SAE TECHNICAL PAPER SERIES
2004-01-2787
A Study on Low Frequency Drum Brake Squeal Shih-Wei Kung, Greg Stelzer and Kelly A. Smith Delphi Corporation
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2004-01-2787
A Study on Low Frequency Drum Brake Squeal Shih-Wei Kung, Greg Stelzer and Kelly A. Smith
Delphi Corporation
Copyright © 2004 SAE International
ABSTRACT Low frequency drum brake squeal is often very intense and can cause high levels of customer complaints. During a noise event, vehicle framework and suspension components are excited by the brake system and result in a violent event that can be heard and felt during a brake application. This paper illustrates the experimental and analytical studies on a low frequency drum brake squeal problem that caused high warranty cost. First the environmental condition was identified and noise was reproduced. Vehicle tests were performed and operating deflection shapes were acquired. The sensitivity of the lining material to different environmental conditions was investigated. With the use of complex eigenvalue method, models were constructed to obtain further understanding of the phenomena. Finally, the squeal mechanism of a drum brake system is discussed and various solution techniques for low frequency drum brake noise are evaluated.
INTRODUCTION Among various types of brake noise, squeal is seen in a wide range of frequencies starting from the first elastic mode of the major brake component to the audible limit of the human ears. For a disc brake, the lower limit of a brake squeal is often defined at 1 or 2 kHz because the first elastic mode of a rotor is in that frequency range. On the other hand, the first elastic mode of a drum is between 500 Hz to 1000 Hz. Brake noise in this frequency range that involves elastic modes of the drum and backing plate should also be categorized as squeal. For a drum brake squeal lower than 1 kHz, the interaction between the brake system and the vehicle framework and suspension is often very substantial. The result is a violent event that can be heard and felt during a brake application. As a result, this type of noise often brings high customer compliant and causes high warranty cost. Unfortunately, to solve this type of squeal problem is also difficult because of the large number of components involved. Dynamometer tests may not be able to
reproduce the noise due to the lack of suspension components. Even in a case where the noise is reproduced on a dynamometer, the noise fix that works on a dynamometer may not be a fix when applied to the vehicle [1]. A similar situation is often found in the finite element analysis. When suspension components are not included in the model, predicted unstable modes may still show up in the problem frequency. However, the prediction does not reflect the actual situation. Thus, suggested noise fixes may not show improvements on the vehicle. Because of these issues, the study of a low frequency drum brake noise has become a challenging task that requires large amounts of experimental and numerical efforts. Many of the latest measuring techniques have been implemented to study low frequency drum brake squeal. Felske [2] used holographic analysis to study drum brake noise in the range of 1-2 kHz, finding that the majority of the noise is transmitted from the backing plate. Yuuji Suzuki and Hideo Ohno [3] studied a drum brake noise at 500 Hz. The interaction between the shoe deformation and the second order radial motion of the drum were investigated. Using the holographic interferometry technique, Fieldhouse [1,4-5] performed a series of investigations on drum brake noise. It was observed that the influence of backing plate is more significant for low frequency squeal, while that of the drum is more significant in the higher frequency region [4]. It was also found that the inclusion of suspension in the test rig changed the noise frequency [1]. A 400 Hz moan was generated when no suspension was attached. However, a low frequency squeal at 960 Hz was found with the suspension system in the test rig. In addition to experimental studies, many analytical efforts have also been carried out on drum brake squeal using the complex eigenvalue approach [6-10]. Jiang et al. [6] developed a dynamic drum brake model with a closed form solution. Hamabe et al. [7] used the complex eigenvalue method to study drum brake squeal and then
calculated modal participation to derive design solutions. Somnay and Shih [8] performed a parametric design study on low frequency drum brake squeal of a commercial vehicle. Ioannidis [9] analyzed a drum brake with a dominant squeal frequency of 750 Hz that was generated without suspension components. Various pressure levels and lining contact conditions were incorporated in the complex eigenvalue analysis. This paper demonstrates the experimental and analytical efforts in solving a low frequency drum brake squeal. First, a spike in warranty cost brought a specific vehicle platform into attention. A statistical engineering team was then set up to identify the noise problem and the environmental conditions needed to reproduce the problem. Experimental investigations including frequency response tests, lining friction test, dynamometer test, and vehicle test were carried out to further understand the brake system and the interaction of the brake system with the suspension links. A nonlinear transient dynamic model was used to peer into the affect of a stick-slip situation on the drum brake system. Complex eigenvalue analysis was used as the primary numerical tool to simulate the modal coupling mechanism and to evaluate design modifications. Several noise solutions for low frequency drum brake noise were examined and verified. Finally, lessons learned from this low frequency noise are discussed.
investigation showed the noisy stops were most prominent under the following conditions: • • • • • •
Wet conditions (high humidity) Cold temperatures Light pressure brake apply (10~20 bar) Low vehicle speeds (about 10 km/h) First few drive stops in the morning after overnight static conditioning Independent of vehicle direction
Figure 1. Rear drum brake and suspension assembly of the vehicle under investigation.
PROBLEM DESCRIPTIONS OVERVIEW Brake noise (squeak/squeal) has been identified as one of the top warranty returns for the brake supplier industry. Brake noise warranty issues have cost the industry millions of dollars. The focus of this study is on a particular vehicle platform that showed a peak on the warranty cost in November of each year. The brake noise problem on this type of vehicle was also reported in J.D. Power Customer Satisfaction Surveys. A statistical engineering team was assembled to identify the brake noise problems on this particular vehicle. The team was tasked to identify the frequency content of the noise and to determine the environmental conditions needed to reproduce the problem noise. Noise was found to come from the rear brakes. The rear brake of this vehicle is a leading-trailing drum brake with sliding abutments [10]. The backing plate assembly is mounted on a knuckle that connects to a strut and three suspension links. An illustration of the brake system along with the suspension links is shown in Figure 1. Preliminary acoustic measurements identified the noise at 760 ~ 800 Hz with higher harmonics. Sound data from a noisy stop can be seen in Figure 2. Testing showed that different vehicle platforms using this identical drum brake system do not experience this problem. Further
Figure 2. Sound measurement of a noisy stop. (a) Time domain. (b) Frequency domain. The main frequency is at 760 Hz. Other peaks are higher harmonics.
EXPERIMENTAL INVESTIGATIONS FREQUENCY RESPONSE MEASUREMENTS The modal characteristics of major components and subsystems of the brake and suspension were investigated experimentally. First, the drum was measured installed on the vehicle with no brake pressure applied. The accelerometer was placed at the outer rim of the drum and the measurement was taken using an impact hammer in the radial direction. Figure 3 shows the frequency response function of the drum and the second radial mode is found at 620 Hz. Next, pressure was
applied to the brake system and the linings were pressed against the drum. It is seen again in Figure 3 that the mode split into two modes at 708 Hz and 836 Hz when the brake pressure reached 14 bars. The structural dynamics of other major brake components were also measured. Figure 4 shows the measurement of the shoe in a free boundary condition and the peak at 768 Hz was identified as the first twisting mode. The backing plate was measured while installed implementing a fixed boundary condition. The two modes showing in Figure 5 are the second nodal diameter modes.
Figure 3.
Frequency response of an installed drum under various pressure levels.
Figure 6. Frequency response suspension link.
of
the
rear
lateral
Figure 7. The bending mode of the suspension links at 816 Hz.
rear
lateral
DYNAMOMETER TESTING A dynamometer test was performed but no noise was reproduced. Two concerns lead to the questioning of the validity of the dynamometer tests. The reasons are as follow: 1. The test setup was not able to reach the environmental condition needed to reproduce the noise.
Figure 4. Frequency response of a free shoe. The 768 Hz mode is a twisting mode.
2. Suspension components were not part of the dynamometer setup. It is possible that an interaction between the suspension and brake components is needed to produce the noise. Because the dynamometer was unable to reproduce the problem noise, vehicle testing became the primary method of investigation. VEHICLE TESTING
Figure 5. Frequency response of the installed backing plate. The suspension links were also measured at their installed conditions on the vehicle. Both lateral links were found to have their second bending mode in the range of 700Hz ~ 900 Hz. As an example, Figure 6 shows the frequency response function of the rear lateral link and Figure 7 shows the bending mode at 816 Hz.
A test procedure was developed to reproduce the environmental condition identified by the statistical engineering team. The test vehicle was left in the cold chamber with 90% humidity and 3°C for about 16 hours. Once finished with the cold soak, the vehicle was driven out of the cold chamber. Several low speed/low pressure stops were made in both the forward and reverse directions. An AachenHead was used to record noise during the stops. Accelerometers were also placed on various locations at the backing plate, shoes, and suspension links. Signals were recorded using a 16-channel TEAC recorder. The
running mode analysis of the LMS system was used for data processing to obtain the operating deflection shapes (ODS) of the brake and the suspension.
placement of accelerometers on the knuckle and suspension links. In addition, further detail ODS tests showed the motions of the suspension links were close to the second bending mode similar to the mode shapes measured in previous impact hammer tests. These test results suggested that the compliance of the suspension was allowing the knuckle and brake assembly to move tangentially while the out of plane motion of the backing plate was radiating the noise.
Figure 8. Accelerometer location on the backing plate for comparing the tangential and the out-of-plane vibration.
Figure 10. ODS of knuckle and suspension links showed a large torsional motion of the brake corner.
Figure 9. Time capture of acceleration data taken on the backing plate during a noise event. (a) Out-ofplane direction, (b) tangential direction. It was observed that the point on the backing plate (as shown in Figure 8) had the largest vibration amplitude during a noise event among various measuring points described above. It was also seen in the acceleration data shown in Figure 9 that the tangential component of the backing plate vibration had higher amplitude than its out-of-plane component. Further investigation on the ODS identified that the out of plane motion of the backing plate was a second nodal diameter mode. The tangential vibration of the backing plate was found to be the result of the torsional motion of the knuckle and suspension seen in another ODS measurement (Figure 10). Figure 11 shows the
Figure 11. Accelerometer arrangement on the knuckle and suspension links.
LINING MATERIAL TESTING
NUMERICAL STUDIES
Further testing was carried out to understand how the lining material behaved when introduced to the environmental conditions discussed earlier. The dynamometer test was used again and the linings were burnished first and then cooled down to the room temperature. A constant low pressure and low speed drag was applied to the brake for six minutes. Torque on the drive axle was monitored and back calculated to obtain the coefficient of friction. The dotted blue line in Figure 12(a) shows that the coefficient of friction stayed relatively constant at 0.43 during the six minute test even thought the temperature was increased slightly (Figure 12b).
NONLINEAR TRANSIENT DYNAMIC To look at the noise problem from the excitation point of view, the transient dynamic analysis seemed to be a good candidate. A brake model was constructed using LS-DYNA. Braking conditions such as brake pressure and initial speed were incorporated according to the vehicle test data. The stick-slip phenomenon was observed when reviewing the time domain simulation. However, this analysis was not further pursued because the frequency content of the time data did not reflect the squeal frequency. In addition the results were sensitive to simulation parameters such as pressure and speed. Also, it was not practical to run all possible combinations of these parameters to evaluate a design suggestion using this time consuming approach. Therefore, further analysis was carried out with a frequency domain approach using the complex eigenvalue method. COMPLEX EIGENVALUE ANALYSIS Complex eigenvalue method has been a useful tool for brake squeal analysis. In this paper, ABAQUS 6.4 is used as the solver since it provides a straightforward approach that combines nonlinear static analysis and complex eigenvalue extraction [11-13].
Figure 12. Results of the lining friction test at wet and dry conditions. (a) Coefficient of friction, (b) temperature.
For low frequency noise analysis, engineering judgment is important in determining the inclusion of components to be modeled. In this study, two finite element models are used. Model A contains the drum, bearing, shoes, and the backing plate assembly (Figure 13). The fixed boundary condition is applied at the bearing seat. The contact between shoe and backing plate is modeled with gap elements. All other contact areas including the lining and drum interface are modeled with surface contact.
In the second test, water was sprayed on the same linings as an easy way to introduce the moisture condition. The procedure was repeated and the lining friction coefficient and temperature were plotted in solid red lines in Figure 12 (a) and (b). It is seen that the coefficient of friction of the wet linings dropped lower during the first minute and then started to climb up after two minutes. Between 2.5 and 4 minutes, the coefficient of friction stayed high and the peak value was as high as 0.7. The tail end of the six-minute stop showed that the friction coefficient decreased as the moisture in the lining evaporated. The final temperature for the wet condition was also higher because of the larger braking energy resulted from the higher friction.
Figure 13. Model A for the complex eigenvalue analysis.
This test showed that the lining material was sensitive to humidity. With moisture introduced to the lining, the coefficient of friction increased dramatically. Furthermore the self-energizing effect [10] of the leading shoe caused brake torque to rise about four times higher than the baseline case. The resulting forcing function was the root cause of the harsh vibration and noise.
The analysis includes five steps as described below: 1. Nonlinear static step to mount the shoes. Forces are applied at the shoes to simulate the retraction and hold-on spring forces. This step is to initiate contact between the shoes and the backing plate components.
2. Nonlinear static step to initiate drum-lining contact. Pressure is applied at the back side of the pistons to the linings against the drum. 3. Nonlinear static step to impose rotational velocity on the drum. This step forces the nodes in contact at the drum-lining interface to be in a slipping condition. The steady-state equilibrium condition of the applied brake is then calculated. 4. Frequency extraction. The initial stress and preloading stiffness effects in the steady-state equilibrium condition are incorporated in the normal mode analysis. Natural frequencies of the undamped system are extracted to form the basis for the next step. 5. Complex eigenvalue extraction. The friction coupling is generated at the slipping nodes of the lining and drum interface. The resulting unsymmetric system is solved to give eigenvalues in the complex form.
model and results are shown in Figure 16. The major unstable mode is found at 801 Hz. When comparing this result to the prediction in Figure 14, it is seen that the number of over-predictions are reduced.
Figure 15. Model B: ABAQUS complex eigenvalue with suspension members.
The results of Model A are plotted on the complex plane in Figure 14. Each point on the plot indicates an eigenmode. The imaginary part of an eigenvalue is the frequency. The real part is a measure of the instability of the mode. Eigenvalues with positive real parts shown in the right half plane are unstable modes that are used to compare with measured squeal frequencies. It is observed in Figure 14 that the complex results are not symmetrical. Therefore, complex conjugate pairs are not easily identified. This is due to the inclusion of frictional damping that is used to reduce overpredictions. There are several unstable modes in the right hand side of the complex plane. The mode with highest instability is at 823 Hz. It appears that Model A is capable of calculating the squeal frequency. However, the correlation of the squeal frequency doesn’t imply that this model can be used to reflect the effect from structural modifications. This issue will be discussed in the next session.
Figure 16. Complex eigenvalue results of the baseline case with 2.07 MPa brake pressure apply. The complex mode shape of the major unstable mode at 801 Hz is also acquired. The drum is in the second order radial mode as seen in Figure 17. The backing plate motion is dominated by the second nodal diameter mode that correlates to the vehicle test. Mode shapes of the suspension links are also similar to the ODS measurements.
Figure 14. Complex eigenvalue results of Model A with 2.07 MPa brake pressure apply. Model B is constructed by adding the knuckle and the suspension components as shown in Figure 15. The fixed boundary is applied at the pin at the end of each suspension link. The same analysis is performed on this
Figure 17. Mode shape of the drum. Second radial mode.
vibratory energy at low frequencies. With these in mind, one should search for solution techniques from a broader point of view where the “excitation” and “radiation” aspects are also included. According, several possible solutions brought up in this study are discussed as follows. LINING CHANGE
Figure 18. Mode shape of the backing plate. Second nodal diameter mode.
SOLUTION TECHNIQUES OVERVIEW With the information from the experimental and numerical studies, the squeal mechanism can be described using a simple block diagram in Figure 19. The forcing function of the harsh excitation is introduced to the system due to high coefficient of friction and the self-energizing effect of the leading shoe. The system releases its vibratory energy by radiating noise, mostly via the backing plate. The compliance of the suspension allows large tangential motion of the brake assembly to take place. The second radial mode of the drum, second nodal diameter mode of the backing plate and the second bending mode of suspension links are involved in the modal coupling mechanism.
The noise occurs when the lining coefficient of friction becomes very high. Testing has confirmed that this occurs when the lining material is exposed to moisture. Since the coefficient of friction is a dependent on temperature, pressure, velocity and humidity, it is important to understand all possible conditions when selecting a lining material. One potential solution is to change to a lining material that is less sensitive to environmental conditions. However, making a lining change late in a program’s schedule will require the rerunning of a series of durability tests. This delay could cost the program several months. Therefore, this solution is useful only at the early stage of the program or when more information of substitute materials is available. SHOE MODIFICATIONS Component tests have shown that the first bending mode of the shoe is right at the squeal frequency. By stiffening the shoe, it is possible to shift this mode away from the 760 ~ 800 Hz problem range. Figure 20 shows the shoe modification proposal. Finite element analysis shows that the first bending mode is shifted from 760 Hz to 1 kHz.
Figure 19. Block diagram of the noise generation mechanism. Comparing with the solution techniques for high frequency squeal where modal decoupling and damping treatment are frequently used, a low frequency squeal problem is more difficult to deal with. First, shifting modes at low frequency is not as effective as high frequency ones. A 10% shift in frequency means 1000Hz difference for a 10 kHz mode but only changed 80 Hz for an 800 Hz mode. Second, more component rigid body motions are involved in low frequency vibration. The frequencies of these rigid body modes are often dominated by bushings, springs, or contact interfaces that are difficult to change. Third, damping treatments such as insulators are not effective to dissipate large
Figure 20. The proposed shoe modification. This modification is first evaluated using Model A (no suspension) and the results are compared with the baseline data in Figure 21. It is seen that the squeal frequency in the region of 800 Hz is shifted higher and the instability is significantly reduced. However, when Model B (with suspension) is used, the complex eigenvalue analysis does not show any improvement when the shoe modification is included. The comparison based on Model B is shown in Figure 22.
suspension links, the large tangential motion of the knuckle may suggest that torsional compliance of the suspension system is a key factor. In addition to the suspension compliance, the resonance of suspension components may also be a factor. Structural dynamic testing showed the second bending mode of the lateral suspension links in the range of 700 ~ 900 Hz. Based on the operating deflection shape discussed earlier, both lateral suspension links were mass loaded at their antinodes, as shown in Figure 23. Vehicle tests with mass loaded links were conducted and no low frequency noise was experienced.
Figure 21. Comparison of complex eigenvalue results of the stiff shoe case and the baseline case based on the model without suspension.
Figure 23. Mass loaded lateral suspension links.
Figure 22. Comparison of complex eigenvalue results of the stiff shoe case and the baseline case based on the model with suspension. To verify whether the shoe modification improved the low frequency drum brake squeal, modified shoes were manufactured. Structural dynamic testing verified the desired frequency shift. When vehicle tests were run with modified shoes, the problem persisted. Similar to the comments made in Reference [1] in an experimental study, a design suggestion made based on a model without suspension may not reflect the reality for a low frequency drum squeal problem. SUSPENSION MODIFICATIONS It is worth noting that no low frequency noise was reported on two other types of vehicles equipped with the same drum brake. Vehicle tests using the same procedure was also not able to reproduce the noise on these two types of vehicles. One of these two types of vehicles had a rear axle attached to the brakes. The other one has a different design of suspension that was less compliant. This information further confirmed that this low frequency squeal was suspension-related. Recalling the ODS measurement on knuckle and
Increasing the suspension compliance requires increasing the bushing rate. Shifting the modes of the suspension needs to be done by redesigning the suspension components. Either approach results in the change of ride comfort and the overall vehicle dynamic. Therefore, it is suggested that the drum brake low frequency noise issue should be considered in the rear suspension design. BACKING PLATE CONSTRAINTS Because the backing plate was believed to be the major source of noise radiation, efforts have been made to stiffen up the backing plate. However, several stiff backing plate designs were tried but the noise still persisted. Instead of changing the backing plate design, imposing constraints to the backing plate was proposed to reduce the amplitude of vibration. Based on the ODS measurement and the complex eigenvalue mode shapes, braces were designed to constrain the backing plate at some of the anti-node positions of the second nodal diameter mode shown in Figure 18. This modification was evaluated using the complex eigenvalue model with suspension. The results are compared with the baseline case in Figure 23 and a significant reduction in instability is seen. Vehicle test further confirmed that the low frequency drum brake noise was eliminated when the braces were installed on the vehicle.
materials should be tested at all possible environmental and operating conditions such that a better selection of lining can be made. Second, the design process of the suspension system needs to include its related systems such as brakes for NVH consideration [14]. The dynamics of the suspension links and the torsional compliance of the suspension system need to be studies for potential brake noise problems.
REFERENCES
Figure 24. Comparison of complex eigenvalue results of the backing plate constraint case and the baseline case based on the model with suspension. Both experimental and analytical studies validate the concept of applying backing plate constraints to reduce the low frequency squeal. However, efforts are still needed to design a production feasible modification based on this proven concept.
CONCLUSION This paper illustrates the experimental and numerical studies on a low frequency drum brake squeal. Tests were performed from the component level to the vehicle level. Operating deflection shapes were measured to understand component deflection and interaction during a noise event. Tests were also performed to investigate the lining sensitivity to moisture and the environmental condition that caused the squeal. Several analysis techniques were used to help understanding the phenomenon. A transient dynamic analysis was implemented to observe the stick-slip effect and the complex eigenvalue method was used to calculate the instability at the squeal frequency. Several noise solutions were proposed based on the experimental and numerical findings. Lining change accounts for the solution from the excitation point of view. Decoupling modes by shoe modification was proven to be non-effective. This suggests that the finite element model has to include enough components to make better predictions. The influence of suspension compliance is discussed based on vehicle tests of other platforms. The modification of suspension links using mass loadings was examined to be effective. Finally, the concept of constraining the backing plate to reduce noise radiation was verified by both tests and analysis. Some design solutions for this type of noise problem are best implemented when the vehicle is still in the early design stage. Lessons learned from this study are described below. First, the friction coefficient seen in a brake system should be better understood. Potential
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