1.5.2 Steady-state spinning of a disk in contact with a foundation

Product: ABAQUS/Standard  

This example illustrates the nature of viscoelastic material effects in steady-state rolling problems and serves as a validation test for the material convection algorithm used in the steady-state transport procedure. Since the steady-state transport capability uses a kinematic description that implies flow of material through the mesh, convective effects must be considered for history-dependent material response. ABAQUS provides material convection in a steady-state transport analysis for viscoelastic materials. An overview of the capability is provided in Steady-state transport analysis, Section 6.4.1 of the ABAQUS Analysis User's Manual.

We use an independent transient Lagrangian analysis to obtain a reference solution for the validation of the steady-state transport material convection algorithm. A finite element analysis of a similar problem, together with numerical results, has also been published by Oden et al. (1986).

Problem description

Loading

The loading is applied over two analysis steps. In the first step the disk is brought in contact with the foundation by applying a prescribed displacement of 0.3 units to the rigid body reference node on the foundation (Figure 1.5.2–1). The *STATIC, LONG TERM option is used for this analysis. The LONG TERM parameter provides the fully relaxed long-term viscoelastic solution without the need to perform a transient analysis. The long-term solution ensures a smooth transition between the static and slow rolling solutions.

The second analysis step is a *STEADY STATE TRANSPORT analysis. Steady-state solutions at various angular velocities (ranging from 0.001 rad/s to 1000 rad/s) are obtained. The *TRANSPORT VELOCITY option is used for this purpose.

The reference Lagrangian solution is obtained using the *VISCO procedure. The file spinningdisk_visco.inp contains the input data for this analysis.

Results and discussion

Input files

Reference

Figures

Figure 1.5.2–1 Displaced shape of disk ( 0.0 rad/s).

Figure 1.5.2–2 Reaction force normal to the foundation. The bullet points are the transient Lagrangian solution.

Figure 1.5.2–3 Moment around the axle. The bullet points are the transient Lagrangian solution.

Figure 1.5.2–4 Contact pressure.

Figure 1.5.2–5 Radial stress variation along a streamline. Comparison with transient Lagrangian solution (broken line).

Figure 1.5.2–6 Circumferential stress variation along a streamline. Comparison with transient Lagrangian solution (broken line).

Figure 1.5.2–7 Shear stress variation along a streamline. Comparison with transient Lagrangian solution (broken line).