The analysis settings and solution controls differ depending upon the method used to solve a brake-squeal problem. This section describes three possible methods:
A linear non-prestressed modal analysis is effective when the stress-stiffening effects are not critical. This method requires less run time than the other two methods, as Newton-Raphson iterations are not required. The contact-stiffness matrix is based on the initial contact status.
Following is the process for solving a brake-squeal problem using this method:
Perform a linear partial-element analysis with no prestress effects.
Generate the unsymmetric stiffness matrix (NROPT,UNSYM).
Generate sliding frictional force (CMROTATE).
Perform a complex modal analysis using the QRDAMP or UNSYM eigensolver.
When using the QRDAMP solver, you can reuse the symmetric eigensolution from the previous load steps (QRDOPT), effective when performing a friction- sensitive/parametric analysis, as it saves time by not recalculating the real symmetric modes after the first solve operation.
Expand the modes and postprocess the results from Jobname.rst.
For this analysis, the UNSYM solver is selected to solve the problem. (Guidelines for selecting the eigensolver for brake-squeal problems appear in Recommendations.)
The frequencies obtained from the modal solution have real and imaginary parts due the presence of an unsymmetric stiffness matrix. The imaginary frequency reflects the damped frequency, and the real frequency indicates whether the mode is stable or not. A real eigenfrequency with a positive value indicates an unstable mode.
The following input shows the solution steps involved in this method:
Modal Solution
/SOLU ANTYPE, MODAL ! Perform modal solve NROPT, UNSYM ! To generate non symmetric CMSEL, S, C1_R ! Select the target elements of the disc CMSEL, A, C2_R CM, E_ROTOR, ELEM ! Form a component named E_ROTOR with the selected target elements ALLSEL, ALL CMROTATE, E_ROTOR, , , 2 ! Rotate the selected element along global Z using CMROTATE command MODOPT, UNSYM, 30 ! Use UNSYM to extract 30 modes MXPAND, 30 ! Expand 30 modes, do not calculate element results SOLVE FINISH
Use a partial nonlinear perturbed modal analysis when stress-stiffening affects the final modal solution. The initial contact conditions are established, and a prestressed matrix is generated at the end of the first static solution.
Following is the process for solving a brake-squeal problem using this method:
Perform a nonlinear, large-deflection static analysis (NLGEOM,ON).
Use the unsymmetric Newton-Raphson method (NROPT,UNSYM). Specify the restart control points needed for the linear perturbation analysis (RESCONTROL)
Create components for use in the next step.
The static solution with external loading establishes the initial contact condition and generates a prestressed matrix.
Restart the previous static solution from the desired load step and substep, and perform the first phase of the perturbation analysis while preserving the .ldhi, .r
nnnand .rst files (ANTYPE,STATIC,RESTART,,,PERTURB).Initiate a modal linear perturbation analysis (PERTURB,MODAL).
Generate forced frictional sliding contact (CMROTATE), specifying the component names created in the previous step.
The contact stiffness matrix is based only on the contact status at the restart point.
Regenerate the element stiffness matrix at the end of the first phase of the linear perturbation solution (SOLVE,ELFORM).
Obtain the linear perturbation modal solution using the QRDAMP or UNSYM eigensolver (MODOPT).
When using the QRDAMP solver, you can reuse the symmetric eigensolution from the previous load steps (QRDOPT), effective when performing a friction-sensitive/parametric analysis, as it saves time by not recalculating the real symmetric modes after the first solve operation.
Expand the modes and postprocess the results (from the Jobname.rstp file).
The following inputs show the solution steps involved with this method:
Static Solution
ANTYPE, STATIC ! Perform static solve OUTRES, ALL, ALL ! Write all element and nodal solution results for each sub steps NROPT, UNSYM ! Specify unsymmetric Newton-Raphson option to solve the problem RESCONTROL,DEFINE,ALL,1 ! Control restart files NLGEOM, ON ! Activate large deflection AUTOTS, ON ! Auto time stepping turned on TIME, 1.0 ! End time = 1.0 sec CMSEL,S,C1_R ! Select target elements of the disc CMSEL,A,C2_R CM,E_ROTOR,ELEM ! Form a component named E_ROTOR SOLVE ! Solve with prestress
Perturbed Modal Solution
ANTYPE,STATIC,RESTART,,,PERTURB ! Restart from last load step and sub step PERTURB,MODAL ! Perform linear perturbation modal solve CMROT,E_ROTOR,,,2 ! Rotate the target element to generate sliding frictional contact SOLVE,ELFORM ! Regenerate the element stiffness matrix MODOPT,UNSYM,30 ! Use UNSYM eigensolver and extract 30 modes MXPAND,30 ! Expand 30 modes SOLVE ! Solve linear perturbation modal solve
A full nonlinear perturbed modal analysis is the most accurate method for modeling the brake-squeal problem. This method uses Newton-Raphson iterations for both of the static solutions.
Following is the process for solving a brake-squeal problem using this method:
Perform a nonlinear, large-deflection static analysis (NLGEOM,ON).
Use the unsymmetric Newton-Raphson method (NROPT,UNSYM).
Specify the restart control points needed for the linear perturbation analysis (RESCONTROL).
Perform a full second static analysis.
Generate sliding contact (CMROTATE) to form an unsymmetric stiffness matrix.
After obtaining the second static solution, postprocess the contact results.
Determine the status (that is, whether the elements are sliding, and the sliding distance, if any).
Restart the previous static solution from the desired load step and substep, and perform the first phase of the perturbation analysis while preserving the .ldhi, .r
nnnand .rst files (ANTYPE,STATIC,RESTART,,,PERTURB).Initiate a modal linear perturbation analysis (PERTURB,MODAL).
Regenerate the element stiffness matrix at the end of the first phase of the linear perturbation solution (SOLVE,ELFORM).
Obtain the linear perturbation modal solution using the QRDAMP or UNSYM eigensolver (MODOPT).
Expand the modes and postprocess the results (from the Jobname.rstp
The following inputs show the solution steps involved with this method:
First Static Solution
ANTYPE, STATIC ! Perform static solve OUTRES, ALL, ALL ! Write all element and nodal solution results for each substep NROPT, UNSYM ! Specify unsymmetric Newton-Raphson option to solve the problem RESCONTROL,DEFINE,ALL,1 ! Control restart files NLGEOM, ON ! Activate large deflection AUTOTS, ON ! Auto time stepping turned on TIME, 1.0 ! End time = 1.0 sec CMSEL, S, C1_R ! Select the target elements of the disc CMSEL, A, C2_R CM, E_ROTOR, ELEM ! Form a component named E_ROTOR with the selected target elements ALLSEL, ALL SOLVE ! Solve with prestress loading
Second Static Solution
CMROTATE, E_ROTOR, , , 2 ! Rotate the selected element along global Z using CMROTATE command TIME, 2.0 ! End time = 2.0sec SOLVE ! Perform full solve FINISH
Perturbed Modal Solution
ANTYPE,STATIC,RESTART,,,PERTURB ! Restart from last load step and sub step PERTURB,MODAL ! Perform linear perturbation modal solve SOLVE,ELFORM ! Regenerate the element stiffness matrix MODOPT,UNSYM,30 ! Use UNSYM eigensolver and extract 30 modes MXPAND,30 ! Expand 30 modes SOLVE ! Solve linear perturbation modal solve