发动机悬置系统解耦与新型半主动液压悬置设计的关键理论研究
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摘要
发动机悬置系统是连接动力总成与车辆底盘的主要用于隔离发动机振动的弹性装置。它通常由若干橡胶悬置或者液压悬置零部件组成，并且在现代轿车的隔振减振降噪性能上起着重要的作用。另一方面，良好的发动机悬置系统能降低结构的应力以提高结构的耐久性。主要通过优化方法来提高悬置系统相关的性能指标，而其中一个重要的性能是系统的解耦。解耦原理有两种：一种是与刚度中心相关的解耦，另一种的目的是使得激励力只激励出一个模态。利用刚度中心解耦原理优化发动机悬置系统，就是要使得悬置系统的刚度中心与发动机的质量中心重合，但是目前还没有文献对刚度中心进行详细的研究。对于另外一种解耦原理，已有文献[1]中的TRA(Torque RollAxis)方法只考虑了扭矩的影响，没有考虑力的作用，因此在理论上具有一定的局限性。
传统的橡胶隔振器拥有几乎与频率无关的动刚度，它不能满足发动机复杂的工作情况要求。理想的悬置部件应该具有低频大刚度、高频小刚度的频变动刚度特性，而液压悬置拥有比橡胶悬置优秀的频变动刚度特性。由于判断隔振性能的共振曲线是针对传统与频率无关的单自由度系统，它不能快速的判断具有频变特性的隔振器的隔振性能，因此需要开发较为直观的方法。关于液压悬置的研究主要集中在这两个方面：研究既有液压悬置的性能和开发新型的液压悬置。
本文从理论上对悬置系统的两种解耦原理进行研究，研究具有频变动刚度的液压悬置的动态特性，同时设计一种新型的半主动液压悬置。本文主要研究内容和创新性成果如下：
（1）推导广义激励力只激励出一个系统模态的解耦准则。
在平衡位置附近，建立由若干悬置支撑的发动机刚体在质量中心处的动力学方程组。经过Fourier变换，分别考虑非比例阻尼的作用和不考虑阻尼的作用，推导广义激励力（包括力和扭矩）只激励出一个系统模态时系统需要满足的解耦条件。而传统的TRA方法是在状态空间中应用Laplace变换推导而来的，并且只考虑了扭矩的作用。然后介绍这种新解耦准则的特点和物理意义。最后通过某悬置系统的优化算例发现：考虑非比例阻尼时，系统可以完全得到解耦；而不考虑阻尼时，系统不能够完全的得到解耦。
（2）推导悬置系统刚度中心存在的充分必要条件和计算其位置的方法。
刚度中心是这样的一个点：过该点的任意静力将使得刚体只发生平移运动，而绕刚度中心的力偶矩，系统在刚度中心处只有转动。在本文中该点称为严格定义的刚度中心（严格刚度中心）。
利用发动机质心处的静力平衡方程，推导施加静力或者力偶矩位置处的静力学平衡方程。利用刚度中心的定义和反对称矩阵的性质，分别考虑静力和考虑力偶矩作用时，推导系统需要满足的条件。在文中定义一个对称的判断矩阵B，当且仅当B是零矩阵时，刚度中心才存在。并且给出计算严格刚度中心位置的方法。发现对称式配置的隔振系统的严格刚度中心不一定存在。
（3）推导悬置系统弱刚度中心存在的充分必要条件和计算其位置的方法，并研究弱刚度中心存在时系统位移响应的类型。
通常情况下严格刚度中心不存在，但是在一些情况下，过某些点的沿着特定方向的静力会使得系统只发生平移运动，这类点称为弱定义的刚度中心（弱刚度中心）。从这个定义出发，推导弱刚度中心存在时系统需要满足的条件，并且该条件是以判断矩阵B的特征值描述的。根据判断矩阵B的特征值的特征，在弱刚度中心存在时，系统位移响应归纳为若干形式，并介绍计算弱刚度中心位置的方法。通过算例计算系统弱刚度中心的位置，验证所提出的方法。
（4）给出一种快速判断拥有频变动刚度的隔振器的隔振性能的图示法。
利用单自由度隔振模型，介绍拥有频变刚度特性的隔振器的传递动刚度和驱动点动刚度的定义。利用传递动刚度和驱动点动刚度，推导隔振系统的力传递率。定义两条在频率域上描述的曲线：共振曲线和隔振曲线。在不同频段通过判断隔振器的同相动刚度与这两条曲线的关系，快速直观的判断系统性能的好坏。运用图示法，我们发现液压悬置在中频段的隔振性能比橡胶悬置的隔振性能优秀，而在高频段和低频段，前者的隔振性能没有后者的好，并得到验证。
（5）设计一种新型的高性能半主动液压悬置。
利用集总参数模型，推导液压悬置的动刚度表达式。通过比较被动TMD(Tuned Mass Damper)系统的动刚度与液压悬置的动刚度，得到它们之间的不同点与相同点。研究液压悬置的动刚度的三个关键频率点（下凸频率，共振频率和峰值频率）与影响其位置的物理参数（例如惯性通道长度、截面积等）的关系，得到了控制一种参数只能够在有限频段调节液压悬置的这几个关键频率点的结论。给出一种利用螺纹原理以同时控制惯性通道长度和截面积的新型半主动液压悬置的结构。这种液压悬置可以在[0,)范围内调节这三个关键频率点。给出两种节能策略（摩擦自锁和最优调节时机）以最大限度的降低能量消耗。最后通过优化算法计算最优的惯性通道长度和相应的动刚度。结果表明：使用最优的惯性通道参数，可以获得低频大刚度、高频小刚度的理想动刚度曲线。
Engine mounting system is elastic equipment which connects powertrain and thechassis of vehicle to isolate vibration of engine. It is composed of somecomponents, such as rubber mount and hydraulic engine mount, and plays animportant role in vibration isolation, vibration reduction and noise reductionperformance for modern passenger vehicle. On the other hand, better enginemounting system can also reduce the stress of structure to increase the durability ofthe components. The optimization is mainly carried out to improve relative indexesof engine mounting system’s performance, where the decoupling of the system isimportant performance. There are two kinds of decoupling principles: one is thedecoupling of the system associating with Center of Rigidity (CR), the other is toachieve that only one model shape is excited by the exciting force. Theoptimization of engine mounting system by the decoupling principle associatedwith CR is to make CR of engine mounting system coincide with center of mass ofthe engine, but there are no articles that study CR completely. For the otherdecoupling principle, the method called TRA (Torque Roll Axis) in current articlesonly considers the influence of torque without force, so it is limited in theory.
Traditional rubber mount has nearly frequency-independent dynamic stiffness,and it cannot fulfill the complex work conditions of engine. Ideal engine mountshould have large stiffness at low frequency and small dynamic stiffness at highfrequency, and hydraulic engine mount has better frequency-dependent dynamicstiffness than rubber mount. Resonant curves which are used to judge the vibrationisolation performance are suitable for traditional frequency-independent systemwith single degree of freedom or they cannot be used to judge the performance offrequency-dependent isolator rapidly, so new method should be developed. The research on hydraulic engine mount focuses on: studying the performance ofcurrent hydraulic mount and developing novel hydraulic mount.
The paper theoretically studies the two decoupling principles of enginemounting system, researches the dynamic characteristic of hydraulic engine mountwith frequency-dependent dynamic stiffness and designs a novel semi-activehydraulic engine mount. The main contents and some creative conclusions in thepaper are as follows:
(1) Derive decoupling criteria for a general exciting force to excite onlyone model shape.
Dynamic equations are set up at the center of mass around equilibriumposition of the rigid engine which is supported by some mounts. Considering or notconsidering the influence of disproportional damping respectively, the decouplingcriteria that the system should meet are derived through Fourier transformation sothat a general exciting force (including force and torque) excites only one modelshape. Traditional TRA method is derived through Laplace transformation in statespace and only considers the influence of torque without force. Then the featuresand physical meaning of the decoupling criteria are introduced. Throughoptimization of engine mounting system, the system can be fully decoupledconsidering the influence of disproportional damping, whereas the system cannotbe fully decoupled without considering the influence of damping.
(2) Derive the sufficient and necessary condition for the existence of CRand the method to calculate the location of CR.
Center of rigidity is a point: arbitrary static force along CR can make the rigidbody have only translational displacement, whereas the torque along CR can makethe rigid body have only rotational angles at CR. This kind of CR is called CR withstrict definition in the paper.
Using equations of static equilibrium at center of mass of engine, theequations of static equilibrium are set up at the point where force and torque is applied. From the definition of CR and the characteristic of anti-symmetric matrix,the conditions that the system should meet are derived under static force conditionand torque condition respectively. A symmetric judging matrix B is defined in thepaper, and CR with strict definition exists only when matrix B is null. Themethod to calculate its position is given. It is found that CR with strict definitionfor the isolation system with the symmetric layout may not exist sometimes.
(3) Derive the sufficient and necessary conditions for the existence of CRwith weak definition and the method to calculate its location, and research thecharacteristic of displacement response when CR with weak definition exists.
Generally, CR with strict definition does not exist, but a static force alongcertain point may have only translational displacement of the system, and this kindof point is called CR with weak definition. From this definition, the conditions thatthe system should satisfy for the existence of CR with weak definition aredescribed by the eigenvalue of judging matrix B. According to the characteristicof eigenvalue of judging matrix B, when CR with weak definition exists, thebehaviors of displacement response are classified into some types and the methodto get the location of CR with weak definition is introduced. A sample is given tocalculate CR with weak definition of the system and validates the proposedmethod.
(4) Give a graphical presentation method to rapidly judge the vibrationisolation performance for the isolator with frequency-dependent dynamicstiffness.
Using vibration isolation model with single degree of freedom, the definitionsof transfer dynamic stiffness and drive-point dynamic stiffness of isolator withfrequency-dependent dynamic stiffness are introduced. The force transmissibility ofthe vibration isolation system is derived by using transfer dynamic stiffness anddrive-point dynamic stiffness. Two curves are defined in frequency domain:resonant curve and vibration isolation curve. The vibration isolation performance can be concluded rapidly by judging relationships between the dynamic stiffnessin-phrase of the isolator and the two defined curves in various frequency bands. Bythis graphical presentation method, we find that hydraulic engine mount can havebetter vibration isolation performance in middle frequency band whereas thevibration isolation performance for hydraulic mount is worse than that for rubbermount in low and high frequency band, and this conclusion is validated.
(5) Design a novel semi-active hydraulic mount with high performance.
The expression of dynamic stiffness of hydraulic is derived by making use oflumped parameter model. The differences and comparisons between passive TMD(Tuned Mass Damper) system and hydraulic engine mount are obtained bycomparing the two concepts of dynamic stiffness between them. The relationshipsbetween the three key frequency points (notch frequency, resonant frequency andpeak frequency) of dynamic stiffness for hydraulic mount and physical parameters(such as length or cross section of inertia track) that influence their locations areresearched, and it is concluded that tuning only one parameter can only tune thesaid frequency points in narrow frequency band. A novel configuration ofsemi-active hydraulic mount is given, and this mount can tune both cross sectionand length of inertia track with the help of screw thread at the same time. Thehydraulic mount can tune the three frequency points as wide as [0,). Two energyconservations (friction self-lock and optimal tuning time) are applied to decreaseenergy consumed. Finally, the optimal length of inertial track and correspondingdynamic stiffness are gotten by optimal algorithm. The result shows that: withoptimal length of inertial track, the ideal dynamic stiffness which is large at lowfrequency and small at high frequency can be gotten.
传统的橡胶隔振器拥有几乎与频率无关的动刚度，它不能满足发动机复杂的工作情况要求。理想的悬置部件应该具有低频大刚度、高频小刚度的频变动刚度特性，而液压悬置拥有比橡胶悬置优秀的频变动刚度特性。由于判断隔振性能的共振曲线是针对传统与频率无关的单自由度系统，它不能快速的判断具有频变特性的隔振器的隔振性能，因此需要开发较为直观的方法。关于液压悬置的研究主要集中在这两个方面：研究既有液压悬置的性能和开发新型的液压悬置。
本文从理论上对悬置系统的两种解耦原理进行研究，研究具有频变动刚度的液压悬置的动态特性，同时设计一种新型的半主动液压悬置。本文主要研究内容和创新性成果如下：
（1）推导广义激励力只激励出一个系统模态的解耦准则。
在平衡位置附近，建立由若干悬置支撑的发动机刚体在质量中心处的动力学方程组。经过Fourier变换，分别考虑非比例阻尼的作用和不考虑阻尼的作用，推导广义激励力（包括力和扭矩）只激励出一个系统模态时系统需要满足的解耦条件。而传统的TRA方法是在状态空间中应用Laplace变换推导而来的，并且只考虑了扭矩的作用。然后介绍这种新解耦准则的特点和物理意义。最后通过某悬置系统的优化算例发现：考虑非比例阻尼时，系统可以完全得到解耦；而不考虑阻尼时，系统不能够完全的得到解耦。
（2）推导悬置系统刚度中心存在的充分必要条件和计算其位置的方法。
刚度中心是这样的一个点：过该点的任意静力将使得刚体只发生平移运动，而绕刚度中心的力偶矩，系统在刚度中心处只有转动。在本文中该点称为严格定义的刚度中心（严格刚度中心）。
利用发动机质心处的静力平衡方程，推导施加静力或者力偶矩位置处的静力学平衡方程。利用刚度中心的定义和反对称矩阵的性质，分别考虑静力和考虑力偶矩作用时，推导系统需要满足的条件。在文中定义一个对称的判断矩阵B，当且仅当B是零矩阵时，刚度中心才存在。并且给出计算严格刚度中心位置的方法。发现对称式配置的隔振系统的严格刚度中心不一定存在。
（3）推导悬置系统弱刚度中心存在的充分必要条件和计算其位置的方法，并研究弱刚度中心存在时系统位移响应的类型。
通常情况下严格刚度中心不存在，但是在一些情况下，过某些点的沿着特定方向的静力会使得系统只发生平移运动，这类点称为弱定义的刚度中心（弱刚度中心）。从这个定义出发，推导弱刚度中心存在时系统需要满足的条件，并且该条件是以判断矩阵B的特征值描述的。根据判断矩阵B的特征值的特征，在弱刚度中心存在时，系统位移响应归纳为若干形式，并介绍计算弱刚度中心位置的方法。通过算例计算系统弱刚度中心的位置，验证所提出的方法。
（4）给出一种快速判断拥有频变动刚度的隔振器的隔振性能的图示法。
利用单自由度隔振模型，介绍拥有频变刚度特性的隔振器的传递动刚度和驱动点动刚度的定义。利用传递动刚度和驱动点动刚度，推导隔振系统的力传递率。定义两条在频率域上描述的曲线：共振曲线和隔振曲线。在不同频段通过判断隔振器的同相动刚度与这两条曲线的关系，快速直观的判断系统性能的好坏。运用图示法，我们发现液压悬置在中频段的隔振性能比橡胶悬置的隔振性能优秀，而在高频段和低频段，前者的隔振性能没有后者的好，并得到验证。
（5）设计一种新型的高性能半主动液压悬置。
利用集总参数模型，推导液压悬置的动刚度表达式。通过比较被动TMD(Tuned Mass Damper)系统的动刚度与液压悬置的动刚度，得到它们之间的不同点与相同点。研究液压悬置的动刚度的三个关键频率点（下凸频率，共振频率和峰值频率）与影响其位置的物理参数（例如惯性通道长度、截面积等）的关系，得到了控制一种参数只能够在有限频段调节液压悬置的这几个关键频率点的结论。给出一种利用螺纹原理以同时控制惯性通道长度和截面积的新型半主动液压悬置的结构。这种液压悬置可以在[0,)范围内调节这三个关键频率点。给出两种节能策略（摩擦自锁和最优调节时机）以最大限度的降低能量消耗。最后通过优化算法计算最优的惯性通道长度和相应的动刚度。结果表明：使用最优的惯性通道参数，可以获得低频大刚度、高频小刚度的理想动刚度曲线。
Engine mounting system is elastic equipment which connects powertrain and thechassis of vehicle to isolate vibration of engine. It is composed of somecomponents, such as rubber mount and hydraulic engine mount, and plays animportant role in vibration isolation, vibration reduction and noise reductionperformance for modern passenger vehicle. On the other hand, better enginemounting system can also reduce the stress of structure to increase the durability ofthe components. The optimization is mainly carried out to improve relative indexesof engine mounting system’s performance, where the decoupling of the system isimportant performance. There are two kinds of decoupling principles: one is thedecoupling of the system associating with Center of Rigidity (CR), the other is toachieve that only one model shape is excited by the exciting force. Theoptimization of engine mounting system by the decoupling principle associatedwith CR is to make CR of engine mounting system coincide with center of mass ofthe engine, but there are no articles that study CR completely. For the otherdecoupling principle, the method called TRA (Torque Roll Axis) in current articlesonly considers the influence of torque without force, so it is limited in theory.
Traditional rubber mount has nearly frequency-independent dynamic stiffness,and it cannot fulfill the complex work conditions of engine. Ideal engine mountshould have large stiffness at low frequency and small dynamic stiffness at highfrequency, and hydraulic engine mount has better frequency-dependent dynamicstiffness than rubber mount. Resonant curves which are used to judge the vibrationisolation performance are suitable for traditional frequency-independent systemwith single degree of freedom or they cannot be used to judge the performance offrequency-dependent isolator rapidly, so new method should be developed. The research on hydraulic engine mount focuses on: studying the performance ofcurrent hydraulic mount and developing novel hydraulic mount.
The paper theoretically studies the two decoupling principles of enginemounting system, researches the dynamic characteristic of hydraulic engine mountwith frequency-dependent dynamic stiffness and designs a novel semi-activehydraulic engine mount. The main contents and some creative conclusions in thepaper are as follows:
(1) Derive decoupling criteria for a general exciting force to excite onlyone model shape.
Dynamic equations are set up at the center of mass around equilibriumposition of the rigid engine which is supported by some mounts. Considering or notconsidering the influence of disproportional damping respectively, the decouplingcriteria that the system should meet are derived through Fourier transformation sothat a general exciting force (including force and torque) excites only one modelshape. Traditional TRA method is derived through Laplace transformation in statespace and only considers the influence of torque without force. Then the featuresand physical meaning of the decoupling criteria are introduced. Throughoptimization of engine mounting system, the system can be fully decoupledconsidering the influence of disproportional damping, whereas the system cannotbe fully decoupled without considering the influence of damping.
(2) Derive the sufficient and necessary condition for the existence of CRand the method to calculate the location of CR.
Center of rigidity is a point: arbitrary static force along CR can make the rigidbody have only translational displacement, whereas the torque along CR can makethe rigid body have only rotational angles at CR. This kind of CR is called CR withstrict definition in the paper.
Using equations of static equilibrium at center of mass of engine, theequations of static equilibrium are set up at the point where force and torque is applied. From the definition of CR and the characteristic of anti-symmetric matrix,the conditions that the system should meet are derived under static force conditionand torque condition respectively. A symmetric judging matrix B is defined in thepaper, and CR with strict definition exists only when matrix B is null. Themethod to calculate its position is given. It is found that CR with strict definitionfor the isolation system with the symmetric layout may not exist sometimes.
(3) Derive the sufficient and necessary conditions for the existence of CRwith weak definition and the method to calculate its location, and research thecharacteristic of displacement response when CR with weak definition exists.
Generally, CR with strict definition does not exist, but a static force alongcertain point may have only translational displacement of the system, and this kindof point is called CR with weak definition. From this definition, the conditions thatthe system should satisfy for the existence of CR with weak definition aredescribed by the eigenvalue of judging matrix B. According to the characteristicof eigenvalue of judging matrix B, when CR with weak definition exists, thebehaviors of displacement response are classified into some types and the methodto get the location of CR with weak definition is introduced. A sample is given tocalculate CR with weak definition of the system and validates the proposedmethod.
(4) Give a graphical presentation method to rapidly judge the vibrationisolation performance for the isolator with frequency-dependent dynamicstiffness.
Using vibration isolation model with single degree of freedom, the definitionsof transfer dynamic stiffness and drive-point dynamic stiffness of isolator withfrequency-dependent dynamic stiffness are introduced. The force transmissibility ofthe vibration isolation system is derived by using transfer dynamic stiffness anddrive-point dynamic stiffness. Two curves are defined in frequency domain:resonant curve and vibration isolation curve. The vibration isolation performance can be concluded rapidly by judging relationships between the dynamic stiffnessin-phrase of the isolator and the two defined curves in various frequency bands. Bythis graphical presentation method, we find that hydraulic engine mount can havebetter vibration isolation performance in middle frequency band whereas thevibration isolation performance for hydraulic mount is worse than that for rubbermount in low and high frequency band, and this conclusion is validated.
(5) Design a novel semi-active hydraulic mount with high performance.
The expression of dynamic stiffness of hydraulic is derived by making use oflumped parameter model. The differences and comparisons between passive TMD(Tuned Mass Damper) system and hydraulic engine mount are obtained bycomparing the two concepts of dynamic stiffness between them. The relationshipsbetween the three key frequency points (notch frequency, resonant frequency andpeak frequency) of dynamic stiffness for hydraulic mount and physical parameters(such as length or cross section of inertia track) that influence their locations areresearched, and it is concluded that tuning only one parameter can only tune thesaid frequency points in narrow frequency band. A novel configuration ofsemi-active hydraulic mount is given, and this mount can tune both cross sectionand length of inertia track with the help of screw thread at the same time. Thehydraulic mount can tune the three frequency points as wide as [0,). Two energyconservations (friction self-lock and optimal tuning time) are applied to decreaseenergy consumed. Finally, the optimal length of inertial track and correspondingdynamic stiffness are gotten by optimal algorithm. The result shows that: withoptimal length of inertial track, the ideal dynamic stiffness which is large at lowfrequency and small at high frequency can be gotten.
引文
[1] Jae-Yeol Park, Rajendra Singh. Effect of non-proportional damping on thetorque roll axis decoupling of an engine mounting system[J]. Journal ofSound and Vibration，2008，313（3-5）:841-857.
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[3] Michael Woon, Sidharth Nakra, Andrej Ivanco, et al. Series hydraulic hybridsystem for a passenger car: design, integration and packaging study[J]. SAE2012-01-1031，2012.
[4]胡金芳.计及弹性基础的动力总成悬置系统特性分析与解耦研究[D].合肥:合肥工业大学,2012.
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