VM274
VM274
Stabilizing Squeal Damping
Overview
| Reference: | Any Dynamics Textbook |
| Analysis Type(s): | |
| Element Type(s): | |
| Input Listing: | vm274.dat |
Test Case
A rigid block (Young’s modulus E, Poisson ratio ν, density ρ, length of edge a, area A) is elastically supported by a spring-damper element and guided by a rail with a velocity υ. The whole assembly is sliding on the rough ex-ey-plane (coefficient of friction μ, normal pressure p). Linear perturbation modal analysis is performed using the DAMP eigensolver to determine the damped frequency and modal damping ratio, which is then compared against analytical results.
| Material Properties | Geometric Properties | Loading |
|---|---|---|
|
E = 21 x 1010 N/m2 ν = 0.3 μ = 0.5 ρ = 8000 kg/m3 m = 8kg |
a = 0.1m A = 0.01m |
υ = 10 m/s k = 315 N/m p = 100 Pa |
Analysis Assumptions and Modeling Notes
The rigid block is modeled and meshed with SOLID185 elements. The block is constrained on all degrees of freedom at location y=0. The pilot node is created using TARGE170 elements. Mass is defined on the pilot node using MASS21 elements. A spring element with stiffness ‘k’ is created using COMBIN14 elements to support the block. One end of the spring element is connected to the pilot node and the other end is fixed. Stabilizing squeal damping is activated using real constant FDMS of the contact elements. Remote force is applied on the block using the pilot node and contact elements. A non-linear static analysis is performed with two load steps. In the first load step, the remote force is applied. In the second load step, the velocity is applied through the CMROTATE command. A linear perturbation modal analysis is performed from the base non-linear static solve using the DAMP eigensolver to determine the damped modes and modal damping ratio. The damped frequency originating from friction is calculated using the following formula:
 | (274–1) |
Where:
| No (force) = 1N |
| μ (friction) = 0.5 |
| c (spring stiffness) = 315 N/m |
| m (mass) = 8 Kg |
| υo (velocity) = 10 m/s |
Substituting these parameters in the above equation yields:
| λ1,2 = 0.003125±6.274949i |
Converting radians/seconds to hertz:
| (1/2π)λ1,2 = 0.000497±0.998287i |
| Damping ratio = 0.0004980 |