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Documentation

Validation Case: Quarter Shaft Subjected to a Fixed Rotation

This validation case belongs to solid mechanics. The aim of this test case is to validate the following parameters:

  • Cyclic symmetry
  • Rotating motion

The simulation results of SimScale were compared to the results presented in [Roark’s]\(^1\).

Geometry

The geometry used for the case is as follows:

sketch of a quarter shaft used for validating simscale with bottom edges labeled a to c and top surface a' to c'
Figure 1: Sketch of a quarter shaft

The quarter shaft has a radius (\(r\)) of 0.1 \(m\) and a length (\(l\)) of 0.5 \(m\).

Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Static – linear

Mesh and Element Types:

The standard mesh was created with the Standard meshing algorithm in SimScale.

CaseMesh TypeNumber of NodesElement Type
A1st order standard8682Standard
B2nd order standard63084Standard
C1st order hexahedral2730Standard
D2nd order hexahedral10527Standard
Table 1: Mesh used for simulation of all cases
first order standard mesh generated with simscale's standard mesher which has 8682 nodes
Figure 2: Generated standard mesh used for cases A and B
uploaded mesh which has 2730 nodes
Figure 3: Uploaded hexahedral mesh used for case C and D

Simulation Setup

Material/Fluid:

  • Steel (linear elastic)
    • Isotropic: \(E\) = 205 \(GPa\), \(\nu\) = 0.3 , \(G\) = 80 \(GPa\)

Boundary Conditions:

  • Constraints:
    • Fixed: Face ABC
    • Fixed rotation:
      • Face A’B’C’: rotation with an angle of (\(\theta\)) 2e-3 \(rad\) around the z-axis

Contacts

  • Cyclic Symmetry
    • Face AA’BB’ tied to face AA’CC’
    • Rotation axis: z-axis
    • Sector angle: 90°

Reference Solution

The reference solution for maximum stress etc. is given by the following equation:

$$\tau_{max} = \theta.G.r.l = 32\ GPa$$

Result Comparison

Comparison of the maximum shear stress (\(\tau_{max}\)) obtained from SimScale against the reference results obtained from [Roark] is given below:

Case[Roark]SimScaleError [%]
A3231.794-0.64
B3231.564-1.36
C32320.00
D3232.059-0.18
Table 2: Comparison of shear stress.

The visualization of the cauchy shear stress [SIYZ] contours in Pascals as in the SimScale post-processor:

visualization of cauchy stress after rotation is applied to the shaft
Figure 4: Cauchy shear stress distribution contours across the quarter shaft

Note

If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

Last updated: July 28th, 2020

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