Brake squeal workflow performance improvements

The brake squeal workflow in Abaqus is based on a combination of nonlinear static analysis steps and complex eigenvalue extraction. A typical analysis includes:

1. Several nonlinear static preloading steps, in which various contact conditions and other nonlinear effects can be taken into account to set up a base state for a complex eigenvalue problem.

2. Solution of a symmetrized natural frequency extraction problem. This step creates a projection subspace that will be used to solve a complex eigenvalue problem by the subspace projection method.

3. Mass, damping, and unsymmetrical stiffness matrices of the original system are projected onto the subspace; and the reduced unsymmetrical complex eigenvalue problem is solved.

Complex modal analysis can be repeated as many times as needed for different friction-induced and other contact conditions. Due to the repetitive executions, complex modal analysis may require significant computational resources and can become very expensive for realistic industrial models.

In Abaqus 2018 the performance of the complex eigenvalue extraction phase of a brake squeal workflow has been improved as follows:

• Improved performance and scaling of matrix operations.

• Improved logic to avoid redundant operations: several analysis phases were re-implemented or completely eliminated.

• Enabled control over the stiffness operator projection. This feature can dramatically improve performance of the complex eigenvalue extraction phase when asymmetry in the stiffness operator is caused by contact elements only. A new parameter on the complex frequency extraction procedure instructs Abaqus whether it should perform full stiffness operator projection (default), focus on the contact elements only to accommodate the asymmetry of the stiffness operator, or ignore the asymmetry of the stiffness operator.

The performance improvement in the brake squeal Abaqus workflow has been demonstrated on three benchmark models, described in Table 1.

Figure 1 and Figure 2 illustrate performance improvements in the brake squeal workflow for several releases, including comparison using the new option for fast stiffness operator projection: project stiffness for the contact elements only. Each analysis included all restart jobs. Each restart job included (a) a general static step changing the base state; (b) a frequency extraction step that computes the subspace basis vectors; and (c) a complex frequency extraction step that solves the reduced unsymmetrical eigenvalue problem.