Impact Analysis of Brake Pad Backplate Structure and Friction Lining Material on Disc-Brake Noise

,is study proposes a three-layer brake pad design, on which a six-DOF dynamicmodel of brake disc-brake pad is established, and the factors affecting the system instability are analyzed. ,e analysis shows that the change of mass and stiffness of the brake pad will affect the stability of the system. From the linear complex eigenvalue analysis, the unstable vibration modes of the brake system are predicted, and the effectiveness of the complex mode analysis model is verified by the brake system bench test. Brake pads with different structural shapes are designed, and their influence on the stability of the brake system is analyzed. ,e results show that the design of the three-layer structure and the slotting design of the brake pad can effectively reduce the occurrence of the brake squeal, especially that of the high-frequency squeal noise.


Introduction
Since the early 1920s, automotive disc-brake squeal noise has been a widespread concern of academics and automobile manufacturers all over the world because brake squeal is an important cause of customer dissatisfaction and warranty problems.In the past three decades, the proportion of disc brake used in sedan has increased year by year.It can be assumed that disc brakes will gradually replace drum brakes in sedan.However, the problem of brake noise of disc brakes still exists, and many brake noise phenomena have not been explained rationally so far [1][2][3].Automobile braking process will produce vibration, and unstable vibration will not only lead to noise that both affects the comfort of driving and causes acoustic pollution to the surrounding environment but it will also cause fatigue wear on the automobile brake system [4].
Lars have slotted and surfaced the surface of the brake disc and proved by experiment that improved brake disc can reduce the occurrence of the brake squeal [5].Oberst and Lai used chaos theory to study the mechanism of braking noise, which is of great guiding significance [6].Kung et al. calculated the free modal of the components in the brake and obtained the components and related modalities with the largest contribution rate of unstable mode by the complex eigenvalue analysis [7].In addition to using the complex eigenvalue analysis to study the brake noise, the transient dynamic analysis is first used by Nagy et al.
e four mode frequencies extracted from the results of transient dynamic analysis coincide with the experimental noise [8].e disadvantages of transient dynamics are that it takes too much computation time and takes up a lot of disk space, and it is also hard for the data to be used directly for design changes.Besides, because of the high frequency of brake squeal, the explicit integral time step is very small, whereas the implicit integral can have a large time step, but it will attenuate the high-frequency mode.Complex eigenvalue analysis and transient dynamic analysis are used by AbuBakar and Ouyang [9] to study the brake squeal, under the same model and boundary condition.e results of the above two analyses are identical with the different contact mechanism and integral method.In the analysis of the brake system noise, the use of complex eigenvalue analysis, combined with a reasonable combination of transient dynamic analysis, may be a way to analyze the noise generation mechanism.
In the friction-slip experiment of the flat plate, Chen [3] found that the instantaneous squeal may not be caused by the modal coupling, and the transient excitation between the disc and block may be the key mechanism of the squeal.However, this kind of alternating load excitation is a transient process difficult to capture through experiments.
e transient dynamic analysis may more clearly show the process and reveal the reasons of this phenomenon.For the dynamic model of the brake disc and brake pad, a four-DOF self-excited frictional oscillator model was proposed by Zhang et al. [10] to explore the difference between the linear analysis and nonlinear analysis on the brake system noise, and corresponding improvement measures are given.
In this context, based on the modal coupling theory, a sixdegree-of-freedom motion model of the brake disc and brake pad is established.Combined with finite element complex modal analysis and bench test, it is of great guiding significance to improving the NVH performance by improving the material properties of the brake pad and optimizing the backplate structure of the brake pad to inhibit the brake squeal noise and to exploring the inhibition mechanism of noise, which provides a theoretical basis for reducing the noise of brake squeal.

Six-DOF Kinematics Model of Brake Disc-Brake Pad
e brake coupling model built by Festjens et al. [11] shows that the structure and damping of backplate of the brake pad have an important influence on the brake noise.Similarly, the damping size of the friction lining material will also have a significant influence on brake noise.rough the research studied by Ruhai et al. [12], it is known that adding a certain proportion of viscoelastic material to the friction lining could reduce the resonance tendency between the brake pad and the brake disc, thereby inhibiting the brake squeal to some extent.Based on the important influence of the friction lining, it is divided into two parts, namely, lining substrate and friction lining mixture.Since the material composition of lining substrate has stronger damping characteristics than the friction lining mixture, it should be treated differently during the modeling and simulating process.
A six-DOF kinematics model of brake disc-brake pad is depicted in Figure 1.Due to the small damping of the system, the effect of damping is neglected in the kinematics analysis.
e brake pad is composed of the brake pad backplate m b , lining substrate m u , and friction lining mixture m l .m b has a z-direction degree of freedom z 1 ; m u has a z-direction degree of freedom z 2 ; and m l has a z-direction degree of freedom z 3 and an x-direction degree of freedom x 3 ; e brake disc m d has two degrees of freedom, respectively, x-direction of x d and z-direction of z d .μ, P, and N are friction coefficient, force of piston acting on the brake pad, and positive force acting on the brake disc, respectively.
e kinematic equation can be obtained from the kinematic model of Figure 1: In this formula, u � (z 1 , z 2 , z 3 , x 3 , z d , x d ) T and (•) is the differentiation with respect to time.e mass matrix

and [K]
is the stiffness matrix: In the initial stage, the system is in a stable steady state, the brake disc rotates at a constant speed, and the system does not produce vibration, so the steady-state equation can be obtained.Assuming that the brake disc and brake pad are not separated during the process of vibration, the constraint condition is z d � z 3 , and then we know Taking (3) into the steady-state equation, we obtain 2 Advances in Materials Science and Engineering Equation ( 4) is the kinematic equation of the brake discbrake pad system.It can be found that the mass matrix and the sti ness matrix of the kinematic equation of system are both asymmetric due to the existence of friction, so the eigenvalues of the system may be complex numbers.e eigenvalues of the system can be obtained by complex modal analysis, where the imaginary part of eigenvalue represents the modal frequency and the real part represents the tendency of instability.At the same time, it can be found that the change of friction coe cient and the change of mass and sti ness of the brake pad will lead to the change of system mass matrix and the sti ness matrix, so as to change the system eigenvalue and a ect the stability of the system.Based on the above, this study will change the system's mass matrix and sti ness matrix by changing the geometric characteristics of the brake pad backplate, thus a ecting the stability tendency of the system, to nd out which structural feature of the backplate can reduce the brake system squeal.

Finite Element Model.
Using CATIA to model the braking system, the HyperMesh is used to establish the mesh models, as shown in Figure 2.Among them, the brake caliper adopts the tetrahedral mesh (C3D4) due to the irregular structure, the remaining parts mainly adopt hexahedral unit (C3D8), supplemented with pentahedron unit (C3D6) and terahedral unit (C3D4), and the total number of model units is 327,568.Besides, the contact relationship between the components has been labelled in Figure 2.

De ning Material Properties.
De ne the material properties of each component, including Density, Young's modulus, and Poisson's ratio, as shown in Table 1.

Setting of Analysis.
e nite element model, which has de ned the material properties and assembled, is introduced into the ANSYS for complex eigenvalue analysis.Some nonlinear perturbation modal analysis is used to extract the unstable modes of the brake system.e brake disc cap portion is bolted to the hub, but the brake disc can rotate along the z-axis, thus restraining the ve degrees of freedom of the disc cap portion except for the z-direction of rotation.
e anchor is bolted to the frame to restrain the six degrees of freedom of the cage bolt hole.

Setting of Load.
In order to quantitatively study the relationship between friction coe cient, braking pressure, and brake noise, a brake system test was carried out under 9 operating conditions: by speed: 60 rpm, 120 rpm, and 180 rpm, and by hydraulic pressure: 1.5 MPa, 2.0 MPa, and 2.5 MPa.

Bench Test Veri cation of Brake Complex Modal Analysis
Model.
e test standard of brake noise is the NVH test standard of the Society of Automotive Engineers, namely, SAE J2521 test standard [13]; the microphone is placed at 10 cm in the horizontal direction of the brake system, and the vertical distance is 50 cm (Figures 3(a)and 3(b)).
In the whole experimental process, 18 stages of braking conditions of the noise test were measured and the total braking process was 1,430 times.Since the initial temperature of this test starts from zero, there is no need to determine the noise in the cold state.
e test data were processed to obtain part of the results of bench test shown in Figure 4 (the braking pressure is 2.0 MPa, and the rotational speed is 120 rpm), which is representative.4 Advances in Materials Science and Engineering each sound pressure level at the same frequency.It can be found from Figure 4 and Table 2 that there are ve di erent frequencies of squeals in the braking process, and the frequencies of squeals are mainly distributed around 4.1 kHz, 7.5 kHz, and 12.7 kHz.e test results at the braking pressure of 1.5 MPa, 2.0 MPa, and 2.5 MPa and ction coe cient of 0.8, 0.7, and 0.6 were, respectively, extracted, and the test results were compared with the unstable modal frequency of brake system obtained by simulating to verify the validity and accuracy of the model, as shown in Table 3. e results show that all the brake squeal frequencies in the test can be predicted by simulation, and the error is controlled within 0.1%.However, the phenomenon of overprediction appeared in the simulation; this is mainly due to the fact that the model of complex eigenvalue analysis does not take into account   Advances in Materials Science and Engineering factors such as the thermomechanical coupling, the frictional characteristics, and the time-varying characteristics of material properties in the actual braking process, which is mentioned in many literatures, so the model could predict the brake squeal accurately.

Verification of Brake Pad
e brake pad is mainly composed of three parts, namely, backplate, lining substrate, and friction lining mixture, as shown in Figure 5.Because of the simple structure and regular shape of the brake pad, the hexahedral mesh is selected to mesh.e material properties of each component are shown in Table 4.
From the results of real modal analysis of the brake pad, the typical vibration modes of natural frequencies within 10 kHz are extracted, as shown in Table 5, which are mainly manifested as bending and torsional vibration modes.e accuracy of the natural frequency of the brake pad was verified by the FRF resonance tester.As shown in Table 6, Advances in Materials Science and Engineering the natural frequency error of the simulation and experiment was found to be within 2%.At the same time, the laser vibrometer is used to verify the vibration mode.As shown in Table 5, the typical modes measured by the laser vibrometer are exactly the same as those of the simulation vibration mode, so the results of the real modal analysis are accurate and the model of the brake pad is effective.

Slotting Designs on Brake Pad Backplate
According to the theory of structural dynamic design, changes in the mass of the system or the shape of the structure will lead to the change of system stiffness and damping, which will affect the natural frequency of the system [14].According to the difficulty of backplate processing and the manufacturing process of the brake pad, five types of slotting methods are designed in this study, as shown in Figures 6-10.e effects of the five types of slotting designs on the natural frequencies and vibration modes of the brake pad are analyzed to determine whether the brake squeal noise will be further affected.e effective total area of the backplate is 4615 mm 2 .e design dimension of horizontal slot is 80 × 4 mm, and single horizontal slot, double horizontal slots, and three horizontal slots are designed on the backplate.e ratio of the slotted area to the total area of the backplate is 6.9%, 13.9%, and 20.8%, respectively.
e design dimension of longitudinal slot is 40 × 4 mm, and four longitudinal slots and six longitudinal slots are designed on the backplate.e ratio of the slotted area to the total area of the backplate is 13.9% and 20.8%, respectively.e depth of slotting designs is both 1 mm.In addition, the large size of the slotting on the backplate will cause the stiffness of the brake pad to drop sharply and affect the manufacturing process of the brake pad, so the ratio of the slotting area of the backplate should not be larger than 25% [15].e free mode characteristics of the above five slotted backplates are calculated in the frequency range of 10∼16 kHz.
en, the six-order critical modal frequencies were extracted and compared with the free modal frequencies of the unslotted backplate, as shown in Table 7. e bench test of the brake system has shown that the frequency of the brake squeal is mainly distributed around 4.1 kHz, 7.5 kHz, and 12.7 kHz.As can be found in Table 7, Sample 3, Sample 4, and Sample 5 are significantly improved for the critical frequency of 4.1 kHz and 7.5 kHz, but only Sample 3 has the best improvement effect on the critical frequency of 12.7 kHz, and Sample 4 and Sample 5 have barely any improvement on the critical frequency of 12.7 kHz.erefore, Sample 3 was selected for further study.e model of Sample 3 was made into a test piece (Figure 11), and the bench test was performed.e test results are shown in Figure 12. e test time for these tests shown in Figure 12 is close to that for those tests shown in Figure 4. Table 8 shows the main four test operations and test times of      From the test results, the brake pad with three horizontal slots on the backplate could e ectively reduce the occurrence of brake squeal noise, especially that of the high-frequency squeal noise, and greatly reduce the noise points above 80 dB sound pressure level.

Results and Discussion
e change rate of the critical frequency between the unslotted brake pad and Sample 3 could be calculated from Table 7. e frequency changes of the Sample 3 are −91.5 Hz, −455.8Hz, and −770 Hz, respectively, as shown in Table 9.From Figure 12, it could be found that the original squeal frequency near 7.5 kHz disappears and the new squeal noise is generated near 6.8 kHz.Similarly, the original noise frequency around 4.1 kHz disappears and the new noise is generated near 3.9 kHz.Besides, high-frequency squeal of noise points near 12.7 kHz disappears completely.
e vibration mode of unstable modal frequency at 12,752.6 Hz is extracted from the results of complex modal analysis, as shown in Figure 13.e mode coupling between the brake pad and the brake disc resulting in resonance and the energy generated by the resonance which cannot be dissipated in time are the root causes of concentration near the high frequency 12.7 kHz.e design of three horizontal slots on the brake pad backplate makes the critical frequency change 770 Hz, which leads to the decoupling of the brake pads and the brake disc.Besides, the lining substrate of the brake pad contributes to the dissipation of energy generated by resonance.Similarly, the decoupling between the brake pads and the brake disc is also achieved at frequencies of

Figure 3 :
Figure 3: (a, b) Location of microphone and picture of real product and (c) disc brake assembled on test bench.

Figure 4 :
Figure 4: Noise frequency distribution and sound pressure level.

Figure 13 :
Figure 13: Unstable vibration mode at the braking pressure of 2.0 MPa (at 12,752.6Hz).

Table 2
shows the noise occurrence rate at di erent frequency bands.e row data in the table indicate the occurrence rate of noise under each frequency band at the same sound pressure level, and the column data indicate the occurrence rate of noise under

Table 1 :
Material properties of brake components.

Table 2 :
Noise occurrence rate at di erent frequency bands.

Table 3 :
Comparison between the results of complex eigenvalue analysis and the bench test of brake squeal.

Table 4 :
Material properties of each component of brake pad.

Table 5 :
Experimental verification on simulation vibration mode of the brake pad.

Table 6 :
Experimental verification on simulation modal frequency of the brake pad.

Table 7 :
Comparison of critical modal frequencies between slotted backplate and unslotted backplate.

Table 8 :
Bench test of Sample 3.

Table 9 :
Critical frequency change rate between unslotted backplate and Sample 3.