Transient Structural Analysis of a Universal Joint

Transient Structural Analysis of a Universal Joint

Objective: To perform a transient structural analysis on a universal joint by assigning different materials to the model and comparing the Total Deformation, Equivalent Stress and Equivalent Elastic Strain obtained in each case.

Geometry: The model consists of a universal joint with one end (or one shaft) connected to a gear and the other end (or shaft) connected to a spring with three coils.

Joint Definition: A number of joints are defined in the model. The end shafts (connected to the gear and spring) are assigned Body-Ground Revolute joints.

The spring at the end it provided a fixed joint to constrain all its degrees of freedom.

The circular slots on the yoke and end shafts are assigned Body-Body Revolute joint with the pins as reference bodies.

Meshing: The entire model is meshed with an adaptive element size of 3.0mm, keeping in mind the node/element limit imposed by the student licence. The smoothening is set to medium.

Analysis Settings: The simulation is run in 5 steps with each step ending at 1s. A constant time step of 0.1s is introduced.

Large deflection is toggled on and all the outputs, except Contact Miscellaneous, are requested to be written to the result file.

Joint Rotation: The revolute joint on the shaft with the gear is provided a total rotation of 150 degrees in increments of 30 degrees over the 5 steps.

Material Definition: For the analysis, three different materials are assigned for three different simulations. The material definition is changed only for the shaft with the spring attached to its end.

Case1: For this run, \"Structural Steel\" is assigned for all the parts of the assembly.

Particulars	Magnitude	Unit
Density	7.85E-06	Kg/mm3
Young’s Modulus	2.00E+05	MPa
Shear Modulus	76923	MPa
Bulk Modulus	166670	MPa
Poisson’s Ratio	0.3
Yield Strength	250	MPa
Ultimate Strength	460	MPa

Case2: for this case, the shaft with the spring at its end is assigned Stainless Steel (Austenitic). The rest of the parts are assigned structural steel as the working material.

Particulars	Magnitude	Unit
Density	7.90E-06	Kg/mm3
Young’s Modulus	1.98E+05	MPa
Shear Modulus	77953	MPa
Bulk Modulus	143480	MPa
Poisson’s Ratio	0.27
Yield Strength	243	MPa
Ultimate Strength	546	MPa

Case3: For this case, the material is changed to Titanium, which possesses the following properties

Particulars	Magnitude	Unit
Density	4.51E-06	Kg/mm3
Young’s Modulus	1.02E+05	MPa
Shear Modulus	37500	MPa
Bulk Modulus	121430	MPa
Poisson’s Ratio	0.36
Yield Strength	315	MPa
Ultimate Strength	411	MPa

Results:

The Total Deformation, Equivalent Stress and Equivalent Elastic Strain obtained for the three cases have been tabulated below

Particular	Case1	Case2	Case3
Total Deformation (mm)	38.637	38.637	38.637
Equivalent Stress (MPa)	1607.6	1581.1	840.04
Equivalent Elastic Strain	8.9746E-02	8.9207E-02	9.1526E-02

1) Total Deformation: The maximum and minimum total deformations are same in all the cases. A maximum of 38.637mm of total deformation is computed for all the cases.

The green, blue and red lines indicate the respective maximum, average and minimum total deformations computed during the run.

2) Equivalent Stress: For all the cases, the region experiencing maximum Von-Mises Stress is the same-in the second loop of the spring, with the highest stress being recorded for the first case. Since no contacts are defined, no stresses are generated at the cross pin joints and the yoke.

Case1

Case2

Case3

The green, blue and red lines indicate the respective maximum, average and minimum Equivalent Stress computed during the run.

3) Equivalent Elastic Strain: The region experiencing the highest lowest strains are the same as that of equivalent strain, with the highest strain being experienced in case of the model with Titanium as the working material.

Case1

Case2

Case3

The green, blue and red lines indicate the respective maximum, average and minimum Equivalent Elastic Strain computed during the run.

Inference:

On analyzing the results obtained from the run, the following deductions are drawn:

• The total deformation computed is independent of the materials assigned to the model. This is because the \"total deformation\" measures the displacement of a point on the model fron its initial position. For this case, the maximum displacement is observed on the gear teeth which displaces by 38.637mm (a little short of its diameter of 40mm) by the end of the simulation.
• Equivalent Elastic Strain is computed as:

...............(i)

Where 𝜀1.𝜀2 𝑎𝑛𝑑 𝜀3 are the maximum, middle and minimum strains in a three dimensional system

𝜈′ is termed as the effective poisson’s ratio.

The individual Principal elastic strains are computed as:

..................................(ii)

From eqn (ii), it can be seen that for a given value of poisson\'s ratio and computed principal stresses, the principal strain value increases for a lower value of Young\'s Modulus.

Since the Young\'s Modulus value is lowest for Titanium , hence the equivalent elastic strain is the highest for Titanium.

• The model does not show any visible deformations even though the Yield strength values have been exceeded during the simulation. This is because, being a linear model, Ansys Mechanical APDL solves the problem in a similar way i.e. it considers the stresses and strains to have a linear function through out the run and the model does not deform even though the yield and ultimate strengths have been exceeded.