K-5
K. Description of the Ball ScrewK
5FeaturesoftheBallS
crew
1. Features of the Ball Screw1. Features of the Ball Screw
With the Ball Screw, balls roll between the screw shaft and the nut to achieve high efficiency.
Its required driving torque is only one third of the conventional sliding screw (Fig. 1 and 2). As
a result, it is capable of not only converting rotational motion to linear motion, but also easily
converting linear motion to rotational motion.
1.1. Driving Torque One Third of the Sliding Screw1.1. Driving Torque One Third of the Sliding Screw
μ=0.003
μ=0.01
μ=0.2μ=
0.1
μ=0.005
100
90
80
70
60
50
40
30
20
10
Ball Screw
Sliding screw
10 2 3 4 5 6 7 8 9 10
Lead angle (degree)
Positive efficiency η1(%)
μ=0.1
μ=0.003
μ=0.01μ=0.005
Ball Screw
Sliding screw
100
90
80
70
60
50
40
30
20
10
10 2 3 4 5 6 7 8 9 10
Lead angle (degree)
Negative efficiency η2(%)
Fig. 1 Positive Efficiency (Rotational to Linear) Fig. 2 Negative Efficiency (Linear to Rotational)
1.1.1. Calculating the Lead Angle
………(1)
where
β :Lead angle (degree)
dP :Ball center diameter (mm)
R :Feed screw lead (mm)
tanβ = Rπ · dP
K-6
The torque or thrust generated when thrust or torque is applied is obtained from equations (2) to (4).
1.1.2. Relationship between Thrust and Torque
Driving Torque Required to Gain Thrust
Fa:Frictional resistance
T:Driving torqueFeed screw
m:Mass
Guide surface
………(2)
where
T :Driving torque (N・mm)
Fa :Frictional resistance on the guide surface(N)
Fa=μ×mg
μ :Friction coefficient of the guide surface
g :Gravitational acceleration (9.8m/s2)
m :Mass of the transferred object (kg)
R :Lead of the feed screw (mm)
η1:Positive efficiency of feed screw
(Fig. 1 on page K-5)
T = Fa · R2π · η1
Thrust Generated When Torque is Applied
………(3)
where
Fa :Thrust generated (N)
T :Driving torque (N・mm)
R :Lead of the feed screw (mm)
η1:Positive efficiency of feed screw
(Fig. 1 on page K-5)
Fa = 2π · η1 · TR
………(4)
where
T :Torque generated (N・mm)
Fa :Thrust input (N)
R :Lead of the feed screw (mm)
η2:Negative efficiency of feed screw
(Fig. 2 on page K-5)
Torque Generated When Thrust is Applied
T = R · η2 · Fa2π
K-7
K. Description of the Ball ScrewK
7FeaturesoftheBallS
crew
When moving an object with a mass of 500 kg using a screw with an effective diameter of 33 mm and a leadlength of 10 mm (lead angle: 5°30'), the required torque is obtained as follows.
Rolling guide (μ= 0.003)
Ball Screw (from μ= 0.2, η= 0.32)
■Examples of Calculating Driving Torque
Fa:Frictional resistance
T:Driving torquem:Mass
Feed screw
Guide surface
(24N・mm)
(14.7N)
(Ball Screw efficiency η= 96%)
(Rolling friction coefficient μ= 0.003)
(500kg)
Fa:Frictional resistance
T:Driving torque Feed screw
Guide surface
(73N・mm)
(14.7N)
(Sliding screw efficiency η= 32%)
(Rolling friction coefficient μ= 0.003)
m:Mass(500kg)
Fa = 0.003 ✕ 500 ✕ 9.8 = 14.7 N
Frictional resistance of the guide surface
T = = 24 N · mm14.7 ✕ 10
2π ✕ 0.96
Driving torque
Fa = 0.003 ✕ 500 ✕ 9.8 = 14.7 N
Frictional resistance of the guide surface
T = = 73 N · mm14.7 ✕ 10
2π ✕ 0.32
Driving torque
Rolling guide (μ= 0.003)
Ball Screw (from μ= 0.003, η= 0.96)
K-8
20
10
0
-10
-20
Lead error(μm)
+MAX a = 0.9
–MAX a = –0.8
0 100 200 300 400 500Length(mm)
ACCUMULATED LEAD
1.2. Ensuring High Accuracy1.2. Ensuring High Accuracy
The Ball Screw is ground with highest-level facilities and equipment at a strictly temperature-controlled factory,
and its accuracy is assured under a thorough quality control system that covers assembly to inspection.
Automatic lead measuring machine using laser
Fig. 3 Lead Accuracy Measurement Data
Standard value
STANDARD
0
±0.011
0.008
Directional target value
Representative travel distance error
Fluctuation
DIRECTIONAL
TARGET POINT
OVERALL
LEAD DEVIATION
RELATIVE
LEAD VARIATION
–0.0012
0.0017
Actual measurement
DATA
Model No.
TYPEBIF3205-10RRG0+903LC2
Unit: mm
K-9
K. Description of the Ball ScrewK
9FeaturesoftheBallS
crew
1.3. Capable of Fine Feed1.3. Capable of Fine Feed
The Ball Screw requires a minimal starting torque thanks to its rolling motion, and does not cause
a slip, which is inevitable with sliding motion. Therefore, it is capable of accurate fine feeding.
Fig. 4 shows a travel distance of the Ball Screw in one-pulse, 0.1-μm feeding (LM Guide is used
for the guide surface).
0.2μm
Time(sec)
Travel distance(μm)
Fig. 4 Data on Travel in 0.1-μm Feeding
K-10
Since the Ball Screw is capable of receiving a preload, the axial clearance can be reduced to below zero and high rigidity
is achieved because of the preload. In Fig. 5, when an axial load is applied in the positive (+) direction, the table is dis-
placed in the same (+) direction. When an axial load is provided in the reverse (-) direction, the table is displaced in the
same (-) direction. Fig. 6 shows the relationship between the axial load and the axial displacement. As indicated in Fig.
6, as the direction of the axial load changes, axial clearance occurs as a displacement. In addition, when the Ball Screw
is provided with a preload, it gains higher rigidity and smaller axial displacement than zero clearance in the axial direction.
Axial displacement
(+)
(+)
( ) ー
( ) ー
Axial loadAxial displacement
(+) ( ) ー
(+)
( ) ー
Axial load
:0Axial load
:0.02
Applied prel
oad(0.1×
Ca)
Axial clearance
Fig. 6 Axial Displacement in Relation to Axial Load
Fig. 5
1.4. High Rigidity without Backlash1.4. High Rigidity without Backlash
K-11
K. Description of the Ball ScrewK
11FeaturesoftheBallS
crew
1.5. Capable of Fast Feed1.5. Capable of Fast Feed
Since the Ball Screw is highly efficient and generates little heat, it is capable of fast feed.
■Example of High SpeedFig. 7 shows a speed diagram for a large-lead rolled Ball Screw operating at 2 m/s.
■Example of Heat GenerationFig. 9 shows data on heat generation from the screw shaft when a Ball Screw is used in an
operating pattern indicated in Fig. 8.
Time(msec) 2000ms
0
2
Speed(m/s)
Time
Speed(m/s)
(s)
t1 = 0.2t2 = 1.4, 1.3t3 = 0.2 wqq
t2 = 1.3t2 = 1.4t1 t3t3 t1
0.217m/s
0.0042m/s
t = 19.6 x 3 cycles0.1
1.915.9
Time(min)
30
25
200 30 60 90 120 150 180
Temperature(℃)
Fig. 7 Speed Diagram
Fig. 8 Operating Pattern
Fig. 9 Ball Screw Heat Generation Data
Maximum speed 2m/s(Ball Screw rotation speed: 2,000 min-1)
Ball ScrewLarge-lead rolled Ball ScrewWTF3060 (shaft diameter: 30 mm; lead: 60 mm)
Guide surfaceLM Guide: model SR25W
Ball ScrewDouble-nut precision Ball ScrewModel BNFN4010-5
(Shaft diameter: 40 mm; lead: 10 mm; applied preload: 2,700 N)
Maximum speed: 0.217m/s(13m/min)(Ball Screw rotation speed: 1,300 min-1)
Low speed 0.0042m/s(0.25m/min)(Ball Screw rotation speed: 25 min-1)
Guide surfaceLM Guide model HSR35CA
LubricantLithium-based grease (No. 2)
K-12
Pipe presser Screw shaft
Return pipe
QZ Lubricator
QZ Lubricator
Wiper ring
Ball screw nut
Ball cageBall
Use of a ball cage in the Ball Screw with Ball Cage eliminates collision and friction between
balls and increases grease retention. This makes it possible to achieve low noise, low torque
fluctuation and long-term maintenance-free operation.
In addition, this Ball Screw is superbly capable of responding to high speed because of an ideal
ball circulation structure, a strengthened circulation path and adoption of the ball cage.
Fig. 1 Structure of High-Speed Ball Screw with Ball Cage Model SBN
2. Structure and Features of the Ball Screw with Ball Cage®2. Structure and Features of the Ball Screw with Ball Cage®
K-13
K. Description of the Ball ScrewK
13Stru
cture
andFeaturesoftheBallS
crewwith
BallC
age
●Low noise, acceptable running soundUse of the ball cage has eliminated collision
noise between balls. Additionally, as balls are
picked up in the tangential direction, collision
noise from ball circulation has also been elimi-
nated.
●Long-term maintenance-free operationFriction between balls has been eliminated,
and grease retention has been improved
through the provision of grease pockets. As
a result, long-term maintenance-free opera-
tion (i.e., lubrication is unnecessary over a
long period) is achieved.
●Smooth motionUse of the ball cage eliminates friction
between balls and reduces torque fluctuation,
thus to achieve smooth motion.
2.1. Caged Ball® Technology2.1. Caged Ball® Technology
Point (metal) contact
Oil filmGrease pocket
Conventional structure
Structure of the Ball Screw with Ball Cage
2.1.1. Caged Ball Technology
K-14
●Low Noise■Low noise level dataSince the balls in the Ball Screw with Ball Cage do not collide with each other, they do not pro-
duce a metallic sound and a low noise level is achieved.
[Noise measurement]
Tested products: Ball Screw with Ball Cage model HBN3210-5
Conventional type: model BNF3210-5
[Conditions]
Stroke 600mm
Lubrication Grease lubrication (lithium-based grease containing extreme pressure agent)
90
85
80
75
70
65
60
55
50
45
4010000 100000
Ball diameter x ball center diameter x rotation speed
Noise level[dB(A)]
1000000 10000000
Conventional type (BNF3210-5) Model HBN (HBN3210-5)
Ball Screw Noise Level
Noise meter
Soundproof material1000mm
M
FFT
Noise Measuring Equipment
K-15
K. Description of the Ball ScrewK
15Stru
cture
andFeaturesoftheBallS
crewwith
BallC
age
●Long-term Maintenance-free Operation■High speed, load-bearing capacityThanks to the ball circulating mechanism supporting high speed and the caged ball technology,
the Ball Screw with Ball Cage excels in high speed and load-bearing capacity.
High Speed Durability Test
[Test conditions]
【Test result】Shows no anomaly after running 10,000 km.
【Test result】Shows no anomaly after running a distance 2.5 timesthe calculated service life.
Description
High-Speed Ball Screw with Ball Cage model
SBN3210-7
3900(min–1)(DN value*: 130,000)
400mm
AFG Grease
12cm3(lubricated every 1,000 km)
1.73kN
1G
Item
Tested article
Speed
Stroke
Lubricant
Quantity
Applied load
Acceleration
Load Bearing Test
[Test conditions]
Description
High-Speed Ball Screw with Ball Cage model
SBN3210-7
1500(min–1)(DN value*: 50,000)
300mm
AFG Grease
12cm3
17.3kN(0.5Ca)
0.5G
Item
Tested article
Speed
Stroke
Lubricant
Quantity
Applied load
Acceleration
–1.0
–0.5
0
0.5
1.0
Time(S)
Torque(N・m)
Torque Fluctuation Data
20 40 60
Model SBNConventional type
0
Description
32/10mm
60min–1
Item
Shaft diameter/lead
Shaft rotation speed
* DN value: Ball center diameter x rotation speed per minute
●Smooth Motion■Low torque fluctuationThe caged ball technology allows smoother motion than the conventional type to be achieved,
thus to reduce torque fluctuation.
K-16
2.2. Types of Ball Screws with Ball Cage®2.2. Types of Ball Screws with Ball Cage®
Ball track with less stress than the conventional type
Matches the lead angleReturn pipe
Screw shaft
Ball screw nut
Tangential direction Large p
ick-up angle
Return pipe
Screw shaft
Ball screw nut
Lead angle
Pitch PitchPitch
(Pitch + preload) PitchPitch
Applied preloadApplied preload
Ball screw nut
Fig. 2 Circulation Structure of Model SBN Fig. 3 Circulation Structure of Conventional Type
●Structure and FeaturesHigh-Speed Ball Screw with Ball Cage model SBN has a circulation structure where balls are
picked up at the tangential direction (Fig. 2), has a strengthened circulation path and uses a
ball cage, thus to achieve a DN value* of 130,000 (* DN value = ball center diameter x rotation speed
per minute).
As a result of adopting the offset preloading method (Fig. 4), which shifts the lead in the cen-
tral area of the ball screw nut, its overall ball screw nut length is shorter and its body is more
compact than the double-nut type, which uses the spacer-based preloading method.
Optionally, QZ Lubricator for Ball Screws (see page K-98), which has been developed for long-
term maintenance-free operation, and a wiper ring (see page K-102), which prevents foreign
matter from entering the ball screw nut, are available.
Fig. 4 Offset Preloading Method
High-Speed Ball Screw with Ball Cage Model SBN
K-17
K. Description of the Ball ScrewK
17Stru
cture
andFeaturesoftheBallS
crewwith
BallC
age
Lead angleBall track with less stress than the conventional type Return piece
Screw shaftBall screw nut
Small pick-up angle
Large pick-up angle Lead angleReturn piece
Screw shaft
Ball screw nut
Fig. 5 Circulation Structure of Model HBN Fig. 6 Circulation Structure of the Conventional Type
●Structure and FeaturesHigh-Load Ball Screw with Ball Cage model HBN has a rated load more than twice greater that
the conventional type because of the optimal design (in ball cage, ball diameter, groove curva-
ture radius, contact angle between ball and groove, and number of turns) for high loads.
In addition, it has a circulation structure where balls are picked up at the near-tangential direc-
tion (Fig. 5), has a strengthened circulation path and uses a ball cage, thus to achieve a DN
value of 130,000.
High-Load Ball Screw with Ball Cage Model HBN
Circulate toward the tangential direction Circulate toward the lead angle direction
Fig. 7 Circulation Structure of Model SBK
K-18
●Structure and FeaturesModel SBK has a circulation structure where balls are picked up at the tangential direction (Fig.
7), has a strengthened circulation path and uses a ball cage, thus to achieve a DN value of
160,000.
As a result of adopting the offset preloading method (Fig. 4 on page K-16), which shifts the lead
in the central area of the ball screw nut, its overall ball screw nut length is shorter and its body
is more compact than the double-nut type, which uses the spacer-based preloading method.
High-Speed Ball Screw with Ball Cage Model SBK
K-21
K. Description of the Ball ScrewK
21FlowChartforSelectin
gaBallS
crew
K-20
3. Flow Chart for Selecting a Ball Screw3. Flow Chart for Selecting a Ball Screw
Steps for Selecting a Ball Screw
When selecting a Ball Screw, it is necessary to make a selection from various angles. The fol-
lowing is a flow chart as a measuring stick for selecting a Ball Screw.
Studying the rotational torque
Calculating the torque from the preload on the Ball Screw
Calculating the frictional torque from an external load
Safety design
Studying the lubrication and the dust prevention
Calculating the torque required for acceleration
5 2 3( )
3 4 5( )
1 3 4( 5)
2 3 5( )
Selection Starts
Selection Completed
Selecting service conditions
Estimating the shaft length
Studying the permissible axial load
Selecting a permissible rotation speed
Axial clearance of precision Ball Screw
Axial clearance of rolled Ball Screw
Selecting axial clearance
Selecting a lead2
Selecting a shaft diameter3
Selecting a method for mounting the screw shaft4
3 2 4
Calculating the permissible axial load
Studying the service life
Studying the rigidity
Studying the positioning accuracy
Studying the rotational torque
Studying the drive motor( )
5 2 3( )
3 4( )
Selecting a model number (type of nut)5
Selecting Ball Screw accuracy
Lead accuracy1Studying the rigidity
Calculating the rigidity of the nut
Calculating the axial rigidity of the screw shaft
Calculating the rigidity of the support bearing
K-69 -
K-68 -
K-98 -
K-69 -
K-22
K-37 -K-62 -
K-55 -
K-43 -
K-45 -
K-53 -
K-70 -
K-48 -
K-23 -
K-31K-31
K-39 -
K-39 -
K-41 -
K-60 -
K-58 -
K-61 -
K-22
[Service Conditions of the Ball Screw]
The following conditions are required when selecting a Ball Screw.
Transfer orientation (horizontal, vertical, etc.)
Transferred mass m(kg)
Table guide method (sliding, rolling)
Friction coefficient of the guide surface μ(-)
Resistance of the guide surface f(N)
External load in the axial direction F(N)
Desired service life time Lh(h)
Stroke length Rs(mm)
Operating speed Vmax(m/s)
Acceleration time t1(s)
Even speed time t2(s)
Deceleration time t3(s)
Acceleration(m/s2)
Acceleration distance R1=Vmax×t1×1000/2(mm)
Even speed distance R2=Vmax×t2×1000(mm)
Deceleration distance R3=Vmax×t3×1000/2(mm)
Reciprocations per minute n(min-1)
Positioning accuracy (mm)
Positioning repeatability (mm)
Backlash (mm)
Minimum feed distance s(mm/pulse)
Drive motor (AC servomotor, stepping motor, etc.)
Motor rated rotation speed NMO(min-1)
Motor inertial moment JM(kg・m2)
Motor resolution (pulse/rev.)
Reduction ratio A(-)
(mm)
(m/s)
(mm)
(s)
Speed Diagram
R1 R2 R3
t1
Vmax
Vmax
t2 t3
R1 R2 R3
t1 t2
RS RS
t3
α =Vmax
t1
K-23
K. Description of the Ball ScrewK
23AccuracyoftheBallS
crew
4. Accuracy of the Ball Screw4. Accuracy of the Ball Screw
4.1. Lead Accuracy4.1. Lead Accuracy
The accuracy of the Ball Screw in lead is controlled in accordance with JIS standards (JIS B
1192 - 1997). Accuracy grades C0 to C5 are defined in linearity and directional property, and
C7 to C10 in travel distance error in relation to 300 mm.
Effective thread length
Nominal travel distance
Reference travel distance
Actual travel distance
Representative travel distance Representative travel distance error
Travel distance error
Target value for reference travel distance
Fluctuation/2π
Fluctuation
●Actual travel distanceAn error in travel distance measured with an
actual Ball Screw.
●Reference travel distanceGenerally, it is the same as nominal travel
distance, but can be an intentionally correct-
ed value of nominal travel distance according
to the intended use.
●Target value for reference travel distanceYou may provide tension in order to prevent
the screw shaft from running out, or set the
reference travel distance in "negative" or
"positive" value in advance given possible
expansion/contraction from external load or
temperature. In such cases, indicate a target
value for the reference travel distance.
●Representative travel distanceIt is a straight line representing the tendency in actual trav-
el distance, and obtained with the least squares method
from the curb that indicates the actual travel distance.
●Representative travel distance error (in ±)Difference between the representative travel
distance and the reference travel distance.
●FluctuationIt is the maximum width of the actual travel dis-
tance between two straight lines drawn in par-
allel with the representative travel distance.
●Fluctuation/300It indicates a fluctuation against a given thread length of 300 mm.
●Fluctuation/2πIt is a fluctuation in one revolution of the screw shaft.
Fig. 1 Terms on Lead Accuracy
K-24
Table 2 Fluctuation in Thread Length of 300 mm and in One Revolution (permissible value) Unit: mm
Table 1 Lead Accuracy (permissible value) Unit: mm
Precision Ball Screw
Rolled Ball Screw
C10C8C7C5C3C2C1C0Accuracy gradeEffective
thread lengthRepresentactive traveldistanceerror
Fluctu-ation
Representactive traveldistanceerror
Fluctu-ation
Representactive traveldistanceerror
Fluctu-ation
Representactive traveldistanceerror
Fluctu-ation
Representactive traveldistanceerror
Fluctu-ation
Travel distanceerror
Travel distanceerror
Travel distanceerrorAbove Or less
—
100
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
100
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
10000
3
3.5
4
5
6
6
7
8
9
11
—
—
—
—
—
—
—
—
3
3
3.5
3.5
4
4
5
6
6
7
—
—
—
—
—
—
—
—
3.5
4.5
6
7
8
9
10
11
13
15
18
22
26
30
—
—
—
—
5
5
5
5
5
6
7
8
9
10
11
13
15
18
—
—
—
—
5
7
8
9
10
11
13
15
18
21
25
30
36
44
52
65
—
—
7
7
7
7
7
8
9
10
11
13
15
18
21
25
30
36
—
—
8
10
12
13
15
16
18
21
24
29
35
41
50
60
72
90
110
—
8
8
8
10
10
12
13
15
16
18
21
24
29
35
41
50
60
—
18
20
23
25
27
30
35
40
46
54
65
77
93
115
140
170
210
260
18
18
18
20
20
23
25
27
30
35
40
46
54
65
77
93
115
140
±50
300mm
±100
300mm
±210
300mm
Note: Unit of effective thread length: mm
Accuracy grade
Fluctuation/300 mm
Fluctuation/2π
C0 C1 C2 C3 C5 C7 C8 C10
3.5 5 7 8 18 — — —
3 4 5 6 8 — — —
K-25
K. Description of the Ball ScrewK
25AccuracyoftheBallS
crew
Example: When the lead of a Ball Screw manufactured is measured with a target value for ref-
erence travel distance being -9 μm/500 mm, the following data are obtained.
The measurement data are expressed in a graph as shown in Fig. 2.
The positioning error (A-B) is indicated as the actual travel distance while the straight line rep-
resenting the tendency of the (A-B) graph refers to the representative travel distance.
The difference between the reference travel distance and the representative travel distance
appears as the representative travel distance error.
Table 3 Measurement Data on Travel Distance Error
Command position (A)
Travel distance (B)
Travel distance error (A-B)
0 50 100 150
0 49.998 100.001 149.996
0 –0.002 +0.001 –0.004
200 250 300 350
199.995 249.993 299.989 349.885
–0.005 –0.007 –0.011 –0.015
400 450 500
399.983 449.981 499.984
–0.017 –0.019 –0.016
+10
–10
–20
–30
0100 200 300 400 500
8.8μmFluctuation
Actual travel distanceRepresentative travel distance
Target value for reference travel distance
Representative travel distance error–7μm
–9μm/500mm
(A-B)
Measurement point on the thread(mm)
Travel distance error(μm)
Measurement result - representative travel distance:-7μmFluctuation:8.8μm
Unit: mm
Fig. 2 Measurement Data on Travel Distance Error
K-26
4.2. Accuracy of the Mounting Section4.2. Accuracy of the Mounting Section
The accuracy of the Ball Screw mounting section complies with JIS standard (JIS B 1192).
Table 8 C
Table 7 C
CE
C
Table 6 G
GF
Table 5 EF
Table 5 EFTable 4 EF Note EF
Table 4 EF
Square nut
Fig. 3 Accuracy of the Mounting Section of the Ball Screw
Note: For the overall run-out of the screw shaft axis in the radial direction, refer to JIS B 1192.
K-27
K. Description of the Ball ScrewK
27AccuracyoftheBallS
crew
4.2.1. Accuracy Standards for the Mounting Section
Tables 4 to 8 show accuracy standards for the mounting sections of the precision Ball Screw.
Example: model No. DIK2005-6RRGO+500LC5
Table 4 Radial Run-out of the Circumference of the Thread Root inRelation to the Support Portion Axis of the Screw Shaft
Unit: μmScrew shaft outer diameter(mm)
Above
—
8
12
20
32
50
80
8
12
20
32
50
80
100
3
4
4
5
6
7
—
5
5
6
7
8
9
10
7
7
8
9
10
11
12
8
8
9
10
12
13
15
10
11
12
13
15
17
20
14
14
14
20
20
20
30
Or less C0 C1 C2 C3 C5 C7
Run-out (Maximum)
Note: The measurements on these items include the effect of the run-out of thescrew shaft diameter. Therefore, it is necessary to obtain the correctionvalue from the overall run-out of the screw shaft axis, using the ratio ofthe distance between the fulcrum and measurement point to the overallscrew shaft length, and add the obtained value to the table above.
L=500
L1=80
E1 E-F E2 E-F
V blockSurface tableMeasurement point
= ✕ 0.06
= 0.01
= 0.022
E1 = 0.012 + 0.01
E1 = e + �e
80500
�e = ✕ E2L1
LE2:Overall radial run-out of the screw shaft axis(0.06) where
e :Standard value in table 4(0.012) where
�e:Correction value
K-28
Table 5 Perpendicularity of the Supporting Portion End ofthe Screw Shaft to the Supporting Portion Axis
Unit: μmScrew shaft outer diameter (mm)
Above
—
8
12
20
32
50
80
8
12
20
32
50
80
100
2
2
2
2
2
3
—
3
3
3
3
3
4
4
3
3
3
3
3
4
5
4
4
4
4
4
5
6
5
5
5
5
5
7
8
7
7
7
7
8
10
11
Or less C0 C1 C2 C3 C5 C7
Perpendicularity (Maximum)
Table 6 Perpendicularity of the Flange Mounting Surfaceof the Screw Shaft to the Screw Shaft Axis
Unit: μmNut outer diameter (mm)
Above
—
20
32
50
80
125
160
20
32
50
80
125
160
200
5
5
6
7
7
8
—
6
6
7
8
9
10
11
7
7
8
9
10
11
12
8
8
8
10
12
13
14
10
10
11
13
15
17
18
14
14
18
18
20
20
25
Or less C0 C1 C2 C3 C5 C7
Perpendicularity (Maximum)
Table 7 Radial Run-out of the Nut Circumferencein Relation to the Screw Shaft Axis
Unit: μmNut outer diameter (mm)
Above
—
20
32
50
80
125
160
20
32
50
80
125
160
200
5
6
7
8
9
10
—
6
7
8
10
12
13
16
7
8
10
12
16
17
20
9
10
12
15
20
22
25
12
12
15
19
27
30
34
20
20
30
30
40
40
50
Or less C0 C1 C2 C3 C5 C7
Run-out (Maximum)
Table 8 Parallelism of the Nut Circumference (FlatMounting Surface) to the Screw Shaft Axis
Unit: μmMounting reference length (mm)
Above
—
50
100
50
100
200
5
7
—
6
8
10
7
9
11
8
10
13
10
13
17
17
17
30
Or less C0 C1 C2 C3 C5 C7
Parallelism (Maximum)
4.2.2. Method for Measuring Accuracy of the Mounting Section
●Radial Run-out of the Circumference of the Part Mounting Section inRelation to the Supporting Portion Axis of the Screw Shaft (Table 4)
Support the supporting portion of the screw shaft with V blocks. Place a probe on the circum-
ference of the part mounting section, and read the largest difference on the dial gauge as a
measurement when turning the screw shaft by one revolution.
Dial gauge
V block V block
Surface table
K-29
K. Description of the Ball ScrewK
29AccuracyoftheBallS
crew
●Radial Run-out of the Circumference of the Thread Root inRelation to the Support Portion Axis of the Screw Shaft (Table 4)
Support the supporting portion of the screw shaft with V blocks. Place a probe on the circumference of the nut, and read the
largest difference on the dial gauge as a measurement when turning the screw shaft by one revolution without turning the nut.
Dial gauge
V block V block
Surface table
Dial gauge
V block V block
Surface table
Dial gauge
V block V block
Surface table
●Perpendicularity of the Supporting Portion End of theScrew Shaft to the Supporting Portion Axis (Table 5)
Support the supporting portion of the screw shaft with V blocks. Place a probe on the screw shaft's supporting portion
end, and read the largest difference on the dial gauge as a measurement when turning the screw shaft by one revolution.
●Perpendicularity of the Flange Mounting Surface of theScrew Shaft to the Screw Shaft Axis (Table 6)
Support the nut of the screw shaft with V blocks. Place a probe on the flange end, and read the largest difference
on the dial gauge as a measurement when simultaneously turning the screw shaft and the nut by one revolution.
K-30
●Radial Run-out of the Nut Circumference in Relation tothe Screw Shaft Axis (Table 7)
Support the thread of the screw shaft with V blocks near the nut. Place a probe on the circumference of the nut, and read the
largest difference on the dial gauge as a measurement when turning the nut by one revolution without turning the screw shaft.
Dial gauge
V block V block
Surface table
Dial gauge
V block V block
Surface table
Dial gauge
V block V block
Surface table
●Parallelism of the Nut Circumference (Flat MountingSurface) to the Screw Shaft Axis (Table 8)
Support the thread of the screw shaft with V blocks near the nut. Place a probe on the circumference of the nut (flat mounting sur-
face), and read the largest difference on the dial gauge as a measurement when moving the dial gauge in parallel with the screw shaft.
●Overall Radial Run-out of the Screw Shaft AxisSupport the supporting portion of the screw shaft with V blocks. Place a probe on the circum-
ference of the screw shaft, and read the largest difference on the dial gauge at several points
in the axial directions as a measurement when turning the screw shaft by one revolution.
Note: For the overall radial run-out of the screw shaft axis, refer to JIS B 1192.
K-31
K. Description of the Ball ScrewK
31AccuracyoftheBallS
crew
4.3. Axial Clearance4.3. Axial Clearance
4.3.1. Axial Clearance of the Precision Ball Screw
Table 9 shows axial clearance of the precision Screw Ball. If the manufacturing length exceeds the
value in table 10, the resultant clearance may partially be negative (preload applied).
Table 9 Axial Clearance of the Precision Ball Screw Unit: mmClearance symbol
Axial clearance
Table 10 Manufacturing-limit Length of the Precision Ball Screw in Axial Clearance Unit: mm
Table 11 Axial Clearance of the Rolled Ball ScrewUnit: mm
Screw shaft
outer
diameter
4 to 6
8 to 10
12 to 16
18 to 25
28 to 32
36 to 45
50 to 70
80 to 100
80
250
500
800
900
1000
1200
—
100
200
400
700
800
800
1000
—
80
250
500
800
1100
1300
1600
1800
100
250
500
700
900
1000
1300
1500
80
250
700
1000
1400
2000
2500
4000
100
300
600
1000
1200
1500
2000
3000
120
300
500
1000
1200
1500
2000
3000
Overall thread length
Clearance GT
C0 to C3 C5 C0 to C3 C5 C0 to C3 C5 C7
Clearance G1 Clearance G2
G0 GT G1 G2 G3
0 or less 0 to 0.005 0 to 0.01 0 to 0.02 0 to 0.05
* When manufacturing the Ball Screw of precision-grade accuracy C7 with clearance GT or G1, the resultant clearanceis partially negative.
4.3.2. Axial Clearance of the Rolled Ball Screw
Table 11 shows axial clearance of the rolled Ball Screw.
Screw shaft outer diameter
6 to 12
14 to 28
30 to 32
36 to 45
50
Axial clearance (maximum)
0.05
0.1
0.14
0.17
0.2
K-32
4.4. Preload4.4. Preload
A preload is provided in order to eliminate axial clearance and minimize the displacement under
an axial load.
When performing highly accurate positioning, a preload is generally provided.
4.4.1. Method for Providing a Preload
Fixed-point Preloading
●Double-nut method (models BNFN, DKN and BLW)This method provides a preload by inserting a spacer between two nuts.
4 x pitch + preload
4 x pitch
Screw shaft
Applied preloadApplied preloadNut BNut A
Spacer
●Offset preloading (models SBN, BIF, DIK, SBK and DIR)More compact than the double-nut method, the offset preloading provides a preload by chang-
ing the groove pitch in the middle of the nut without using a spacer.
Model BNFN Model DKN Model BLW
Pitch + preload
Pitch
Screw shaft
Applied preloadApplied preloadNut
Model BIFModel SBN
Model DIRModel SBK
Model DIK
K-33
K. Description of the Ball ScrewK
33AccuracyoftheBallS
crew
Constant-pressure Preloading Model JPF
A spring structure is established almost in the middle of the nut, and the groove pitch is
changed in the middle of the nut to provide a preload.
3 x pitch
Screw shaft
Pitch - preload
Applied preloadApplied preloadNut
Model JPF
4.4.2. Rigidity of the Ball Screw under a Preload
When a preload is provided to the Ball Screw, the rigidity of the nut is increased.
Fig. 4 shows elastic displacement curbs of the Ball Screw under a preload and without a preload.
Without a preload
With a preload
Parallel
Axial load
2�ao
0
�ao
Ft=3Fao
Axial displacement
Fig. 4 Elastic Displacement of the Ball Screw
�A�a0
�B�a0
�a
Nut BNut AAxial displacement
Fa'
Fa0
Fa
Ft
FB
FA
Fa.Fa'Displacement of nut B Di
splacement of nut A
Axial load
K-34
Nut B Nut ASpacer
Nut BNut A
Spacer
External load: 0
External load: Fa
Fa
Fa0Fa0
FAFB
Fig. 5 Fig. 6
Nuts A and B are provided with preload Fa0 from the spacer. Because of the preload, nuts A
and B are elastically displaced by �a0 each. If an axial load (Fa) is applied from outside in this
state, the displacement of nuts A and B is calculated as follows.
�A = �a0 + �a �B = �a0 - �aIn other words, the loads on nut A and B are expressed as follows:
FA = Fa0 + (Fa - Fa') FB = Fa0 - Fa'Therefore, under a preload, the load that nut A receives equals to Fa - Fa'. This means that
since load Fa', which is applied when nut A receives no preload, is deducted from Fa, the dis-
placement of nut A is smaller.
This effect extends to the point where the displacement (�a0) caused by the preload applied on
nut B reaches zero.
To what extent is elastic displacement reduced? The relationship between the axial load on
the Ball Screw under no preload and the elastic displacement can be expressed by �a∝Fa2/3.
From Fig. 6, the following equations are established.
Thus, the Ball Screw under a preload is displaced by �a0 when an axial load (Ft) approximately three times
greater than the preload is provided from outside. As a result, the displacement of the Ball Screw under a
preload is half the displacement (2�a0) of the Ball Screw without a preload.
As stated above, since the preloading is effective up to approximately three times the applied preload, the
optimum preload is one third of the maximum axial load.
Note, however, that an excessive preload adversely affects the service life and heat generation. As a
guideline, the maximum preload should be set at 10% of the basic dynamic load rating (Ca) at a maximum.
�a0 = KFa02/3 (K: constant)
2�a0 = KFt2/3
= 2 Ft = 23/2 ✕ Fa0 = 2.8Fa0 ≒ 3Fa0
Ft
Fa0( )
23
Fig. 5 shows a double-nut type of Ball Screw.
K-35
K. Description of the Ball ScrewK
35AccuracyoftheBallS
crew
4.4.3. Preload Torque
The preload torque of the Ball Screw in lead is controlled in accordance with JIS standard (JIS B 1192).
Starting actual torque
Starting actual torque
Negative actual-torque fluctuation
Positive actual-torque fluctuation
Actual torque
Actual torque (minimum)
Actual torque (maximum)
Actual torque
Effective travel distance of the nut
Effective travel distance of the nut
(Forward)
(Backward)
0
(-)
(+)
(-)
(+)
Average actual torque
Average actual torque
Reference torque
Reference torque
Torque fluctuation
Torque fluctuation
Friction torque
●Dynamic preload torqueA torque required to continuously rotate the
screw shaft of a Ball Screw under a given
preload without an external load applied.
●Actual torqueA dynamic preload torque measured with an
actual Ball Screw.
●Torque fluctuationVariation in a dynamic preload torque set at a
target value. It can be positive or negative in
relation to the reference torque.
●Coefficient of torque fluctuationRatio of torque fluctuation to the reference torque.
●Reference torqueA dynamic preload torque set as a target.
●Calculating the reference torqueThe reference torque of a Ball Screw provid-
ed with a preload is obtained in the following
equation (5).
………(5)
where
Tp :Reference torque (N・mm)
β :Lead angle
Fa0 :Applied preload (N)
R :Lead (mm)
Fig. 7 Terms on Preload Torque
Tp = 0.05 (tanβ)–0.5 Fa0 ·R2π
K-36
Table 12 Tolerance Range in Torque Fluctuation
Reference torque
N・mm
Above Or less
Effective thread length
4,000 mm or lessAbove 4,000 mm and
10,000 mm or less
――Thread length
≦ 40screw shaft outer diameter
Accuracy grade
C0 C1 C2, C3 C5 C0 C1 C2, C3 C5 C2, C3 C5
±35%
±25%
±20%
±15%
±10%
—
±40%
±30%
±25%
±20%
±15%
—
±45%
±35%
±30%
±25%
±20%
±15%
±55%
±45%
±35%
±30%
±25%
±20%
±45%
±38%
±30%
±25%
±20%
—
±45%
±38%
±30%
±25%
±20%
—
±55%
±45%
±35%
±30%
±25%
±20%
±65%
±50%
±40%
±35%
±30%
±25%
—
—
±40%
±35%
±30%
±25%
—
—
±45%
±40%
±35%
±30%
Accuracy grade Accuracy grade
40 <Thread length
< 60screw shaft outer diameter
200
400
600
1000
2500
6300
400
600
1000
2500
6300
10000
Example: When a preload of 3,000 N is provided to Ball Screw model BNFN4010-5G0 + 1500LC3
with a thread length of 1,300 mm (shaft diameter: 40 mm; ball center diameter: 41.75
mm; lead: 10 mm), the preload torque of the Ball Screw is calculated in the steps below.
β :Lead angle
Fa0 :Applied preload =3000N
R :Lead =10mm
Thus, with the reference torque in table 12 being between 600 and 1,000 N-mm, effective
thread length 4,000 mm or less and accuracy grade C3, the coefficient of torque fluctuation is
obtained as ±30%.
As a result, the torque fluctuation is calculated as follows,
865 ✕ (1 ± 0.3) = 606 N · mm to 1125 N · mm
Reference torque: 865 N-mn
Torque fluctuation: 606 N-mm to 1,125 N-mm
tanβ = = = 0.0762lead
π ✕ ball center diameter
10π ✕ 41.75
Tp = 0.05 (tanβ)–0.5 = 0.05 (0.0762)–0.5 = 865N · mmFa0 · R2π
3000 ✕ 102π
= = 32.5 ≦ 40thread length
screw shaft outer diameter
130040
Calculating the Reference Torque
Calculating the Torque Fluctuation
Result
K-37
K. Description of the Ball ScrewK
37Selectin
gaScrewShaft
5. Selecting a Screw Shaft5. Selecting a Screw Shaft
5.1. Maximum Manufacturing Length of the Screw Shaft5.1. Maximum Manufacturing Length of the Screw Shaft
The manufacturing limit length of the precision Ball Screw by accuracy grade is shown in table 1,
and that of the rolled Ball Screw in table 2 on page K-38.
If the shaft dimensions exceed the manufacturing limit in table 1 or 2, contact .
Screw shaft
outer diameter
4
6
8
10
12
13
14
15
16
18
20
25
28
30
32
36
40
45
50
55
63
70
80
100
90
150
230
350
440
440
530
570
620
720
820
1100
1300
1450
1600
2000
110
170
270
400
500
500
620
670
730
840
950
1400
1600
1700
1800
2100
2400
2750
3100
3450
4000
120
210
340
500
630
630
770
830
900
1050
1200
1600
1900
2050
2200
2550
2900
3350
3800
4150
5200
6300
120
210
340
500
680
680
870
950
1050
1220
1400
1800
2100
2300
2500
2950
3400
3950
4500
5300
5800
6450
7900
10000
120
210
340
500
680
680
890
980
1100
1350
1600
2000
2350
2570
2800
3250
3700
4350
5000
6050
6700
7650
9000
10000
120
210
340
500
680
680
890
1100
1400
1600
1800
2400
2700
2950
3200
3650
4300
5050
5800
6500
7700
9000
10000
Overall screw shaft length
Table 1 Manufacturing Limit Length of the Precision Ball Screw by Accuracy Grade Unit: mm
C0 C1 C2 C3 C5 C7
K-38
Screw shaft
outer diameter
6 to 8
10 to 12
14 to 15
16 to 18
20
25
28
30
32 to 36
40
45
50
320
500
1500
1500
2000
2000
3000
3000
3000
3000
3000
3000
320
1000
1500
1800
2200
3000
3000
3000
4000
5000
5500
6000
—
—
1500
1800
2200
3000
3000
4000
4000
5000
5500
6000
Overall screw shaft length
Table 2 Manufacturing Limit Length of the Rolled Ball Screw by Accuracy GradeUnit: mm
C7 C8 C10
K-39
K. Description of the Ball ScrewK
39Selectin
gaScrewShaft
5.2. Standard Combinations of Shaft Diameter and Lead for the Precision Ball Screw5.2. Standard Combinations of Shaft Diameter and Lead for the Precision Ball Screw
Table 3 shows standard combinations of shaft diameter and lead for the precision Ball Screw.
If desiring a Ball Screw not covered by the table, contact .
Table 3 Standard Combinations of Screw Shaft and Lead (Precision Ball Screw)
Screw shaft
outer diameter
4
5
6
8
10
12
13
14
15
16
18
20
25
28
30
32
36
40
45
50
55
63
70
80
100
Lead
1
●
●
●
●
2
●
●
●
●
4
●
●
○
○
○
○
5
●
●
●
●
●
○
●
○
○
6
○
○
○
●
●
○
○
○
8
●
●
○
○
○
○
○
○
○
○
10
●
●
●
○
●
●
●
○
●
●
●
○
●
○
○
○
○
12
○
○
○
○
○
●
○
○
○
○
○
○
15
○
16
●
○
○
○
○
○
○
○
20
○
●
●
●
○
○
○
○
○
○
○
○
○
○
24
○
○
25 30
○
○
○
○
32
○
36
○
○
○
40
○
○
○
50
○
○
60
○
○
80
○
90
○
100
○
For combinations marked with "●," off-the-shelf products (standard-stock products equipped with standardized screw shafts -shaft ends unfinished and finished) are available.
K-40
5.3. Standard Combinations of Shaft Diameter and Lead for the Rolled Ball Screw5.3. Standard Combinations of Shaft Diameter and Lead for the Rolled Ball Screw
Table 4 shows standard combinations of shaft diameter and lead for the rolled Ball Screw.
Table 4 Standard Combinations of Screw Shaft and Lead (Rolled Ball Screw)
Screw shaft
outer diameter
6
8
10
12
14
15
16
18
20
25
28
30
32
36
40
45
50
Lead
1
●
●
●
●
● ●
●
●
●
○
●
○
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
2 4 5 6 8 10 12 16 20 24 25 30 32 36 40 50 60 80 100
For combinations marked with "●," off-the-shelf products are available.
K-41
K. Description of the Ball ScrewK
41Selectin
gaScrewShaft
5.4. Method for Mounting the Screw Shaft5.4. Method for Mounting the Screw Shaft
Figures 1 to 4 show representative mounting methods for the screw shaft.
Permissible axial load and permissible rotation speed vary with mounting methods for the screw shaft.
Therefore, it is necessary to select an appropriate mounting method according to the service conditions.
Center distance (permissible rotation speed)
Center distance (permissible axial load)
Fixed Fixed Free
Center distance (permissible axial load)
Center distance (permissible rotation speed)
Fixed SupportedFixed
Fig. 1 Screw Shaft Mounting Method: Fixed - Free
Fig. 2 Screw Shaft Mounting Method: Fixed - Supported
K-42
Center distance (permissible axial load)
Center distance (permissible rotation speed)
FixedFixed Fixed
Center distance (permissible axial load)
FixedFixed
Fixed
Fig. 3 Screw Shaft Mounting Method: Fixed - Fixed
Fig. 4 Screw Shaft Mounting Method for Rotary Nut Ball Screw: Fixed - Fixed
K-43
K. Description of the Ball ScrewK
43Selectin
gaScrewShaft
5.5. Permissible Axial Load5.5. Permissible Axial Load
5.5.1. Buckling Load on the Screw Shaft
With the Ball Screw, it is necessary to select a screw shaft so that it will not buckle when the maxi-
mum compressive load is applied in the axial direction.
Fig. 5 on page K-44 shows the relationship between the screw shaft diameter and a buckling load.
If determining a buckling load by calculation, it can be obtained from the equation (6) below. Note
that in this equation, a safety factor of 0.5 is multiplied to the result.
………(6)
where
P1 :Buckling load (N)
Ra :Center distance (mm)
E :Young's modulus (2.06×105 N/mm2)
I :Minimum geometrical moment of inertia of the screw shaft(mm4)
η1,η2=Factor for mounting method
Fixed - free η1=0.25 η2=1.3
Fixed - supported η1=2 η2=10
Fixed - fixed η1=4 η2=20
If an axial load is applied to the Ball Screw, it is necessary to take into account not only the
buckling load but also the permissible tensile and compressive load in relation to the yielding
stress on the screw shaft.
The permissible tensile-compressive load is obtained from the equation (7).
………(7)
where
P2 :Permissible tensile and compressive load (N)
σ :Permissible tensile-compressive stress(147 N/mm2)
d1 :Screw-shaft thread minor diameter (mm)
P1 = 0.5 = η2 104η1 · π2 · E · I�Ra2
d14
Ra2
d1:Screw-shaft thread minor diameter(mm) I = d14π
64
5.5.2. Permissible Tensile and Compressive Load on the Screw Shaft
P2 = σ d12 = 116d1
2π4
K-44
22210.80.60.4Fixedーfree
10 864864 102
222108642Fixedーsupported
864864 102
42 24210864Fixedーfixed
Mounting method Axial load(kN)
86486 102
103
103
200
400
600
800
1000
2000
4000
6000
8000
10000
φ45
φ80
φ70
φ63
φ55
φ50
φ100
φ40
φ36
φ32
φ30
φ28
φ25φ20
φ18
φ16
φ15φ14
φ12
φ10
φ8
φ6
Center distance(mm)
Fig. 5 Permissible Tensile and Compressive Load Diagram
K-45
K. Description of the Ball ScrewK
45Selectin
gaScrewShaft
5.6. Permissible Rotation Speed5.6. Permissible Rotation Speed
5.6.1. Critical Speed of the Screw Shaft
When the rotation speed reaches a high level, the Ball Screw may resonate and eventually become
unable to operate due to the screw shaft's natural frequency. Therefore, it is necessary to select a
model so that it is used below the resonance point (critical speed).
Fig. 6 on page K-47 shows the relationship between the screw shaft diameter and a critical speed.
If determining a critical speed by calculation, it can be obtained from the equation (8) below. Note
that in this equation, a safety factor of 0.8 is multiplied to the result.
………(8)
where
N1 :Permissible rotation speed determined by critical speed(min-1)
Rb :Center distance (mm)
E :Young's modulus (2.06×105 N/mm2)
I :Minimum geometrical moment of inertia of the screw shaft(mm4)
� :Density (specific gravity) (7.85×10-6 kg/mm3)
A :Screw shaft sectional area (mm2)
λ1,λ2:Factor for mounting method
Fixed - free λ1=1.875 λ2=3.4
Supported - supported λ1=3.142 λ2=9.7
Fixed - supported λ1=3.927 λ2=15.1
Fixed - fixed λ1=4.73 λ2=21.9
N1 = ✕ ✕ 0.8 = λ2 · · 10760 · λ12
2π ·Rb2
d1
Rb2
E ✕ 103· I� · A
�������
d1:Screw-shaft thread minor diameter(mm) I = d14
π
64
A = d12
π
4
The permissible rotation speed of the Ball Screw must be obtained from the critical speed of
the screw shaft and the DN value.
The permissible rotation speed determined by the DN value is obtained using the equations (9)
to (13) below.
●Models SBN and HBN
………(9)
where
N2 :Permissible rotation speed determined by DN value (min-1(rpm))
D :Ball center diameter
(Described in the dimensional table for the respective model number in the "
General Catalog - Product Specifications," provided separately.)
●Model SBK
………(10)
………(11)
(excluding large-lead type)
………(12)
………(13)
Of the permissible rotation speed determined by critical speed (N1) and the permissible rotation
speed determined by DN value (N2), the lower rotation speed is regarded as the permissible
rotation speed.
If the working rotation speed exceeds N2, a high-speed type Ball Screw is available. Contact
for details.
K-46
5.6.2. DN Value
N2 = 70000D
N2 = 50000D
N2 = 70000D
N2 = 130000D
N2 = 160000D
Ball Screw with Ball Cage
Precision Ball Screw
Rolled Ball Screw
Large-Lead Rolled Ball Screw
K-47
K. Description of the Ball ScrewK
47Selectin
gaScrewShaft
4 46 8 2 2102 6 8 103Fixedーfree
2 4 6 8 2103 4 6 8 104Fixedーsupported
42 26 8 1044 6 8 103Fixedーfixed
Mounting method
Rotation speed(min-1)
200
400
600
800
1000
2000
4000
6000
8000
10000
φ100φ80φ70φ63φ55φ50φ45φ40
φ32φ30φ28φ25
φ18φ16φ15φ14φ12
φ36
φ20
φ10φ8φ6
Center distance(mm)
Fig. 6 Permissible Rotation Speed Diagram
K-49
K. Description of the Ball ScrewK
49TypesofBallS
crews
K-48
6. Types of Ball Screws6. Types of Ball Screws
Classification of Ball Screws
For Ball Screws, a broad array of types are offered as standard so that the optimal
product can be selected to meet diversified applications. By ball circulation method, the Ball
Screws are divided into return-pipe type, deflector type and end-cap type. And by preloading
method, fixed-point preloading (double-nut method, offset preloading) and constant-pressure
preloading are selectable.
By screw shaft, they are divided into precision Ball Screws, which are ground with precision
(six accuracy grades from C7 to C0), and rolled Ball Screws, which are formed through rolling
with high accuracy (three accuracy grades from C10 to C7).
Also, a series of nut-rotating Ball Screws, which are optimal for usage based on nut rotation, are
also offered in addition to those types designed for conventional use based on axial rotation.
In addition, also offers support units, which are incorporated with nut bracket, rock nut
and support bearing, as peripherals for Ball Screws as standard.
BallScrews
Standard-Lead
Precision BallScrew
Standard-Lead RolledBall Screw
Large-LeadPrecisionBall Screw
Large-Lead Rolled Ball Screw
RotaryNut Series
Shaft end unfinished typeModels MDK, MBF, BNF, BIF and BNFNStandard off-the-shelf
Type Equipped withShaft
Standard Nut Type
Standard Nut Type
Ball Screws/Splines
Rotary Nut PrecisionBall Screw
Rotary NutRolled Ball Screw
Standard Nut Type
Rolled Shaft and NutStandard off-the-shelf Type
Shaft end finished typeModel BNK
Preload typeModels SBN, DIK, DKN, BIF and BNFN
Non-preload typeModels HBN, DK, BNF and BNT
Preload typeModel JPF
Non-preload typeModels MTF, BTK and BNT
Preload typeModels SBK and BLW
Non-preload typeModels BLK and WGF
Non-preload typeModels BLK, WTF and CNF
Standard-lead, preload typeModel DIR
Large-lead, non-preload typeModel BLR
Large-lead, non-preload typeModel BLR
Stroke, rotation typeModels BNS and BNS-A
Stroke typeModels NS and NS-A
Rolled Shaft and NutStandard off-the-shelf Type
K-50
7. Selecting a Nut7. Selecting a Nut
7.1. Types of Nuts7.1. Types of Nuts
Nuts of Ball Screws are categorized by ball circulation method into return-pipe type, deflector
type and end cap type. These three nut types are described as follows.
In addition to circulation methods, Ball Screws are categorized also by preloading method.
7.1.1. Types by Ball Circulation Method
These nuts are most suitable for fast feed.
Balls are picked up with an end cap, pass
through the through hole of the nut, and
return to their original positions to complete
infinite motion.
These are the most compact type of nut.
Balls change their traveling direction with a
deflector, pass over the circumference of the
screw shaft, and return to their original posi-
tions to complete infinite motion.
These are most common types of nuts that
use a return pipe for ball circulation. The
return pipe allows balls to be picked up, pass
through the pipe, and return to their original
positions to complete infinite motion.
Pipe presser
Return pipe
Screw shaft
BallKey
Labyrinth seal
Spacer (shim plate)
Ball screw nut
Ball screw nut
Deflector Screw shaft
Ball
Greasing hole
Labyrinth seal
Ball screw nut
End cap
Ball screw
Ball
Greasing hole
End cap
Ball screw nut
Example of Structure of Return-pipe Nut
Example of Structure of Simple Nut
Example of Structure of Large-lead Nut
Return-pipe Type(Models SBN, BNF, BNT, BNFN, BIF and BTK)
Return-piece Type (Model HBN)
Deflector Type: Simple Nut (Models DK, DKN, DIK, JPF and DIR)
End-cap Type: Large-lead Nut(Models SBK, BLK, WGF, BLW, WTF, CNF and BLR)
K-51
K. Description of the Ball ScrewK
51Selectin
gaNut
7.1.2. Types by Preloading Method
Fixed-point Preloading
●Double-nut Method (Models BNFN, DKN and BLW)A spacer is inserted between two nuts to provide a preload.
(3.5 to 4.5)pitch + preloadSpacer
Applied preload Applied preload
Model BNFN Model DKN Model BLW
K-52
Constant-pressure Preloading (Model JPF)
With this method, a spring structure is installed almost in the middle of the nut, and it provides
a preload by changing the groove pitch in the middle of the nut.
Four pitches - preload
Applied preloadApplied preloadApplied preloadApplied preload Applied preloadApplied preload
Spring sectionModel JPF
Model DIRModel SBK
●Offset Preloading (Models SBN, BIF, DIK, SBK and DIR)It allows more compact design than the double-nut method. This method provides a preload by
changing the groove pitch in the middle of the nut without using a spacer.
0.5 pitch + preload
Applied preload Applied preload
Model BIFModel SBN Model DIK
K-53
K. Description of the Ball ScrewK
53Selectin
gaNut
7.2. Calculating the Axial Load7.2. Calculating the Axial Load
7.2.1. In Horizontal MountWith ordinary conveyance systems, the axial load (Fan) applied when horizontally reciprocating
the workpiece is obtained in the equation below.
Fa1 = μ · mg + f + mα………………(14)
Fa2 = μ · mg + f………………………(15)
Fa3 = μ · mg + f - mα ………………(16)
Fa4 = -μ · mg - f - mα………………(17)
Fa5 = -μ · mg - f ……………………(18)
Fa6 = -μ · mg - f + mα………………(19)
Maximum speed Vmax (m/s)
Acceleration time t1 (m/s)
Acceleration(m/s2)
Axial load during forward acceleration Fa1 (N)
Axial load during forward uniform motion Fa2 (N)
Axial load during forward deceleration Fa3 (N)
Axial load during backward acceleration Fa4 (N)
Axial load during uniform backward motion Fa5 (N)
With ordinary conveyance systems, the axial load (Fan) applied when vertically reciprocating
the workpiece is obtained in the equation below.
Fa1 = mg + f + mα……………………(20)
Fa2 = mg + f……………………………(21)
Fa3 = mg + f - mα ……………………(22)
Fa4 = mg - f - mα ……………………(23)
Fa5 = mg - f……………………………(24)
Fa6 = mg - f + mα ……………………(25)
Maximum speed Vmax (m/s)
Acceleration time t1 (m/s)
Acceleration(m/s2)
Axial load during upward acceleration Fa1 (N)
Axial load during uniform upward motion Fa2 (N)
Axial load during upward deceleration Fa3 (N)
Axial load during downward acceleration Fa4 (N)
Axial load during uniform downward motion Fa5 (N)
Axial load: FanMass: m
Guide surface Friction coefficient :μ Resistance without load: f
Axial load:Fan
Mass: m
Guide surface Friction coefficient:μ Resistance without load: f
Ascent / descent
7.2.2. In Vertical Mount
Axial load during backward deceleration Fa6 (N)
Transferred mass m (kg)
Friction coefficient of the guide surface μ (-)
Resistance of the guide surface (without load) f (N)
Axial load during downward deceleration Fa6 (N)
Transferred mass m (kg)
Resistance of the guide surface (without load) f (N)
α =Vmax
t1
α =Vmax
t1
K-54
7.3. Static Safety Factor7.3. Static Safety Factor
* The basic static load rating (C0a) is a static load with a constant direction and magnitude
whereby the sum of the permanent deformation of the rolling element and that of the raceway
on the contact area under the maximum stress is 0.0001 times the rolling element diameter.
With the Ball Screw, it is defined as the axial load.
Specific values of each Ball Screw model are indicated in the dimensional table for the corre-
sponding model number in the " General Catalog - Product Specifications," provided
separately.
The basic static load rating (C0a) generally equals to the permissible axial load of a Ball Screw.
Depending on the service conditions, it is necessary to take into account the following static
safety factor against the calculated load. When the Ball Screw is stationary or operative,
unexpected external force may be applied through inertia caused by impact or start/stop.
………(26)
where
Famax :Permissible axial load (kN)
C0a :Basic static load rating* (kN)
fS :Static safety factor (see table 1)
Famax = C0afs
Machine using theLM system Load conditions Lower limit
of fs
Table 1 Static Safety Factor (fs)
General industrial
machinery
Machine tools
Without vibrations or impact
With vibrations or impact
Without vibrations or impact
With vibrations or impact
1 to 1.3
2 to 3
1 to 1.5
2.5 to 7
K-55
K. Description of the Ball ScrewK
55Selectin
gaNut
7.4. Studying the Service Life7.4. Studying the Service Life
7.4.1. Service Life of the Ball Screw
The Ball Screw in motion under an external load receives repeated stress on its raceways and
balls. When the stress reaches the limit, the raceways break from fatigue and their surfaces
partially exfoliate in flakes. This phenomenon is called flaking. The service life of the Ball Screw
is the total number of revolutions until the first flaking occurs on any of the raceways or the
balls as a result of rolling fatigue of the material.
The service life of the Ball Screw varies from unit to unit even if they are manufactured in the
same process and used in the same operating conditions. For this reason, when determining the
service life of a Ball Screw unit, the rated life as defined below is used as a guideline.
The rated life is the total number of revolutions that 90% of identical Ball Screw units in a group
achieve without developing flaking (scale-like exfoliation of a metallic surface) after they inde-
pendently operate in the same conditions.
* The basic dynamic load rating (Ca) is used in calculating the service life when a Ball Screw
operates under a load.
The basic dynamic load rating is a load with constant direction and magnitude under which
the rated life (L) equals to 106rev. when a group of the same Ball Screw units independently
operate. (Specific basic dynamic load ratings (Ca) are indicated in the dimensional tables of
the corresponding model numbers in the " General Catalog - Product Specifications,"
provided separately.)
The service life of the Ball Screw is calculated from the equation (27) below using the basic
dynamic load rating (Ca) and the applied axial load.
………(27)
where
L :Rated life (total number of revolutions)(rev)
Ca :Basic dynamic load rating* (N)
Fa :Applied axial load (N)
fw :Load factor (see table 2)
7.4.2. Calculating the Rated Life
Rated Life (Total Number of Revolutions)
L = ( )3 ✕ 106Ca
fW · Fa
Table 2 Load Factor (fW)
Faint
Weak
Medium
Strong
Very low
V≦0.25m/s
Low
0.25<V≦1m/s
Moderate
1<V≦2m/s
High
V>2m/s
1 to 1.2
1.2 to 1.5
1.5 to 2
2 to 3.5
Vibrations/impact Speed(V) fW
K-56
Service Life TimeIf the rotation speed per minute is determined, the service life time can be calculated from the
equation (28) below using the rated life (L).
………(28)
where
Lh :Service life time (h)
N :Rotation speed per minute (min-1)
n :Reciprocations per minute (min-1)
R :Lead of the Ball Screw (mm)
RS :Stroke length (mm)
The service life in travel distance can be calculated from the equation (29) below using the
rated life (L) and the Ball Screw lead.
………(29)
where
LS :Service life in travel distance (km)
R :Ball Screw lead (mm)
If the Ball Screw is used under a preload (medium load), it is necessary to consider the applied
preload in calculating the service life since the ball screw nut already receives an internal load.
For details on applied preload for a specific model number, contact .
If an axial load acting on the Ball Screw is present, it is necessary to calculate the service life
by determining the average axial load.
The average axial load (Fm) is a constant load that equals to the service life in fluctuating load
conditions.
If the load changes in steps, the average axial load can be obtained from the equation below.
………(30)
where
Fm :Average axial load (N)
Fan :Fluctuating load (N)
Rn :Distance traveled under a load (Fn)
R :Total travel distance
Lh = =L
60 ✕ NL ✕ R
2 ✕ 60 ✕ n ✕ RS
Service Life in Travel Distance
LS = L ✕ R106
Applied Load and Service Life with a Preload Taken into Account
Average Axial Load
Fm = (Fa13R1 + Fa2
3R2 + · · · · + Fan3Rn)1
L
3
���������������������
K-57
K. Description of the Ball ScrewK
57Selectin
gaNut
To determine the average axial load using a rotation speed and time, instead of a distance, cal-
culate the average axial load by determining the distance in the equation below.
where
R = R1 + R2 + · · ·Rn
R1 = N1 · t1
R2 = N2 · t2
Rn = Nn · tn
N:Rotation speed
t:Time
■When the Applied Load Sign ChangesWhen all signs for fluctuating loads are the same, the
equation (30) applies without problem. However, if
the sign for the fluctuating load changes according
to the operation, it is necessary to calculate both the
average axial load of the positive-sign load and that
of the negative-sign load while taking in to account
the load direction (when calculating the average
axial load of the positive-sign load, assume the nega-
tive-sign load to be zero). Of the two average axial
loads, the greater value is regarded as the average
axial load for calculating the service life.
Example:
Calculate the average axial load with the following load conditions.
* The subscripts of the fluctuating load symbol and the travel distance symbol indicate operation numbers.
Average axial load of positive-sign load* To calculate the average axial load of the positive-sign load, assume Fa3 and Fa4 to be zero.
Average axial load of negative-sign load* To calculate the average axial load of the negative-sign load, assume Fa1 and Fa2 to be zero.
Accordingly, the average axial load of the positive-sign load (Fm1) is adopted as the average
axial load (Fm) for calculating the service life.
Positive-sign load
Negative-sign load
Operation
No.
No.1
No.2
No.3
No.4
10
50
–40
–10
10
50
10
70
Fluctuating load
Fan(N)
Travel distance
Rn(mm)
������������Fm1 = = 35.5NFa1
3 ✕ R1 + Fa23 ✕ R2
R1 + R2 + R3 + R4
3
Fa3
3 ✕ R3 + Fa4 3 ✕ R4
R1 + R2 + R3 + R4������������
Fm2 = = 17.2N
3
K-58
8. Studying the Rigidity8. Studying the RigidityTo increase the positioning accuracy of feed screws in NC machine tools or precision
machines, or to reduce the displacement cause by the cutting force, it is necessary to design
the rigidity of the components in a well-balanced manner.
K-58
The axial rigidity of a screw shaft varies depending on the method for mounting the shaft.
………(33)
where
A :Sectional area of the screw shaft(mm2)
d1:Screw-shaft thread minor diameter(mm)
E :Young's modulus (2.06×105 N/mm2)
L :Center distance (mm)
Fig. 1 shows an axial rigidity diagram for the
screw shaft.
When the axial rigidity of a feed screw system is K, the elastic displacement in the axial direc-
tion can be obtained using the equation (31) below.
………(31)
where
� :Elastic displacement of a feed screw system in the axial direction(μm)
Fa :Applied axial load (N)
The axial rigidity (K) of the feed screw system is obtained using the equation (32) below.
………(32)
where
K :Axial rigidity of the feed screw system (N/μm)
KS :Axial rigidity of the screw shaft (N/μm)
KN :Axial rigidity of the nut (N/μm)
KB :Axial rigidity of the support bearing (N/μm)
KH :Rigidity of the nut bracket and the support bearing bracket (N/μm)
8.1. Axial Rigidity of the Feed Screw System8.1. Axial Rigidity of the Feed Screw System
� = FaK
1K
1KS
1KN
1KB
1KH
= + + +
8.1.1. Axial Rigidity of the Screw Shaft
For Fixed-Supported (or -Free) Configuration
L
Fixed Supported(free)
Ks = A · E1000 · L
A = d12π
4
K-59
K. Description of the Ball ScrewK
59StudyingtheRigidity
………(34)
Fig. 2 on page K-60 shows an axial rigidity dia-
gram of the screw shaft in this configuration.
For Fixed-Fixed Configuration
Fixed Fixed
La b
Ks = A · E · L1000 · a · b
a = b =
KS becomes the lowest and the elastic displacement in the
axial direction is the greatest at the position of .L2
KS = 4A · E1000L
φ100
φ80φ70φ63
φ55φ50φ45φ40φ36φ32φ30φ28φ25
φ20φ18φ16φ15
φ14φ12
φ10φ8
φ6φ4
108
6 4
2
186
4
8
8
6
6
4
4
2
2
10-1
102 86 103 42 86 104
Center distance(mm)
Rigidity of the screw shaft(kN/μm)
Fig. 1 Axial Rigidity of the Screw Shaft (Fixed-Free, Fixed-Supported)
K-60
φ55φ63
φ70
φ80φ100
φ50φ45φ40φ36φ32φ30φ28φ25
φ20φ18φ16φ15φ14φ12
φ10φ8
φ6
φ4
1086 4
2
186
4
8
6
4
2
10-1
86 42102 86 103 42 86 104
Center distance(mm)
Rigidity of the screw shaft(kN/μm)
Fig. 2 Axial Rigidity of the Screw Shaft (Fixed-Fixed)
8.1.2. Axial Rigidity of the NutThe axial rigidity of the nut varies widely with preloads.
The logical rigidity in the axial direction when an axial load accounting for 30% of the basic dynamic load rating
(Ca) is applied is indicated in the dimensional table of the corresponding model number in the " General
Catalog - Product Specifications," provided separately. This value does not include the rigidity of the components
related to the nut-mounting bracket. Therefore, generally set the rigidity at roughly 80% of the value in the table.
The rigidity when the applied axial load is not 30% of the basic dynamic load rating (Ca) is calculated using the
equation (35) below.
………(35)
where
KN :Axial rigidity of the nut (N/μm)
K :Rigidity value in the dimensional table in the " General Catalog - Product Specifications,"
provided separately (N/μm)
Fa :Applied axial load (N)
Ca :Basic dynamic load rating (N)
Non-preload Type
KN = K ✕ 0.8Fa
0.3Ca( )13
K-61
K. Description of the Ball ScrewK
61StudyingtheRigidity
The logical rigidity in the axial direction when an axial load accounting for 10% of the basic
dynamic load rating (Ca) is applied is indicated in the dimensional table of the corresponding
model number in the " General Catalog - Product Specifications," provided separately.
This value doe not include the rigidity of the components related to the nut-mounting bracket.
Therefore, generally set the rigidity at roughly 80% of the value in the table.
The rigidity when the applied preload is not 10% of the basic dynamic load rating (Ca) is calcu-
lated using the equation (36) below.
………(36)
where
KN :Axial rigidity of the nut (N/μm)
K :Rigidity value in the dimensional table in the " General Catalog - Product Specifications,"
provided separately (N/μm)
Fa0 :Applied preload (N)
Ca :Basic dynamic load rating (N)
Take this factor into consideration when designing your machine. Set the rigidity as high as possible.
The rigidity of the Ball Screw support bearing varies depending on the support bearing used.
The calculation of the rigidity with a representative angular ball bearing is shown in the equa-
tion (37) below.
………(37)
KB :Axial rigidity of the support bearing (N/μm)
Fa0 :Applied preload of the support bearing (N)
�a0 :Axial displacement (μm)
Q :Axial load (N)
Da :Ball diameter of the support bearing (mm)
α :Initial contact angle of the support bearing (degree)
Z :Number of balls
For details of a specific support bearing, contact its manufacturer.
Preload Type
KN = K ✕ 0.8Fa0
0.1Ca( )13
8.1.3. Axial Rigidity of the Support Bearing
8.1.4. Axial Rigidity of the Nut Bracket and the Support Bearing Bracket
KB ≒ 3Fa0
�a0
�a0 =0.45sinα
Q2
Da( )13
Q =Fa0
Zsinα
K-62
9. Studying the Positioning Accuracy9. Studying the Positioning Accuracy
9.1. Causes of Error in Positioning Accuracy9.1. Causes of Error in Positioning Accuracy
Causes of error in the positioning accuracy include lead accuracy, axial clearance and axial
rigidity of the feed screw system. Other important factors include thermal displacement from
heat and orientation change of the guide system during traveling.
K-62
9.2. Studying the Lead Accuracy9.2. Studying the Lead Accuracy
It is necessary to select the correct accuracy grade of the Ball Screw that satisfies the required
positioning accuracy from Ball Screw accuracies (table 1 on page K-24). Table 1 shows exam-
ples of selecting accuracy grades by application.
K-62
9.3. Studying the Axial Clearance9.3. Studying the Axial Clearance
The axial clearance is not a factor of positioning accuracy in single-directional feed. However,
it will cause backlash when the feed direction is inversed or the axial load is inversed. Select
an axial clearance that meets the required backlash from tables 9 and 11 on page K-31.
Table 1 Examples of Selecting Accuracy Grades by Application
Application
Axis
Accuracygrade
C0
C1
C2
C3
C5
C7
C8
C10
Lathe
NC machine tools
X Z XY Z XY Z XY Z X Y Z X Z XY Z XY Z UV XY
Machiningcenter
Drillingmachine
Jigborer
Surfacegrinder
Cylindergrinder
Electric
dischargemachine
Electric
dischargemachine
Wirecutting
Punchingpress
○○○○
○○
○○○
○○○
○○ ○○
○○
○○
○○
○○○○
○○○○
○○○
○○○
○○○○○○○
○○○
○○○○
○○○ ○
○○
Application
Axis
Accuracygrade
C0
C1
C2
C3
C5
C7
C8
C10
Laserprocessing
machine
X Z Assembly Other Assembly OtherWoodworkingmachine
General-purposemachine;
dedicatedmachine
Cartesian
coordinate
Vertical
articulatedtype
Officeequipment
Injectionmoldingmachine
Imageprocessingmachine
3Dmeasuringinstrument
Electroniccomponentinserter
Printedboarddrillingmachine
Prober
Wirebonder
Chemicaltreatmentmachine
Photolithographymachine
Cylindricalcoordinate
○○○
○○○
○○○○
○○○○○
○○○○
○○○○
○○○
○○
○○○
○○○○○○○○
○○
○○○○
○○○○○
○○○○
○○○
○○○
○○○
○○○○
NC machine tools Industrial robots Semiconductor related machines
K-64
9.4. Studying the Axial Rigidity of the Feed Screw System9.4. Studying the Axial Rigidity of the Feed Screw System
Of the axial rigidities of the feed screw system, the axial rigidity of the screw shaft fluctuates
according to the stroke position. When the axial rigidity is large, such change in the axial rigidi-
ty of the screw shaft will affect the positioning accuracy. Therefore, it is necessary to take
into account the rigidity of the feed screw system (pages K-58 to K-61).
Example: Positioning error due to the axial rigidity of the feed screw system during vertical transfer
L
1000N
500N
[Service conditions]
Transferred weight: 1,000 N; table weight: 500 N
Ball Screw used: model BNF2512 - 2.5 (screw-shaft thread minor diameter d1 = 21.9 mm)
Stroke length: 600 mm(L=100 mm to 700 mm)
Screw shaft mounting type: fixed-supported
■ConsiderationThe difference in axial rigidity between L = 100 mm and L = 700 mm applied only to the axial
rigidity of the screw shaft. Therefore, positioning error due to the axial rigidity of the feed
screw system equals to the difference in the axial displacement of the screw shaft between L
= 100 mm and L = 700 mm.
K-65
K. Description of the Ball ScrewK
65StudyingthePositio
ningAccuracy
■Axial Rigidity of the Screw Shaft (see pages K-58 and K-59)
① When L = 100 mm
② When L = 700 mm
■Axial Displacement due to Axial Rigidity of the Screw Shaft① When L = 100 mm
② When L = 700 mm
■Positioning Error due to Axial Rigidity of the Feed Screw SystemPositioning accuracy=�1-�2=1.9-13.5
=-11.6μm
Therefore, the positioning error due to the axial rigidity of the feed screw system is 11.6 μm.
Ks = = =1000LA · E
4π
4π1000 ✕ L
376.5 ✕ 2.06 ✕ 105 L
77.6 ✕ 103
A = d1
2 = ✕ 21.92 = 376.5mm2
E = 2.06 ✕ 105 N/mm2
KS1 = = 776 N/μm100
77.6 ✕ 103
KS2 = = 111 N/μm700
77.6 ✕ 103
�1 = = = 1.9μmKS1
Fa776
1000 + 500
�2 = = = 13.5μmKS2
Fa111
1000 + 500
K-66
9.5. Studying the Thermal Displacement through Heat Generation9.5. Studying the Thermal Displacement through Heat Generation
If the temperature of the screw shaft increases during operation, the screw shaft is elongated
due to heat thereby to lower the positioning accuracy. The expansion and contraction of the
screw shaft is calculated using the equation (38) below.
�RR = ρ×�t×RR ………(38)
where
�R :Axial expansion/contraction of the screw shaft(mm)
ρ :Thermal expansion coefficient (12×10-6/℃)
�t :Temperature change in the screw shaft (℃)
R :Effective thread length (mm)
Thus, if the temperature of the screw shaft increases by 1℃, the screw shaft is elongated by
12 μm per meter. Therefore, the faster the Ball Screw travels, the more heat is generated.
And, the higher the temperature, the lower the positioning accuracy become. Accordingly, if
high accuracy is required, it is necessary to take a measure to cope with temperature
increase.
●Minimize preloads on the Ball Screw and the support bearing.●Increase Ball Screw lead and reduce rotation speed.●Select a correct lubricant (see page A-109).●Cool the circumference of the screw shaft with a lubricant or air.
●Set a negative target value for the reference traveldistance of the Ball Screw.
Generally, set a negative target value for the reference travel distance assuming atemperature increase of 2℃ to 5℃ by heat.(-0.02 mm to -0.06 mm/m)
●Pretension the screw shaft (see Fig. 3 of the struc-ture on page K-42).
9.5.1. Measures to Cope with Temperature Rise
Minimize Heat Generation
Avoid Effect of Temperature Rise through Heat Generation
K-67
K. Description of the Ball ScrewK
67StudyingthePositio
ningAccuracy
9.6. Studying Orientation Change during Traveling9.6. Studying Orientation Change during Traveling
The lead accuracy of the Ball Screw equals to the positioning accuracy of the shaft center of
the Ball Screw. Normally, the point where the highest positioning accuracy is required
changes according to the ball screw center and the vertical or horizontal direction. Therefore,
orientation change during traveling affects the positioning accuracy.
The largest factor of orientation change affecting the positioning accuracy is pitching if the
change occurs in the ball screw center and the vertical direction, and yawing if the change
occurs in the horizontal direction.
Accordingly, it is necessary to study the orientation change (accuracy in pitching, yawing,
etc.) during traveling on the basis of the distance from the ball screw center to the location
where positioning accuracy is required.
Positioning error due to pitching and yawing is obtained using the equation (39) below.
A = RR✕ sinθ………(39)
where
A :Positioning accuracy due to pitching (or yawing) (mm)
R :Vertical (or horizontal) distance from the ball screw center (mm)(see Fig. 1)
θ :Pitching (or yawing) (℃)
θ
θ
R
A
A
R
Fig. 1
K-68
10. Studying the Rotation Torque10. Studying the Rotation TorqueThe rotation torque required to convert rotational motion of the Ball Screw into linear motion is
obtained using the equation (40) below.
●During uniform motionTt = T1 + T2 + T4 ………(40)
where
Tt :Rotation torque required during uniform motion(N-mm)
T1 :Friction torque due to external load (N-mm)
T2 :Preload torque of the Ball Screw (N-mm)
T4 :Other torque (N-mm)
(friction torque of the support bearing and oil seal)
●During accelerationTK = Tt + T3 ………(41)
where
TK :Rotation torque required during acceleration(N-mm)
T3 :Torque required for acceleration (N-mm)
●During decelerationTg = Tt - T3 ………(42)
where
Tg :Rotation torque required for deceleration(N-mm)
K-68
Of the turning forces required for the Ball Screw, the rotation torque needed for an external
load (guide surface resistance or external force) is obtained using the equation (43) below
………(43)
where
T1 :Friction torque due to an external load (N-mm)
Fa :Axial load (N)
R :Ball Screw lead (mm)
η :Ball Screw efficiency (0.9 to 0.95)
A :Reduction ratio
10.1. Friction Torque Due to an External Load10.1. Friction Torque Due to an External Load
T1 = · A2π · η Fa · R
K-69
K. Description of the Ball ScrewK
69StudyingtheRotatio
nTorque
10.2. Torque Due to a Preload on the Ball Screw10.2. Torque Due to a Preload on the Ball Screw
For a preload on the Ball Screw, see "Preload Torque" on page K-35.
T2 = Td · A ………(44)
where
T2 :Torque due to a preload on the Ball Screw (N-mm)
Td :Preload torque of the Ball Screw (N-mm)
A :Reduction ratio
K-69
K. Description of the Ball ScrewK
69StudyingtheRotatio
nTorque
10.3. Torque Required for Acceleration10.3. Torque Required for Acceleration
T3 = J×ω'×103 ………(45)
where
T3 :Torque required for acceleration (N-mm)
J :Inertial moment (kg-m2)
ω' :Angular acceleration (rad/sec2)
m :Transferred mass (kg)
R :Ball screw lead (mm)
JS :Inertial moment of the screw shaft (kg-m2)
(indicated in the dimensional table of the respective model number in the " General
Catalog - Product Specifications," provided separately)
A :Reduction ratio
JA :Inertial moment of gears, etc. attached to the screw shaft side (kg-m2)
JB :Inertial moment of gears, etc. attached to the motor side(kg-m2)
Nm:Motor rotation speed per minute (min-1)
t :Acceleration time (sec)
[Ref.]Inertial moment of a round object
J :inertial moment (kg-m2)
m :Mass of a round object (kg)
D :Screw shaft outer diameter (mm)
J = m · A2 · 10-6 + JS · A2 + JA · A2 + JB
2πR( )
2
ω' = 60t2π · Nm
J = 8 · 106
m · D2
K-70
11. Studying the Driving Motor11. Studying the Driving MotorWhen selecting a driving motor required to rotate the Ball Screw, normally take into account
the rotation speed, rotation torque and minimum feed distance.
K-70
11.1. When Using a Servomotor11.1. When Using a Servomotor
11.1.1. Rotation Speed
The rotation speed required for the motor is obtained using the equation (46) based on the
feed speed, Ball Screw lead and reduction ratio.
………(46)
where
NM :Required rotation speed of the motor (min-1)
V :Feed speed (m/s)
R :Ball Screw lead (mm)
A :Reduction ratio
The rated rotation speed of the motor must be equal to or above the calculated value (NM) above.
NM≦NR
Where
NR :The rated rotation speed of the motor (min-1)
11.1.2. Required Resolution
Resolutions required for the encoder and the driver are obtained using the equation (47) based
on the minimum feed distance, Ball Screw lead and reduction ratio.
………(47)
where
B :Resolution required for the encoder and the driver(p/rev)
R :Ball Screw lead (mm)
A :Reduction ratio
S :Minimum feed distance (mm)
NM = ✕ R
V ✕ 1000 ✕ 60A1
B = S
R · A
K-71
K. Description of the Ball ScrewK
71StudyingtheDriv
ingMotor
11.1.3. Motor Torque
The torque required or the motor differs between uniform motion, acceleration and deceleration.
To calculate the rotation torque, see "Studying the Rotation Torque" on page K-68.
a Maximum torque
The maximum torque required for the motor must be equal to or below the maximum instan-
taneous torque of the motor.
Tmax≦Tpmax
where
Tmax :Maximum torque acting on the motor
Tpmax :Maximum instantaneous torque of the motor
b Effective value of the torque
The effective value of the torque required for the motor must be calculated. The effective value
of the torque is obtained using the equation (48) below.
………(48)
where
Trms :Effective value of the torque (N-mm)
Tn :Fluctuating torque (N-mm)
tn :Time during which the torque Tn is applied(s)
t :Cycle time (s)
(t=t1+t2+t3)
The calculated effective value of the torque must be equal to or below the rated torque of the
motor.
Trms≦TR
where
TR :Rated torque of the motor (N-mm)
Trms = T1
2 ✕ t1 + T22 ✕ t2 + T3
2 ✕ t3
t����������������
11.1.4. Inertial Moment
The inertial moment required for the motor is obtained using the equation (49) below.
………(49)
where
JM :Inertial moment required for the motor (kg-m2)
C :Factor determined by the motor and the driver
(It is normally between 3 to 10. However, it varies depending on the motor and the driver. Check
the specific value in the catalog by the motor manufacturer.)
The inertial moment of the motor must be equal to or above the calculated JM value.
JM = CJ
K-72
11.2. When Using a Stepping Motor (Pulse Motor)11.2. When Using a Stepping Motor (Pulse Motor)
11.2.1. Minimal Feed (Feed per Step)
The step angle required for the motor and the driver is obtained using the equation (50) below
based on the minimum feed distance, Ball Screw lead and reduction ratio.
………(50)
where
E :Step angle required for the motor and the driver (degree)
S :Minimum feed distance (mm)
(feed per step)
R :Ball Screw lead (mm)
A :Reduction ratio
11.2.2. Pulse Speed and Motor Torque
a Pulse speed
The pulse speed is obtained using the equation (51) below based on the feed speed and the
minimum feed distance.
………(51)
where
f :Pulse speed (Hz)
V :Feed speed (m/s)
S :Minimum feed distance (mm)
b Torque required for the motor
The torque required for the motor differs between uniform motion, acceleration and decelera-
tion. To calculate the rotation torque, see "Studying the Rotation Torque" on page K-68.
Thus, the pulse speed required for the motor and the required torque can be calculated in the
manner described above.
Although the torque varies depending on the motor used, normally the calculated torque should
be doubled to ensure safety. Check if the torque can be used in the motor speed-torque curve.
E = R · A360S
f =S
V ✕ 1000
K-73
K. Description of the Ball ScrewK
73ExamplesofSelectin
gaBallS
crew
12. Examples of Selecting a Ball Screw12. Examples of Selecting a Ball Screw
12.1. High Speed Conveyance System (Horizontal Use)12.1. High Speed Conveyance System (Horizontal Use)
12.1.1. Selection Conditions
Table mass m1 =60kg
Workpiece mass m2 =20kg
Stroke length RS =1000mm
Maximum speed Vmax =1m/s
Acceleration time t1 =0.15s
Deceleration time t3 =0.15s
Reciprocations per minute n =8min-1
Backlash 0.15mm
Positioning accuracy ±0.3 mm/1000 mm
(Perform positioning from
the negative direction)
Positioning repeatability ±0.1 mm
Minimum feed distance s =0.02mm/pulse
Desired service life time 30000h
Driving motor AC servomotor
Rated rotation speed: 3,000 min-1
Motor inertial moment Jm =1×10-3 kg・m2
Deceleration mechanism None (direct coupling) A=1
Friction coefficient of the guide surface
μ =0.003 (rolling)
Resistance of the guide surface f =15 N (without load)
12.1.2. Selection Items
Screw shaft diameter
Lead
Nut model No.
Accuracy
Axial clearance
Screw shaft support method
Driving motor
Workpiece mass+
+Table mass
m2m1
Ball screw nutBall screw shaftMotor
K-74
12.1.3. Selecting Lead Accuracy and Axial Clearance
●Selecting lead accuracyTo achieve positioning accuracy of ±0.3 mm/1,000 mm:
The lead accuracy must be ±0.09 mm/300 mm or higher.
Therefore, the accuracy grade of the Ball Screw (see table 1 on page K-24) needs to be:
C7 (travel distance error: ±0.05 mm/300 mm)
Accuracy grade C7 is available for both Rolled and Precision Ball Screws. Assume that a
Rolled Ball Screw is selected here because it is less costly.
●Selecting axial clearanceTo satisfy the backlash of 0.15 mm, it is necessary to select a Ball Screw with an axial clear-
ance of 0.15 mm or less.
Therefore, a Rolled Ball Screw model with a screw shaft diameter of 32 mm or less that meets
the axial clearance of 0.15 mm or less (see table 11 on page K-31) meets the requirements.
Thus, a Rolled Ball Screw model with a screw shaft diameter of 32 mm or less and accuracy
grade of C7 is selected.
12.1.4. Selecting a Screw Shaft
●Assuming the screw shaft lengthAssume the overall nut length to be 100 mm and the screw shaft end length to be 100 mm.
Therefore, the overall length is determined as follows based on the stroke length of 1,000 mm.
1000 + 200 = 1200 mmThus, the screw shaft length is assumed to be 1,200 mm.
●Selecting leadWith the driving motor's rated rotation speed being 3,000 min-1 and the maximum speed 1 m/s,
the Ball Screw lead is obtained as follows:
Therefore, it is necessary to select a type with a lead of 20 mm or longer.
In addition, the Ball Screw and the motor can be mounted in direct coupling without using a
reduction gear. The minimum resolution per revolution of an AC servomotor is obtained based
on the resolution of the encoder (1,000 p/rev; 1,500 p/rev) provided as a standard accessory
for the AC servomotor, as indicated below.
1000±0.3
300±0.09
=
1 ✕ 1000 ✕ 60
3000 = 20 mm
K-75
K. Description of the Ball ScrewK
75ExamplesofSelectin
gaBallS
crew
1000 p/rev(without multiplication)
1500 p/rev(without multiplication)
2000 p/rev(doubled)
3000 p/rev(doubled)
4000 p/rev(quadrupled)
6000 p/rev(quadrupled)
To meet the minimum feed distance of 0.02 mm/pulse, which is the selection requirement, the
following should apply.
Lead20mm ―― 1000 p/rev
30mm ―― 1500 p/rev
40mm ―― 2000 p/rev
60mm ―― 3000 p/rev
80mm ―― 4000 p/rev
●Selecting a screw shaft diameterThose Ball Screw models that meet the requirements defined in Section 12.1.3.: screw shaft
diameter of 32 mm or less and being a rolled Ball Screw; and the requirement defined in
Section 12.1.4.: lead being 20, 30, 40, 60 or 80 mm (see table 4 on page K-40) are as fol-
lows.
Shaft diameter Lead
15mm ―― 20mm
15mm ―― 30mm
20mm ―― 20mm
20mm ―― 40mm
30mm ―― 60mm
Since the screw shaft length has to be 1,200 mm as indicated in Section 12.1.4., the shaft diam-
eter of 15 mm is insufficient. Therefore, the Ball Screw should have a screw shaft diameter of 20
mm or greater.
Accordingly, there are three combinations of screw shaft diameters and leads that meet the
requirements: screw shaft diameter of 20 mm/lead of 20 mm; 20 mm/40 mm; and 30 mm/60 mm.
●Selecting a screw shaft support methodSince the assumed type has a long stroke length of 1,000 mm and operates at high speed of 1
m/s, select either the fixed-supported or fixed-fixed configuration for the screw shaft support.
However, the fixed-fixed configuration requires a complicated structure, needs high accuracy
in the installation and is costly.
Accordingly, the fixed-supported configuration is selected as the screw shaft support method.
K-76
●Studying the permissible axial load■Calculating the maximum axial load
Guide surface resistance f =15 N(without load)
Table mass m1 =60 kg
Workpiece mass m2 =20 kg
Friction coefficient of the guide surface μ =0.003
Maximum speed Vmax =1 m/s
Gravitational acceleration g =9.807 m/s2
Acceleration time t1 =0.15 s
Hence,
Acceleration:
During forward acceleration:
Fa1 = μ · (m1 + m2) g + f + (m1 + m2) · α = 550 N
During forward uniform motion:
Fa2 = μ · (m1 + m2) g + f = 17 N
During forward deceleration:
Fa3 = μ · (m1 + m2) g + f – (m1 + m2) · α = –516 N
During backward acceleration:
Fa4 = –μ · (m1 + m2) g – f – (m1 + m2) · α = –550 N
During uniform backward motion:
Fa5 = –μ · (m1 + m2) g – f = – 17 N
During backward deceleration:
Fa6 = –μ · (m1 + m2) g – f + (m1 + m2) · α = 516 N
Thus, the maximum axial load applied on the Ball Screw is as follows:
Famax = Fa1 = 550 N
The smaller the screw shaft diameter, the smaller the permissible axial load on the shaft
becomes. Therefore, if there is no problem with a shaft diameter of 20 mm and a lead of 20
mm (smallest thread minor diameter of 17.5 mm), then the screw shaft diameter of 30 mm
should meet the requirements. Thus, the following calculations for the buckling load and the
permissible compressive and tensile load of the screw shaft are performed while assuming a
screw shaft diameter of 20 mm and a lead of 20 mm.
α = = 6.67 m/s2Vmax
t1
K-77
K. Description of the Ball ScrewK
77ExamplesofSelectin
gaBallS
crew
■Buckling load of the screw shaftCoefficient determined by the mounting method: η2=20(see page K-43)
Since the mounting method for the section between the nut and the bearing, where buck-
ling is to be considered, is "fixed-fixed:"
Center distance: Ra=1100 mm(estimate)
Thread minor diameter: d1=17.5 mm
■Permissible compressive and tensile load of the screw shaftP2 = 116 ✕ d1
2 = 116 ✕ 17.52 = 35500 NThus, the buckling load and the permissible compressive and tensile load of the screw shaft
are at least equal to the maximum axial load. Therefore, a Ball Screw that meets these require-
ments can be used without a problem.
●Studying the permissible rotation speed■Maximum rotation speedScrew shaft diameter: 20 mm; lead: 20 mm
Maximum speed: Vmax=1 m/s
Lead: R=20 mm
Screw shaft diameter: 20 mm; lead: 40 mmMaximum speed: Vmax=1 m/s
Lead: R=40 mm
Screw shaft diameter: 30 mm; lead: 60 mmMaximum speed: Vmax=1 m/s
Lead: R=60 mm
Nmax = = 3000 min–1Vmax ✕ 60 ✕ 103
R
Nmax = = 1500 min–1Vmax ✕ 60 ✕ 103
R
Nmax = = 1000 min–1Vmax ✕ 60 ✕ 103
R
P1 = η2 · ✕ 104 = 20 ✕ ✕ 104 = 15500 Nd14
Ra2
17.54
11002
K-78
■Permissible rotation speed determined by the critical speed of the screw shaftCoefficient determined by the mounting method: λ2=15.1(see page K-45)
Since the mounting method for the section between the nut and the bearing, where critical
speed is to be considered, is "fixed-supported:"
Center distance: Rb=1100 mm(estimate)
Screw shaft diameter: 20 mm; lead: 20mm and 40 mmScrew shaft thread minor diameter: d1=17.5mm
Screw shaft diameter: 30 mm; lead: 60 mmScrew shaft thread minor diameter: d1=26.4 mm
■Permissible rotation speed determined by the DN valueScrew shaft diameter: 20 mm; lead: 20 mm and 40mm (large-lead Ball Screw)
Ball center diameter: D=20.75 mm
Screw shaft diameter: 30 mm; lead: 60 mm (large-lead Ball Screw)Ball center diameter: D=31.25 mm
Thus, with a Ball Screw having a screw shaft diameter of 20 mm and a lead of 20 mm, the
maximum rotation speed exceeds the critical speed.
In contrast, a combination of a screw shaft diameter of 20 mm and a lead of 40 mm, and
another of a screw shaft diameter of 30 mm and a lead of 60 mm, meet the critical speed and
the DN value.
Accordingly, a Ball Screw with a screw shaft diameter of 20 mm and a lead of 40 mm, or with
a screw shaft diameter of 30 mm and a lead of 60 mm, is selected.
N1 = λ2 ✕ 107 = 15.1 ✕ ✕ 107 = 2180 min–1
Rb2
d1
11002
17.5
N1 = λ2 ✕ 107 = 15.1 ✕ ✕ 107 = 3294 min–1
Rb2
d1
11002
26.4
N2 = = = 3370 min–1 D
7000020.7570000
N2 = = = 2240 min–1 D
7000031.2570000
K-79
K. Description of the Ball ScrewK
79ExamplesofSelectin
gaBallS
crew
12.1.5. Selecting a Nut
●Selecting a Nut Model NumberRoller Ball Screw models with a screw shaft diameter of 20 mm and a lead of 40 mm, or with a
screw shaft diameter of 30 mm and a lead of 60 mm, are large-lead Rolled Ball Screw model
WTF variations. The following variations are selected.
WTF2040-2
(Ca=5.4 kN, C0a=13.6 kN)
WTF2040-3
(Ca=6.6 kN, C0a=17.2 kN)
WTF3060-2
(Ca=11.8 kN, C0a=30.6 kN)
WTF3060-3
(Ca=14.5 kN, C0a=38.9 kN)
●Studying the Permissible Axial LoadStudy the permissible axial load of model WTF2040-2 (C0a = 13.6 kN).
Assuming that this model is used in a high-speed conveyance system and an impact load is
applied during deceleration, set the static safety factor (fS) at 2.5 (see table 1 on page K-54).
The obtained permissible axial load is greater than the maximum axial load of 550 N, and there-
fore, there will be no problem with this model.
■Calculating the travel distanceMaximum speed: Vmax =1 m/s
Acceleration time: t1 =0.15 s
Deceleration time: t3 =0.15 s
Travel distance during acceleration
Travel distance during uniform motion
Travel distance during deceleration
C0afS
13.62.5
= = 5.44 kN = 5440 N
R1,4 = ✕ 103 = ✕ 103 = 75 mm2
Vmax · t1
21 ✕ 0.15
R2,5 = R3 – ✕ 103 = 1000 – ✕ 103 = 850 mm2
Vmax · t1 + Vmax · t3
21 ✕ 0.15 + 1 ✕ 0.15
R3,6 = ✕ 103 = ✕ 103 = 75 mm2
Vmax · t3
21 ✕ 0.15
K-80
Based on the conditions above, the relationship between the applied axial load and the travel
distance is shown in the table below.
* The subscript (N) indicates a motion number.
Since the load direction (as expressed in positive or negative sign) is reversed with Fa3, Fa4
and Fa5, calculate the average axial load in the two directions.
■Average axial loadAverage axial load in the positive direction
Since the load direction varies, calculate the average axial load while assuming Fa3,4,5 = ON.
Average axial load in the negative direction Since the load direction varies, calculate the average axial load while assuming Fa1,2,6 = ON.
Since Fm1 = Fm2, assume the average axial load to be Fm = Fm1 = Fm2 = 225 N.
■Rated lifeLoad factor: fW=1.5 (see table 2 on page K-55)
Average load: Fm=225 N
Rated life L(rev.)
Motion
No.1:During forward acceleration
No.2:During forward uniform motion
No.3:During forward deceleration
No.4:During backward acceleration
No.5:During backward uniform motion
No.6:During backward deceleration
550
17
–516
–550
–17
516
75
850
75
75
850
75
Applied axial load
FaN(N)
Travel distance
RN(mm)
�����������������Fm1 = = 225 NFa1
3 ✕ R1 + Fa23 ✕ R2 + Fa6
3 ✕ R6
R1 + R2 + R3 + R4 + R5 + R6
3
Fa3
3 ✕ R3 + Fa4 3 ✕ R4 + Fa5
3 ✕ R5
R1 + R2 + R3 + R4 + R5 + R6������������������
Fm2 = = 225 N
3
L = ✕ 106
fw · Fm
Ca( )3
Model No. under
consideration
WTF 2040-2
WTF 2040-3
WTF 3060-2
WTF 3060-3
5400
6600
11800
14500
4.10 ✕ 109
7.47 ✕ 109
4.27 ✕ 1010
7.93 ✕ 1010
Dynamic load rating
Ca(N)
Rated life
L(rev.)
K-81
K. Description of the Ball ScrewK
81ExamplesofSelectin
gaBallS
crew
■Reciprocations per minuteReciprocations per minute: n=8 min-1
Stroke: RS=1000 mm
Lead :R=40 mm
Lead :R=60 mm
■Calculating the service life time on the basis of the rated lifeWTF2040-2
Rated life: L=4.1×109 rev.
Average rotation speed per minute: Nm=400 min-1
WTF2040-3Rated life: L=7.47×109 rev.
Average rotation speed per minute: Nm=400 min-1
WTF3060-2Rated life: L=4.27×1010 rev.
Average rotation speed per minute: Nm=267 min-1
WTF3060-3Rated life: L=7.93×1010 rev.
Average rotation speed per minute: Nm=267 min-1
Nm = = = 267 min–1
R
2 ✕ n ✕ Rs
602 ✕ 8 ✕ 1000
Lh = = = 171000 h60 ✕ Nm
L60 ✕ 4004.1 ✕ 109
Lh = = = 2670000 h60 ✕ Nm
L60 ✕ 267
4.27 ✕ 1010
Lh = = = 4950000 h60 ✕ Nm
L60 ✕ 267
7.93 ✕ 1010
Lh = = = 311000 h60 ✕ Nm
L60 ✕ 4007.47 ✕ 109
Nm = = = 400 min–1
R
2 ✕ n ✕ Rs
402 ✕ 8 ✕ 1000
K-82
■Calculating the service life in travel distance on the basis of the rated lifeWTF2040-2
Rated life: L=4.1×109 rev.
Lead: R=40 mm
LS = L ✕ R ✕ 10 – 6 = 164000 km
WTF2040-3Rated life: L=7.47×109 rev.
Lead: R=40 mm
LS = L ✕ R ✕ 10 – 6 = 298800 km
WTF3060-2Rated life: L=4.27×1010 rev.
Lead: R=60 mm
LS = L ✕ R ✕ 10 – 6 = 2562000 km
WTF3060-3Rated life: L=7.93×1010 rev.
Lead: R=60 mm
LS = L ✕ R ✕ 10 – 6 = 4758000 km
With all the conditions stated above, the following models satisfying the desired service life
time of 30,000 hours are selected.
WTF 2040-2
WTF 2040-3
WTF 3060-2
WTF 3060-3
K-83
K. Description of the Ball ScrewK
83ExamplesofSelectin
gaBallS
crew
12.1.6. Studying the RigiditySince the conditions for selection do not include rigidity and this element is not particularly
necessary, it is no described here.
12.1.7. Studying the Positioning Accuracy●Studying the lead accuracyAccuracy grade C7 was selected in Section 12.1.3.
C7 (travel distance error:±0.05mm/300mm)
●Studying the axial clearanceSince positioning is performed in a given direction only, axial clearance is not included in the
positioning accuracy. As a result, there is no need to study the axial clearance.
WTF2040: axial clearance: 0.1 mm
WTF3060: axial clearance: 0.14 mm
●Studying the axial rigiditySince the load direction does not change, it is unnecessary to study the positioning accuracy
on the basis of the axial rigidity.
●Studying the thermal displacement due to heatAssume the temperature rise during operation to be 5℃.
The positioning accuracy based on the temperature rise is obtained as follows:
�R = ρ ✕ �t ✕ R= 12 ✕ 10-6 ✕ 5 ✕ 1000= 0.06 mm
●Studying the orientation change during travelingSince the ball screw center is 150 mm away from the point where the highest accuracy is
required, it is necessary to study the orientation change during traveling. Assume that pitch-
ing can be done within ±10 seconds because of the structure. The positioning error due to
the pitching is obtained as follows:
�a = R ✕ sinθ= 150 ✕ sin(±10'')= ± 0.007 mm
Thus, the positioning accuracy (�p) is obtained as follows:
Accordingly, the selection requirements are met.
Since models WTF2040-2, WTF2040-3, WTF3060-2 and WTF3060-3 meet the selection
requirements throughout the studying process in Section 12.1.3. to Section 12.1.7., the most
compact model WTF2040-2 is selected.
�p = ± 0.007 + 0.06 = 0.234 mm± 0.05 ✕ 1000300
K-84
12.1.8. Studying the Rotation Torque
●Friction torque due to an external torqueThe friction torque is obtained as follows:
●Torque due to a preload on the Ball ScrewThe Ball Screw is not provided with a preload.
●Torque required for accelerationInertial moment:
The inertial moment per unit length of the screw shaft can be specified as follows.
Since 1.23×10-3 kg・cm2/mm(see the dimensional table in the " General Catalog -
Product Specifications," provided separately), the inertial moment of the screw shaft with an
overall length of 1,200 mm is obtained as follows.
Js = 1.23 ✕ 10-3 ✕ 1200 = 1.48 kg · cm2
= 1.48 ✕ 10-4 kg · m2
Angular acceleration:
Based on the above, the torque required for acceleration is obtained as follows.
T2 = (J + Jm) ✕ ω´ = (3.39 ✕ 10– 3 + 1 ✕ 10– 3) ✕ 1050 = 4.61N · m= 4.61 ✕ 103 N · mm
Therefore, the required torque is specified as follows.
During acceleration:
Tk = T1 + T2 = 120 + 4.61×103 = 4730 N · mmDuring uniform motion:
Tt = T1 = 120 N・mmDuring deceleration:
Tg = T1 – T2 = 120 – 4.61×103 = – 4490 N · mm
T1 = · A = × 1 = 120 N · mm2π · η Fa · R
2×π×0.917×40
J = (m1 + m2) · A2 ✕ 10–6 + Js · A2 = (60 + 20) ✕ 12
✕ 10–6 + 1.48 ✕ 10–4 ✕ 12
= 3.39 ✕ 10–3 kg · m2
2 ✕ πR( )
2
2 ✕ π40( )
2
ω' = = = 1050 rad/s2
60 · t1
2π · Nm60 ✕ 0.152π ✕ 1500
K-85
K. Description of the Ball ScrewK
85ExamplesofSelectin
gaBallS
crew
12.1.9. Studying the Driving Motor
●Rotation speedSince the Ball Screw lead is selected based on the rated rotation speed of the motor, it is
unnecessary to study the rotation speed of the motor.
Maximum working rotation speed:1500 min-1
Rated rotation speed of the motor:3000 min-1
●Minimum feed distance:As with the rotation speed, the Ball Screw lead is selected based on the encoder normally used
for an AC servomotor. Therefore, it is unnecessary to study this factor.
Encoder resolution:1000 p/rev
Doubled:2000 p/rev
●Motor torque:The torque during acceleration calculated in Section 12.1.8. is the required maximum torque.
Tmax = 4730 N · mmTherefore, the instantaneous maximum torque of the AC servomotor needs to be at least
4,730 N-mm.
●Effective torque valueThe selection requirements and the torque calculated in Section 12.1.8. can be expressed as
follows.
During acceleration:
Tk = 4730 N · mmt1 = 0.15 s
During uniform motion:
Tt = 120 N · mmt2 = 0.85 s
During deceleration:
Tg = 4490 N · mmt3 = 0.15 s
When stationary:
TS = 0t4 = 2.6 sec
K-86
Therefore, the effective torque is obtained as follows.
Accordingly, the rated torque of the motor must be 1,305 N-mm or greater.
●Inertial momentThe inertial moment applied to the motor equals to the inertial moment calculated in Section
12.1.8.
J = 3.39 ✕ 10-3 kg · m2
Normally, the motor needs to have an inertial moment at least one tenth of the inertial moment
applied to the motor, although the specific value varies depending on the motor manufacturer.
Therefore, the inertial moment of the AC servomotor must be 3.39×10-4kg-m2 or greater.
The selection has been completed.
Trms = =Tk
2 · t1 + Tt2 · t2 + Tg
2 · t3 + Ts2 · t4
t1 + t2 + t3 + t4 0.15 + 0.85 + 0.15 + 2.6= 1305 N · mm
47302 ✕ 0.15 + 1202 ✕ 0.85 + 44902 ✕ 0.15 + 0��������������� ���������������������
K-87
K. Description of the Ball ScrewK
87ExamplesofSelectin
gaBallS
crew
12.2. Vertical Conveyance System12.2. Vertical Conveyance System
12.2.1. Selection Conditions
Table mass m1 =40 kg
Workpiece mass m2 =10 kg
Stroke length Rs =600 mm
Maximum speed Vmax =0.3 m/s
Acceleration time t1 =0.2 s
Deceleration time t3 =0.2 s
Reciprocations per minute n =5 min-1
Backlash 0.1 mm
Positioning accuracy ±0.7 mm/600 mm
Positioning repeatability ±0.05 mm
Minimum feed distance s =0.01 mm/pulse
Service life time 20000 h
Driving motor AC servomotor
Rated rotation speed:3000 min-1
Inertial moment of the motor Jm =5×10-5 kg・m2
Reduction mechanism None (direct coupling)
Frictional coefficient of the guide surface
μ =0.003 (rolling)
Resistance of the guide surface f =20 N (without load)
12.2.2. Selection Items
Screw shaft diameter
Lead
Nut model No.
Accuracy
Axial clearance
Screw shaft support method
Driving motor
m2
m1
600
K-88
12.2.3. Selecting Lead Accuracy and Axial Clearance
●Selecting lead accuracyTo achieve positioning accuracy of ±0.7 mm/600 mm:
The lead accuracy must be ±0.35 mm/300 mm or higher.
Therefore, the accuracy grade of the Ball Screw (see table 1 on page K-24) needs to be C10
(travel distance error: ±0.21 mm/300 mm).
Accuracy grade C10 is available for low-priced, Rolled Ball Screws. Assume that a Rolled Ball
Screw is selected.
●Selecting axial clearanceThe required backlashes is 0.1 mm or less. However, since an axial load is constantly applied
in a single direction with vertical mount, the axial load does not serve as a backlash no matter
how large it is.
Therefore, a low price, rolled Ball Screw is selected since there will not be a problem in axial
clearance.
12.2.4. Selecting a Screw Shaft
●Assuming the screw shaft lengthAssume the overall nut length to be 100 mm and the screw shaft end length to be 100 mm.
Therefore, the overall length is determined as follows based on the stroke length of 600 mm.
600 + 200 = 800 mmThus, the screw shaft length is assumed to be 800 mm.
●Selecting leadWith the driving motor's rated rotation speed being 3,000 min-1 and the maximum speed 0.3
m/s, the Ball Screw lead is obtained as follows:
Therefore, it is necessary to select a type with a lead of 6 mm or longer.
In addition, the Ball Screw and the motor can be mounted in direct coupling without using a
reduction gear. The minimum resolution per revolution of an AC servomotor is obtained based
on the resolution of the encoder (1,000 p/rev; 1,500 p/rev) provided as a standard accessory
for the AC servomotor, as indicated below.
600±0.7
300±0.35=
0.3 ✕ 60 ✕ 1000
3000 = 6 mm
K-89
K. Description of the Ball ScrewK
89ExamplesofSelectin
gaBallS
crew
1000 p/rev(without multiplication)
1500 p/rev(without multiplication)
2000 p/rev(doubled)
3000 p/rev(doubled)
4000 p/rev(quadrupled)
6000 p/rev(quadrupled)
To meet the minimum feed distance of 0.010 mm/pulse, which is the selection requirement,
the following should apply.
Lead 6mm ―― 3000 p/rev
8mm ―― 4000 p/rev
10mm ―― 1000 p/rev
20mm ―― 2000 p/rev
40mm ―― 2000 p/rev
However, with a lead being 6 mm or 8 mm, the feed distance is 0.002 mm/pulse, and the start-
ing pulse of the controller that issues commands to the motor driver needs to be at least 150
kpps, and the cost of the controller may be higher.
In addition, if the lead of the Ball Screw is greater, the torque required for the motor is also
greater, and thus the cost will be higher.
Therefore, select 10 mm for the Ball Screw lead.
●Selecting a screw shaft diameterThose Ball Screw models that meet the lead being 10 mm as described in Section 12.2.3. and
Section 12.2.4. (see table 4 on page K-40) are as follows.
Shaft diameter Lead
15mm ―― 10mm
20mm ―― 10mm
25mm ―― 10mm
Accordingly, the combination of a screw shaft diameter of 15 mm and a lead 10 mm is selected.
●Selecting a screw shaft support methodSince the assumed Ball Screw has a stroke length of 600 mm and operates at a maximum
speed of 0.3 m/s (Ball Screw rotation speed: 1,800 min-1), select the fixed-supported configu-
ration for the screw shaft support.
K-90
●Studying the permissible axial load■Calculating the maximum axial load
Guide surface resistance f =20 N(without load)
Table mass m1 =40 kg
Workpiece mass m2 =10 kg
Maximum speed Vmax =0.3 m/s
Acceleration time t1 =0.2 s
Hence,
Acceleration:
During upward acceleration:
Fa1 = (m1 + m2) · g + f + (m1 + m2) · α = 585 N
During upward uniform motion:
Fa2 = (m1 + m2) · g + f = 510 N
During upward deceleration:
Fa3 = (m1 + m2) · g + f - (m1 + m2) · α = 435 N
During downward acceleration:
Fa4 = (m1 + m2) · g - f - (m1 + m2) · α = 395 N
During downward backward motion:
Fa5 = (m1 + m2) · g - f = 470 N
During downward deceleration:
Fa6 = (m1 + m2) · g - f + (m1 + m2) · α = 545 N
Thus, the maximum axial load applied on the Ball Screw is as follows:
Famax = Fa1 = 585 N
α = = 1.5 m/s2Vmax
t1
K-91
K. Description of the Ball ScrewK
91ExamplesofSelectin
gaBallS
crew
■Buckling load of the screw shaftCoefficient determined by the mounting method: η2=20 (see page K-43)
Since the mounting method for the section between the nut and the bearing, where buck-
ling is to be considerd, is "fixed-fixed:"
Center distance: Ra=700 mm (estimate)
Thread minor diameter: d1=12.5 mm
■Permissible compressive and tensile load of the screw shaftP2 = 116d1
2 = 116 ✕ 12.52 = 18100 NThus, the buckling load and the permissible compressive and tensile load of the screw shaft
are at least equal to the maximum axial load. Therefore, a Ball Screw that meets these require-
ments can be used without a problem.
●Studying the permissible rotation speed■Maximum rotation speedScrew shaft diameter: 15 mm; lead: 10 mm
Maximum speed: Vmax=0.3 m/s
Lead: R=10 mm
■Permissible rotation speed determined by the critical speed of the screw shaft Coefficient determined by the mounting method: λ2=15.1(see page K-45)
Since the mounting method for the section between the nut and the bearing, where critical
speed is to be considered, is "fixed-supported:"
Center distance: Rb=700 mm (estimate)
Screw shaft diameter: 15 mm; lead: 10 mmScrew shaft thread minor diameter d1=12.5 mm
■Permissible rotation speed determined by the DN valueScrew shaft diameter: 15 mm; lead: 10 mm (large-lead Ball Screw)
Ball center diameter: D=15.75 mm
Thus, the critical speed and the DN value of the screw shaft are met.
P1 = η2 · ✕ 104 = 20 ✕ ✕ 104 = 9960 Nd14
Ra2
12.54
7002
Nmax = = 1800 min–1Vmax ✕ 60 ✕ 103
R
N1 = λ2 ✕ 107 = 15.1 ✕ ✕ 107 = 3852 min–1
Rb2
d1
7002
12.5
N2 = = = 4444 min–1 D
7000015.7570000
K-92
●Selecting a Nut Model NumberThe Roller Ball Screw model with a screw shaft diameter of 15 mm and a lead of 10 mm is
large-lead Rolled Ball Screw model BLK1510-5.6.
(Ca=9.8 kN、C0a=25.2 kN)
●Studying the Permissible Axial LoadAssuming that an impact load is applied during acceleration and deceleration, set the static
safety factor (fS) at 2 (see table 1 on page K-54).
The obtained permissible axial load is greater than the maximum axial load of 585 N, and there-
fore, there will be no problem with this model.
●Studying the Service Life■Calculating the travel distance
Maximum speed: Vmax =0.3 m/s
Acceleration time: t1 =0.2 s
Deceleration time: t3 =0.2 s
Travel distance during acceleration
Travel distance during uniform motion
Travel distance during deceleration
Based on the conditions above, the relationship between the applied axial load and the travel
distance is shown in the table below.
* The subscript (N) indicates a motion number.
12.2.5. Selecting a Nut
C0afS
25.22
Famax = = = 12.6 kN = 12600 N
R1,4 = ✕ 103 = ✕ 103 = 30 mm2
Vmax · t1
20.3 ✕ 0.2
R2,5 = RS – ✕ 103 = 600 – ✕ 103 = 540 mm2
Vmax · t1 + Vmax · t3
20.3 ✕ 0.2 + 0.3 ✕ 0.2
R3,6 = ✕ 103 = ✕ 103 = 30 mm2
Vmax · t3
20.3 ✕ 0.2
Motion
No.1:During upward acceleration
No.2:During upward uniform motion
No.3:During upward deceleration
No.4:During downward acceleration
No.5:During downward uniform motion
No.6:During downward deceleration
585
510
435
395
470
545
30
540
30
30
540
30
Applied axial load
FaN(N)
Travel distance
RN(mm)
K-93
K. Description of the Ball ScrewK
93ExamplesofSelectin
gaBallS
crew
■Average axial load
■Rated lifeDynamic load rating: Ca=9800 N
Load factor: fW=1.5(see table 2 on page K-55)
Average load: Fm=492 N
Rated life L(rev.)
■Reciprocations per minuteReciprocations per minute: n=5 min-1
Stroke: RS=600 mm
Lead: R=10 mm
■Calculating the service life time on the basis of the rated lifeRated life: L=2.34×109 rev.
Average rotation speed per minute: Nm=600 min-1
■Calculating the service life in travel distance on the basis of the rated lifeRated life: L=2.34×109 rev.
Lead: R=10 mm
LS = L ✕ R ✕ 10– 6 = 23400 km
With all the conditions stated above, model BLK1510-5.6 satisfies the desired service life time
of 20,000 hours.
�������������������������Fm = (Fa1
3 ·R1 + Fa23 ·R2 + Fa3
3 ·R3 + Fa43 ·R4 + Fa5
3 ·R5 + Fa63 ·R6) = 492N1
2 ✕RS
3
L = ✕ 106 = ✕ 106 = 2.34 ✕ 109 rev.fw・Fm
Ca( )3
1.5 ✕ 4929800( )
3
Lh = = = 65000h60 · Nm
L60 ✕ 6002.34 ✕ 109
Nm = = = 600min–1
R
2 ✕ n ✕ Rs
102 ✕ 5 ✕ 600
K-94
12.2.6. Studying the Rigidity
Since the conditions for selection do not include rigidity and this element is not particularly
necessary, it is no described here.
12.2.7. Studying the Positioning Accuracy
12.2.8. Studying the Rotation Torque
●Studying the lead accuracyAccuracy grade C10 was selected in Section 12.2.3.
C10 (travel distance error:±0.21mm/300mm)
●Studying the axial clearanceSince the axial load is constantly present in a given direction only because of vertical mount,
there is no need to study the axial clearance.
●Studying the axial rigiditySince the lead accuracy is achieved at a much higher degree than the required positioning
accuracy, there is no need to study the positioning accuracy determined by axial rigidity.
●Studying the thermal displacement due to heatSince the lead accuracy is achieved at a much higher degree than the required positioning accuracy,
there is no need to study the positioning accuracy determined by heat generation.
●Studying the orientation change during travelingSince the lead accuracy is achieved at a much higher degree than the required positioning accuracy,
there is no need to study the positioning accuracy.
●Friction torque due to an external torqueDuring upward acceleration:
During upward uniform motion:
T1 = = = 1030 N · mm2×π×η Fa1 · R
2×π×0.9585×10
T2 = = = 900 N · mm2×π×η Fa2 · R
2×π×0.9510×10
K-95
K. Description of the Ball ScrewK
95ExamplesofSelectin
gaBallS
crew
Similarly,
During upward deceleration:
T3 = 770 N · mmDuring downward acceleration:
T4 = 700 N · mmDuring downward uniform motion:
T5 = 830 N · mmDuring downward deceleration:
T6 = 960 N · mm
●Torque due to a preload on the Ball ScrewThe Ball Screw is not provided with a preload.
●Torque required for accelerationInertial moment:
The inertial moment per unit length of the screw shaft can be specified as follows.
Since 3.9×10-4kg-cm2/mm (see the dimensional table in the " General Catalog - Product
Specifications," provided separately), the inertial moment of the screw shaft with an overall
length of 800 mm is obtained as follows.
JS = 3.9 ✕ 10-4 ✕ 800 = 0.31 kg · cm2
= 0.31 ✕ 10-4 kg · m2
Angular acceleration:
Based on the above, the torque required for acceleration is obtained as follows.
T7 = (J + Jm) · ω' = (1.58 + 10–4 + 5 ✕ 10–5) ✕ 942 = 0.2 N · m = 200 N · mmTherefore, the required torque is specified as follows.
During upward acceleration:
Tk1 = T1 + T7 = 1030 + 200 = 1230 N · mmDuring upward uniform motion:
Tt1 = T2 = 900 N · mmDuring upward deceleration:
Tg1 = T3 – T7 = 770 – 200 = 570 N · mm
J = (m1 + m2) · A2 10–6 + JS · A2 = (40 + 10) ✕ 12
✕ 10–6 + 0.31 ✕ 10–4 ✕ 12
= 1.58 ✕ 10–4 kg · m2
2 ✕ πR( )
2
2 ✕ π10( )
2
ω' = = = 942 rad/s2
60 · t2π · Nm
60 ✕ 0.22π ✕ 1800
K-96
Similarly,
During downward acceleration:
Tk2 = 500 N · mmDuring downward uniform motion:
Tt2 = 830 N · mmDuring downward deceleration:
Tg2 = 1160 N · mm
12.2.9. Studying the Driving Motor
●Rotation speedSince the Ball Screw lead is selected based on the rated rotation speed of the motor, it is
unnecessary to study the rotation speed of the motor.
Maximum working rotation speed :1800min-1
Rated rotation speed of the motor :3000min-1
●Minimum feed distance:As with the rotation speed, the Ball Screw lead is selected based on the encoder normally used
for an AC servomotor. Therefore, it is unnecessary to study this factor.
Encoder resolution :1000 p/rev.
●Motor torque:The torque during acceleration calculated in Section 12.2.8. is the required maximum torque.
Tmax = Tg2 = 1160 N · mmTherefore, the instantaneous maximum torque of the AC servomotor needs to be at least
1,160 N-mm.
●Effective torque valueThe selection requirements and the torque calculated in Section 12.2.8. can be expressed as
follows.
During upward acceleration:
Tk1 = 1100 N · mmt1 = 0.2 s
During upward uniform motion:
Tt1 = 900 N · mmt2 = 1.8 s
During upward deceleration:
Tg1 = 700 N · mmt3 = 0.2 s
K-97
K. Description of the Ball ScrewK
97ExamplesofSelectin
gaBallS
crew
During downward acceleration:
Tk2 = 500 N · mmt1 = 0.2 s
During downward uniform motion:
Tt2 = 830 N · mmt2 = 1.8 s
During downward deceleration:
Tg2 = 1160 N · mmt3 = 0.2 s
When stationary(m2=0):
TS = 830 N · mmt4 = 7.6s
Therefore, the effective torque is obtained as follows.
Accordingly, the rated torque of the motor must be 846 N-mm or greater.
●Inertial momentThe inertial moment applied to the motor equals to the inertial moment calculated in Section
12.2.8.
J = 1.58 ✕ 10–4 kg · m2
Normally, the motor needs to have an inertial moment at least one tenth of the inertial moment
applied to the motor, although the specific value varies depending on the motor manufacturer.
Therefore, the inertial moment of the AC servomotor must be 1.58×10-5kg-m2 or greater.
The selection has been completed.
Trms =Tk1
2 · t1 + Tt12 · t2 + Tg1
2 · t3 + Tk22 · t1 + Tt2
2 · t2 + Tg22 · t3 + Ts
2 · t1
t1 + t2 + t3 + t1 + t2 + t3 + t7
=
= 846 N · mm
11002 ✕ 0.2 + 9002 ✕ 1.8 + 7002 ✕ 0.2 + 5002 ✕ 0.2 + 8302 ✕ 1.8 + 11602 ✕ 0.2 + 8302 ✕ 7.60.2 + 1.8 + 0.2 + 0.2 + 1.8 + 0.2 + 7.6
����������������������������
������������������������������������
K-98
13. Safety Design13. Safety Design
13.1. Lubrication13.1. Lubrication
To maximize the performance of the Ball Screw, it is necessary to select a lubricant and a lubri-
cation method according to the service conditions.
For types of lubricants, characteristics of lubricants and lubrication methods, see page A-109.
Also, QZ Lubricator is available as an optional accessory that significantly increases the main-
tenance interval.
13.1.1. QZ LubricatorTM for the Ball Screw
QZ Lubricator feeds a right amount of lubricant to the ball raceway of the ball screw shaft.
This allows an oil film to be formed between the balls and the ball raceway and significantly
extends the lubrication maintenance interval.
Its structure consists of major three components: ① a highly oil-impregnated fiber net (function
to store a lubricant), ② a high-density fiber net (function to apply the lubricant to the raceway)
and ③ an oil control plate (function to control the flow of the lubricant). The lubricant con-
tained in QZ Lubricator is fed based on the principle of capillary action, which is used in felt-tip
pens and other products.
Features●Since it supplements an oil loss, the lubrication maintenance interval can significantly be
extended.
●Since the right amount of lubricant is applied to the ball raceway, an environmentally friendly
lubrication system that does not contaminate the surroundings is achieved.
●Enables selection of a lubricant that meets the intended use.
Note: For model numbers supported for QZ Lubricator, see the section on the respective model number in the " GeneralCatalog - Product Specifications," provided separately.
QZ Lubricator
QZ Lubricator
QZ securing screw
Ball screw shaft
Ball
Ball screw nut
Model number indication Flow of lubricant ③Oil control plate②High-density fiber net
①Highly oil-impregnated fiber net
Applied directly to the raceway
Ball screw shaft
Sealed case Ball screw nut
Outline drawing Structural drawing
K-99
K. Description of the Ball ScrewK
99Safety
Design
■Significantly extended maintenance intervalSince QZ Lubricator continuously feed a lubricant over a long period, the maintenance interval
can significantly be extended.
Still traveling at 3,500 km
Still traveling at 1,500 km
Oxidized wear dust generated at 100 km
Distance traveled km (linear travel distance)
0 500 1000 1500 2000 2500 3000 3500
QZ Lubricator + AFA Grease
QZ Lubricator only
No lubrication
BIF2505-5
3000min–1
500mm
0.46kN (with an internal preload)
Ball Screw
Rotation speed
Stroke
Load
■Environmentally friendly lubrication systemSince QZ Lubricator feeds the right amount of lubricant directly to the raceway, the lubricant
can effectively be used without waste.
Model No.: BNFN3612-5G0+1500LC5 Travel distance: 20km/day Travel distance: 2500km
QZ Lubricator
15000
32
Forced lubrication
0 5000 10000 15000
Amount of oil cm3
QZ Lubricator + AFA Grease
32cm3
(QZ Lubricator attached to both ends of the ball screw nut)
Forced lubrication
0.25cm3/3min×24hour×125day
=15000cm3
Comparison
K-100
13.1.2. Amount of Lubricant
If the amount of lubricant to the Ball Screw is insufficient, it may cause oil film break, and if it is
excessive, it may cause heat to be generated and resistance to be increased. It is necessary
to select an amount that meets the service conditions.
The feed amount of grease is generally approximately one third of the special volume inside the nut.
Table 1 shows a guideline for the feed amount of oil.
Note, however, that the amount varies according to the stroke, oil type and service conditions
(e.g., suppressed heat generation).
Table 1 Guideline for the Feed Amount of Oil(Interval: 3 minutes)
Shaft diameter(mm)
4 to 8
10 to 14
15 to 18
20 to 25
28 to 32
36 to 40
45 to 50
55 to 63
70 to 100
Amount of lubricant(cc)0.03
0.05
0.07
0.1
0.15
0.25
0.3
0.4
0.5
Grease
Oil
K-101
K. Description of the Ball ScrewK
101Safety
Design
13.2. Dust Prevention13.2. Dust Prevention
Dust and foreign matter that enter the Ball Screw may cause accelerated wear and breakage,
as with roller bearings. Therefore, where contamination by dust or foreign matter (e.g., cutting
chips) is predicted, screw shafts must always be completely covered by dust prevention
devices (e.g., bellows, screw cover, wiper ring).
If the Ball Screw is used in an atmosphere free from foreign matter but with suspended dust, a
labyrinth seal (for precision Ball Screw) and a brush seal (for rolled Ball Screw) can be used in
place of dust prevention devices. When placing an order, indicate the respective model number.
The labyrinth seal is designed to maintain a slight clearance between the seal and the screw
shaft raceway so that torque does not develop and no heat is generated, though its effect in
dust prevention is limited.
With Ball Screws except the large-lead and super-lead types, there is no difference in nut dimen-
sions between those with and without a seal.
With the wiper ring, special resin with high wear resistance and low dust generation removes
foreign matter while closely contacting the circumference of the ball screw shaft and the screw
thread. It is capable of preventing foreign matter from entering the Ball Screw even in harsh
environments.
Screw cover Bellows
Fig. 1 Dust Prevention Cover
K-102
Features●A total of eight slits on the circumference remove foreign matter in succession, and prevents entrance of foreign matter.
●Contacts the ball screw shaft to reduce the flowing out of grease.
●Contacts the ball screw shaft at a constant pressure level using a spring, thus to minimize heat generation.
●Since the material is highly resistant to wear and chemicals, its performance will not easily be deteriorated even if it is
used over a long period.
Seal snap ring
Seal snap ring
Ball screw shaft
Ball screw nut
Wiper ring
Wiper ring
Grease nipple
Spring Multi-slit
Multi-slitA
Foreign matter
Ball screw shaft
Rotational directionDetail drawing of section A
Outline drawing Structural drawing
13.2.1. Wiper Ring W for the Ball Screw
With the wiper ring, special resin with high wear resistance and low dust generation removes
foreign matter and prevents foreign matter from entering the ball screw nut while elastically
contacting the circumference of the ball screw shaft and the screw thread.
■Test in an environment exposed to foreign matter
[Test conditions]
Wiper ring
Labyrinth seal
0 400 800 1200 1600 2000200 600 1000 1400 1800
Distance traveled km
Flaking occurs on the ball shaft racewayNo problem Flaking occurs on the ball
[Test result]
Description
BIF3210-5G0+1500LC5
1000min–1
10m/min
1.8m/s
60ms
1s
900mm
1.31kN
AFG Grease 8cm3
Initial lubrication to the ball screw nut only.
FCD400 average particle diameter: 250μm
5g/h
Item
Model No.
Maximum speed
Time constant
Dowel
Stroke
Load
(through internal load)
Grease
Foundry dust
(1)Wiper ring specificationsSlight flaking occurred in the ball screw shaft at travel distantof 1,000 km.
(2)Labyrinth seal specificationsFlaking occurred throughout the circumference of the screwshaft raceway at travel distance of 200 km.Flaking occurred on the balls after traveling 1,500 km.
Maximum rotation speed
Maximum circumferential speed
Volume of foreignmatter per shaft
K-103
K. Description of the Ball ScrewK
103Safety
Design
00
2
4
6
8
10
12
500 1000 1500 2000Distance traveled(km)
Wear of ball(μm)
Labyrinth
Wiper ring
(1)Wiper ring typeWear of balls at a travel distance of 2,000 km: 1.4μm.
(2)Labyrinth seal typeStarts to be worn rapidly after 500 km, and the ball wearamount at the travel distance of 2,000 km: 11 μm.
After traveling 2,000 km
●Discolored, but no breakage ●Flaking occurs
(1)Wiper ring type (2)Labyrinth seal type
Ball
■Heat generation test
[Test conditions] [Test result]
Description
BLK3232DG0+1426LC5
1000min–1
32m/min
1.7m/s
100ms
1000mm
0.98kN
AFG Grease 5cm3
(contained in the ball screw nut)
Item
Model No.
Maximum speed
Time constant
Stroke
Load
(through internal load)
Grease
00
10
20
30
40
50
60
15 30 45 60 75 90Travel time(min)
Unit: ℃
Temperature at shaft center area(℃)
Heat generation temperature
Temperature rise
With wiper ring 37.1 12.2
Without wiper ring 34.5 8.9
With wiper ring
Without seal
Unused ball Ball after traveling Unused ball Ball after traveling
Maximum rotation speed
Maximum circumferential speed
K-104
(Band type) (Flanged type)
MAXMIN
φ
4-φ
φODφID φ
φ
φ
MAXMIN
L
Bellows Dimensions
Stroke mm MAX. mm MIN. mm
Permissible outer diameter Desired inner diameter
How It Is Used
Orientation (horizontal, vertical, slant) Speed( )mm/sec. min.
Motion (reciprocation, vibration)
Service Conditions
Oil/water resistance (necessary, not necessary) Oil name
Chemical resistance Name × %
Location (indoor, outdoor)
Remarks Number of units to be manufactured
φIDφOD
Bellows Specifications
K-105
K. Description of the Ball ScrewK
105Precautio
nsonUsingtheBallS
crew
a Disassembling components may cause dust to enter the system or degrade mounting accu-
racy of parts. Do not disassemble the product.
s Tilting the screw shaft and the ball screw nut may cause them to fall by their self-weights.
d Dropping or hitting the Ball Screw may damage the ball circulation section, which may cause
functional loss. Giving an impact to the product could also cause damage to its function
even if the product looks intact.
14. Precautions on Using the Ball Screw14. Precautions on Using the Ball Screw
Handling
a Thoroughly remove anti-corrosion oil and feed lubricant before using the product.
s Do not mix lubricants of different physical properties.
d In locations exposed to constant vibrations or in special environments such as clean rooms, vacu-
um and low/high temperature, normal lubricants may not be used. Contact for details.
f When planning to use a special lubricant, contact before using it.
g Lubrication interval varies according to the service conditions. Contact for details.
Lubrication
a Do not remove the ball screw nut from the ball screw shaft. Doing so may cause the balls or the nut to fall off.
s Entrance of foreign matter to the ball screw nut may cause damage to the ball circulating path or
functional loss. Prevent foreign matter, such as dust or cutting chips, from entering the system.
d If foreign matter adheres to the product, replenish the lubricant after cleaning the product.
f When planning to use the product in an environment where the coolant penetrates the spline nut, it may
cause trouble to product functions depending on the type of the coolant. Contact for details.
g Do not use the product at temperature of 80℃ or higher. When desiring to use the system
at temperature of 80℃ or higher, contact in advance.
h If using the product with vertical mount, the ball screw nut may fall by its self-weight.
Attach a mechanism to prevent it from falling.
j Using the product at speed exceeding the permissible rotation speed may cause breakage of a com-
ponent or accident. Be sure to use the product within the specification range designated by .
k Forcibly driving in the ball screw shaft or the ball screw nut may cause an indentation on the
raceway. Use care when mounting components.
l If an offset or skewing occurs with the ball screw shaft support and the ball screw nut, it
may substantially shorten the service life. Pay much attention to components to be mount-
ed and to the mounting accuracy.
¡0 When using the product in locations exposed to constant vibrations or in special environ-
ments such as clean rooms, vacuum and low/high temperature, contact in advance.
¡1 Letting the ball screw nut overrun will cause balls to fall off or the ball-circulating component
to be damaged. Be sure not to let it overrun.
Precautions on Use
When storing the Ball Screw, enclose it in a package designated by and store it in a
horizontal orientation while avoiding high temperature, low temperature and high humidity.
Storage