Chapter 39: Brake Squeal Analysis

39 Brake Squeal Analysis

Summary 580

Introduction 581

Modeling Details 581

Results 586

Modeling Tips 588

Input File(s) 588

Reference 588

Video 588

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SummaryTitle Chapter 39: Brake Squeal Analysis

Contact features Contact friction induced dynamic instability leading to brake squeal

Geometry

Model Courtesy ofDr. Lin Jun Seng of TRW

Automotive

Material properties • Back plate E = 2.07x108 kg/(mm-sec2), = 0.28, = 7.82x10-6 kg/mm3

• Insulator: E = 2.07x108 kg/(mm-sec2), = 0.28, = 7.82x10-6 kg/mm3

• Pad: Anisotropic Organic Material

• Rotor: E = 1.25x108 kg/(mm-sec2), = 0.24, = 7.2x10-6 kg/mm3

Boundary conditions • Constraints to simulate caliper guided brake pad motion• Contact between the two deformable bodies with µ = user selected

Applied loads Piston pressure normal to pad surface

Element types 8-node solid element HEXA and PENTA

FE results The unstable mode at 1.953 Hz in the analysis when = 0.3.

R = 144

t = 20

Units: mm, kg, sec

Pad

Rotor

Back_Plate

Insulator

X Y

Z

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IntroductionBrake squeal is the unpleasant high frequency vibrations (2000 to 10000 Hz) that occur in disk brake systems. Application of the brakes causes an increase in line pressure which results in the caliper piston (s) to push the pads against the spinning rotor. A valuable review paper by Kinkaid et al. (Kinkaid 2003) provide a comprehensive review and bibliography of research on disc brake squeal. The high pitch noise or squeal occurs when a specific combination of piston pressure, friction and damping effects cause two stable modes to merge or coalesce into a single unstable mode.

The solution to preventing modal coalescence is to modify the design. This would include, but is not limited to, material changes, design changes and the addition or modification of present damping components. However the analysis of disk brake systems has been challenging due to the complexity of the structure, material properties and loading environment.

Brake squeal analysis models require not only the typical FEM mesh of the components (pads and rotor at a minimum), but also the representation of the contact/frictional connection between the pad and rotor. This contact/friction is represented by an unsymmetric stiffness matrix. Previously in Nastran there were restrictions imposed by this method that included:

• The meshed contact area between the rotor and pad must be congruent

• Separation is not allowed; full contact is maintained

• The contact matrix is supplied as a DMIG generated outside of the normal FEM calculations

• Each contact condition involving the friction coefficient and loading (magnitude and pattern) required a unique DMIG

Typically, the generation of the DMIG entries required days to weeks of analysis time. Interested users are directed to Section 5.3 of the Advanced Dynamic Analysis Users Guide for a description on manual generation of the contact/friction connection DMIG entries.

The introduction of the brake squeal analysis capability in this release has eliminated all of the previous restrictions. In addition, the user now has the capability to examine various combinations of friction values, loading, and contact definitions in a single execution. Further, the system matrices can include, at user request, differential stiffness due to preloading, large displacement effects and full nonlinear property definitions. No longer is the brake squeal analysis limited to a string of single shot runs or multiple restarts. This example features the following: 3-D deformable-deformable contact with friction, multiple SUBCASE/STEP analysis, user selectable complex solution domain - real or modal space, choice of complex Lanczos or Hessenberg solver, and full user control of contact parameters.

Modeling DetailsBrake squeal analysis is activated in MD Nastran's Advanced Nonlinear solution sequence (SOL 400) with the Bulk Data entry BSQUEAL. The BSQUEAL entry is selectable within the Case Control section at the SUBCASE level. With the analysis chaining capability complex eigenvalues can be computed at user selected load factors.

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The case control loading and modal extraction requests are shown in the listing that follows. This example demonstrates the extraction of complex modes at specific piston load points

SUBCASE 100 $ SUBTITLE = Nonlinear static analysis SPC = 2 METHOD = 100 $ Modal Approach CMETHOD = 200 AUTOSPC(noprint) = YES RESVEC = NO $ STEP 1 LABEL = Nonlinear Static Step NLPARM = 2 $ Ten load increments BCONTACT = 1 BOUTPUT = NONE $ No contact surface output SPC = 2 LOAD = 200 $$ STEPs for complex eigenvalue extraction$ STEP 2 LABEL = Brake Squeal modes at 20% piston load 0.3 friction coeff ANALYSIS=MCEIG BSQUEAL = 900 NLIC STEP 1 LOADFAC 0.2$ STEP 3 LABEL = Brake Squeal modes at 50% piston load 0.3 friction coeff ANALYSIS=MCEIG BSQUEAL = 900 NLIC STEP 1 LOADFAC 0.5$ STEP 4 LABEL = Brake Squeal modes at 80% piston load 0.3 friction coeff ANALYSIS=MCEIG BSQUEAL = 900 NLIC STEP 1 LOADFAC 0.8BEGIN BULK...

The analysis contains a single SUBCASE with four STEPs. Step 1 performs the nonlinear loading in 10 steps. Contact bodies are selected with the BCONTACT where the contact friction values are defined on the Bulk Data BCTABLE. This step performs a normal nonlinear 3-D contact analysis that allows separation of the contact surfaces.

Steps 2 through 4 perform a complex eigenvalue extraction at selected load points. The methods used to extract the modes are defined above all the STEP definitions. Activation is done with the ANALYSIS=MFREQ entry which requires a normal modes and complex modes selection which in this example is above all STEP definitions. The user has access to all of the MD Nastran modern modal methods: Lanczos, complex Lanczos, and Hessenberg.

Load steps selected for complex mode extraction is defined by the NLIC entry. This entry selects the loading STEP and the load increment - LOADFAC. The allowable values for LOADFAC are determined by the INC value defined on the

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Bulk Data NLPARM entry. The BSQUEAL entry is also present to select the variables such as friction value to be used in generating the contact stiffness matrix between the pad and rotor. As the example shows, complex modes are extracted for a defined friction value of 0.3 at piston loads of 20, 50, and 80 percent of the maximum. This then allows, in one execution, monitoring the complex modes for possible coalesce of two modes which signals the onset of brake squeal.

Modeling ContactContact is easily defined in MD Nastran. The Bulk Data pair BCBODY/BSURF to designate the type of contact body (deformable) and the elements comprising the contact body. The contact algorithms locate the element faces that will potentially participate in contact surfaces. There is no need for user effort to limit the elements listed on the BSURF entry to aid the contact algorithms. For example, all of the elements in the rotor are selected in BCBODY/BSURF 4 of the larger model, and there is no need to painstaking pick only those elements that might contact the pads; similarly for the pads.

The contact bodies for this example model are shown in Figure 39-1. Note that the elements defining the contact body can be groups of discontinuous elements as shown by the brake pads.

Figure 39-1 Contact Bodies

Additional contact bodies are permitted. With disk brake systems, other components would be (but not limited to) the caliper, pistons, guide pins, and steering knuckle. The BCTABLE collects the contact bodies and assigns various parameters related to the surface contact. In the example below, there are four contact bodies. Contact between the pads and pistons are defined as glued contact - integer 1 in field 8. Glued contact also has the feature of eliminating the requirement of matching mesh gridpoints between the bodies. Pad and rotor contact is defined as full nonlinear contact with a frictional value of 0.3.

If the contact surfaces are a mixture on glued (pistons to pads) and full nonlinear contact (pads to rotor) the BCPARAM entry is also required.

BCPARA 0 nlglue 1

bsurf-4

bsurf-5

bsurf-6

X Y

Z

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This ensures that a contact body that participate in glued and full nonlinear contact will maintain the full nonlinear contact status in all STEPs.

$ Contact bodies (see BCBODY/BSURF) - all deformable$ BODY 4 - Rotor$ BODY 5 - Outer pad$ BODY 6 - Inner pad$ Body ID Fric Glued$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------BCTABLE 0 2 SLAVE 6 0. 0. 0.3 0. 0 0. 2 2 0 MASTERS 4 SLAVE 5 0. 0. 0.3 0. 0 0. 2 2 0 MASTERS 4BCTABLE 1 2 SLAVE 6 0. 0. 0.3 0. 0 0. 2 2 0 MASTERS 4 SLAVE 5 0. 0. 0.3 0. 0 0. 2 2 0 MASTERS 4BCTABLE 2 2 SLAVE 6 0. 0. 0.4 0. 0 0. 2 2 0 MASTERS 4 SLAVE 5 0. 0. 0.4 0. 0 0. 2 2 0 MASTERS 4 BCTABLE 3 2 SLAVE 6 0. 0. 0.5 0. 0 0. 2 2 0 MASTERS 4 SLAVE 5 0. 0. 0.5 0. 0 0. 2 2 0 MASTERS 4 ...$$ Rotor deformable contact body$BCBODY 4 3D DEFORM 4 0BSURF 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...(rest of elements omitted)$ Outer pad deformable contact body$ BCBODY 5 3D DEFORM 5 0BSURF 5 24400 24401 24402 24403 24404 24405 24406 24407 24408 24409 24410 24411 24412 24413 24414...(rest of elements omitted)$$ Inner pad deformable contact body$BCBODY 6 3D DEFORM 6 0BSURF 6 20704 20705 20706 20707 20708 20709 20710 20711 20712 20713 20714 20715 20716 20717 20718...(rest of elements omitted)

BCTABLE with ID 0 is used to define the touching conditions at the start of the analysis. This is a mandatory option required in SOL 400 for contact analysis, and it is flagged in the case control section through the optional BCONTACT = 0 option. The BCTABLE with ID 1 is used to define the touching conditions for later increments in the analysis, and it is flagged using BCONTACT = 1 in the case control section. Also, the SLAVE-MASTER combination defines that the nodes for body 1 are nodes belonging to the slave body. This in literature is referred by various terminologies as either

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contacting body nodes or tied nodes (imagining the situation of multi-point constraints). The nodes belonging to body 2 are said to belong to the master body which are also referred to as the contacted body nodes or the retained nodes (imagining the situation of multi-point constraints)

The definition of the contact bodies (defined as Rotor and Pads in Figure 39-1 above) as stated above use the BCBODY/BSURF Bulk Data pair. The BCBODY options define the deformable body including the body ID, dimensionality, type of body, type of contact constraints and friction, etc. BSURF identifies the elements forming a part of the deformable body and includes the convenient THRU option when listing the element ID's.

Brake Squeal ParametersThe BSQUEAL Bulk Data entry supplies information specific for forming the brake squeal analysis.

$ ID OMETH AVSTIFBSQUEAL 900 0.5 1.e+5 0.0 0.0 1.0 0.0 0.0 0.0

AVSTIF is the average stiffness on a per unit basis between the pad and disk. This variable is under user control instead of a hidden predefined value. This stiffness is used in forming the penalty contact stiffness between the pad and rotor. Thus AVSTIF has a direct influence over the overall stability of the model and the values of the brake squeal modes. The default value is 1.0E+4 however it is advised that until the user is comfortable with the calculated results, several additional brake squeal runs be performed using alternate AVSTIF values.

Evaluation of the proper value for AVSTIF (or if the default is appropriate) can be easily accomplished with the STEP command. As the BSQUEAL is called from the Case Control section, a series of STEPs can be defined each calling a BSQUEAL Bulk Data entry with a unique AVSTIF.

The second line of data defines the rotational axis of the rotor; all reference from the basic rectangular coordinate system. The first three values define the cosines of the rotation axis. The second three values represent a point on the rotation axis. As the rotor spins about the Z direction, only the Z cosine is supplied. Any point coordinate on the Z axis would be acceptable for the three values as the rotor straddles the Z=0.0 plane.

Loading and Boundary ConditionsThe displacements for the pads simulate the guidance of the brake caliper system. This is best described in Figure 39-2.

Figure 39-2 Displacement Constraints

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Pressure is applied to the backside of each brake pad. This is best described in Figure 39-3.

Figure 39-3 Piston Pressure on Brake Pads

Solution ProcedureThe nonlinear procedure used is defined through the following NLPARM entry:

NLPARM 2 FNT PV YES

FNT represents Full Newton Raphson technique wherein the stiffness is reformed at every iteration. KSTEP (field after FNT) is left blank, and in conjunction with FNT, it indicates that stiffness needs to be reformed between the end of the load step and the start of next load increment. The maximum number of allowed recycles for every increment is left at the default of 25. If more than 25 recycles is exceeded, the load step would be cut-back and the increment repeated. PV indicates that the maximum norm of vector component of the incremental loads will be checked for convergence. YES indicates that intermediate output will be produced after every increment. The second line of NLPARM is not defined indicating that default tolerances will be used for convergence checking.

The number of increments is provided in the 3rd field of the NLPARM option. The default is 10 and this ties back to the allowable values for LOADFAC on the NLIC entry.

ResultsFigure 39-4 shows the displacement (contours and physical shape) of the brake pads due to the pressure load at 100% magnitude. The undeformed shape is represented by the unshaded wireframe. This information is available for each load increment (10 as NINC was defaulted to 10.)

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Figure 39-4 Displaced Shape at 100% Load

Figure 39-5 is an example of the modal shape of the first unstable complex mode when is 0.3. The mode shapes are available for every complex mode calculated at each STEP where the BSQUEAL is present.

Figure 39-5 First Unstable Complex Mode Shape at 1953 Hz

The SUBCASE/STEP combination provides the user with the powerful capability to evaluate multiple combinations of friction, load patterns, and contact properties. In Table 39-1 a simple comparison between two friction values has been summarized.

Table 39-1 Summary of First Unstable Mode Results

Piston Load

First Unstable Mode Frequency

HzDamping

Coefficient

First Unstable Mode Frequency

HzDamping

coefficient

10% 1914.56 -0.014863 1914.90 -0.027065

20% 1914.55 -0.014855 1914.89 -0.027062

50% 1914.50 -0.014833 1914.84 -0.027052

100% 1914.42 -0.014796 1914.77 -0.027007

0.30= 0.50=

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Modeling TipsStart with the smaller demonstration model (small_brake_squeal.dat). This model can be run locally on a PC machine and runs fast. Data generation is reasonable even with a large number of output requests, then migrate to the larger model.

Input File(s)

ReferenceKinkaid, N. M. O’Reilly, O. M. Papadopoulos, P. (2003) Automotive disc brake squeal. Journal of Sound and Vibration 267, 105-166.

VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately four minutes and explains how the steps are performed.

Figure 39-6 Video of the Above Steps

File Description

nug_39a.dat Simple brake squeal model. Runs fast and users encouraged to evaluate analysis procedures/selections with this model.

nug_39b.dat This is the large brake squeal model shown in the figures. Although it runs relatively fast it can generate vast amounts of data, particularly if the print or punch options are chosen.

R = 144

t = 20

Units: mm, kg, sec

Pad

Rotor

Back_Plate

Insulator

X Y

Z