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Machine Tool Spindles The key to improve

productivity

and

performance

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Performance featuresTo increase productivity and performance of spindles, certain features that are to considered are as follows :

•Desired spindle power both peak and continuous.

•Maximum spindle load both axial and radial.

•Minimum size and weight

•Maximum torque over a broad range of speeds

•Speed allowed

•Tooling style

•Belt driven or integral motor-spindle design

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Factors considered for spindles design

Besides the above-mentioned performance features, other factors that will affect the ultimate

spindle design are as follows :

Amount of available space in the head

Complexity

Purpose and application

Cost considerations

Market demands

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Benefits of spindlesCertain benefits of spindles are as follows :

Machine tool spindles reduce the number of cuts in mfg by half.

Spindles provide position and transmit power to a tool

They hold a rotating workpiece .

They hold cutting tools and spin them at high torque and speed.

Spindles support many key machining tasks.

Allow flexibility in cutting a variety of materials.

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Uses of spindles

Spindles are used to perform variety of tasks like as follows :

Grinding Milling Engraving Drilling Boring Turning

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Machine Tool SpindleFunction of machine spindle

The function of the main spindle of metal cutting machine tools are:

1. The guiding of tool and/or work at the cutting point with adequate kinematic accuracy.

2. The absorption of externally applied forces such as the weight of the work and cutting forces with minimum static, dynamic and thermal distortion.

Other Factors

The dimensional accuracy and surface finish of the work being machined, as well as the rate of metal removal of a machine tool, are among other factors directly governed by the static, dynamic and thermal behavior of the spindle bearing unit.

In this way, spindle deflection strongly affects the production accuracy of the machine tool, and for this reason, it must be designed to be stiff enough

The deformation of the a spindle depends not only on its own stiffness, but also upon the stiffness of its bearing and that of the housing.

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Spindle Mounting

Forces acting on a machine tool spindle

1. Cutting force F acts at the spindle nose. This force has a radial Fcr and axial Fa, respectively.

2. Driving force Fd, acts radially, between bearings

Fixed (locating) bearing: is the bearing that takes the axial force component. It should prevent the spindle from moving axially in both directions. (source of heat generation).

Floating (Non locating) bearing: takes a radial force component only. It can not prevent spindle from moving axially.

The reaction of the radial component at each spindle bearing can be calculated simply.

The axial component is taken only by one bearing, either he front or rear bearing.

Spindle-bearing arrangement with front fixed point is commonly used in machine tools. It leads to:

Higher nose stiffness Lower thermal expansion Higher machining accuracy

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Spindle DesignDesign Criteria1. Static Criteria: stiffness – strength

2. Dynamic criteria: Natural frequency - Damping – Mode Shape – dyn. Amplitude

Machine spindle may be classified into two categories:

1. Hollow of stepped cross section: Ex. Horizontal milling machine, vertical milling machine, lathe, turret lathe.

2. Solid of uniform cross section: Ex. Boring machine, Drilling machine, Grinding machine.

In the following analysis, for simplicity, it will be be assumed that:

1. the spindle has a uniform cross section (hollow or solid).

2. The effect of the driving force is neglected.

3. The reactive moment of the fixed bearing is neglected

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The accuracy of the work accuracy produced by the main spindle is governed by the total deflection of the spindle at the point of force application in the radial direction.

The total nose deflection at the spindle nose is:

Y = y1 + y2 + y3

Where:

y 1 : the contribution due to shaft deflection

y2 : the contribution due to bearing deflection

y3 : the contribution due to housing deflection

Because of the series connection of the individual contributions to the total flexure, the total flexibility at the point of force application is given by:

1/k = 1/k1 + 1/k2 + 1/k3

= y1/F + y2/F + y3/F

= (y1 + y2 + y3)/F = y/F

Spindle design on the stiffness criterion

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Spindle nose deflection y1

For an infinity stiff bearing, the spindle nose deflection y1 is given by:

Where:

Fcr : radial cutting force at spindle nose

E :Modulus of elasticity of spindle material

I : Area moment of inertia of spindle

cross section

l : spindle span (distance bet. bearings)

c : spindle overhang length

Spindle nose deflection y1

).(.3

21 clc

EIFy cr

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Nose deflection y2 due bearing deflectionFor an infinity rigid spindle, the nose deflection y2 due to bearing can be derived as follows.

First : calculate bearing reactions

Rf = Fc (l+c)/l & Rr = Fc.c/l

Second: bearing deflections

yf = Rf /kf = Fcr (l+c)/l .kf

yr = Rr /kr = Fcr.c/l.Kr

Third: From triangle similarity in the lower figure

Spindle deflection y2

Derivation of spindle deflection y2lcl

yyyy

rf

r

)()( 2

rrf ylclyyy

)(2

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rcr

rcr

fcr

r

r

r

r

f

f

klcF

lcl

klcF

klclFy

kR

lcl

kR

kR

y

..).

..

..(

).(

2

2

})(.{

.)(.

..)(.)(.

22

22

2

2

2

2

2

22

2

2

rf

cr

r

cr

f

cr

r

cr

r

cr

f

cr

kc

kcl

lFy

lc

kF

lcl

kFy

lkcF

lclc

kF

lcl

kFy

The contribution of the total nose deflection by the deflection of the frame (bearing housing) y3 is difficult to calculate by the normal method, but the finite element method may by

applied.spindle design

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It is clear from the previous equations that the total spindle nose deflection and also the total spindle –bearing system depends upon the combined effect of:

The bearing stiffness,

The span; the center distance between bearings l,

The length of the overhang length c and

The geometry of the spindle.

The experiment studies showed that :

1.The front bearing stiffness kf has great effect on the total flexibility of a particular spindle-bearing system

2.Also, a bearing stiffness kf >750 N/m

Note that the frame stiffness is not presented in this curves

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Optimum span length

The optimum span length that gives minimum deflection at the point of force application, (given that all other parameters are unchanged) can be derived from the equation of the total deflection.

If this equation is differentiated with respect to the bearing span l, and equating to zero (maximum or minimum), then a cubic expression is obtained for the span l. the solution for l. with minimum computer, the value of the optimum span length l can be obtained.

In general, the span length l should be greater than three times the overhang length, i.e., l 3c

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Recommended Values of Spindle Nose Stiffness

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Spindle Design Guidelines1. Higher spindle stiffness is achieved by choosing

higher bearing stiffness and higher cross section

2. Dimensions C and l have direct influence on the accuracy of machine tool

3. Dimension C should be as small as possible

4. Optimum dimension of the the length l should be

calculated l / C >3

5. Spindle with large diameter is recommended

6. Hollow spindle gives higher spindle stiffness.spindle design

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20 spindle design

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SHAFTING, Hollow vs. Solid Sect .

“When comparing a solid shaft with a hollow shaft of equal section modulus, both will transmit the torque with equal stress levels, but the hollow shaft will be stiffer, or rather will deflect less under the same overhung moment”. The following is an engineering analysis to support this statement :

Section modulus = I /c Where I = Moment of Inertia c= Distance to extreme fiber = D/2

Hollow Shaft : O.D.= 6.625”, I.D. = 5.761 ”Moment of inertia for hollow shaft I = 0.049087 x (OD4 − ID4 ) = 40.4904 Section modulus for hollow shaft = I / c = 12.2

4.99 ”dia. Solid Shaft :Moment of inertia for 4.99” solid shaft =0.785398 x R4 = 30.4349Section modulus for 4.99” solid shaft = I / c = I / R = 12.2

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Exercise

1.Go to the machining workshop

2.Select any machine tool

3.Draw its spindle mounting

4.Represent the bearing mounting

5.Represent a part of housing

6.Use a suitable scale