View
220
Download
0
Category
Tags:
Preview:
Citation preview
1
Design for DifferentType of Loading
Lecture NotesDr. Rakhmad Arief Siregar
Kolej Universiti Kejuruteraan Utara Malaysia
Machine Element in Mechanical Design
Fourth Edition in SI UnitRobert L. Mott
Chapter 5
2
Chapter 5 Design for Different Types of Loading
Objectives: Identify various kinds of loading commonly
encountered by machine parts, including static, repeated and reversed, fluctuating, shock or impact and random
Define the term stress ratio and compute its value for the various kinds of loading
Define the concept of fatigue Define the material property of endurance strength
and determine estimates of its magnitude for different materials
Recognize the factors that affect the magnitude of endurance strength
3
Chapter 5 Design for Different Types of Loading
Objectives: Define the term design factor Specify a suitable value for the design factor Define the maximum normal stress theory of failure
and the modified Mohr method for design with brittle materials
Define maximum shear stress theory of failure Define he distortion energy theory, also called the von
Mises theory or the Mises-Hencky theory Describe the Goodman method and apply it to the
design of parts subjected to fluctuating stresses Consider statistical approaches, finite life and damage
accumulation method for design
4
Types of Loading & Stress Ratio
Types of loading: Static: when a part is subjected to a load that is
applied slowly, without shock, and is held at constant value.
Repeated and Reversed: when a part is subjected to a certain level of tensile stress followed by the same level of compressive stress
Fluctuating stress: when a load-carrying member is subjected to an alternating stress with a nonzero mean.
Shock or impact: loads applied suddenly and rapidly cause shock or impact, i.e., hammer blow, weight falling
Random: when varying loads are applied that are not regular in their amplitude
5
Figures
See Fig. 5-1 for static stress See Fig. 5-2 for repeated, reversed
stress See Fig. 5-4 for Fluctuating stress
6
Impact Load
Strain Gage A Strain Gage B
Signal Conditioner
Digital Oscilloscope
Striker Bar
Input Bar Output BarV
Photodiode velocity sensor
(a)
7
Impact Load
-60
-40
-20
0
20
40
60
Str
ess
[ M
Pa
]
10008006004002000
Time [ sec ]
Incident wave Transmitted wave x 20%
8
Stress ratio
Stress ratio is one of method to characterize variation of stresses.
Maximum stress, max Minimum stress, min Mean stress, m Alternating stress, a (stress amplitude)
max
min
RrationStress
m
aArationStress
2
minmax
m
2minmax
a
9
Photographs of failed parts
Failure of a truck drive shaft spline due to corrosion fatigue
10
Photographs of failed parts
Failure of a stamped steel bracket due to residual stresses
11
Photographs of failed parts
Failure of an automotive drag link (steering wheel)
12
Photographs of failed parts
Failure of bolt in the overhead-pulley
13
Photographs of failed parts
Automotive rocker-arm articulation-joint fatigue failure
14
Photographs of failed parts
Valve-spring failure caused by spring surge in an over speed engine
15
Photographs of failed parts
Brittle facture of a lock washer in one-half cycle
16
Failure resulting from static loading
Static loading Direct tension and compression Direct shear Torsional shear Vertical shearing stresses Bending Buckling
How to predict failure if the component is subjected to combine loading?
17
Ductile materialsMaximum shear stress
Also known as Tresca theory The maximum shear stress hypothesis states
that yielding begin “whenever the maximum shear stress in any element becomes equal to the maximum shear stress in a tension test specimen of the same material when specimen begins to yield”
yy SorS
21max 2
ysy SS 5.0
18
Triaxial shear stresses
221
2/1
232
3/2
231
3/1
The maximum shear stress graphically represented in three dimensions
19
Biaxial stress1
2
-Sy
-Sy
Sy
Sy
yy SorS
21max 2
ysy SS 5.0
20
Ductile materialsDistortion energy
Also known as von Misses – Hencky theory The maximum strain energy hypothesis
predicts failure by yielding occurs “when distortion energy in a unit volume equals the distortion energy in the same when uniaxially stressed to the yield strength”
yS
2
213
232
221
21
Ductile materialsDistortion energy
Under the name of octahedral shear stress this theory predicts failure occurs “whenever the octahedral shear stress for any stress state equal or exceeds the octahedral shear stress for the simple tension test at failure”
yoct S
2132
322
213
1 oct
22
Triaxial stress3
2
1
The distortion energy theory graphically represented in three dimensions
23
Biaxial stress
1
2Sy
Sy
-Sy
-Sy
yS
2221
21
24
Problem 1
A hot-rolled steel is subjected to principle stress 1 = 210 MPa, 1 = 480 MPa and 3 = 0 MPa. By utilizing UTM the hot-rolled steel has a yield strength of Syt=Syc = 690 MPa and a true strain at fracture of f = 0.55. Estimate the factor of safety.
25
Solution
Maximum shear stress theory
Distortion energy theory
MPa8.416
2
48000210210480 222
66.18.416
690
ySSF
2402
0480
221
max
44.12402
690
2 max
ySSF
26
Brittle materialsMaximum normal stress
Also known as Rankine theory The maximum normal stress hypothesis
predicts failure occurs “whenever one of the three principle stresses equals or exceeds the strength”
Suppose we arrange: 1 > 2 > 3
ycyt SnSn 31
Note: n = safety factor
27
Brittle materialsModification of Mohr
Coulomb-Mohr
Mod. I-Mohr
ututut SSn
S 211 00
utucutuc
B
ut
SSSnSS
211 0
1
utututut SSSn
S 211 0
utucututcu
utuc
utcu
ut SSSSSn
SS
SS
S
21
21 0
)(
28
Brittle materialsModification of Mohr
Mod. II-Mohr
utututut SSSn
S 211 0
utucututcu
ut
ut
SSSSS
Sn
S
n
21
2
11 01
29
Problem 2
A cast iron is subjected to principle stress 1 = 210 MPa, 1 = 480 MPa and 3 = 0 MPa.
By utilizing UTM the cast iron has a yield strength of Sut=215 MPa and Suc = 750 MPa. Estimate the factor of safety by using:(1) Coulomb-Mohr failure model(2) Mod. I-Mohr failure model(3) Mod. II-Mohr failure model
30
Solution
Maximum shear stress theory
Distortion energy theory
MPa8.416
2
48000210210480 222
66.18.416
690
ySSF
2402
0480
221
max
44.12402
690
2 max
ySSF
31
Fatigue
A machine components often subjected to dynamic loading such as: variable, repeated alternating or fluctuating stresses.
In most cases machine members are found to have failed under the action of repeated or fluctuating stresses.
The analysis reveals that the actual maximum stresses were below the ultimate strength of the material and quite frequently even below the yield stress
32
Fatigue
This kind failure CAN NOT be detected by naked eye and even quite difficult to locate in a Magnaflux or X-ray inspection
This failure called as fatigue failure. Begins with a small crack and develops a point
of discontinuity in materials such as change in cross section, a keyway or a hole.
Once developed, the stress-concentration effect becomes greater and crack progresses more rapidly
33
Endurance strength
Endurance strength of material is its ability to withstand fatigue loads.
Endurance strengths are usually charted on a graph like shown in Fig. 5-7, called as S-N diagram.
Factors affecting endurance strength: Surface finish Material factor Type of stress factor Reliability Factor Size Factor
Recommended