Designof an Industrial automobile Shaft
Theaim of my project is to design an axle shaft for an industrial carrunning on wheels under particular loading conditions. Failurescaused due to the existence of pure bending, pure torsion, shearloading, axial loading and varying type of these loadings areevaluated separately or in a combined manner for a certain situation.The effect of mentioned types of loading may cause different failuresunder specific conditions such as creep failure, fatigue failure,bending failure or compressive and tensile failure.
Mydesign procedure is majorly going to focus in the aspect of failuredue to fatigue since it is dominant this situation. This is becausesome stresses play more effective roles on a design failure than theother ones for a specific loading condition.
Mechanicaldesign is referred to as the formulation of a plan to gratify acertain need, imaginary or real. Engineering design is defined as theprocess of applying engineering methods and science to prescribe asystem or a component in sufficient details to permit itsrealization. Mechanical design refers to the design of system andcomponents of a mechanical nature devices, structures, machines andinstrument.
Thereare so many factors to be considered, even for very simple load casesdesign. The characteristics of a machine parts is completelydifferent when they are subjected to time- varying loading besidesother loading types. The methods of fatigue failure analysisrepresent a combination of science and mechanical engineering.Science usually fails to give a complete answer that is required.
Myproject is to design an industrial automobile axle running on rails,when a load of 10 KN is applied on each wheel.
Inmy design the axle is a rotating component therefore we havereversed bending stresses due to the load, torsion stresses and shearstresses. After understanding the rotational behavior of the axle andthe stresses acting on it, the next thing is to find out the dominantstress component on the axle. I carried out a static failure analysiswhich I used to estimate the axle diameter. I also carried outfatigue failure analysis and used the analysis to evaluate thedesired diameter of the axle then determined the location of themaximum deflection point due to stresses on my shaft. I carried outthis analysis because of the varying bending stress component whichgreatly affects the fatigue life of the shaft.
Thenext step was to decide the most effective and appropriate stresscomponent causing the deflection. After this decision was made I usedCastigliano’s Energy Theorem to calculate the maximum deflection onmy shaft. I carried the
Figure1: Sectionview of the loading on the axle is shown below:
Table1: Theproperties of the shaft
D1= 0.8 D
D2 =1.2 D
Factor of safety
Fatigue life (cycle)
Filet radius (mm)
Modulus of elasticity
E = 207 GPa
Modulus of rigidity
G = 79 GPa
Sy = 430MPa
Sut = 570MPa
3.1.1Static Failure Analysis
Afterdrawing a Free Body Diagram (FBD) and moment, shear diagrams. Sizethe shaft first based on the possibility of a static failure. SinceI/c, the allowable stress is =M/(I/c).
Fromthe free body diagram, moment and loading diagrams it appears thatpart C (150 mm) is vital, for safety of our design calculations,let’s find out.
AB= 75 mm
BC= 75mm, AC = 150 mm
Mmax= Ra LARGEST
CD= 200 mm, AD = 350 mm
Finallywe can confirm our assumption from the above calculations.
3.1.2Fatigue Failure Analysis
Atthis moment we will size the shaft to find diameter and criticalsection for the static failure.
Theproperties of material are taken from the table 1 above:
Sy= 430MPa, Sut=570MPa, E=213GPa, G=79GPa
Havingthe safety factor as n= 1.5
Anapproximate value of the shaft is established from failure due tostatic loading.
Thenext factor to check is the diameter and length of the shaft based onthe chance of a fatigue failure. The bending load will give differentstresses because of rotation this process makes analysis of fatigueunavoidable. Bending is the principal stress on the fatigue failure.By ignoring shear and torsion and using Marin factors, it is possibleto approximate the endurance limit.
Butfor these calculations we need to know the diameter, to get an ideawe will use the diameter calculated from the analysis of staticfailure and then we proceed by checking safety factor of 1.5.
a= 1.58b = 0.085 this is taken from Appendix Table 4 forground surface
Reliabilityfactor, kc = 0.814 (Appendix Table 6)
Temperaturefactor, kd = 1 supposing the condition at which the shaft isoperating in is at room temperature
Stressconcentration factor, ke =1/Kf Kf = 1+q (Kt-1)
Ktfrom Appendix Table 7
Accordingto r/d =3/40 =0.075, D/d =1.2 interpolating Kt= 1.808
Qfrom Appendix Table 2
Accordingto r =3mm and Sut = 570 MPa from interpolation twice q = 0.8
Miscellaneousfactors, kf = 1this is because there is no other conditions that areknown.
Nowthat we have Martin factor calculated, we estimate the endurancelimit
Whenthe car axle rotates, the bending load becomes completely reversedand alternating component of the stress being equal to maximumstresses.
Thenext step the fatigue strength is evaluated for a finite life of 500cycles:
TakingSu from Appendix Table 1, we have
b= -0.208, C= 3.28 and Sf = 124.34 MPa
Sincewe have only alternating component of stress, as per secondCastigliano’stheorem
Introducen =1.5 and solve for d
Tofind the exact diameter desired for factor of safety
Asthe desired size, if we choose d=58mm, we have to check ourcalculations to see our design safety factor.
Thechange in diameter has negligible effect on stress concentrationfactors, due filet radius is evaluated in terms of radius. But thediameter change effect on the size factor must be calculated.
Thenew endurance limit value will be:
Safetyfactor and fatigue strength are calculated again by replacing Se withthe new one
b= -0.213, c =3.3 and Sf = 121.93 MPa
3.1.3Fatigue failure analysis with torsion
Amorereliable drive shaft design (axle) should include torsion forcesacting on the axle. Because of the nature of the vehicle this torquealternates between peak and zero value and frequently changes. Theradical force also has effect on the shaft and shear forces ispresent already. Because the shaft has a finite life we should alsolook at the damage done due to cumulative fatigue on the axle.Consequently the endurance limit reduces and the subsequent lifereduces.
Theindustrial car moving on rail will not move at high velocity but maybe used in a plant for transportation as a conveyor. Therefore forlocomotives high engine torque will be needed roughly 20kNm on eachwheel. In my case I choose a torque of 100N as my average valueapplied on the axle. In order to know how much of my assumption isaccepted I rearrange my calculations.
Twodifferent loads will give different stress concentration factors andsize factors.
Fromfailure analysis we take the d=58mm, to evaluate Marin factors asfollows:
a= 1.58 b= 0.085 from Appendix Table 4 for ground finish then,
Reliabilityfactor, kc=0.814 obtained from the Appendix Table 6
Temperaturefactor, kd = 1 (considering room temperature working conditions)
ke=1/Kf Formula for calculating stress concentration factor.
TakeKf=1. Therefore ke=1.
Enduringlimit is evaluated after Marin factor has been calculated.
Stressconcentration factor Kfs for torsion load is calculated
FromAppendix Table 5
Nextusing, Appendix Table 1 q=1 for torsion with a notch radius of 3 mm.
Then,Kfs=1+q(Kt – 1) = 1.576,Kf = 1.64
Fromour earlier calculations we know
Thisis because it is repeated type torsion.
TheVon Misses stress components,
Fatiguesafety factor and strength are recalculated by replacing Se with newone.
b= -0.142, C = 3.08 and Sf = 186.52Mpa
Asper the modified Goodman theory
60mmwill give a safety factor of n = 1.59 if the same procedure isfollowed.
Fromthe free body diagram we can agree that the maximum deflection occursat the middle of the shaft, due to the symmetric loading. By usingCastigliano’s Second Theorem we can determine the maximumdeflection that will occur at the middle of the shaft. This can bedone by placing fictitious force Q at the shaft centre. And then byfinding the complementary energy of the shaft through calculation andtaking derivative with respect to the fictitious force Q will getdeflection at the application of the fictitious force Q. Thisdeflection is the maximum deflection. Below is a free body diagramwith fictitious force Q.
FromA to B
3.2.1DeflectionAnalysis with pure bending
Where:isdeflection because of bending and is corresponding energy stored because of bending. The length todiameter ratio in our case is 700/58 =12 therefore we can ignore theshear effect.
WhereU = is the total corresponding energy stored in the shaft. A=0. B=75,C= 150, D=350, P=10Kn, Q=0, E and G are obtained from Appendix Table1. And id obtained by substituting values into the equation and findingdeflection
3.2.2Deflection Analysis due to bending and shear
Deflectioncaused by bending calculated while the effects due to shear isignored. Now let us think about the effect of shear on deflection andfind out if our assumption is right.
WhereUs=is the corresponding energy stored because of shear,is deflection because of shear k=1.33 for solid cross sectionscircles from Borassi.
Theerror obtained for this scenario is only 0.029% which can be easilyignored, therefore our assumption is applicable.
Onthis paper we have discussed the process of designing an industrialcar axle. As we stated earlier in section 1 fatigue failure analysisand static failure analysis should be determined for this kind ofloading including varying stresses on the shaft. Sadly there is alimit for all the calculations you can make, this is because a lot ofuncertainties lack scientific expressions. Therefore in ourcalculations we have made assumptions in order to simplify ourcalculations, also again there some factors which change depending onthe working condition from time to time such as temperature andhumidity. However, we must come up with a good and safe shaft design.This project demonstrates how to evaluate our shaft diameter in theaspect of a safety factor thus overcoming uncertainties. In section3.1.3 and section 3.2wealso evaluated our assumption through further analysis of deflectionanalysis and fatigue failure analysis. In this way for any loadingsituation is considered while we designed our shaft. We also find andcarefully select our safety factor since determining safety factor initself is an important concept in engineering design. Under anacceptable factor of safety we can conclude our design.
Inthis day and age technology serves a great deal of prospect forconquering uncertainties and assessing design analysis. Simulatorsand Computer Aided Design replicate the working conditions in a veryclose manner as in the real life. Also to add on that there aresingle purposes softwares that make possible analysis of certaindesign problems. Proengineer, Delmia are such programs used formodeling assemblies and parts. Abacas, Ansys, Autoform, Delmia andDynaform are some of the programs used for analysis of particularproblems and general ones. Using these softwares and programs indesign, increases the design reliability and reduces time foranalysis and test.
AnselC. Ugural, 2014: Mechanical Design of Machine Components 2ndEdition: Online
VijayK. Goyal, 2012: Elements of Machine Design I. Online
Accordingto the Free Body Diagram of the axle, moment and shear diagrams areshown
Table1:Notch sensitivity curves for materials undergoing reversed torsion.
Source:Shigley’s book, 7thedition figure 7-12
Table2:Notch sensitivity for 2024 wrought Aluminium and steel alloy underreversed bending and axial loads.
Source:Filiz’s Problem book Table A3-17
Table3:Stress concentration factors for shafts with shoulder filletsubjected to bending load
Source:Filiz’s Problem book Table A3-17
Table4: Marinparameters for surface modification factor
Source:Shigley’s book, 7thedition figure 7-12
Table5: Stressconcentration factors for shafts with shoulder fillet subjected totorsion
Source:Filiz’s Problem book Table A3-9
Table6: Reliabilityfactor corresponding to 8% Standard deviation of the endurance limit
Source:Shigley’s book, 7thedition figure 7-7
Table7: Modificationfactors for steels surface finish
Source:Filiz’s Problem book Table A3-16