Simulation Driven Innovation 1

Robustness Studies of the Disc Brake Rotor and Structural Modifications for Squeal Reduction Using Radioss

Sanjay Chincholi

Specialist Satyam- Venture Engg Services Secunderabad - 500 003 India

Praveen Kumar Abburi Specialist

Satyam- Venture Engg Services Secunderabad - 500 003 India

Vijayasaradhi. T Asst.Project Manager

Satyam- Venture Engg Services Secunderabad - 500 003 India

Nomenclature: C damping matrix K stiffness matrix k spring stiffness Kf friction coupling matrix M mass matrix u displacement vector ω angular frequency µ coefficient of friction

Abstract

The brake rotor is one of the active components of the disc brake assembly. During braking friction between the pad and disc it can induce

dynamic instability. Many studies associate the squeal phenomenon to the coalescence of two Eigen frequencies of the system as a result of

friction induced vibration. Rotors exhibit varying material characteristics and tolerances based on the manufacturing process of each supplier. A

small deviation in geometric shape and mass may alter the dynamic behavior of the brake assembly.

To make a robust design regardless of the manufacturing tolerances and wear etc, a simple method to update the material properties and evaluate

the design sensitivities with respect to squeal of the brake rotor is discussed. The finite element model for various manufacturing tolerances is

generated by morphing shapes using Hypermesh. Radioss solver is used to analyze the model using complex eigenvalue analysis and identify

potential squeal frequencies. The robustness analysis is done using Hyperstudy.

Keywords: Squeal, Disc brake, design sensitivity, finite element, NVH Introduction: Disc brake squeal is an undesirable noise emitting from the car due to friction induced vibration. The disc brake squeal continues to be the major problem concern for automotive industry despite efforts to reduce its occurrence during the past decades. There are several factors that influence both high and low frequency squeal, which are the rubbing surface thickness, hat structure or vane pattern structure and materials used for production [5]. Studies have shown that variation of stiffness of the Disc and Backplate also have significant sensitivity for squeal. The NVH characteristics of the brake system may be altered for variations in material and tolerances. The brake design system must accommodate these variations in the design phase itself so as to minimize the cost escalations. In present work, attempt is made to study the influence of variation of geometry, friction and disc stiffness on disc squeal. Finite element modeling, shape morphing, DOE studies and simulation using Radioss are done seamlessly within the HyperWorks environment.

Simulation Driven Innovation 2

Background theory: Nack [3] conducted a new finite element complex Eigen value analysis of a disc brake system in the year 2000, where the stiffness matrix of the finite element system was directly modified to include the friction coupling. The equation of motion for the free vibration of a multi-degree-of-freedom system is given by 0 KuuCuM (1) Where ‘M’ is the mass matrix, ‘C’ is the damping matrix, ‘K’ is the stiffness matrix and ‘u’ is the displacement vector. The contact at the brake pad/rotor interface is simulated by connecting coincident nodes on the pad and the disc with linear springs. The springs prevent penetration of pad into the rotor and have a contact stiffness value based on the stiffness of the adjacent pad elements. In order to simulate friction coupling between the pad and the rotor, a simple friction law of the following form is used for the friction force. )( )1( yiiyjyx uukff (2) Where fx

is the friction force, fy is the normal force at the friction interface, µ is the coefficient of friction, Kj is the

contact stiffness and ui’s are the displacements of the coincident nodes. In equation [2], the pad has been assumed to be in constant sliding contact with the disc and that the tangential vibration velocities are small in comparison to the sliding velocity so that the friction force does not reverse direction. This friction force provides a forcing function for Equation [1], which can be rearranged as 0][ uKKuCuM f (3) Where, Kf is friction stiffness matrix, which couples forces in the friction interface normal direction to the tangential direction and is asymmetric. By solving Equation (3) as an eigenvalue problem, complex eigen values can be obtained consisting of real and imaginary parts. For a particular mode the Eigen value pair is ii i 2,1 (4) Where αi and ωi are the damping coefficient (real part) and damped natural frequency (the imaginary part) describing the damped sinusoidal motion. A positive damping coefficient causes the amplitude of oscillations to increase with time. Therefore, the system is not stable and damping coefficient is positive. By examining the real part of the system Eigen values the modes that are unstable and are likely to produce squeal are revealed. Damping ratio can be defined as -2α / |ω| , which is negative in case of instability.

Updating the FE Model: Ideally correlation criteria should quantify the ability of test and FE models to make the same predictions. A correlation with FRF’s is common comparison criteria performed for both identification and finite element updating purposes. Model updating works by modifying the mass, stiffness, and damping parameters of the FE model until an improved agreement between FEA data and test data is achieved. The following error function λdB is used in the "decibel method."

M

m mdbndbdb XA1

2|)()(| (5)

where Adb(ωm) and Xdb(ωm) are the measured and model FRF in decibel respectively, ωm is the angular frequency. By taking the differences in the decibel, the model should be fitted to the measured FRF independently on the levels of the measured FRF at individual components. Finite Element Modeling: A simplified model with disc and pad assembly is considered for this study for two reasons: 1. Major source for the friction induced squeal is at the pad / rotor interface

2. The CPU time for study of the changes in the geometric tolerances and material properties is reduced allowing more configurations to be computed. FE mesh in Radioss bulk data format is generated for the rotor and pad assembly with higher order tetrahedral elements. The rotor cheeks at outer and inner sides are coupled to pads with 1D linear contact springs. The pad is

Simulation Driven Innovation 3

allowed to move in the axial direction while the rotor is constrained at bolt locations. It is assumed that friction forces are acting equally on both the outer and inner pads. Process Methodology :

The nominal values of material parameters are presented in the Table 1:

Component Young's Modulus (Mpa)

Poisson's Ratio Density (Kg/mm3)

Disc material (cast iron) 100000 0.3 7.1 E-06 Pad lining material 800 0.3 2.8 E-06 Backplate material 200000 0.3 7.8 E-06

Table 1: Material properties of components [2]

In the present study, influence of shape changes on the disc squeal behavior is taken up. The vented disc parameters are identified for analyzing the disc squeal behavior listed in Table 2.

Figure 3: Disc Brake geometric parameters

Figure 3 shows the section details for the typical vented disc with reference to the feature labels from Table 2. The regions in the Table 2 are morphed and saved as shapes using HyperMorph module. The design variables for the morphed shapes are created in the optimization panel. The design variables, shape files and the finite element information are exported with analysis code set to Optistruct. HyperStudy provides environment where the finite element shape modifications are achieved by creating input decks for the variants automatically for the study setup based on bounds specified and runs linked to a particular solver. The study setup process is shown in figure 4.

p4

p1

p2 p3

p5

Simulation Driven Innovation 4

Label Parameter Region

P1 m_1_shape1

P2 m_1_shape2

P3 m_1_shape3

P4 m_1_shape4

P5 m_1_shape5

Table 2: Hyperstudy setup and template input file creation

Simulation Driven Innovation 5

A full factorial design evaluates the response of every possible combination of factors and factor levels. For the present problem, the design of experiments (DOE) is setup as full factorial class in HyperStudy with total of 32 runs (5 shape variables).

Figure 4: HyperStudy setup and template input file creation

Figure 5: DOE setup using HyperStudy

The HyperStudy also provides an elegant mechanism for extracting the responses. For the present study frequency responses were extracted at all the runs.

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Figure 6: Extraction of the responses in Hyperstudy

Mode shapes: Results of the mode shapes for the Radioss complex Eigen value solution can be viewed in HyperView by reading the h3d result file.

Figure 7: Shape plot for instable mode (negative damping)

In the HyperStudy environment it is possible to generate an automated report for the design study. The images of correlations, regression and surface plot of the parameter interaction can be added to the report. Results & Discussions:

Material Influence of disc stiffness on squeal:

The material properties of the disc were evaluated for young’s modulus varying from 70,000MPa to 140,000 MPa to study the squeal occurrence.

Simulation Driven Innovation 7

6319

7410

7608

7936

8609

8777

9434

9495

9648

9887

9906

Disc E= 70 GPa

Disc E= 90 GPa

Disc E= 110 GPa

Disc E= 130 GPa0.00

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Influence of disc stiffness on prediction of results of squeal using the simplified model

Disc E= 70 GPa

Disc E= 80 GPa

Disc E= 90 GPa

Disc E= 100 GPa

Disc E= 110 GPa

Disc E= 120 GPa

Disc E= 130 GPa

Disc E= 140 GPa

Figure 8: Influence of disc stiffness on the prediction of the squeal using the simplified model

From figure 8, it can be noted that the squeal occurrence and squeal intensities are shifted with increase in disc stiffness. Material Influence of shape variations on the disc:

Influence of the shape variations on the squeal prediction results using the simplified model

0.00

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6000 6500 7000 7500 8000 8500 9000 9500 10000 10500

Frequency (Hz)

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tive

dam

ping

rat

io

Model 1Model 2Model 3Model 4Model 5Model 6Model 7Model 8Model 9Model 10Model 11Model 12

Figure 9: Influence of shape variations on the squeal prediction results using the simplified model

From figure 9, one can see that the squeal events in some of the squeal zones have shifted to nearby frequencies due to shape variations; in general these squeal events are sensitive to shape variations. To make the design robust the squeal occurrence influences of the instability spread due to manufacturing tolerances that has to be taken into account.

Simulation Driven Innovation 8

Predicted unstable Eigenvalue variation due to shape variations on the simplified model

6000

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Shape variation model number

Freq

uenc

y (H

z)

Squeal freq 1Squeal freq 2Squeal freq 3Squeal freq 4Squeal freq 5Squeal freq 6Squeal freq 7Squeal freq 8Squeal freq 9

Figure 10. Predicted unstable eigenvalue variation due to shape variations

Figure 10, shows the Eigen values at which instability are predicted for the shape variational models obtained from the DOE setup. Response selection for the post processing is done based on the mode number for the predicted zone squeal frequency. For the variation of the shapes results are tabulated from the Hyperstudy postprocessor as shown in the figure 11 to figure 13

Figure 11: Distribution of response for first squealing frequency

Figure 12: Distribution of response for second squealing frequency

Simulation Driven Innovation 9

Figure 13: Distribution of response for third squealing frequency

Benefits Summary

The finite element brake assembly can be analyzed with respect to squeal frequencies for shape various configurations within the HyperWorks framework with the integration of Radioss complex Eigen value solver.

The sensitivity analysis will give sufficient information on the required design changes. Morphing removes the dependency on CAD, thereby reducing the cycle time.

Conclusions

The design of the brake rotor is studied for the variations in shape and material parameters The squeal prediction is made for changes in shape parameters within the specified tolerance The responses from the DOE iterations provide the shapes tend to shift the squeal occurrence The entire process of squeal prediction and modifications can be done within HyperWorks environment.

REFERENCES [1] Nack W., Joshi, A..M., "Friction induced vibration: Brake Moan”, SAE paper, 951095, 1995 [2] Chen G, Wu P, Dai H., "Comparative study on the complex eigen value prediction of brake squeal by two infinite element modeling

approaches”, Chinese Journal of Mechanical engineering, Vol 23 , 2010 [3] Cao Q.,, Ouyang H et al .,”Linear eigenvalue analysis of the disc brake squeal problem”, Int J. Numer. Mech Engng 2004: 61:1546-1563 [4] Antti T.P., Joseph C.S L et al., ”Vibro-Acoustic studies of the brake squeal”, Proc. of Acoustics, 2004 [5] Hassan Z M, “ Experimental modal analysis of brake squeal noise”, http://eprints.um.edu.my/484/1/Poster9.pdf [6] Ouyang H, Nack W.,”On Automotive Disc Brake SquealPart II: Simulation and Analysis”, SAE paper, 2003-01-0684