CN104123411A

CN104123411A - Automobile powertrain system rotational inertia synthetic method

Info

Publication number: CN104123411A
Application number: CN201410335649.9A
Authority: CN
Inventors: 伍建伟; 刘夫云; 杨运泽; 汪沙娜; 甘林
Original assignee: Guilin University of Electronic Technology
Current assignee: Guilin University of Electronic Technology
Priority date: 2014-07-15
Filing date: 2014-07-15
Publication date: 2014-10-29
Anticipated expiration: 2034-07-15
Also published as: CN104123411B

Abstract

The invention discloses a method for synthesizing moment of inertia of an automobile powertrain system, comprising: inputting known parameters of mass, center of mass, inertia and Euler angle of an engine and a gearbox into an EXCEL table, so as to facilitate data import and modification; Using the method of solving the center of mass in theoretical mechanics, according to the mass and center of mass of the engine and gearbox, the coordinates of the combined center of mass are obtained; the coordinate system of the orientation parallel to the overall coordinate system is established from the coordinates of the total center of mass; the vector is represented by a coordinate matrix, Establish the relationship between the coordinate matrices of the same vector in different coordinate systems, and use linear algebra related theoretical methods to derive the relationship of inertia matrices in different coordinate systems, that is, establish the relationship between the moment of inertia and product of inertia of rigid bodies in the coordinate system; according to the derived matrix expression , using computer language to compile corresponding programs to calculate the synthesis results. The present invention adopts the derivation in matrix form, which has the characteristics of simplicity and intuition, and the conclusion has an extremely concise form, which is easy to use computer language to solve.

Description

A method for synthesizing moment of inertia of automobile powertrain system

技术领域technical field

本发明属于汽车工程技术领域，尤其涉及一种汽车动力总成系统转动惯量合成方法。The invention belongs to the technical field of automobile engineering, and in particular relates to a method for synthesizing moment of inertia of an automobile power assembly system.

背景技术Background technique

物体的转动惯量在机械设计中是一个十分重要的参数，它的正确获取是机械系统进行静力学、运动学分析和动力学分析设计的前提。The moment of inertia of an object is a very important parameter in mechanical design, and its correct acquisition is the premise of statics, kinematics analysis and dynamics analysis and design of the mechanical system.

在汽车动力总成系统(由发动机、变速箱和悬置元件等组成的系统)中，发动机和变速箱(由于刚度大，可视为刚体)一般来自不同的厂家，厂家会提供相应的惯性参数(质量、质心和转动惯量)。但是，在汽车动力总成系统中，需要先将发动机和变速箱两个物体的质量、质心和转动惯量进行合成，得到合成数据才能便于供动力学分析使用。多刚体的质量和质心的合成较为简单，而转动惯量的合成，由于厂家给出的惯量参数是在不同坐标系下给出的(一般以过质心相对于整车坐标系的欧拉角表示)。因此，这给合成造成了一定的困难，故本文也重点介绍的是转动惯量的合成方法。In the automotive powertrain system (system composed of engine, gearbox and suspension components, etc.), the engine and gearbox (which can be regarded as rigid bodies due to their high stiffness) generally come from different manufacturers, and the manufacturers will provide corresponding inertia parameters. (mass, center of mass and moment of inertia). However, in the automotive powertrain system, the mass, center of mass, and moment of inertia of the two objects, the engine and the gearbox, need to be synthesized first, so that the synthesized data can be used for dynamic analysis. The synthesis of mass and center of mass of multi-rigid bodies is relatively simple, and the synthesis of moment of inertia, because the inertia parameters given by the manufacturer are given in different coordinate systems (generally represented by the Euler angle of the center of mass relative to the vehicle coordinate system) . Therefore, this has caused certain difficulties to the synthesis, so this article also focuses on the synthesis method of the moment of inertia.

目前，转动惯量合成的方法有两种：一种是通过实验的方法，另一种是通过专业性较强的大型商业软件(如ADAMS)，在软件中建立相应的模型，利用相关的命令进行合成。At present, there are two methods for synthesizing the moment of inertia: one is through experiments, and the other is through professional large-scale commercial software (such as ADAMS), establishing corresponding models in the software, and using related commands. synthesis.

大型商业软件合成的方法也有很大的缺陷，它不仅需要操作人员熟练使用该软件，并且还要具备一定的专业技术能力，更重要的是需要在软件中建立相应的模型。同时，合成的转动惯量相对于质心，以便于系统的动力学分析。因此，通过软件合成需要进行两次，才有它实际的意义。先一次合成找到质心，然后再以该质心为基准进行二次合成，得到的转动惯量才相对于该总质心。The method of large-scale commercial software synthesis also has great defects. It not only requires operators to be proficient in using the software, but also has a certain professional technical ability, and more importantly, it needs to establish a corresponding model in the software. At the same time, the resultant moment of inertia is relative to the center of mass to facilitate the dynamic analysis of the system. Therefore, the software synthesis needs to be carried out twice before it has practical significance. Find the center of mass in the first synthesis, and then perform the second synthesis based on the center of mass, so that the obtained moment of inertia is relative to the total center of mass.

显然，实验的方法，耗时耗力耗资金，而通过大型商业软件合成却又操作复杂、对专业技术水平有一定的要求，不便于非技术人员的使用。实际上，对于发动机和变速箱而言，厂家分别提供了实验所得到的质心、质心坐标和转动惯量这些参数，只是在原有的基础上进行叠加(尽管存在欧拉角的问题)，根本没有必要再次实验的方法来进行这些参数的合成。Obviously, the experimental method is time-consuming, labor-intensive and capital-intensive, but the synthesis through large-scale commercial software is complicated to operate and requires a certain level of professional skills, which is not convenient for non-technical personnel to use. In fact, for the engine and the gearbox, the manufacturer provided the parameters of the center of mass, the coordinates of the center of mass and the moment of inertia obtained from the experiment, but superimposed on the original basis (although there is a problem with the Euler angle), it is not necessary at all Experimental methods are again used to synthesize these parameters.

因此，迫切需要找到一种适用于汽车动力总成系统的转动惯量合成方法，即不用建立模型，只需输入发动机和变速箱各自的参数，然后利用计算机程序来实现质量、质心和转动惯量合成。Therefore, there is an urgent need to find a method for synthesizing the moment of inertia suitable for the automotive powertrain system, that is, without building a model, only need to input the respective parameters of the engine and gearbox, and then use a computer program to realize the synthesis of mass, center of mass and moment of inertia.

发明内容Contents of the invention

本发明实施例的目的在于提供一种汽车动力总成系统转动惯量合成方法，旨在解决现有的转动惯量合成方法存在的操作复杂，费时费力，操作成本高的问题。The purpose of the embodiments of the present invention is to provide a method for synthesizing the moment of inertia of an automobile powertrain system, aiming to solve the problems of complicated operation, time-consuming and labor-intensive, and high operating costs in the existing method for synthesizing the moment of inertia.

本发明实施例是这样实现的，一种汽车动力总成系统转动惯量合成方法，该汽车动力总成系统转动惯量合成方法包括以下步骤：The embodiment of the present invention is achieved in this way, a method for synthesizing the moment of inertia of a powertrain system of an automobile, the method for synthesizing the moment of inertia of the powertrain system of an automobile comprises the following steps:

步骤一，将已知的发动机和变速箱质量、质心、惯量和欧拉角参数输入到EXCEL表中，以便于数据的导入与修改；Step 1, input the known engine and gearbox mass, center of mass, inertia and Euler angle parameters into the EXCEL table, so as to facilitate data import and modification;

步骤二，利用理论力学中求解质心的方法，根据发动机和变速箱的质量和质心，求出合成后总质心的坐标；由总质心的坐标建立方位与总体坐标系平行的坐标系；Step 2, using the method for solving the center of mass in theoretical mechanics, according to the mass and the center of mass of the engine and gearbox, obtain the coordinates of the total center of mass after synthesis; establish a coordinate system parallel to the overall coordinate system with the orientation from the coordinates of the total center of mass;

步骤三，将矢量用坐标阵来表示，建立不同坐标系下相同矢量的坐标阵之间的关系，线性代数的相关理论方法推导不同坐标系下惯量矩阵的关系，即建立坐标系下刚体转动惯量和惯量积关系；Step 3: Express the vector with a coordinate matrix, establish the relationship between the coordinate matrix of the same vector in different coordinate systems, and use the related theoretical methods of linear algebra to derive the relationship of the inertia matrix in different coordinate systems, that is, establish the moment of inertia of the rigid body in the coordinate system and inertia product relationship;

步骤四，根据推导的矩阵表达式 $J_{c}^{a} = J_{c} + J_{c}^{'} = J_{c b_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T},$ 利用计算机语言编制相应的程序计算合成结果。Step 4, according to the derived matrix expression $J_{c}^{a} = J_{c} + J_{c}^{'} = J_{c b_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T},$ Use computer language to compile corresponding programs to calculate the synthesis results.

进一步，该汽车动力总成系统转动惯量合成方法的具体步骤如下：Further, the specific steps of the method for synthesizing the moment of inertia of the automobile powertrain system are as follows:

步骤一、将已知的发动机和变速箱质量、质心、惯量和欧拉角参数输入到EXCEL表中，以便于数据的导入与修改。Step 1. Input the known mass, center of mass, inertia and Euler angle parameters of the engine and gearbox into the EXCEL table, so as to facilitate data import and modification.

步骤二、利用理论力学中求解质心的方法，根据发动机和变速箱的质量和质心，求出合成后总质心的坐标；由总质心的坐标建立方位与总体坐标系平行的坐标系c-x^ry^rz^r；Step 2. Using the method of solving the center of mass in theoretical mechanics, according to the mass and center of mass of the engine and gearbox, find the coordinates of the combined center of mass; establish a coordinate system cx ^r y ^r parallel to the overall coordinate system from the coordinates of the total center of mass z ^r ;

步骤三、将矢量用坐标阵来表示，建立不同坐标系下相同矢量的坐标阵之间的关系，线性代数的相关理论方法推导不同坐标系下惯量矩阵的关系，即建立c-x^ry^rz^r坐标系与坐标系下刚体转动惯量和惯量积关系；Step 3. Express the vector with a coordinate matrix, establish the relationship between the coordinate matrix of the same vector in different coordinate systems, and use the relevant theoretical methods of linear algebra to derive the relationship of the inertia matrix in different coordinate systems, that is, establish cx ^r y ^r z ^r coordinate system with The relationship between the moment of inertia and the product of inertia of a rigid body in the coordinate system;

步骤四、根据矩阵表达式 $J_{c}^{a} = J_{c} + J_{c}^{'} = J_{c b_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T},$ 利用计算机语言编制相应的程序计算合成结果。Step 4. According to the matrix expression $J_{c}^{a} = J_{c} + J_{c}^{'} = J_{c b_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T},$ Use computer language to compile corresponding programs to calculate the synthesis results.

进一步，该汽车动力总成系统转动惯量合成方法的矩阵表达式推导过程如下：Further, the derivation process of the matrix expression of the rotational inertia synthesis method of the automobile powertrain system is as follows:

第一步，已知：发动机的质量m，质心坐标相对于的转动惯量和惯量积为J_xx,J_yy,J_zz,J_xy,J_xz,J_yz，惯量参数坐标系相对于总体坐标系下的方位用欧拉角表示为变速箱的质量为m'，质心坐标为相对于的转动惯量和惯量积为J'_xx,J'_yy,J'_zz,J'_xy,J'_xz,J'_yz，惯量参数坐标系相对于总体坐标系下的方位用欧拉角表示为先利用理论力学的方法，根据发动机和变速箱的质量和质心，求出合成后总质心的坐标，由总质心的坐标建立方位与总体坐标系平行的坐标系c-x^ry^rz^r；The first step is known: the mass m of the engine, the coordinates of the center of mass compared to The moment of inertia and product of inertia are J _xx , J _yy , J _zz , J _xy , J _xz , J _yz , and the orientation of the inertia parameter coordinate system relative to the global coordinate system is expressed as The mass of the gearbox is m', and the coordinates of the center of mass are compared to The moment of inertia and product of inertia are J' _xx , J' _yy , J' _zz , J' _xy , J' _xz , J' _yz , and the orientation of the inertia parameter coordinate system relative to the global coordinate system is expressed as First use the method of theoretical mechanics, according to the mass and center of mass of the engine and gearbox, find the coordinates of the combined total center of mass, and establish a coordinate system cx ^r y ^r z ^r parallel to the overall coordinate system from the coordinates of the total mass center;

第二步，然后推导出发动机相对于总质心坐标系的惯量矩阵，同理可以得到变速箱相对于总质心坐标系的惯量矩阵：In the second step, the inertia matrix of the engine relative to the total center of mass coordinate system is derived. Similarly, the inertia matrix of the gearbox relative to the total center of mass coordinate system can be obtained:

发动机的惯量矩阵为：The inertia matrix of the engine is:

$J J = = (\begin{matrix} {J J}_{xx xx} & - - {J J}_{xy xy} & - - {J J}_{xz xz} \\ - - {J J}_{xy xy} & {J J}_{yy yy} & - - {J J}_{yz yz} \\ - - {J J}_{xz xz} & - - {J J}_{yz yz} & {J J}_{zz zz} \end{matrix}) - - - - - - ((11))$

由于刚体是特殊的质点系，设刚体1由n个质点的质点系组成，第i个质点为R_i，第i个质点相对于坐标为它的坐标方阵为：Since the rigid body is a special particle system, let the rigid body 1 consist of a particle system of n particles, the i-th particle is R _i , and the i-th particle is relative to The coordinates are Its coordinate matrix is:

${\overset{~ ~}{R R}}_{i i}^{{c c}_{11}} = = (\begin{matrix} 00 & {z z}_{i i} & - - {y the y}_{i i} \\ - - {z z}_{i i} & 00 & {x x}_{i i} \\ {y the y}_{i i} & - - {x x}_{i i} & 00 \end{matrix}) - - - - - - ((22))$

根据惯量的定义，惯量矩阵用质点系表示为：According to the definition of inertia, the inertia matrix is expressed as:

$\begin{matrix} J J = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} (\begin{matrix} {y the y}_{i i}^{22} + + {z z}_{i i}^{22} & - - {x x}_{i i} {y the y}_{i i} & - - {x x}_{i i} {z z}_{i i} \\ - - {x x}_{i i} {y the y}_{i i} & {x x}_{i i}^{22} + + {z z}_{i i}^{22} & - - {y the y}_{i i} {z z}_{i i} \\ - - {x x}_{i i} {z z}_{i i} & - - {y the y}_{i i} {z z}_{i i} & {x x}_{i i}^{22} + + {y the y}_{i i}^{22} \end{matrix}) = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(\begin{matrix} 00 & {z z}_{i i} & - - {y the y}_{i i} \\ - - {z z}_{i i} & 00 & {x x}_{i i} \\ {y the y}_{i i} & - - {x x}_{i i} & 00 \end{matrix})}^{T T} (\begin{matrix} 00 & {z z}_{i i} & - - {y the y}_{i i} \\ - - {z z}_{i i} & 00 & {x x}_{i i} \\ {y the y}_{i i} & - - {x x}_{i i} & 00 \end{matrix}) \\ = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{R R}}_{i i}^{{c c}_{11}}))}^{T T} {\overset{~ ~}{R R}}_{i i}^{{c c}_{11}} \end{matrix} - - - - - - ((33))$

根据坐标系之间的关系，考虑到欧拉角已知，故相对于的方向余弦阵为：According to the relationship between coordinate systems, considering that the Euler angles are known, so compared to The direction cosine matrix of is:

由式(4)可得在坐标系下第i个质点的坐标阵、坐标方阵和坐标方阵的转置为：From formula (4) can be obtained in The coordinate matrix, the coordinate matrix and the transposition of the coordinate matrix of the i-th particle in the coordinate system are:

${R R}_{i i}^{{b b}_{11}} = = {A A}^{{b b}_{11} {c c}_{11}} {R R}_{i i}^{{c c}_{11}} = = A A {R R}_{i i}^{{c c}_{11}} - - - - - - ((55))$

${\overset{~ ~}{R R}}_{i i}^{{b b}_{11}} = = {A A}^{{b b}_{11} {c c}_{11}} {\overset{~ ~}{R R}}_{i i}^{{c c}_{11}} {A A}^{{c c}_{11} {b b}_{11}} = = A A {\overset{~ ~}{R R}}_{i i}^{{c c}_{11}} {A A}^{T T} - - - - - - ((66))$

${(({\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} = = {((A A | | {\overset{~ ~}{R R}}_{i i}^{{c c}_{11}} {A A}^{T T}))}^{T T} = = A A {(({\overset{~ ~}{R R}}_{i i}^{{c c}_{11}}))}^{T T} {A A}^{T T} - - - - - - ((77))$

由式(3)，根据(6)和(7)得到：From formula (3), according to (6) and (7):

${J J}_{{b b}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} A A {(({\overset{~ ~}{R R}}_{i i}^{{C C}_{11}}))}^{T T} {A A}^{T T} A A {\overset{~ ~}{R R}}_{i i}^{{c c}_{11}} {A A}^{T T} = = A A (({Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{R R}}_{i i}^{{c c}_{11}}))}^{T T} {\overset{~ ~}{R R}}_{i i}^{{c c}_{11}})) {A A}^{T T} = = {AJA AJA}^{T T} - - - - - - ((88))$

有矢量关系：There is a vector relation:

$\overset{&RightArrow; &Right Arrow;}{{cR c}_{i i}} = = \overset{&RightArrow; &Right Arrow;}{{cb cb}_{11}} + + - - {\overset{&RightArrow; &Right Arrow;}{{b b}_{11} R R}}_{i i} - - - - ((99))$

同样，它们的坐标方阵也存在同样的对应关系：Similarly, their coordinate matrix also has the same corresponding relationship:

${\overset{~ ~}{R R}}_{i i}^{c c} = = {\overset{~ ~}{cb cb}}_{11} + + {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}} - - - - - - ((1010))$

$\begin{matrix} {J J}_{c c} = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{R R}}_{i i}^{c c}))}^{T T} {\overset{~ ~}{R R}}_{i i}^{c c} = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{cb cb}}_{11} + + {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} (({\overset{~ ~}{cb cb}}_{11} + + {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}})) \\ = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} (({\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{cb cb}}_{11} + + {\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}} + + {(({\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} {\overset{~ ~}{cb cb}}_{11} + + {(({\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}})) \end{matrix} - - - - - - ((1111))$

考虑到为常向量，并且b₁为发动机的质心，则有如下的关系：considering is a constant vector, and b ₁ is the center of mass of the engine, the relationship is as follows:

${Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}} = = {\overset{~ ~}{cb cb}}_{11}^{T T} {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}} = = 00_{33 \times \times 33} - - - - - - ((1212))$

${Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} {\overset{~ ~}{cb cb}}_{11} = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {(({\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} = = {(({\overset{~ ~}{cb cb}}_{11}^{T T} {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} = = 00_{33 \times \times 33} - - - - - - ((1313))$

得到：get:

${J J}_{c c} = = {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} (({\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{cb cb}}_{11} + + {(({\overset{~ ~}{R R}}_{i i}^{{b b}_{11}}))}^{T T} {\overset{~ ~}{R R}}_{i i}^{{b b}_{11}})) - - - - - - ((1414))$

考虑到为常向量，即为常矩阵，记：considering is a constant vector, that is, is a constant matrix, remember:

${J J}_{{cb cb}_{11}} = = {m m \overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{cb cb}}_{11} - - - - - - ((1515))$

故：Therefore:

${J J}_{c c} = = {\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{cb cb}}_{11} {Σ Σ}_{i i = = 11}^{n no} {m m}_{i i} + + {J J}_{{b b}_{11}} = = m m {\overset{~ ~}{cb cb}}_{11}^{T T} {\overset{~ ~}{cb cb}}_{11} + + {AJA AJA}^{T T} = = {J J}_{{cb cb}_{11}} + + {AJA AJA}^{T T} - - - - - - ((1616))$

同理，推导出变速箱在c-x^ry^rz^r坐标系下的惯量矩阵：In the same way, the inertia matrix of the gearbox in the cx ^r y ^r z ^r coordinate system is derived:

${J J}_{c c}^{' '} = = {J J}_{{cb cb}_{22}}^{' '} + + {A A}^{' '} {J J}^{' '} {(({A A}^{' '}))}^{T T} - - - - - - ((1717))$

将发动机和变速箱在该坐标系下的惯量矩阵求和，就得到了这两个刚体相对于坐标系c-x^ry^rz^r总的惯量矩阵，再根据式(1)就得到相对于坐标系c-x^ry^rz^r总的转动惯量和惯量积；Summing the inertia matrices of the engine and gearbox in this coordinate system, the total inertia matrix of the two rigid bodies relative to the coordinate system cx ^r y ^r z ^r is obtained, and then according to the formula (1), the relative coordinate system cx ^r y ^r z ^r total moment of inertia and product of inertia;

${J J}_{c c}^{a a} = = {J J}_{c c} + + {J J}_{c c}^{' '} = = {J J}_{{cb cb}_{22}}^{' '} + + {A A}^{' '} {J J}^{' '} {(({A A}^{' '}))}^{T T} + + {J J}_{{cb cb}_{11}} + + {AJA AJA}^{T T} - - - - - - ((1818)) . .$

进一步，该汽车动力总成系统转动惯量合成方法的采用如下的步骤来完成惯量参数的输入与合成：Further, the method for synthesizing the rotational inertia of the automobile powertrain system adopts the following steps to complete the input and synthesis of the inertia parameters:

首先，在MATLAB开发平台中，编制相应的程序，开发图形用户界面，然后，将已知的数据输入到用户图形界面中即显示合成的结果，最后，为了进一步方便操作人员的使用，添加了EXCEL表格导入数据的形式，使在相应的EXCEL表格中输入或修改数据，就将数据导入到图形用户界面中。First, in the MATLAB development platform, compile the corresponding program, develop the graphical user interface, and then input the known data into the user graphical interface to display the synthesized results. Finally, in order to further facilitate the use of operators, add EXCEL The form of importing data from a form enables the data to be imported into the graphical user interface after inputting or modifying data in the corresponding EXCEL form.

本发明提供的汽车动力总成系统转动惯量合成方法，利用惯量的定义，采用矩阵形式推导，有着简洁、直观的特点，结论具有极其简明的形式，很容易利用计算机语言进行求解；本发明目的是克服实验法和大型商业软件合成方法的缺点，使其能更高效、更方便地服务于汽车动力总成系统的动力学分析和优化。The method for synthesizing moment of inertia of automobile powertrain system provided by the invention utilizes the definition of inertia and adopts matrix form to derive, which has the characteristics of simplicity and intuition, and the conclusion has an extremely concise form, which can be easily solved by computer language; the purpose of the invention is to Overcome the shortcomings of experimental methods and large-scale commercial software synthesis methods, so that they can serve the dynamic analysis and optimization of automotive powertrain systems more efficiently and conveniently.

本发明较实验方法和大型商业软件合成方法有三个显著优点：The present invention has three significant advantages compared with experimental method and large-scale commercial software synthesis method:

一，无需建立刚体的模型，只要输入它们相应参数即可进行质量、质心和转动惯量的合成；First, there is no need to establish a rigid body model, as long as their corresponding parameters are input, the mass, center of mass and moment of inertia can be synthesized;

二，合成的方法采用矩阵形式推导，得到了极为简明的结论，方便于计算机程序的实现，高效且适用性强；Second, the synthesis method is deduced in the form of a matrix, and a very concise conclusion is obtained, which is convenient for the realization of computer programs, high efficiency and strong applicability;

三，采用EXCEL表格读取数据方式，修改简单、使用方便、运行可靠，可以为非专业人士使用。该方法现已利用计算机语言开发成转动惯量合成软件，它是汽车动力总成系统的动力学分析和悬置系统的解耦优化前期处理工作。3. Using the EXCEL form to read data, it is simple to modify, easy to use, reliable in operation, and can be used by non-professionals. The method has been developed into a moment of inertia synthesis software using computer language, which is the pre-processing work of the dynamic analysis of the vehicle powertrain system and the decoupling optimization of the suspension system.

目前已经在汽车动力总成悬置系统的解耦优化中取得了良好的效果。At present, it has achieved good results in the decoupling optimization of the automotive powertrain suspension system.

附图说明Description of drawings

图1是本发明实施例提供的汽车动力总成系统转动惯量合成方法流程图；Fig. 1 is a flow chart of a method for synthesizing moment of inertia of an automobile powertrain system provided by an embodiment of the present invention;

图2是本发明实施例提供的发动机和变速箱及其坐标系；Fig. 2 is the engine and gearbox and coordinate system thereof provided by the embodiment of the present invention;

图3是本发明实施例提供的汽车动力总成系统转动惯量合成方法实施例的流程图。Fig. 3 is a flow chart of an embodiment of a method for synthesizing a moment of inertia of a powertrain system of an automobile provided by an embodiment of the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

下面结合附图及具体实施例对本发明的应用原理作进一步描述。The application principle of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

如图1所示，本发明实施例的汽车动力总成系统转动惯量合成方法包括以下步骤：As shown in Figure 1, the method for synthesizing the moment of inertia of the automobile powertrain system in the embodiment of the present invention comprises the following steps:

S101：将已知的发动机和变速箱质量、质心、惯量和欧拉角参数输入到EXCEL表中，以便于数据的导入与修改；S101: input the known mass, center of mass, inertia and Euler angle parameters of the engine and gearbox into the EXCEL table, so as to facilitate data import and modification;

S102：利用理论力学中求解质心的方法，根据发动机和变速箱的质量和质心，求出合成后总质心的坐标；由总质心的坐标建立方位与总体坐标系平行的坐标系；S102: Using the method of solving the center of mass in theoretical mechanics, according to the mass and center of mass of the engine and gearbox, find the coordinates of the combined total center of mass; establish a coordinate system whose orientation is parallel to the overall coordinate system from the coordinates of the total center of mass;

S103：将矢量用坐标阵来表示，建立不同坐标系下相同矢量的坐标阵之间的关系，线性代数的相关理论方法推导不同坐标系下惯量矩阵的关系，即建立坐标系下刚体转动惯量和惯量积关系；S103: Represent the vector with a coordinate matrix, establish the relationship between the coordinate matrix of the same vector in different coordinate systems, and use the relevant theoretical methods of linear algebra to derive the relationship of the inertia matrix in different coordinate systems, that is, establish the rigid body moment of inertia and product of inertia relationship;

S104：根据推导的矩阵表达式，利用计算机语言编制相应的程序计算合成结果。S104: According to the derived matrix expression, use computer language to compile a corresponding program to calculate the synthesis result.

本发明的具体步骤如下：Concrete steps of the present invention are as follows:

一、将已知的发动机和变速箱质量、质心、惯量和欧拉角参数输入到EXCEL表中，以便于数据的导入与修改。1. Input the known engine and gearbox mass, center of mass, inertia and Euler angle parameters into the EXCEL table to facilitate data import and modification.

二、利用理论力学中求解质心的方法，根据发动机和变速箱的质量和质心，求出合成后总质心的坐标。由总质心的坐标建立方位与总体坐标系平行的坐标系c-x^ry^rz^r，见图2。2. Using the method of solving the center of mass in theoretical mechanics, according to the mass and center of mass of the engine and gearbox, find the coordinates of the total center of mass after synthesis. The coordinate system cx ^r y ^r z ^r with orientation parallel to the global coordinate system is established from the coordinates of the total center of mass, see Figure 2.

三、将矢量用坐标阵来表示，建立不同坐标系下相同矢量的坐标阵之间的关系，线性代数的相关理论方法推导不同坐标系下惯量矩阵的关系，即建立c-x^ry^rz^r坐标系与坐标系下刚体转动惯量和惯量积关系。3. Represent the vector with a coordinate matrix, establish the relationship between the coordinate matrix of the same vector in different coordinate systems, and use the relevant theoretical methods of linear algebra to derive the relationship of the inertia matrix in different coordinate systems, that is, establish cx ^r y ^r z ^r coordinates Department with The relationship between the moment of inertia and the product of inertia of a rigid body in the coordinate system.

四、根据本发明的方法推导的极其简明结论——矩阵表达式式(18)，利用计算机语言编制相应的程序计算合成结果。Four, according to the extremely concise conclusion of method derivation of the present invention---matrix expression formula (18), utilize computer language to compile corresponding program and calculate synthetic result.

五、为了方便操作人员的使用，将本发明方法的开发出图形用户界面，界面的操作步骤如下：Five, in order to facilitate the use of operators, a graphical user interface is developed by the inventive method, and the operation steps of the interface are as follows:

(1)在EXCEL表中相应的位置输入发动机和变速箱各自的质量、质心坐标和转动惯量参数值，也可以在所开发的图形用户界面中输入相应的参数。(1) Input the respective mass, center of mass coordinates and moment of inertia parameter values of the engine and gearbox at corresponding positions in the EXCEL table, or input corresponding parameters in the developed graphical user interface.

(2)在软件的界面中点击按键“从EXCEL中导入数据”，等待约10秒钟即可将数据导入到软件中。(2) Click the button "Import data from EXCEL" in the software interface, and wait for about 10 seconds to import the data into the software.

(3)如需要修改发动机和变速箱的参数值，也可以在界面中修改。(3) If you need to modify the parameter values of the engine and gearbox, you can also modify them in the interface.

(4)点击合成，即可得到合成后的质量、质心和转动惯量。(4) Click Synthesize to get the mass, center of mass and moment of inertia after synthesis.

本发明的实施例：Embodiments of the invention:

实施例1：Example 1:

本发明利用惯量的定义，采用矩阵形式推导，有着简洁、直观的特点，其结论具有极其简明的形式，很容易利用计算机语言进行求解，本发明目的是克服实验法和大型商业软件合成方法的缺点，使其能更高效、更方便地服务于汽车动力总成系统的动力学分析和优化；The present invention utilizes the definition of inertia, adopts matrix form derivation, has the characteristics of succinct, intuitionistic, its conclusion has extremely concise form, is easy to utilize computer language to solve, and the purpose of the present invention is to overcome the shortcoming of experimental method and large-scale commercial software synthesis method , so that it can serve the dynamic analysis and optimization of the automotive powertrain system more efficiently and conveniently;

如图3所示，为实现上述目的，本发明的惯量合成的方法涉及如下三个基本原理：第一，利用惯量的定义以矩阵形式推导了不同坐标系下的惯量矩阵表达，第二，利用线性代数中的数学方法，对转动惯量矩阵进行相似变换，得到新坐标系下的转动惯量矩阵表达，第三，在同一坐标系下利用叠加原理将两个刚体的质量、质心和转动惯量进行合成，具体的技术方案如下：As shown in Figure 3, in order to achieve the above object, the method of inertia synthesis of the present invention involves following three basic principles: the first, utilize the definition of inertia to deduce the inertia matrix expression under different coordinate systems in matrix form, the 2nd, utilize The mathematical method in linear algebra is to similarly transform the moment of inertia matrix to obtain the expression of the moment of inertia matrix in the new coordinate system. Third, use the superposition principle to synthesize the mass, center of mass and moment of inertia of two rigid bodies in the same coordinate system , the specific technical scheme is as follows:

步骤一，已知：发动机的质量m，质心坐标相对于的转动惯量和惯量积为J_xx,J_yy,J_zz,J_xy,J_xz,J_yz，惯量参数坐标系相对于总体坐标系下的方位用欧拉角表示为变速箱的质量为m'，质心坐标为相对于的转动惯量和惯量积为J'_xx,J'_yy,J'_zz,J'_xy,J'_xz,J'_yz，惯量参数坐标系相对于总体坐标系下的方位用欧拉角表示为发动机和变速箱及其坐标系如图2所示，先利用理论力学的方法，根据发动机和变速箱的质量和质心，求出合成后总质心的坐标，由总质心的坐标建立方位与总体坐标系平行的坐标系c-x^ry^rz^r；Step 1, known: the mass m of the engine, the coordinates of the center of mass compared to The moment of inertia and product of inertia are J _xx , J _yy , J _zz , J _xy , J _xz , J _yz , and the orientation of the inertia parameter coordinate system relative to the global coordinate system is expressed as The mass of the gearbox is m', and the coordinates of the center of mass are compared to The moment of inertia and product of inertia are J' _xx , J' _yy , J' _zz , J' _xy , J' _xz , J' _yz , and the orientation of the inertia parameter coordinate system relative to the global coordinate system is expressed as The engine, gearbox and their coordinate system are shown in Figure 2. Firstly, using the method of theoretical mechanics, according to the mass and center of mass of the engine and gearbox, the coordinates of the combined total center of mass are obtained, and the orientation and overall coordinates are established from the coordinates of the total center of mass The parallel coordinate system cx ^r y ^r z ^r ;

步骤二，然后推导出发动机相对于总质心坐标系的惯量矩阵，同理可以得到变速箱相对于总质心坐标系的惯量矩阵：Step 2, and then derive the inertia matrix of the engine relative to the total center of mass coordinate system, and similarly, the inertia matrix of the gearbox relative to the total center of mass coordinate system can be obtained:

发动机的惯量矩阵为：The inertia matrix of the engine is:

由式(3)，根据(6)和(7)得到：From formula (3), according to (6) and (7):

由图1，有矢量关系：From Figure 1, there is a vector relationship:

得到：get:

故：Therefore:

同理，可以推导出变速箱在c-x^ry^rz^r坐标系下的惯量矩阵：In the same way, the inertia matrix of the gearbox in the cx ^r y ^r z ^r coordinate system can be derived:

采用矩阵形式推导的结论式(18)具有极其简明的形式，可以极大地方便计算机语言的实现，因此，还需根据推导的结论，采用如下的步骤来完成惯量参数的输入与合成；The conclusion formula (18) deduced in matrix form has an extremely concise form, which can greatly facilitate the realization of computer language. Therefore, according to the deduced conclusion, the following steps are used to complete the input and synthesis of inertia parameters;

首先，在MATLAB开发平台中，编制相应的程序，开发图形用户界面，然后，将已知的数据输入到用户图形界面中即可显示合成的结果，最后，为了进一步方便操作人员的使用，添加了EXCEL表格导入数据的形式，使其可以在相应的EXCEL表格中输入或修改数据，就可以将数据导入到图形用户界面中。First, in the MATLAB development platform, compile the corresponding program, develop the graphical user interface, and then input the known data into the user graphical interface to display the synthesized results. Finally, in order to further facilitate the use of operators, add The form of importing data from an EXCEL form makes it possible to input or modify data in the corresponding EXCEL form, and then the data can be imported into the graphical user interface.

本发明与传统的实验方法和大型商业软件合成方法有三个显著优点，The present invention has three significant advantages with traditional experimental method and large-scale commercial software synthesis method,

三，采用EXCEL表格读取数据方式，修改简单、使用方便、运行可靠，可以为非专业人士使用。本发明现已利用计算机语言开发成转动惯量合成软件，它是汽车动力总成系统的动力学分析和悬置系统的解耦优化前期处理工作。3. Using the EXCEL form to read data, it is simple to modify, easy to use, reliable in operation, and can be used by non-professionals. The present invention has been developed into moment of inertia synthesis software by using computer language, which is the preliminary processing work of dynamic analysis of automobile power assembly system and decoupling optimization of suspension system.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims

1. a powertrain system of automobile moment of inertia synthetic method, is characterized in that, this powertrain system of automobile moment of inertia synthetic method comprises the following steps:

Step 1, is input to known engine and wheel box quality, barycenter, inertia and Eulerian angle parameter in EXCEL table, so that the importing of data and modification;

Step 2, utilizes the method that solves barycenter in theoretical mechanics, according to the quality of engine and wheel box and barycenter, obtains the coordinate of synthetic rear total barycenter; By the coordinate of total barycenter, set up the orientation coordinate system parallel with global coordinate;

Step 3, vector is represented by coordinate battle array, set up the relation between the coordinate battle array of identical vector under different coordinates, under the correlation theory method derivation different coordinates of linear algebra, the relation of inertia matrix, sets up solid moment of inertia and product of inertia relation under coordinate system;

Step 4, according to the matrix expression of deriving

J_{c}^{a} = J_{c} + J_{c}^{'} = J_{c b_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T},

Utilize computerese to work out corresponding program and calculate synthetic result.

2. powertrain system of automobile moment of inertia synthetic method as claimed in claim 1, is characterized in that, the concrete steps of this powertrain system of automobile moment of inertia synthetic method are as follows:

Step 1, known engine and wheel box quality, barycenter, inertia and Eulerian angle parameter are input in EXCEL table, so that the importing of data and modification;

Step 2, utilize the method that solves barycenter in theoretical mechanics, according to the quality of engine and wheel box and barycenter, obtain synthetic after the coordinate of total barycenter; By the coordinate of total barycenter, set up the orientation coordinate system c-x parallel with global coordinate ^ry ^rz ^r;

Step 3, vector is represented by coordinate battle array, set up the relation between the coordinate battle array of identical vector under different coordinates, under the correlation theory method derivation different coordinates of linear algebra, the relation of inertia matrix, sets up c-x ^ry ^rz ^rcoordinate system with solid moment of inertia and product of inertia relation under coordinate system;

Step 4, according to matrix expression

J_{c}^{a} = J_{c} + J_{c}^{'} = J_{c b_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T},

3. powertrain system of automobile moment of inertia synthetic method as claimed in claim 1, is characterized in that, the matrix expression derivation of this powertrain system of automobile moment of inertia synthetic method is as follows:

The first step, known: the quality m of engine, center-of-mass coordinate with respect to moment of inertia and product of inertia be J _xx, J _yy, J _zz, J _xy, J _xz, J _yz, inertia parameter coordinate system is expressed as by Eulerian angle with respect to the orientation under global coordinate the quality of wheel box is m', and center-of-mass coordinate is with respect to moment of inertia and product of inertia be J' _xx, J' _yy, J' _zz, J' _xy, J' _xz, J' _yz, inertia parameter coordinate system is expressed as by Eulerian angle with respect to the orientation under global coordinate first utilize the method for theoretical mechanics, according to the quality of engine and wheel box and barycenter, obtain the coordinate of synthetic rear total barycenter, by the coordinate of total barycenter, set up the orientation coordinate system c-x parallel with global coordinate ^ry ^rz ^r;

Second step, then derives engine with respect to the inertia matrix of total geocentric coordinate system, in like manner can obtain wheel box with respect to the inertia matrix of total geocentric coordinate system:

The inertia matrix of engine is:

J = (\begin{matrix} J_{xx} & - J_{xy} & - J_{xz} \\ - J_{xy} & J_{yy} & - J_{yz} \\ - J_{xz} & - J_{yz} & J_{zz} \end{matrix}) - - - (1)

Because rigid body is special system of particles, to establish rigid body 1 and formed by the system of particles of n particle, i particle is R _i, i particle with respect to coordinate is its coordinate square formation is:

{\tilde{R}}_{i}^{c_{1}} = (\begin{matrix} 0 & z_{i} & - y_{i} \\ - z_{i} & 0 & x_{i} \\ y_{i} & - x_{i} & 0 \end{matrix}) - - - (2)

According to the definition of inertia, inertia matrix is expressed as with system of particles:

\begin{matrix} J = Σ_{i = 1}^{n} m_{i} (\begin{matrix} {y_{i}}^{2} + {z_{i}}^{2} & - x_{i} y_{i} & - x_{i} z_{i} \\ - x_{i} y_{i} & {x_{i}}^{2} + {z_{i}}^{2} & - y_{i} z_{i} \\ - x_{i} z_{i} & - y_{i} z_{i} & {x_{i}}^{2} + {y_{i}}^{2} \end{matrix}) = Σ_{i = 1}^{n} m_{i} {(\begin{matrix} 0 & z_{i} & - y_{i} \\ - z_{i} & 0 & x_{i} \\ y_{i} & - x_{i} & 0 \end{matrix})}^{T} (\begin{matrix} 0 & z_{i} & - y_{i} \\ - z_{i} & 0 & x_{i} \\ y_{i} & - x_{i} & 0 \end{matrix}) \\ = Σ_{i = 1}^{n} m_{i} {({\tilde{R}}_{i}^{c_{1}})}^{T} {\tilde{R}}_{i}^{c_{1}} \end{matrix} - - - (3)

According to the relation between coordinate system, consider that Eulerian angle are known, therefore with respect to direct cosine matrix be:

Can be by formula (4) under coordinate system, the transposition of the coordinate battle array of i particle, coordinate square formation and coordinate square formation is:

R_{i}^{b_{1}} = A^{b_{1} c_{1}} R_{i}^{c_{1}} = A R_{i}^{c_{1}} - - - (5)

{\tilde{R}}_{i}^{b_{1}} = A^{b_{1} c_{1}} {\tilde{R}}_{i}^{c_{1}} A^{c_{1} b_{1}} = A {\tilde{R}}_{i}^{c_{1}} A^{T} - - - (6)

{({\tilde{R}}_{i}^{b_{1}})}^{T} = {(A | {\tilde{R}}_{i}^{c_{1}} A^{T})}^{T} = A {({\tilde{R}}_{i}^{c_{1}})}^{T} A^{T} - - - (7)

By formula (3), according to (6) and (7), obtain:

J_{b_{1}} = Σ_{i = 1}^{n} m_{i} {({\tilde{R}}_{i}^{b_{1}})}^{T} {\tilde{R}}_{i}^{b_{1}} = Σ_{i = 1}^{n} m_{i} A {({\tilde{R}}_{i}^{C_{1}})}^{T} A^{T} A {\tilde{R}}_{i}^{c_{1}} A^{T} = A (Σ_{i = 1}^{n} m_{i} {({\tilde{R}}_{i}^{c_{1}})}^{T} {\tilde{R}}_{i}^{c_{1}}) A^{T} = {AJA}^{T} - - - (8)

There is vector correlation:

\overset{&RightArrow;}{{cR}_{i}} = \overset{&RightArrow;}{{cb}_{1}} + - {\overset{&RightArrow;}{b_{1} R}}_{i} - - (9)

Equally, also there is same corresponding relation in their coordinate square formation:

{\tilde{R}}_{i}^{c} = {\tilde{cb}}_{1} + {\tilde{R}}_{i}^{b_{1}} - - - (10)

\begin{matrix} J_{c} = Σ_{i = 1}^{n} m_{i} {({\tilde{R}}_{i}^{c})}^{T} {\tilde{R}}_{i}^{c} = Σ_{i = 1}^{n} m_{i} {({\tilde{cb}}_{1} + {\tilde{R}}_{i}^{b_{1}})}^{T} ({\tilde{cb}}_{1} + {\tilde{R}}_{i}^{b_{1}}) \\ = Σ_{i = 1}^{n} m_{i} ({\tilde{cb}}_{1}^{T} {\tilde{cb}}_{1} + {\tilde{cb}}_{1}^{T} {\tilde{R}}_{i}^{b_{1}} + {({\tilde{R}}_{i}^{b_{1}})}^{T} {\tilde{cb}}_{1} + {({\tilde{R}}_{i}^{b_{1}})}^{T} {\tilde{R}}_{i}^{b_{1}}) \end{matrix} - - - (11)

Consider for constant vector, and b ₁for the barycenter of engine, there is following relation:

Σ_{i = 1}^{n} m_{i} {\tilde{cb}}_{1}^{T} {\tilde{R}}_{i}^{b_{1}} = {\tilde{cb}}_{1}^{T} Σ_{i = 1}^{n} m_{i} {\tilde{R}}_{i}^{b_{1}} = 0_{3 \times 3} - - - (12)

Σ_{i = 1}^{n} m_{i} {({\tilde{R}}_{i}^{b_{1}})}^{T} {\tilde{cb}}_{1} = Σ_{i = 1}^{n} m_{i} {({\tilde{cb}}_{1}^{T} {\tilde{R}}_{i}^{b_{1}})}^{T} = {({\tilde{cb}}_{1}^{T} Σ_{i = 1}^{n} m_{i} {\tilde{R}}_{i}^{b_{1}})}^{T} = 0_{3 \times 3} - - - (13)

Obtain:

J_{c} = Σ_{i = 1}^{n} m_{i} ({\tilde{cb}}_{1}^{T} {\tilde{cb}}_{1} + {({\tilde{R}}_{i}^{b_{1}})}^{T} {\tilde{R}}_{i}^{b_{1}}) - - - (14)

Consider for constant vector, for normal matrix, note:

J_{{cb}_{1}} = {m \tilde{cb}}_{1}^{T} {\tilde{cb}}_{1} - - - (15)

Therefore:

J_{c} = {\tilde{cb}}_{1}^{T} {\tilde{cb}}_{1} Σ_{i = 1}^{n} m_{i} + J_{b_{1}} = m {\tilde{cb}}_{1}^{T} {\tilde{cb}}_{1} + {AJA}^{T} = J_{{cb}_{1}} + {AJA}^{T}

(16) in like manner, derive wheel box at c-x ^ry ^rz ^rinertia matrix under coordinate system:

J_{c}^{'} = J_{{cb}_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} - - - (17)

The inertia matrix summation under this coordinate system by engine and wheel box, has just obtained these two rigid bodies with respect to coordinate system c-x ^ry ^rz ^rtotal inertia matrix, more just obtain with respect to coordinate system c-x according to formula (1) ^ry ^rz ^rtotal moment of inertia and product of inertia;

J_{c}^{a} = J_{c} + J_{c}^{'} = J_{{cb}_{2}}^{'} + A^{'} J^{'} {(A^{'})}^{T} + J_{{cb}_{1}} + {AJA}^{T} - - - (18) .

4. powertrain system of automobile moment of inertia synthetic method as claimed in claim 3, is characterized in that, the following step of employing of this powertrain system of automobile moment of inertia synthetic method completes the input of inertia parameter with synthetic:

First, in MATLAB development platform, work out corresponding program, development graph user interface, then, known data are input to and in graphical interface of user, show synthetic result, finally, in order to further facilitate operating personnel's use, added the form of Microsoft Excel importing data, make input or Update Table in corresponding Microsoft Excel, just by data importing in graphic user interface.