Influence of contact parameters on the radiated noise from an automotive drum brake

Ramesh, Ananthapadmanabhan 1

Indian Institute of Technology Tirupati Tirupati, Andhra Pradesh India-517506

Rangamani, Aditya 2

Indian Institute of Technology Tirupati Tirupati, Andhra Pradesh India-517506

Sundar, Sriram 3

Indian Institute of Technology Tirupati Tirupati, Andhra Pradesh India-517506

ABSTRACT Drum brakes are the major source of noise and vibrations in the automobile as the drum acts as a significant source of the noise. High-frequency noises are generated at the interfacial contact between the brake shoe and brake drum. Hence, the variation in the contact parameters (friction, contact sti ff ness, and contact damping) will significantly a ff ect the vibro-acoustic noise emanating from the drum brake. The current work quantifies the variation in vibro-acoustic noise due to an asymmetry in the contact of leading and trailing shoes with the drum. The overall sound pressure level is estimated numerically using a finite element model of the drum brake. Multiple spring-like components in parallel between the brake shoe and the drum imitate the contact in real drum brakes. The numerical model predicts the noise generated by a symmetric system (without any asymmetry defects) and a system with controlled asymmetric defects introduced into the model. The results show that the overall sound pressure level is a strong function of the contact parameters. The current research is envisioned to better the selection of contact parameters and hence the drum and shoe properties.

1 me17ms001@iittp.ac.in

2 me19b046@iittp.ac.in

3 sriram@iittp.ac.in

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

1. INTRODUCTION

Drum brake noise is a significant problem in many automobiles ranging from lightweight vehicles like cars to heavyweight vehicles like trucks and buses [1]. These are high-pitched noises in the frequency range of 20 Hz to 20 kHz, mainly due to the frictional interaction between the brake drum and brake shoes. Previously researchers have developed the Finite Element Model (FEM) of drum brake to perform complex eigenvalue analysis to identify the unstable modes which are likely to produce noise [2]. Further, the model was used to analyze the influence of various parameters like drum sti ff ness, brake lining sti ff ness, and coe ffi cient of friction on squeal noise (in terms of the real part of the eigenvalue). Kung et al. [3] performed experimental and numerical studies on low- frequency drum brake squeal and proposed various solutions like modification of backing plate, brake shoes, and lining for reducing noise. Ramesh et al. [4] have developed an integrated framework of a non-linear vibration analytical model and a numerical acoustic model of drum brake to quantify the drum brake vibro-acoustic noise over the audible frequency range. Further, the e ff ect of change in parameters like damping ratio and actuation force on overall sound pressure level was quantified. However, most of the drum brake models (FEM and Analytical) developed by previous researchers were under the assumption that there are no defects in drum brake [5,6]. Various defects can occur in drum brakes due to manufacturing errors or continuous usage like cracks, out of roundness, etc. For instance, Ramesh et al. [7] have studied the variation in vibro-acoustic noise emitting from the drum brake due to the asymmetry in the shoe’s pivot location and initial angular orientation of the shoe. However, other parameters and defects strongly influence vibro-acoustic noise. Hence, the current study aims to analyze the influence of contact parameters such as contact sti ff ness, contact damping, and coe ffi cient of friction on the radiated vibro-acoustic noise. This is achieved by using a finite element model of the drum brake and integrating harmonic acoustic and transient structural analysis in ANSYS.

2. ESTIMATING ACOUSTIC RESPONSE

To estimate the variation in the sound pressure radiated from the brake drum due to various asymmetry defects, a finite element model of drum brake has been developed in ANSYS. Previously researchers have developed a comprehensive vibro-acoustic model (combining numerical acoustic and non-linear analytical model) for estimating the variation in overall sound pressure level due to asymmetry defect [7]. Calculating the variation in sound pressure level due to asymmetry in the contact parameters is performed in three steps. First, the dynamic forces acting on the brake drum are calculated from the transient structural analysis of the drum brake. Second, transfer functions (ratio of sound pressure level to dynamic force) related to the brake drum have been calculated using harmonic acoustic analysis. Finally, overall sound pressure levels at various microphone locations are calculated from the sum of the products of appropriate transfer functions and dynamic forces in the frequency domain. For calculating the dynamic forces acting on the brake drum at the contact point, transient structural analysis has been performed in ANSYS, as shown in Fig.1. The developed model has a brake drum, leading and trailing shoes, and brake lining. A small gap has been provided between the brake shoe lining and brake drum, which finally reaches zero when the actuation forces are applied. The contact between the brake shoe lining and the brake drum has been modelled using multiple springs arranged in parallel, whose e ff ective sti ff ness will be the contact sti ff ness. The excitation force used for the acoustic analysis is the transient contact force, namely, the normal force ( F n ) and frictional forces ( F f ) acting at the point of contact between the brake drum and brake shoe. The transfer function relating sound pressure level and excitation forces ( F n and F f ) acting at the leading and trailing shoe contact points are calculated using harmonic acoustic analysis. This analysis is similar to the numerical acoustic model developed in the literature [4], and can be referred

to for the assumptions and procedure for calculating the transfer functions. For the current study, two microphone locations were chosen, one along the drum axis at 250 mm from the drum centre (ML1) and the other perpendicular to the drum axis at 250 mm from the drum centre (ML2). Four transfer functions T n l ( ω ), T f l ( ω ), T n r ( ω ) and T f r ( ω ) were calculated in the frequency domain corresponding to the four excitation forces ( F n and F f in leading and trailing shoes).

Figure 1: FEM model of drum brake used for structural transient analysis

Dynamic forces acting at the contact point of the brake drum and brake shoes during a braking event were obtained from transient structural analysis in ANSYS. From the response, it is evident that there are two distinct phases, namely the impact phase, where the brake shoe continuously loses contact with the brake drum and the contact phase, where the brake shoes are always in contact with the brake drum. Since the dynamics of these phases are distinct, the sound pressure levels corresponding to the excitation forces are analyzed separately. For the current study, asymmetry in the contact parameters, namely contact sti ff ness ( k ), contact damping ( c ), and coe ffi cient of friction ( µ ) are analyzed as shown in Table.1. The subscript l and r denotes leading and trailing shoes.

3. EFFECT OF ASYMMETRY IN CONTACT PARAMETERS

The values of various contact parameters in the leading and trailing shoes are varied to understand the influence of asymmetry in contact parameters on the acoustic response of the system. Even though a drum brake has various components like a backing plate, brake shoes, brake lining, etc., for the current study, the noise emanating from the brake drum is only considered. The influence of various asymmetric defects on noise is quantified in terms of overall sound pressure level (SPL). In each study, the SPL from the impact and contact phases were analyzed separately along with the SPL at ML1 and ML2.

Table 1: Cases developed to analyze the e ff ect of asymmetry in contact parameters on drum brake vibro-acoustic noise

k l [Nm − 1 ] k r [Nm − 1 ] c l [Nsm − 1 ] c r [Nsm − 1 ] µ l µ r Asymmetry defect

Symmetric case 2.88x10 7 2.88x10 7 7 7 0.4 0.4

Case 1 3.46x10 7 2.88x10 7 7 7 0.4 0.4 Sti ff ness Asymmetry

Case 2 2.88x10 7 3.46x10 7 7 7 0.4 0.4 Sti ff ness Asymmetry

Case 3 2.88x10 7 2.88x10 7 8.4 7 0.4 0.4 Damping Asymmetry

Case 4 2.88x10 7 2.88x10 7 7 8.4 0.4 0.4 Damping Asymmetry

Case 5 2.88x10 7 2.88x10 7 7 7 0.3 0.4 Friction Asymmetry

Case 6 2.88x10 7 2.88x10 7 7 7 0.4 0.3 Friction Asymmetry

3.1. Asymmetry in contact sti ff ness In this case, asymmetry is caused due to di ff erent values of contact sti ff ness in the leading and trailing shoe contact points. Case 1 corresponds to the condition in which the contact sti ff ness of the leading shoe is higher than the trailing shoe by 20%. From Table 2, it is evident that the value of overall SPL decreased in the impact regime when the leading shoe contact sti ff ness increased. Even though there is an increase in the value of friction and normal forces (in the time domain) in the leading shoe due to high sti ff ness, the overall SPL value still decreases in the impact regime. At the same time, the value of overall SPL increased in the contact regime by 2.9dB when the leading shoe sti ff ness value was high compared to the trailing shoe. Similarly, Case 2 analyzes the condition when the trailing shoe’s contact sti ff ness is higher than the leading shoe by 20 %. Similar to Case 1, the value of overall SPL in the contact regime increased by 3.8 dB, whereas the SPL remained unchanged in the impact regime. In all the cases, the value of overall SPL in the impact regime is greater than the contact regime, which is obvious due to higher force during impacts.

Table 2: Comparison of overall SPL for Case 1 and 2

Overall SPL [dB ref 20 µ Pa]

Symmetric case

Case 1 Change from symmetric case

Case 2 Change from symmetric case

M1 (Impact) 148.3 137.7 -10.60 148.3 0

M2 (Impact) 147.0 136.4 -10.60 147.0 0

M1 (Contact) 57.2 60.1 + 2.90 61.0 + 3.80

M2 (Contact) 44.0 46.9 + 2.90 47.8 + 3.80

3.2. Asymmetry in contact damping Cases 3 and 4 represent the asymmetric condition when the leading and trailing shoe’s contact damping is di ff erent from the symmetric case. From Table 3, it is observed that when the contact

damping of the leading shoe is higher than the trailing shoe (case 3), the value of overall SPL in both impact and contact regime decreased at both microphone locations (ML1 and ML2). Since the amplitude of impacts is higher in the leading shoe than in the trailing shoe due to the self-energizing e ff ect, increasing the value of contact damping significantly a ff ects the vibro-acoustic noise emanating from the brake drum. On the contrary, the value of overall SPL increased in both impact and contact regime when the contact damping of the trailing shoe was higher than the leading shoe (case 4).

Table 3: Comparison of overall SPL for Case 3 and 4

Overall SPL [dB ref 20 µ Pa]

Symmetric case

Case 3 Change from symmetric case

Case 4 Change from symmetric case

M1 (Impact) 148.3 148.1 -0.20 148.4 + 0.05

M2 (Impact) 147.0 146.8 -0.20 147.0 + 0.04

M1 (Contact) 57.2 57.0 -0.24 57.6 + 0.36

M2 (Contact) 44.0 43.7 -1.70 44.4 + 0.36

3.3. Asymmetry in coe ffi cient of friction For the symmetric condition or the brake shoes without any defects, both shoes’ coe ffi cient of friction should be the same. However, continuous interactions of brake shoes with the brake drum can lead to a change in the coe ffi cient of friction. Case 5 and 6 describe the asymmetric condition when the coe ffi cient of friction of the leading and trailing shoe is di ff erent. From Table 4, it can be observed that when the coe ffi cient of friction of the leading shoe is lower than trailing shoe (case 5), the value of overall SPL decreases in the impact regime compared to an increase in the contact regime. Similar results can be observed when the coe ffi cient of friction of the trailing shoe is lower than the leading shoe (case 6).

Table 4: Comparison of overall SPL for Case 5 and 6

Overall SPL [dB ref 20 µ Pa]

Symmetric case

Case 5 Change from symmetric case

Case 6 Change from symmetric case

M1 (Impact) 148.3 148.0 -0.35 147.0 -1.35

M2 (Impact) 147.0 146.2 -0.80 146.2 -0.80

M1 (Contact) 57.2 57.9 + 0.68 57.8 + 0.61

M2 (Contact) 44.0 44.4 + 0.37 44.4 + 0.40

4. CONCLUSIONS

The current study investigates the e ff ect of asymmetry defects in contact parameters on the radiated vibro-acoustic noise from drum brake. A finite element model of drum brake has been developed in

ANSYS to perform harmonic acoustic and transient structural analysis. The normal and frictional force acting at the point of contact between the brake drum and brake shoe was considered as the source for the harmonic acoustic analysis. Various parameters like contact sti ff ness, contact damping, and coe ffi cient of friction were varied to find the impact of contact parameters on the noise. From the results, it is clear that there is a significant change in the radiated vibro-acoustic noise by changing the values of contact sti ff ness. Further, by increasing the damping of the leading shoe contact point, the value of overall SPL can be decreased. In the future, this work can be extended to find the noise radiating from brake shoes, backing plate, and other components in the drum brake. It is envisioned that the current work can be used for calculating vibro-acoustic noise in the time domain.

ACKNOWLEDGEMENTS

We acknowledge the Science Engineering and Research Board (SERB), India (https: // www.serbonline.in / ) for partially supporting this research work under the Startup Research Grant (Grant No. SRG / 2019 / 001172).

REFERENCES

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