鼓式制动器热结构耦合参数化有限元分析
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摘要
鼓式制动器是决定汽车安全性的重要部件之一,由于其造价便宜、制动效能高,被广泛的用于大型客车、重型货车和部分轿车中。通过有限元仿真技术对其工作过程进行准确的再现是一个涉及到温度场和应力应变场的多场耦合问题。为了能在仿真过程中考虑应力应变场和温度场之间的交互作用,则需对鼓式制动器进行动态热-结构耦合分析。在鼓式制动器设计方面,若采用传统的简单计算方法,产品的开发周期长,无法准确预测制动性能,因此,本文在三维参数化建模的基础上,开发了鼓式制动器热-结构耦合参数化有限元分析平台。利用此平台,对轻卡后轮鼓式制动器的整个制动过程进行了动态模拟,并将仿真结果与通过台架试验得到的试验结果进行对比,两者吻合良好。事实证明,利用该参数化有限元仿真平台能够有效地缩短制动器的设计和开发周期,对降低开发成本,提高产品质量具有重要的意义。
本文的主要工作和结论涉及以下几个方面：
(1)鼓式制动器热-结构耦合有限元模型的建立在保证制动器各部分刚度及结构力学特性基本不变的情况下,对制动器的结构进行了适当的简化；利用大型通用有限元软件ABAQUS,建立了鼓式制动器三维接触有限元模型；通过理论分析和试验中所测得的数据确定了仿真过程中的各种边界条件,得到了热-结构耦合分析模型。
(2)鼓式制动器热-结构耦合仿真分析利用热-结构耦合有限元分析模型进行了紧急制动工况下的制动性能模拟,仿真结果表明：制动蹄上最大等效应力出现在领蹄其自身旋转端的位置附近,两制动蹄的受力端也是等效应力较大的部位；领蹄摩擦衬片中下部的等效应力较大,从蹄摩擦衬片中上部的等效应力较大,两摩擦衬片上的等效应力近似呈中心对称分布。在制动鼓上,最大等效应力始终出现在螺栓连接处；分析制动鼓内表面上三向应力结果显示,轴向应力与周向应力较大,均大于径向应力,这解释了在制动鼓内表面上产生沿轴向开裂的主裂纹并贯穿整个制动鼓壁的原因。分析制动鼓法兰根部三向应力结果显示,在径向以及轴向方向上均受到应力循环周期较短的交变应力作用,并且交变应力在径向方向上的作用程度较强烈,零件结构在这种应力作用下容易产生疲劳破坏,这解释了制动鼓的另外一种疲劳失效形式,即制动鼓法兰根部的周圈性开裂。由于受到移动热源以及对流换热作用的影响,制动鼓内表面上节点的温度呈周期性“锯齿状”的上升规律,最高温度并不是出现在制动结束时,而是出现在制动过程中的某一时刻。制动鼓加强筋上的温度由于热传导作用在整个制动过程中一直呈现上升趋势。摩擦衬片与制动表面之间的接触压力主要集中在摩擦衬片的中部,为了改善两者之间的接触压力分布,应适当在制动蹄腹板的两翼增加加强筋以提高制动蹄两侧的刚度,增大摩擦衬片两侧与制动鼓制动表面之间的接触,使接触压力在摩擦衬片的宽度方向上均匀分布,同时使制动鼓外表面上加强筋处于摩擦衬片与制动表面接触区域的中间稍偏向制动鼓“开口端”一侧,从而保证接触区域的制动鼓刚度基本一致。制动鼓加强筋增加了制动鼓外表面的散热面积,使制动鼓上的温度能够尽量的朝加强筋径向和靠近制动鼓“开口端”一侧的轴向方向传导,使热量通过与空气的对流换热作用散失,使热量尽量远离螺栓连接处,改善制动鼓内表面上的温度分布。
(3)鼓式制动器台架试验参考国家汽车行业标准中的“QC／T479-1999货车、客车制动器台架试验方法”对鼓式制动器进行了台架试验,测得了制动力矩,制动鼓内、外表面温度以及制动管路压力等重要试验数据,记录并处理所测得的试验数据,得到相应的试验结果。将仿真结果与试验结果进行对比验证,验证结果表明,制动鼓和制动蹄的结构简化,对仿真结果影响并不大,仿真结果与试验结果吻合良好。
(4)鼓式制动器热-结构耦合参数化有限元分析平台的建立利用Python语言对ABAQUS软件进行二次开发,创建了相应的图形用户界面(GUI),形成了一套适用于鼓式制动器建模和仿真分析的参数化有限元分析平台。平台中包含两个模块,即前处理模块和后处理模块。在前处理模块中可以实现鼓式制动器三维建模参数化、边界条件参数化和网格划分参数化等功能,因此用户可根据要求修改这些定义的参数,得到自己的鼓式制动器热-结构耦合有限元模型。在仿真计算完成后,可以通过后处理模块查看相应的应力场、温度场分布情况,以及得到角速度、角减速度和制动力矩变化的规律曲线。该平台为缩短产品开发周期,提高产品设计质量提供了有效的手段,也为今后鼓式制动器的优化工作打下了基础。
(5)制动性能影响因素分析通过正交试验设计方法研究了促动力、摩擦系数以及摩擦衬片包角对制动性能的影响规律。上述三个因素对于制动性能影响的排序是：摩擦系数>促动力>摩擦衬片包角。制动力矩随着摩擦系数和促动力的增大而增大,并且摩擦系数和促动力越大,制动器的敏感性越强,制动稳定性越差。增大摩擦衬片包角,制动力矩的增加并不显著,这表明当摩擦衬片的包角在一定范围内时,增大或者减小其角度值对制动力矩的影响并不大。
The brake is one of important part in vehicle safety. Drum brakes have many advantages, such as simple structure, low-cost and high brake performance. Considering theses advantages, the brakes of front-and rear-wheels are drum brakes in large-passenger cars and heavy-goods vehicles. Samely, the brakes of rear-wheels are drum brakes in middle-and-low car based on economic and practical aspects. To simulate the whole working process of drum brakes through the finite element simulation skill is a multi-field problem related to the thermal field and the stress-strain field. In order to condider the interaction between the stress-strain field and temperature field simultaneously, the thermo-mechanical coupling method must be applied. In the aspect of drum brake design, traditional design method extended the product development cycle and can not accurately predict the braking performance. So, in this paper, on the basis of three-dimensional parametric modeling, the thermo-mechanical coupling parametric finite element analysis platform was built. Using this platform, the whole braking process of light truck rear drum brake was dynamically simulated. Comparing the simulation results with the test results which were got from the drum brake bench test, the comparison result showed that these two results matched well. Facts showed that, this parametric finite element simulation platform can effectively decrease the product design and development cycles, as far as cost-reduction and quality-improvement is concerned, it has a lot of significance.
The major work involves the following aspects:
(1) Establishment of thermo-mechanical coupling finite element model of drum brake In the stiuation of maintaining stiffness and mechanical properties of the brake parts basically unchanged, the structure of the real brake was simplified. The three-dimensional finite element model of drum brake including brake drum, brake shoes and friction plate was built by the big general finite software ABAQUS. Then all the boundary conditions in simulation process were initially identified by theory analysis and calculation. The Thermo-mechanical coupling finite element model was set based on the these work.
(2) Simulation analysis of drum brake Thermo-mechanical coupling Simulation of the drum brake used in experiment was taken in emergency brake situation. The results shown the maximum equivalent stress of brake shoes was near the end of the rotation of the leading shoe. And the force of two side brake shoe was on the location where the equivalent stress was relatively large. The equivalent stress was relatively large in the lower part of friction lining of leading shoe. While the equivalent stress was relatively large in the upper part of friction lining of trailing shoe. The equivalent stress of the two friction linings was approximately centrosymmetric distributed. In the brake drum, the maximum equivalent stress was always in the bolt connection. The results of three-dimentional stress in axial node of braking surface shown axial stress and circumferential stress were both lager than radial stress. This was the reason why the main crack was generated in the axial direction of brake drum inner surface though the whole brake drum. The result of three-dimensional stress of flange root node showed that in the radial and axial directions node was subjected to alternating stress, and the stress cycle was short. In the radial direction, the effect of the alternating stress was stronger. In this case, the brake drum was prone to generate fatigue failure. That the reason why the brake drum generated cracking in the circumferential direction at flange root generally. As a result of moving heat source and convective heat transfer, the temperature of nodes of brake drum inner surface was increased by periodically "jagged" law. The maximum temperature was not in the end of braking, but in the braking process. The temperature of radial notes of stiffener had been on the rise in the braking process due to thermal conduction. Contact pressure between friction lining and brake surface was mainly in the central part of the friction lining. To improve the distribution of contact pressure between the two, stiffeners should be properly added on the two wings of brake shoe web to increase the stiffness of both side of brake shoe. The contact area between two side of friction lining and the brake surface of brake drum should be increased in order to make the contact pressure distrubuted equably in wide direction of friction lining. At the same time, stiffeners of brake drum outer surface in contact field between friction lining and brake surface should bias "open end" of brake drum a little. So the stiffnesses in the contact field are basiclly the same. Stiffener can increase the heat dissipation area, the temperature of the brake drum can be as much as possible toward the radial ribs and near the brake drum " open end" side of the axial direction of conduction. So the heat is lost by convection with air. Then the heat is away from the bolt connections as possible to improve temperature distribution of the brake drum surface.
(3) Drum Brake Bench Test Bench test of drum brake was taken by QC/T 479-1999 truck and bus brake bench test method in accordance with China auto industry standards. The results showed that the simplified structure of brake drum and brake shoes had little effect on the simulation results. And the simulation results agreeed well with the experimental results.
(4) Establishment of parametic finite element analysis platform of drum brakes related to Thermo-mechanical coupling Python language was used to take secondary development on Abaqus software. At the same time, a appropriate graphical user interface (GUI) was created. So a complete set of parametric finite element analysis platform was obtained to built the drum brake model and simulate. This platform includes two parts, the pre-processing module and post-processing module. The pre-processing module can be achieved in the parametic three-dimentional model of drum brake, parametic boundary conditions and parametic meshing and so on. According to the demand, users can modify these definition parameters to get their own Thermo-mechanical coupling finite element model. After the simulation, post-processing module can view the distribution of stress and thermal fields, as well as angular velocity, angular deceleration and braking torque curve. This platform provide an effective method to shorten product development cycle, reduce the cost of product development and improve product design quality. Also, the research in this thesis has laid a good foundation for the optimization work of future drum brakes.
(5) Analysis of brake preformance factors According to orthogonal experimental design method which studied the impact on brake performance from promote power, friction coefficient and friction lining, the order of three factors is:the friction coefficient> promote power> friction lining corners. Braking torque increased with the friction coefficient and promote power increasing. And with the increase of the friction coefficient and promote power, the sensitivity of brake was greater, the brake stability was worse. Increasing the wrap angle of friction linings, brake torque increase is not significant, suggesting that, when the the wrap angle of friction lining in a certain range, the increase or decrease the angle value of braking torque is not too great. Excessive increase of wrap angle of the friction linings will increase the cost and quality of brake.
本文的主要工作和结论涉及以下几个方面：
(1)鼓式制动器热-结构耦合有限元模型的建立在保证制动器各部分刚度及结构力学特性基本不变的情况下,对制动器的结构进行了适当的简化；利用大型通用有限元软件ABAQUS,建立了鼓式制动器三维接触有限元模型；通过理论分析和试验中所测得的数据确定了仿真过程中的各种边界条件,得到了热-结构耦合分析模型。
(2)鼓式制动器热-结构耦合仿真分析利用热-结构耦合有限元分析模型进行了紧急制动工况下的制动性能模拟,仿真结果表明：制动蹄上最大等效应力出现在领蹄其自身旋转端的位置附近,两制动蹄的受力端也是等效应力较大的部位；领蹄摩擦衬片中下部的等效应力较大,从蹄摩擦衬片中上部的等效应力较大,两摩擦衬片上的等效应力近似呈中心对称分布。在制动鼓上,最大等效应力始终出现在螺栓连接处；分析制动鼓内表面上三向应力结果显示,轴向应力与周向应力较大,均大于径向应力,这解释了在制动鼓内表面上产生沿轴向开裂的主裂纹并贯穿整个制动鼓壁的原因。分析制动鼓法兰根部三向应力结果显示,在径向以及轴向方向上均受到应力循环周期较短的交变应力作用,并且交变应力在径向方向上的作用程度较强烈,零件结构在这种应力作用下容易产生疲劳破坏,这解释了制动鼓的另外一种疲劳失效形式,即制动鼓法兰根部的周圈性开裂。由于受到移动热源以及对流换热作用的影响,制动鼓内表面上节点的温度呈周期性“锯齿状”的上升规律,最高温度并不是出现在制动结束时,而是出现在制动过程中的某一时刻。制动鼓加强筋上的温度由于热传导作用在整个制动过程中一直呈现上升趋势。摩擦衬片与制动表面之间的接触压力主要集中在摩擦衬片的中部,为了改善两者之间的接触压力分布,应适当在制动蹄腹板的两翼增加加强筋以提高制动蹄两侧的刚度,增大摩擦衬片两侧与制动鼓制动表面之间的接触,使接触压力在摩擦衬片的宽度方向上均匀分布,同时使制动鼓外表面上加强筋处于摩擦衬片与制动表面接触区域的中间稍偏向制动鼓“开口端”一侧,从而保证接触区域的制动鼓刚度基本一致。制动鼓加强筋增加了制动鼓外表面的散热面积,使制动鼓上的温度能够尽量的朝加强筋径向和靠近制动鼓“开口端”一侧的轴向方向传导,使热量通过与空气的对流换热作用散失,使热量尽量远离螺栓连接处,改善制动鼓内表面上的温度分布。
(3)鼓式制动器台架试验参考国家汽车行业标准中的“QC／T479-1999货车、客车制动器台架试验方法”对鼓式制动器进行了台架试验,测得了制动力矩,制动鼓内、外表面温度以及制动管路压力等重要试验数据,记录并处理所测得的试验数据,得到相应的试验结果。将仿真结果与试验结果进行对比验证,验证结果表明,制动鼓和制动蹄的结构简化,对仿真结果影响并不大,仿真结果与试验结果吻合良好。
(4)鼓式制动器热-结构耦合参数化有限元分析平台的建立利用Python语言对ABAQUS软件进行二次开发,创建了相应的图形用户界面(GUI),形成了一套适用于鼓式制动器建模和仿真分析的参数化有限元分析平台。平台中包含两个模块,即前处理模块和后处理模块。在前处理模块中可以实现鼓式制动器三维建模参数化、边界条件参数化和网格划分参数化等功能,因此用户可根据要求修改这些定义的参数,得到自己的鼓式制动器热-结构耦合有限元模型。在仿真计算完成后,可以通过后处理模块查看相应的应力场、温度场分布情况,以及得到角速度、角减速度和制动力矩变化的规律曲线。该平台为缩短产品开发周期,提高产品设计质量提供了有效的手段,也为今后鼓式制动器的优化工作打下了基础。
(5)制动性能影响因素分析通过正交试验设计方法研究了促动力、摩擦系数以及摩擦衬片包角对制动性能的影响规律。上述三个因素对于制动性能影响的排序是：摩擦系数>促动力>摩擦衬片包角。制动力矩随着摩擦系数和促动力的增大而增大,并且摩擦系数和促动力越大,制动器的敏感性越强,制动稳定性越差。增大摩擦衬片包角,制动力矩的增加并不显著,这表明当摩擦衬片的包角在一定范围内时,增大或者减小其角度值对制动力矩的影响并不大。
The brake is one of important part in vehicle safety. Drum brakes have many advantages, such as simple structure, low-cost and high brake performance. Considering theses advantages, the brakes of front-and rear-wheels are drum brakes in large-passenger cars and heavy-goods vehicles. Samely, the brakes of rear-wheels are drum brakes in middle-and-low car based on economic and practical aspects. To simulate the whole working process of drum brakes through the finite element simulation skill is a multi-field problem related to the thermal field and the stress-strain field. In order to condider the interaction between the stress-strain field and temperature field simultaneously, the thermo-mechanical coupling method must be applied. In the aspect of drum brake design, traditional design method extended the product development cycle and can not accurately predict the braking performance. So, in this paper, on the basis of three-dimensional parametric modeling, the thermo-mechanical coupling parametric finite element analysis platform was built. Using this platform, the whole braking process of light truck rear drum brake was dynamically simulated. Comparing the simulation results with the test results which were got from the drum brake bench test, the comparison result showed that these two results matched well. Facts showed that, this parametric finite element simulation platform can effectively decrease the product design and development cycles, as far as cost-reduction and quality-improvement is concerned, it has a lot of significance.
The major work involves the following aspects:
(1) Establishment of thermo-mechanical coupling finite element model of drum brake In the stiuation of maintaining stiffness and mechanical properties of the brake parts basically unchanged, the structure of the real brake was simplified. The three-dimensional finite element model of drum brake including brake drum, brake shoes and friction plate was built by the big general finite software ABAQUS. Then all the boundary conditions in simulation process were initially identified by theory analysis and calculation. The Thermo-mechanical coupling finite element model was set based on the these work.
(2) Simulation analysis of drum brake Thermo-mechanical coupling Simulation of the drum brake used in experiment was taken in emergency brake situation. The results shown the maximum equivalent stress of brake shoes was near the end of the rotation of the leading shoe. And the force of two side brake shoe was on the location where the equivalent stress was relatively large. The equivalent stress was relatively large in the lower part of friction lining of leading shoe. While the equivalent stress was relatively large in the upper part of friction lining of trailing shoe. The equivalent stress of the two friction linings was approximately centrosymmetric distributed. In the brake drum, the maximum equivalent stress was always in the bolt connection. The results of three-dimentional stress in axial node of braking surface shown axial stress and circumferential stress were both lager than radial stress. This was the reason why the main crack was generated in the axial direction of brake drum inner surface though the whole brake drum. The result of three-dimensional stress of flange root node showed that in the radial and axial directions node was subjected to alternating stress, and the stress cycle was short. In the radial direction, the effect of the alternating stress was stronger. In this case, the brake drum was prone to generate fatigue failure. That the reason why the brake drum generated cracking in the circumferential direction at flange root generally. As a result of moving heat source and convective heat transfer, the temperature of nodes of brake drum inner surface was increased by periodically "jagged" law. The maximum temperature was not in the end of braking, but in the braking process. The temperature of radial notes of stiffener had been on the rise in the braking process due to thermal conduction. Contact pressure between friction lining and brake surface was mainly in the central part of the friction lining. To improve the distribution of contact pressure between the two, stiffeners should be properly added on the two wings of brake shoe web to increase the stiffness of both side of brake shoe. The contact area between two side of friction lining and the brake surface of brake drum should be increased in order to make the contact pressure distrubuted equably in wide direction of friction lining. At the same time, stiffeners of brake drum outer surface in contact field between friction lining and brake surface should bias "open end" of brake drum a little. So the stiffnesses in the contact field are basiclly the same. Stiffener can increase the heat dissipation area, the temperature of the brake drum can be as much as possible toward the radial ribs and near the brake drum " open end" side of the axial direction of conduction. So the heat is lost by convection with air. Then the heat is away from the bolt connections as possible to improve temperature distribution of the brake drum surface.
(3) Drum Brake Bench Test Bench test of drum brake was taken by QC/T 479-1999 truck and bus brake bench test method in accordance with China auto industry standards. The results showed that the simplified structure of brake drum and brake shoes had little effect on the simulation results. And the simulation results agreeed well with the experimental results.
(4) Establishment of parametic finite element analysis platform of drum brakes related to Thermo-mechanical coupling Python language was used to take secondary development on Abaqus software. At the same time, a appropriate graphical user interface (GUI) was created. So a complete set of parametric finite element analysis platform was obtained to built the drum brake model and simulate. This platform includes two parts, the pre-processing module and post-processing module. The pre-processing module can be achieved in the parametic three-dimentional model of drum brake, parametic boundary conditions and parametic meshing and so on. According to the demand, users can modify these definition parameters to get their own Thermo-mechanical coupling finite element model. After the simulation, post-processing module can view the distribution of stress and thermal fields, as well as angular velocity, angular deceleration and braking torque curve. This platform provide an effective method to shorten product development cycle, reduce the cost of product development and improve product design quality. Also, the research in this thesis has laid a good foundation for the optimization work of future drum brakes.
(5) Analysis of brake preformance factors According to orthogonal experimental design method which studied the impact on brake performance from promote power, friction coefficient and friction lining, the order of three factors is:the friction coefficient> promote power> friction lining corners. Braking torque increased with the friction coefficient and promote power increasing. And with the increase of the friction coefficient and promote power, the sensitivity of brake was greater, the brake stability was worse. Increasing the wrap angle of friction linings, brake torque increase is not significant, suggesting that, when the the wrap angle of friction lining in a certain range, the increase or decrease the angle value of braking torque is not too great. Excessive increase of wrap angle of the friction linings will increase the cost and quality of brake.
引文
[1]刘惟信.汽车制动系的结构分析与设计计算[M].北京：清华大学出版社,2004：7-36.
[2]杨兆军,范久臣,丁树伟,等.鼓式制动器应力场数值模拟[J].电子科技大学学报,2010,39(4)：623-628
[3]袁春静,吴永根,葛振亮,制动鼓瞬态温度场有限元分析[J].科学技术与工程,2006,(8)：1154-1156
[4]Przemyslaw Zagrodzki. Thermoelastic instability in friction clutches and brake-Transient modal analysis revealing mechanisms of excitation of unstable modes[J]. International Journal of Solids and Structures,2006,46:2463-2476.
[5]范久臣.汽车鼓式制动器多物理场仿真研究及数字化分析平台[D].长春：吉林大学,2009.
[6]赵腾伦ABAQUS 6.6在机械工程中的应用[M].北京：中国水利水电出版社,2007：1-3.
[7]古成中,吴新跃.有限元网格划分及发展趋势[J].计算机科学与探索,2008,2(3)：248-259
[8]刘彩霞.基于面向对象技术的起重机参数化设计系统研究[D].大连：大连理工大学,2003.
[9]李响.履带起重机臂架系统有限元参数化方法研究[D].大连：大连理工大学,2007.
[10]G A G Fazekas. Temperature Gradients and Heat Stresses in Brake Drum[J]. SAE,1953,61:279.
[11]Barber J R. The Influence of Thermal Expansion on the Friction and Wear Process[J]. Wear,1967,10:155-159.
[12]R A Burton, V Nerlikar, S R Kilaparti. Thermoelastic instability in a seal-like configuration[J]. Wear,1973,24:177-188.
[13]A E Anderson, R A Knapp. Hot spotting in automotive friction systems[J]. Wear,1990,135:319-337
[14]Kwangjin Lee, J R Barber. Frictionally Excited Thermoelastic Instability in Automotice Disk Brakes[J]. ASME,1993,115:607-614.
[15]P A Fensel. An Axisymmetric Finite Element Analysis of the Mechanical and Thermal Stresses in Brake Drum[J]. SAE,1974,740321.
[16]Kikuo Kishimoto, Hirotsugu Inoue. Boundary element analysis of thermoelastic contact problems[J]. Elsevier,1995,15:329-337
[17]Masashi Daimaruya, Hidetoshi Kobayashi, Khairul Fua. Thermoelasto-plastic stresses and thermal distortions in a brake drum[J]. Journal of Thermal Stresses,1997,20:345-361.
[18]Lee Kwangjin, Dinwiddie R B. Conditions of Frictional Contact in Disk Brakes and Their Effects on Brake Judder[J]. SAE,1998,980598.
[19]C Hohmann, K Schiffner, K Oerter. Contact analysis foe drum brakes and disk brakes using ADINA[J]. Computers & Structures,1999,72:185-198
[20]Kwangjin Lee. Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes[J].ASME,2000,122:849-855.
[21]Malak Naji, M.AL-Nimr. DYNAMIC THERMAL BEHAVIOR OF A BRAKE SYSTEM[J]. International Journal of Heat and Mass Transfer,2001,28(6):835-845.
[22]Ji-Hoon Choi, In Lee. Finite element analysis of transient thermoelastic behaviors in disk brakes[J]. Wear,2002,257:47-58.
[23]H S KIM, C B KIM. QUALITY IMPROVEMENT FOR BRAKE JUDDER USING DESIGN FOR SIX SIGMA WITH RESPONSE SURFACE METHOD AND SIGMA BASED ROBUST DESIGN[J]. International Journal of Automotive Technology,2003,4:193-201
[24]R J TALIB, A MUCHTAR, C H AZHARI. THE EFFECT OF TEMPERATURE ON THE GENERATION OF THERMOINSTABILITY DURING BRAKING OF FRICTION LINING MATERIALS[J]. Jurnal teknologi,2004,40(A):51-66.
[25]Ashwin Hattiangadi, Thomas Siegmund. A numerical study on interface crack growth under heat flux loading[J]. INTERNATIONAL JOURNAL OF SOLIDS and STRUCTURES,2005,42:6335-6355.
[26]Ramesh Edara. Heavy Vehicle Disc Brake Components Design Using CAE Tools[J]. SAE,2006,1:1-6
[27]P Liu, H Zheng, C Cai, Y Y Wang, C Lu, K H Ang, G R Liu. Analysis of disk brake squeal using the complex eigenvalue method[J]. Applied Acoustics,2007,68:603-615.
[28]C.H.Gao, J.M.Huang, X.Z.Lin, et al. Stress Analysis of Thermal Fatigue Fracture of Brake Disks Based on Thermomechanical Coupling[J]. Journal of Tribology,2007,129:536-543.
[29]Jinchun Huang, Charles M.Krousgrill, Anil K.Bajaj. An Efficient Approach to Estimate Critical Value of Friction Coefficient in Brake Squeal Analysis[J]. Journal of Applied Mechanics,2007,74:534-541.
[30]A.Akay, O.Giannini, F.massi, A.Sestieri. Disc brake squeal characterization through simplified test rigs[J]. Mechanical Systems and Signal Processing,2009,23:2590-2607.
[31]D K Kolluri, X.Boidin, Y Desplanques, et al. Effect of Natural Graphite Particle size in friction materials on thermal localisation phenomenon during stop-braking[J]. Wear,2010,268:1472-1482.
[32]付强,李明丽.鼓式制动器尖叫噪声的模态识别[J].汽车技术,1990,10：16-23
[33]管迪华,朱新潮,成波.鼓式制动器结构振动噪声研究[J].汽车工程,1993,15(2)：71-78.
[34]曹立波,郭正康.鼓式制动器制动尖叫的机理及其预防[J].湖南大学学报,1995,22(3)：91-96.
[35]张文明,申炎华,张卫钢,马飞.湿式制动器的制动过程和摩擦温度场的研究[J].有色金属,1997,49(1)14-19.
[36]方明霞,冯奇.鼓式制动器摩擦片的有限元分析[J].重型汽车,1998,47(4)：14-17.
[37]毛智东,王学林,胡于进,等.鼓式制动器接触分析[J].华中科技大学学报(自然科学版),2002,30(7)：71-73.
[38]王步康,董光能,谢友柏.滑动接触中摩擦发热的数值分析[J].中国机械工程,2002,13(21)：1880-1884.
[39]刘立刚,王学林.鼓式制动器的有限元分析[J].专用汽车,2003,3：21-23
[40]吕振华.蹄-鼓式制动器热弹性耦合有限元分析[J].机械强度,2003,25(4)：401-407.
[41]陈兴旺.鼓式制动器温度场的数值模拟分析[J].北京汽车,2005：11-15.
[42]袁春静,吴永根,葛振亮.制动鼓瞬态温度场有限元分析[J].科学技术与工程,2006,6(8)：1154-1156.
[43]郭应时,袁伟,付锐.实验法求解汽车鼓式制动器对流换热系数[J].长安大学学报(自然科学版),2006,26(4)：92-94.
[44]马迅,秦剑.基于有限元法的制动鼓的偶和分析[J].机械设计与研究,2005,21(1)：68-71.
[45]林谢昭,高诚辉,黄健萌.制动工况参数对制动盘摩擦温度场分布的影响[J].工程设计学报,2006,13(1)：45-48.
[46]高诚辉,黄健萌,林谢昭,等.盘式制动器摩擦磨损人动力学研究进展[J].中国工程机械学报,2006,4(1)：83-88.
[47]杨国俊,古正气,李伟平.有限元分析在鼓式制动器设计中的应用[J].机械设计与制造,2007,4：14-15.
[48]王志刚.制动器摩擦副温度场的解析计算[J].机械设计与研究,2007,23(4)：58-60.
[49]管欣,申军烽,管仁梅,等.不同摩擦系数对鼓式制动器低频振动的影响[J].科学技术与工程,2008,8(21)：5867-5871.
[50]王宣锋,粱迎春.控制鼓式制动器力矩波动的研究[J].机械设计与制造,2008,7：131-133.
[51]姚辉学,侯永涛,王国林,等.车辆制动器参数化数据库设计[J].机械工程学报,2008,44(10)：255-259.
[52]黄健萌,高诚辉,唐旭晟,等.盘式制动器热-结构耦合的数值建模与分析[J].机械工程学报,2008,44(2)145-151.
[53]范久臣,杨兆军,刘长亮,等.鼓式制动器刚柔耦合虚拟样机[J].吉林大学学报(工学版),2009,39：183-187.
[54]管欣,申军烽,管仁梅,等.鼓式制动器相关参数对其制动效能的影响[J].科学技术与工程,2009,9(4)：940-942.
[55]赵凯辉,魏朗.鼓式制动器三维热-机耦合温度场仿真[J].农业机械学报,2009,40(2)：32-36.
[56]靳少杰,徐颖强,林富华.鼓式制动器摩擦片-鼓接触点确定方法及变化规律分析[J].2010,32(5)：424-428.
[57]庄茁,张帆,岑松,等.非线性有限元分析与实例[M].北京：科学出版社,2005.
[58]Jung, I Lee. Development of Automotive Braking Performance Analysis Program Considering Dynamic Characteristics[J]. Trans. Korean Society of Automotive Engineers, 2004,12(2):175-181.
[59]Mohammad Haghpanahi.Development of a Parametric Finite Element Model of Lower Cervical Spine in Sagital Plane[C]. Proceeding of the 28 th IEEE,New York City,USA,Aug 30-Sept3,2006,1739-1741.
[60]李亮,宋健,李永,郭振宇.制动器热分析的快速有限元仿真模型研究[J].系统仿真学报,2005,17(12)：2869-2877.
[61]R Limpert. Brake Design and Safety Second Edition[J]. Society of Automotive Engineers, USA,1999.
[62]S P Jung, K J Jun, T W Park, et al. Development of The Brake System Design Program for A Vehicle[J]. International Journal of Automotive Technology,2008,9(1):45-51.
[63]马迅,秦剑.制动鼓的热-结构耦合分析[J].湖北汽车工业学院学报,2004,18(3)：5-9.
[64]Raphael B, Krishanmoorthy C S. Automating finite element development using object oriented techniques[J]. Eng Computation,1993,10:267-278.
[65]张峰,李兆前,黄传真.参数化设计的研究现状与发展趋势[J].机械工程师,2002,1：13-15.
[66]杨秀萍,王鹏林.基于ANSYS APDL语言的零件参数化有限元分析[J].设计与研究,2005,11：10-11.
[67]Abaqus Scripting User's Manual.
[68]Abaqus GUI Toolkit User's Manual.
[69]吴剑增,张炳荣,邓祖国.汽车制动器相关参数关系初探[J].客车技术与研究,2009,6：19-22.
[2]杨兆军,范久臣,丁树伟,等.鼓式制动器应力场数值模拟[J].电子科技大学学报,2010,39(4)：623-628
[3]袁春静,吴永根,葛振亮,制动鼓瞬态温度场有限元分析[J].科学技术与工程,2006,(8)：1154-1156
[4]Przemyslaw Zagrodzki. Thermoelastic instability in friction clutches and brake-Transient modal analysis revealing mechanisms of excitation of unstable modes[J]. International Journal of Solids and Structures,2006,46:2463-2476.
[5]范久臣.汽车鼓式制动器多物理场仿真研究及数字化分析平台[D].长春：吉林大学,2009.
[6]赵腾伦ABAQUS 6.6在机械工程中的应用[M].北京：中国水利水电出版社,2007：1-3.
[7]古成中,吴新跃.有限元网格划分及发展趋势[J].计算机科学与探索,2008,2(3)：248-259
[8]刘彩霞.基于面向对象技术的起重机参数化设计系统研究[D].大连：大连理工大学,2003.
[9]李响.履带起重机臂架系统有限元参数化方法研究[D].大连：大连理工大学,2007.
[10]G A G Fazekas. Temperature Gradients and Heat Stresses in Brake Drum[J]. SAE,1953,61:279.
[11]Barber J R. The Influence of Thermal Expansion on the Friction and Wear Process[J]. Wear,1967,10:155-159.
[12]R A Burton, V Nerlikar, S R Kilaparti. Thermoelastic instability in a seal-like configuration[J]. Wear,1973,24:177-188.
[13]A E Anderson, R A Knapp. Hot spotting in automotive friction systems[J]. Wear,1990,135:319-337
[14]Kwangjin Lee, J R Barber. Frictionally Excited Thermoelastic Instability in Automotice Disk Brakes[J]. ASME,1993,115:607-614.
[15]P A Fensel. An Axisymmetric Finite Element Analysis of the Mechanical and Thermal Stresses in Brake Drum[J]. SAE,1974,740321.
[16]Kikuo Kishimoto, Hirotsugu Inoue. Boundary element analysis of thermoelastic contact problems[J]. Elsevier,1995,15:329-337
[17]Masashi Daimaruya, Hidetoshi Kobayashi, Khairul Fua. Thermoelasto-plastic stresses and thermal distortions in a brake drum[J]. Journal of Thermal Stresses,1997,20:345-361.
[18]Lee Kwangjin, Dinwiddie R B. Conditions of Frictional Contact in Disk Brakes and Their Effects on Brake Judder[J]. SAE,1998,980598.
[19]C Hohmann, K Schiffner, K Oerter. Contact analysis foe drum brakes and disk brakes using ADINA[J]. Computers & Structures,1999,72:185-198
[20]Kwangjin Lee. Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes[J].ASME,2000,122:849-855.
[21]Malak Naji, M.AL-Nimr. DYNAMIC THERMAL BEHAVIOR OF A BRAKE SYSTEM[J]. International Journal of Heat and Mass Transfer,2001,28(6):835-845.
[22]Ji-Hoon Choi, In Lee. Finite element analysis of transient thermoelastic behaviors in disk brakes[J]. Wear,2002,257:47-58.
[23]H S KIM, C B KIM. QUALITY IMPROVEMENT FOR BRAKE JUDDER USING DESIGN FOR SIX SIGMA WITH RESPONSE SURFACE METHOD AND SIGMA BASED ROBUST DESIGN[J]. International Journal of Automotive Technology,2003,4:193-201
[24]R J TALIB, A MUCHTAR, C H AZHARI. THE EFFECT OF TEMPERATURE ON THE GENERATION OF THERMOINSTABILITY DURING BRAKING OF FRICTION LINING MATERIALS[J]. Jurnal teknologi,2004,40(A):51-66.
[25]Ashwin Hattiangadi, Thomas Siegmund. A numerical study on interface crack growth under heat flux loading[J]. INTERNATIONAL JOURNAL OF SOLIDS and STRUCTURES,2005,42:6335-6355.
[26]Ramesh Edara. Heavy Vehicle Disc Brake Components Design Using CAE Tools[J]. SAE,2006,1:1-6
[27]P Liu, H Zheng, C Cai, Y Y Wang, C Lu, K H Ang, G R Liu. Analysis of disk brake squeal using the complex eigenvalue method[J]. Applied Acoustics,2007,68:603-615.
[28]C.H.Gao, J.M.Huang, X.Z.Lin, et al. Stress Analysis of Thermal Fatigue Fracture of Brake Disks Based on Thermomechanical Coupling[J]. Journal of Tribology,2007,129:536-543.
[29]Jinchun Huang, Charles M.Krousgrill, Anil K.Bajaj. An Efficient Approach to Estimate Critical Value of Friction Coefficient in Brake Squeal Analysis[J]. Journal of Applied Mechanics,2007,74:534-541.
[30]A.Akay, O.Giannini, F.massi, A.Sestieri. Disc brake squeal characterization through simplified test rigs[J]. Mechanical Systems and Signal Processing,2009,23:2590-2607.
[31]D K Kolluri, X.Boidin, Y Desplanques, et al. Effect of Natural Graphite Particle size in friction materials on thermal localisation phenomenon during stop-braking[J]. Wear,2010,268:1472-1482.
[32]付强,李明丽.鼓式制动器尖叫噪声的模态识别[J].汽车技术,1990,10：16-23
[33]管迪华,朱新潮,成波.鼓式制动器结构振动噪声研究[J].汽车工程,1993,15(2)：71-78.
[34]曹立波,郭正康.鼓式制动器制动尖叫的机理及其预防[J].湖南大学学报,1995,22(3)：91-96.
[35]张文明,申炎华,张卫钢,马飞.湿式制动器的制动过程和摩擦温度场的研究[J].有色金属,1997,49(1)14-19.
[36]方明霞,冯奇.鼓式制动器摩擦片的有限元分析[J].重型汽车,1998,47(4)：14-17.
[37]毛智东,王学林,胡于进,等.鼓式制动器接触分析[J].华中科技大学学报(自然科学版),2002,30(7)：71-73.
[38]王步康,董光能,谢友柏.滑动接触中摩擦发热的数值分析[J].中国机械工程,2002,13(21)：1880-1884.
[39]刘立刚,王学林.鼓式制动器的有限元分析[J].专用汽车,2003,3：21-23
[40]吕振华.蹄-鼓式制动器热弹性耦合有限元分析[J].机械强度,2003,25(4)：401-407.
[41]陈兴旺.鼓式制动器温度场的数值模拟分析[J].北京汽车,2005：11-15.
[42]袁春静,吴永根,葛振亮.制动鼓瞬态温度场有限元分析[J].科学技术与工程,2006,6(8)：1154-1156.
[43]郭应时,袁伟,付锐.实验法求解汽车鼓式制动器对流换热系数[J].长安大学学报(自然科学版),2006,26(4)：92-94.
[44]马迅,秦剑.基于有限元法的制动鼓的偶和分析[J].机械设计与研究,2005,21(1)：68-71.
[45]林谢昭,高诚辉,黄健萌.制动工况参数对制动盘摩擦温度场分布的影响[J].工程设计学报,2006,13(1)：45-48.
[46]高诚辉,黄健萌,林谢昭,等.盘式制动器摩擦磨损人动力学研究进展[J].中国工程机械学报,2006,4(1)：83-88.
[47]杨国俊,古正气,李伟平.有限元分析在鼓式制动器设计中的应用[J].机械设计与制造,2007,4：14-15.
[48]王志刚.制动器摩擦副温度场的解析计算[J].机械设计与研究,2007,23(4)：58-60.
[49]管欣,申军烽,管仁梅,等.不同摩擦系数对鼓式制动器低频振动的影响[J].科学技术与工程,2008,8(21)：5867-5871.
[50]王宣锋,粱迎春.控制鼓式制动器力矩波动的研究[J].机械设计与制造,2008,7：131-133.
[51]姚辉学,侯永涛,王国林,等.车辆制动器参数化数据库设计[J].机械工程学报,2008,44(10)：255-259.
[52]黄健萌,高诚辉,唐旭晟,等.盘式制动器热-结构耦合的数值建模与分析[J].机械工程学报,2008,44(2)145-151.
[53]范久臣,杨兆军,刘长亮,等.鼓式制动器刚柔耦合虚拟样机[J].吉林大学学报(工学版),2009,39：183-187.
[54]管欣,申军烽,管仁梅,等.鼓式制动器相关参数对其制动效能的影响[J].科学技术与工程,2009,9(4)：940-942.
[55]赵凯辉,魏朗.鼓式制动器三维热-机耦合温度场仿真[J].农业机械学报,2009,40(2)：32-36.
[56]靳少杰,徐颖强,林富华.鼓式制动器摩擦片-鼓接触点确定方法及变化规律分析[J].2010,32(5)：424-428.
[57]庄茁,张帆,岑松,等.非线性有限元分析与实例[M].北京：科学出版社,2005.
[58]Jung, I Lee. Development of Automotive Braking Performance Analysis Program Considering Dynamic Characteristics[J]. Trans. Korean Society of Automotive Engineers, 2004,12(2):175-181.
[59]Mohammad Haghpanahi.Development of a Parametric Finite Element Model of Lower Cervical Spine in Sagital Plane[C]. Proceeding of the 28 th IEEE,New York City,USA,Aug 30-Sept3,2006,1739-1741.
[60]李亮,宋健,李永,郭振宇.制动器热分析的快速有限元仿真模型研究[J].系统仿真学报,2005,17(12)：2869-2877.
[61]R Limpert. Brake Design and Safety Second Edition[J]. Society of Automotive Engineers, USA,1999.
[62]S P Jung, K J Jun, T W Park, et al. Development of The Brake System Design Program for A Vehicle[J]. International Journal of Automotive Technology,2008,9(1):45-51.
[63]马迅,秦剑.制动鼓的热-结构耦合分析[J].湖北汽车工业学院学报,2004,18(3)：5-9.
[64]Raphael B, Krishanmoorthy C S. Automating finite element development using object oriented techniques[J]. Eng Computation,1993,10:267-278.
[65]张峰,李兆前,黄传真.参数化设计的研究现状与发展趋势[J].机械工程师,2002,1：13-15.
[66]杨秀萍,王鹏林.基于ANSYS APDL语言的零件参数化有限元分析[J].设计与研究,2005,11：10-11.
[67]Abaqus Scripting User's Manual.
[68]Abaqus GUI Toolkit User's Manual.
[69]吴剑增,张炳荣,邓祖国.汽车制动器相关参数关系初探[J].客车技术与研究,2009,6：19-22.