﻿ 底盘角系统制动颤振多体动力学建模与分析
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (5): 639-647.  DOI: 10.11908/j.issn.0253-374x.2018.05.011 0

### 引用本文

ZHANG Lijun, YAN Guoming, MENG Dejian, YU Zhuoping. Multi-body Dynamics Modeling of Chassis Corner for Brake Creep Groan and Its Analysis[J]. Journal of Tongji University (Natural Science), 2018, 46(5): 639-647. DOI: 10.11908/j.issn.0253-374x.2018.05.011

### 文章历史

Multi-body Dynamics Modeling of Chassis Corner for Brake Creep Groan and Its Analysis
ZHANG Lijun , YAN Guoming , MENG Dejian , YU Zhuoping
School of Automotive Studies, Tongji University, Shanghai 201804, China
Abstract: Based on the multi-body dynamics method, a transient dynamic model of brake creep groan was proposed. In this model, the brake system, the suspension system, the structure and spatial position of equivalent transmission system and the brake friction characteristics were considered. The driving torque from transmission system and the brake pressure were regarded as inputs. The stick-slip motion and phase diagram of disc against pad, the vibration of key components in brake and suspension system were obtained. In addition, the key transfer path analysis was clarified. The simulation results indicate that the brake creep groan consists of two typical vibration modes. One is the impact mode with large magnitude and short duration, and the other is the periodic mode with lower magnitude but longer duration. The tangential movement dominants the key vibration both in brake and suspension components. The vibration is transferred by the strut and control arm to the body, resulting in the longitudinal movement of the whole vehicle.
Key words: brake creep groan    chassis corner    multi-body dynamic model    stick-slip motion    road test

1 整车道路试验与分析

1.1 试验方案

 图 1 传感器布置 Fig.1 Sensor layout

1.2 试验结果分析

 图 2 制动钳振动加速度时程曲线(试验) Fig.2 Vibration acceleration time history of caliper(test)

 图 3 制动钳振动加速度时程曲线放大图 Fig.3 Detailed vibration acceleration time history of caliper

 图 4 制动钳Z向振动加速度时频图(试验) Fig.4 Time-frequency spectrum of vibration acceleration of caliper in Z direction(test)

 图 5 悬架减振器支柱振动加速度时程曲线 Fig.5 Vibration acceleration time history of strut

 图 6 减振器支柱X向振动加速度时频图(试验) Fig.6 Time-frequency spectrum of vibration acceleration of strut in X direction(test)

2 底盘角刚柔耦合多体动力学建模 2.1 底盘角系统拓扑关系

 图 7 底盘角系统拓扑结构 Fig.7 Topology of chassis corner
2.2 边界条件定义

 ${F_{\rm{n}}} = K{\delta ^n} + C\frac{{{\rm{d}}\delta }}{{{\rm{d}}t}}$ (1)

 ${F_{\rm{f}}} = \mu {F_{\rm{n}}}$ (2)

 $\left\{ \begin{array}{l} \mu \left( {{v_{\rm{s}}}} \right) = {\mu _{\rm{s}}}\\ \mu \left( { - {v_{\rm{s}}}} \right) = {\mu _{\rm{s}}}\\ \mu \left( 0 \right) = 0\\ \mu \left( { - {v_{\rm{d}}}} \right) = {\mu _{\rm{d}}}\\ \mu \left( {{v_{\rm{d}}}} \right) = - {\mu _{\rm{d}}}\\ \mu \left( v \right) = - {\rm{sign}}\left( v \right){\mu _{\rm{d}}}, {\rm{ |}}v| > {v_{\rm{d}}}\\ \mu \left( v \right) = - {\rm{step}}\left( {|v|, {v_{\rm{d}}}, {v_{\rm{s}}}, {\mu _{\rm{d}}}, {\mu _{\rm{s}}}} \right){\rm{sign}}\left( v \right).\\ \begin{array}{*{20}{l}} {{v_{\rm{s}}} \le |v| \le {v_{\rm{d}}}}\\ \begin{array}{l} \mu \left( v \right) = {\rm{step}}(v, - {v_{\rm{s}}}, {\mu _{\rm{s}}}, {v_{\rm{s}}}, - {\mu _{\rm{s}}}), \\ - {v_{\rm{s}}} < v < {v_{\rm{s}}} \end{array} \end{array} \end{array} \right.$ (3)

 图 8 制动盘块摩擦系数测试试验 Fig.8 Friction coefficient test of disc and pad

 图 9 底盘角系统刚柔耦合多体动力学模型 Fig.9 Rigid-flexible coupling multi-body dynamics model of chassis corner
2.3 工况设置

 图 10 驱动力矩、制动力输入设置 Fig.10 Input curves of drive torque and brake force
3 仿真结果分析 3.1 整体特征

 图 11 制动盘角速度时程曲线 Fig.11 Angular velocity time history of disc

(1) 制动停车过程(第Ⅰ阶段).驱动力矩保持恒定，制动盘角速度从无到有后随着制动力矩的施加直至停车.

(2) 驻车制动过程(第Ⅱ阶段).驱动力矩小于制动力矩，制动盘转速为零.

(3) 制动颤振过程(第Ⅲ阶段).制动力矩略大于驱动力矩，制动盘块间产生黏滑振动现象，制动颤振现象产生.

3.2 黏滑振动特征

 图 12 制动盘块相对角速度时程曲线 Fig.12 Relative angular velocity time history of disc and pad
 图 13 7.80~7.90 s制动盘块相对角速度时程曲线 Fig.13 Relative angular velocity time history of disc and pad from 7.80 s to 7.90 s

 图 14 制动盘角速度与制动盘块相对角速度相图 Fig.14 Phase diagram of disc's angular velocity and relative angular velocity of disc and pad
3.3 关键零部件振动特性

3.3.1 制动器振动特性

 图 15 制动钳振动加速度时程曲线(仿真) Fig.15 Vibration acceleration time history of caliper(simulation)

 图 16 制动钳Z向振动加速度时频图(仿真) Fig.16 Time-frequency spectrum of vibration acceleration of caliper in Z direction(simulation)

 图 17 滑动状态第1阶固有频率振型 Fig.17 First vibration mode in sliding state

 图 18 制动盘角加速度时频图 Fig.18 Time-frequency spectrum of angular acceleration of disc
 图 19 制动块角加速度时频图 Fig.19 Time-frequency spectrum of angular acceleration of pad
3.3.2 悬架关键点振动特征分析

 图 20 悬架系统关键点振动加速度时程曲线 Fig.20 Vibration acceleration time history of key points of suspension system

 图 21 减振器支柱X向振动加速度时频图(仿真) Fig.21 Time-frequency spectrum of vibration acceleration of strut in X direction(simulation)

4 结论

(1) 开展了汽车制动颤振整车道路试验，发现制动颤振包含2种典型的振动模式，一种是幅值较大、持续时间较短的冲击振动，另一种是幅值较小、持续时间较长的周期性谐波振动.制动钳和悬架关键部件均以制动盘切向的振动特性为主.

(2) 基于多体动力学方法，考虑制动系统、悬架系统、等效传动系统的具体结构和空间位置以及制动器摩擦特性，以传动系统驱动力矩和制动压力为输入，提出了一种制动颤振瞬态动力学模型.与试验结果对比，发现该模型可再现制动颤振的主要特征，可用于制动颤振的预测与控制.

(3) 以制动盘与制动块间的黏滑运动和相图特性、制动器和悬架系统关键部件振动加速度为评价指标，分析了汽车制动颤振的瞬态动力学特性.结果表明, 制动器和悬架系统关键部件振动趋势和频率成份相似，制动钳的振动特性是制动盘与制动块振动特性的综合体现.最后, 得到了制动颤振的主要传递路径.

 [1] 张立军, 郑一兵, 孟德建, 等. 汽车制动器摩擦颤振综述[J]. 同济大学学报(自然科学版), 2016, 44(3): 420 ZHANG Lijun, ZHENG Yibing, MENG Dejian, et al. Literature survey of friction induced automotive brake groan[J]. Journal of Tongji University (Natural Science), 2016, 44(3): 420 [2] ABDELHAMID M K, BLASCHKE P, WANG A, et al. An overview of brake noise and vibration problems[C]//Proceeding of SPIE. Orlando: Society of Photo-Optical Instrumentation Engineers, 2001: 57-63. [3] LIU P, ZHENG H, CAI C, et al. Analysis of disc brake squeal using the complex eigenvalue method[J]. Applied Acoustics, 2007, 68(6): 603 DOI:10.1016/j.apacoust.2006.03.012 [4] BRECHT J, SCHIFFNER K. Influence of friction law on brake creep-groan[C]// Brake Colloquium and Exhibition. New Orleans: SAE, 2001: 363-377. [5] ABDELHAMID M K. Creep groan of disc brakes[C]//SAE Noise and Vibration Conference and Exposition. Detroit: SAE, 1995: 82-87. [6] NEIS P D, BAETS P, OST W, et al. Investigation of the dynamic response in a dry friction process using a rotating stick-slip tester[J]. Wear, 2011, 271(9): 2640 [7] DUNLAP K B, RIEHLE M A, LONGHOUSE R E. An investigative overview of automotive disc brake noise[R]. Detroit: SAE, 1999. [8] NAKANO K, MAEGAWA S. Safety-design criteria of sliding systems for preventing friction-induced vibration[J]. Journal of Sound & Vibration, 2009, 324(3/4/5): 539 [9] BRECHT J, HOFFRICHTER W, FOHLE A. Mechanisms of brake creep groan[R]. Detroit: SAE, 1997. [10] TONAZZI D, FRANCESCO M, LAURENT B. Experimental and numerical analysis of frictional contact scenarios: from macro stick-slip to continuous sliding[J]. Meccanica, 2015, 50(3): 649 DOI:10.1007/s11012-014-0010-2 [11] XU J J. Disc brake low frequency creep groan simulation using ADAMS[C]//Proceedings of the 2000 ADAMS International User Conference. Orlando: SAE, 2000: 2240-2259. [12] DONLEY M, RIESLAND D. Brake groan simulation for a McPherson strut type suspension[C]//SAE 2003 Noise & Vibration Conference and Exhibition. Traverse City: SAE, 2003: 1627-1636. [13] PURSCHER M, FISCHER P. Creep groan characterization via vehicle corner test[C]//SAE 2017 Brake Colloquium & Exhibition. Orlando: SAE, 2017: 2488-2501. [14] JOO K H, JEON H C, SUNG W, et al. Transfer path analysis of brake creep noise[C]//SAE 2013 Brake Colloquium & Exhibition, 31st Annual. Jacksonville: SAE, 2013: 2036-2050. [15] CROWTHER A R, YOON J, SINGH R. An explanation for brake groan based on coupled brake-driveline system analysis[C]//SAE 2007 Noise and Vibration Conference and Exhibition. St. Charles: SAE, 2007: 2260-2274. [16] MARÍN F, ALHAMA F, MORENO J A. Modelling of stick-slip behavior with different hypotheses[J]. International Journal of Engineering Science, 2012, 60: 13 DOI:10.1016/j.ijengsci.2012.06.002 [17] CROWTHER A.R, SINGH R. Identification and quantification of stick-slip induced brake groan events using experimental and analytical investigations[J]. Noise Control Engineering Journal, 2008, 56(4): 235 DOI:10.3397/1.2955772 [18] FUADI Z, MAEGAWA S, NAKANO K, et al. Map of low-frequency stick-slip of a creep groan[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2010, 224(12): 1235 DOI:10.1243/13506501JET834