Week 8 - Universal Joint

TRANSIENT STRUCTURAL ANALYSIS ON A DOUBLE UNIVERSAL JOINT USING ANSYS WORKBENCH

OBJECTIVE

1. To perform transient structural analysis on a double universal joint with spring for the following three different cases of materials,

1. Case-1: Structural steel
2. Case-2: Stainless steel
3. Case-3: Titanium alloy

2. To find out Total Deformation and Equivalent (v-m) Stress for all the cases and compare the results.

1. THEORY

1.1 Universal Joint:

A universal joint also known as universal coupling, U joint, Cardan joint, Hardy-Spicer joint, or Hooke’s joint is a joint or coupling used to connect rotating shafts that are coplanar, but not coinciding. A universal joint is a positive, mechanical connection used to transmit motion, power or both. Each universal joint assembly consists of three major components: two yokes and a cross trunnion. An automotive flange yoke has a machined flat face which may be affixed through a bolted connection to the rear differential of a vehicle. The cross trunnion is used to deliver rotation from one yoke to another using four needle pin bearings.

Fig.1.1 Universal joint.

The main application of the Universal or Hooke’s joint is found in the transmission from the gear box to the differential or back axle of the automobiles. It is also used for transmission of power to different spindles of multiple drilling machine. It is also used as a knee joint in milling machines.

Universal joints differ in view of their material composition, type of hub and the applications for which they are designed. Steel is the most widely recognized material utilized, either in stainless form or alloyed with different metals to handle more noteworthy torque and temperature.

Fig.1.2 Double universal joint.

In this project, a transient structural analysis is carried out on a double universal joint with spring for three different cases of materials such as structural steel, stainless steel and titanium alloy for joint with spring alone.

2. ANALYSIS SETUP

2.1 Geometry:

Fig.2.1 3D model of double universal joint with spring.

The given 3D model of double universal joint with spring assembly is imported into SpaceClaim. It consists of driver yoke, two cross trunnion, intermediate link and driven yoke with spring.

2.2 Material Properties:

a. Structural steel.

b. Stainless steel.

c. Titanium alloy.

Fig.2.2 Material property details of double universal joint with spring.

The material assigned for joint with spring for each case are as follows,

Case-1: Structural steel

Case-2: Stainless steel

Case-3: Titanium alloy

Note: The analysis setup of case-1 is demonstrated.

2.3 Joint Details:

a. Fixed support applied to free end of spring.

b. Revolute joint specified on the driver yoke.                   c. Revolute joint specified on the driven yoke.

d. Revolute joints specified between driver yoke and trunnion_1.

e. Revolute joints specified between trunnion_1 and intermediate link.

f. Revolute joints specified between intermediate link and trunnion_2.

g. Revolute joints specified between trunnion_2 and driven yoke.

Fig.2.3 Joint details of double universal joint with spring,

The free end surface of spring is fixed. In order to rotate the driver yoke, the revolute type of joint is specified along Z-axis with connection type being body-ground. The driven yoke is specified with revolute type of joint along Z-axis with connection type being body-ground to follow the rotary motion and compress the spring which is attached to it.

The rotary motion of the driver yoke is transferred to the trunnion 1 and later to the intermediate link followed by trunnion 2 and driven link. Hence revolute joint is specified along Z axis with connection type being body-body to transmit the rotary motion of driver yoke to the driven yoke.

2.4 Meshing:

Fig.2.4 Meshing details of double universal joint with spring.

The element size of the double universal joint with spring is chosen as 2 mm.  Under sizing option, use adaptive sizing is set to ‘No’. The total number of nodes and elements generated are 57665 and 34548 respectively.

Note: The academic version of software has the problem size limit of 128k nodes or elements.

2.5 Boundary Conditions:

2.5.1 Analysis settings:

a. Analysis setting for step 1.                                            b. Analysis setting for step 2 to step 5.

Fig.2.5.1 Analysis settings.

In the analysis settings the number of steps considered is 5. which is defined by ‘time’. For step 1, auto time stepping is set to ‘Off’, the time step is considered as 0.1s. For step 2 to step 5, auto time stepping and carry over time step is set to ‘On’, the minimum and maximum time step is 0.1s and 1s respectively. In the solver controls, solver type is chosen as ‘Program controlled’, weak springs is set to ‘Program controlled’ and large deflection is set to ‘On’. Under the output controls, all the required results are set to ‘Yes’.

2.5.2 Boundary condition:

Fig.2.5.2 Joint load applied to driver yoke.

The joint load is applied to driver yoke to rotate it in clockwise direction from 0⁰ to 150⁰, with an increment of 30⁰ in each step.

3. RESULTS AND DISCUSSIONS

3.1 Case-1: Structural steel.

a. Total Deformation                                                                                                                    b. Equivalent (v-m) Stress

3.2 Case-2: Stainless steel.

a. Total Deformation                                                                                                                      b. Equivalent (v-m) Stress

3.3 Case-3: Titanium alloy.

a. Total Deformation.                                                                                                                   b. Equivalent (v-m) Stress.

3.4 Comparison of Results:

From the table, it is observed that, the value of maximum total deformation is same for all the cases.

The maximum v-m stress was developed in the spring for case-1 i.e., 1366.4 MPa, whereas, for case-3 is only 672.33 MPa, because the value of young’s modulus, Poisson’s ratio and compressive yield strength is more in case of Titanium alloy compared to other two given materials.

4. ANIMATION OF RESULTS:

4.1 Case-1:

a. Total Deformation                                                                                          b. Equivalent (v-m) Stress

4.2 Case-2:

a. Total Deformation                                                                                          b. Equivalent (v-m) Stress

4.3 Case-3:

a. Total Deformation                                                                                         b. Equivalent (v-m) Stress

CONCLUSION

1. The transient structural analysis on a double universal joint with spring was carried out successfully for the following three different cases of materials,

1. Case-1: Structural steel
2. Case-2: Stainless steel
3. Case-3: Titanium alloy

2. The maximum value of total deformation is same for all the cases i.e., 38.637 mm.

3. The maximum v-m stress was developed in the spring for case-1 i.e., 1366.4 MPa, whereas, for case-3 is only 672.33 MPa, because the value of young’s modulus, Poisson’s ratio and compressive yield strength is more in case of Titanium alloy compared to other two given materials.