CN104123411A - Automobile powertrain system rotational inertia synthetic method - Google Patents

Abstract

The invention discloses an automobile powertrain system rotational inertia synthetic method. The method comprises the steps of inputting the known parameters including the mass, center of mass, inertia and eulerian angle of an engine and a gear box into an EXCEL so as to facilitate data import and correction; obtaining the coordinates of the main center of mass obtained after synthesis according to the mass and center of mass of the engine and the gearbox by means of the method for solving the center of mass in theoretical mechanics; establishing a coordinate system the orientation of which is parallel to that of a main coordinate system according to the coordinates of the main center of mass; expressing vectors with a coordinate matrix, establishing the relationship between the coordinate matrixes of the same vectors under different coordinate systems, and deducing the relationship between inertia matrixes under different coordinate systems by means of correlation theoretical methods of the linear algebra, namely establishing the relationship between rigid body rotation inertia and the product of inertia under different coordinate systems; calculating a synthesis result by means of a corresponding computer language compile program according to a deduced matrix expression. According to the method, deduction is conducted in the matrix form, briefness and visualization are achieved, the conclusion is in a quite brief form, and a solution can be obtained easily by means of the computer language.

Description

A kind of powertrain system of automobile moment of inertia synthetic method

Technical field

The invention belongs to AE field, relate in particular to a kind of powertrain system of automobile moment of inertia synthetic method.

Background technology

The moment of inertia of object is a very important parameter in Machine Design, and correctly obtaining of it is the prerequisite that mechanical system is carried out statics, kinematics analysis and dynamic analysis design.

In powertrain system of automobile (system being formed by engine, wheel box and suspension members etc.), engine and wheel box are (because rigidity is large, can be considered rigid body) general from different producers, producer can provide corresponding inertial parameter (quality, barycenter and moment of inertia).But, in powertrain system of automobile, need first quality, barycenter and the moment of inertia of engine and two objects of wheel box to be synthesized, obtain generated data and just can be convenient to for dynamic analysis.The quality of many rigid bodies and barycenter synthetic comparatively simple, and moment of inertia is synthetic, the inertia parameter providing due to producer provides (generally to cross barycenter, with respect to the Eulerian angle of car load coordinate system, representing) under different coordinates.Therefore, this gives and syntheticly to have caused certain difficulty, therefore what also introduce herein is the synthetic method of moment of inertia.

At present, the synthetic method of moment of inertia has two kinds: a kind of is method by experiment, and another kind is by highly professional large scale business software (as ADAMS), sets up corresponding model in software, utilizes relevant order to synthesize.

The synthetic method of large scale business software also has very large defect, and it not only needs operating personnel skillfully to use this software, and will possess certain professional technique ability, the more important thing is and need in software, set up corresponding model.Meanwhile, synthetic moment of inertia is with respect to barycenter, so that the dynamic analysis of system.Therefore, by software, synthesize and need to carry out twice, just have the meaning of its reality.First single sintering finds barycenter, and then it is synthetic as benchmark carries out secondary to take this barycenter, and the moment of inertia obtaining is just with respect to this total barycenter.

Obviously, the method for experiment, takes time and effort cost gold, but and by the synthetic complicated operation of large scale business software, level professional technology is had to certain requirement, is not easy to the use of non-technical personnel.In fact, for engine and wheel box, producer provides respectively experiment resulting barycenter, center-of-mass coordinate and these parameters of moment of inertia, just on original basis, superpose (although having the problem of Eulerian angle), the method that at all there is no need again to test is carried out the synthetic of these parameters.

Therefore, in the urgent need to finding a kind of moment of inertia synthetic method that is applicable to powertrain system of automobile, need not set up model, only need input engine and wheel box parameter separately, then utilize computer program to realize quality, barycenter and moment of inertia synthetic.

Summary of the invention

The object of the embodiment of the present invention is to provide a kind of powertrain system of automobile moment of inertia synthetic method, is intended to solve the complicated operation that existing moment of inertia synthetic method exists, waste time and energy, and the problem that running cost is high.

The embodiment of the present invention is achieved in that a kind of powertrain system of automobile moment of inertia synthetic method, and 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 $J_c^a=J_c+J_c^{\′}=J_{c{b}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T,$ Utilize computerese to work out corresponding program and calculate synthetic result.

Further, 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 $J_c^a=J_c+J_c^{\′}=J_{c{b}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T,$ Utilize computerese to work out corresponding program and calculate synthetic result.

Further, 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:

$J=\left(\begin{array}{ccc}{J}_{\mathrm{xx}}& -J_{\mathrm{xy}}& -J_{\mathrm{xz}}\\ -J_{\mathrm{xy}}& J_{\mathrm{yy}}& -J_{\mathrm{yz}}\\ -J_{\mathrm{xz}}& -J_{\mathrm{yz}}& J_{\mathrm{zz}}\end{array}\right)---\left(1\right)$

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:

${\tilde{R}}_i^{c_1}=\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)---\left(2\right)$

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

$\begin{array}{c}J=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i\left(\begin{array}{ccc}{y_i}^2+{z_i}^2& -x_i{y}_i& -x_i{z}_i\\ -x_i{y}_i& {x_i}^2+{z_i}^2& -y_i{z}_i\\ -x_i{z}_i& -y_i{z}_i& {x_i}^2+{y_i}^2\end{array}\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)}^T\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{c_1}\right)}^T{\tilde{R}}_i^{c_1}\end{array}---\left(3\right)$

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:

$R_i^{b_1}=A^{b_1{c}_1}{R}_i^{c_1}=A{R}_i^{c_1}---\left(5\right)$

${\tilde{R}}_i^{b_1}=A^{b_1{c}_1}{\tilde{R}}_i^{c_1}{A}^{c_1{b}_1}=A{\tilde{R}}_i^{c_1}{A}^T---\left(6\right)$

${\left({\tilde{R}}_i^{b_1}\right)}^T={\left(A\right|{\tilde{R}}_i^{c_1}{A}^T)}^T=A{\left({\tilde{R}}_i^{c_1}\right)}^T{A}^T---\left(7\right)$

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

$J_{b_1}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_{i}A{\left({\tilde{R}}_i^{C_1}\right)}^T{A}^{T}A{\tilde{R}}_i^{c_1}{A}^T=A\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{c_1}\right)}^T{\tilde{R}}_i^{c_1}\right)A^T={\mathrm{AJA}}^T---\left(8\right)$

There is vector correlation:

$\stackrel{\→}{{\mathrm{cR}}_i}=\stackrel{\→}{{\mathrm{cb}}_1}+-{\stackrel{\→}{b_{1}R}}_i--\left(9\right)$

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

${\tilde{R}}_i^c={\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1}---\left(10\right)$

$\begin{array}{c}{J}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^c\right)}^T{\tilde{R}}_i^c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{({\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1})}^T({\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1})\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i({\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}+{\left({\tilde{R}}_i^{b_1}\right)}^T{\widetilde{\mathrm{cb}}}_1+{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1})\end{array}---\left(11\right)$

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

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}={\widetilde{\mathrm{cb}}}_1^T\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\tilde{R}}_i^{b_1}=0_{3\×3}---\left(12\right)$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{b_1}\right)}^T{\widetilde{\mathrm{cb}}}_1=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}\right)}^T={\left({\widetilde{\mathrm{cb}}}_1^T\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\tilde{R}}_i^{b_1}\right)}^T=0_{3\×3}---\left(13\right)$

Obtain:

$J_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i({\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1})---\left(14\right)$

Consider for constant vector, for normal matrix, note:

$J_{{\mathrm{cb}}_1}={m\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1---\left(15\right)$

Therefore:

$J_c={\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i+J_{b_1}=m{\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\mathrm{AJA}}^T=J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T---\left(16\right)$

In like manner, derive wheel box at c-x ^ry ^rz ^rinertia matrix under coordinate system:

$J_c^{\′}=J_{{\mathrm{cb}}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T---\left(17\right)$

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;

$J_c^a=J_c+J_c^{\′}=J_{{\mathrm{cb}}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T---\left(18\right).$

Further, the input that the following step of employing of this powertrain system of automobile moment of inertia synthetic method completes inertia parameter is 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.

Powertrain system of automobile moment of inertia synthetic method provided by the invention, utilizes the definition of inertia, adopts matrix form to derive, and has succinctly, feature intuitively, and conclusion has extremely simple and clear form, is easy to utilize computerese to solve; The present invention seeks to overcome the shortcoming of experimental method and large scale business software synthetic method, can serve more efficiently, more easily dynamic analysis and the optimization of powertrain system of automobile.

The present invention has three remarkable advantages compared with experimental technique and large scale business software synthetic method:

One, without the model of setting up rigid body, as long as their relevant parameters of input can carry out the synthetic of quality, barycenter and moment of inertia;

Two, synthetic method adopts matrix form to derive, and has obtained very simple and clear conclusion, is convenient to the realization of computer program, efficient and applicability is strong;

Three, adopt Microsoft Excel reading out data mode, revise simple, easy to use, reliablely, can use for layman.The method has now utilized computerese to be developed to moment of inertia composite software, and it is that the dynamic analysis of powertrain system of automobile and the decoupling zero optimization of suspension system are dealt with the work in earlier stage.

At present in the decoupling zero optimization of automobile power assembly suspension system, obtained good effect.

Accompanying drawing explanation

Fig. 1 is the powertrain system of automobile moment of inertia synthetic method process flow diagram that the embodiment of the present invention provides;

Fig. 2 is engine and wheel box and the coordinate system thereof that the embodiment of the present invention provides;

Fig. 3 is the process flow diagram of the powertrain system of automobile moment of inertia synthetic method embodiment that provides of the embodiment of the present invention.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.

Below in conjunction with drawings and the specific embodiments, application principle of the present invention is further described.

As shown in Figure 1, the powertrain system of automobile moment of inertia synthetic method of the embodiment of the present invention comprises the following steps:

S101: 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;

S102: utilize the method that solves barycenter in 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 parallel with global coordinate;

S103: 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;

S104: according to the matrix expression of deriving, utilize computerese to work out corresponding program and calculate synthetic result.

Concrete steps of the present invention are as follows:

One, 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.

Two, utilize the method that solves barycenter in 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, see Fig. 2.

Three, 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.

Four, extremely terse conclusion---the matrix expression formula (18) that the method according to this invention is derived, utilizes computerese to work out corresponding program and calculates synthetic result.

Five, for handled easily personnel's use, by the graphic user interface of developing of the inventive method, the operation steps at interface is as follows:

(1) corresponding Position input engine and wheel box quality, center-of-mass coordinate and moment of inertia parameter value separately in EXCEL table also can be inputted corresponding parameter in developed graphic user interface.

(2) in the interface of software, click keys " imports data " from EXCEL, waits for that approximately 10 seconds can be by data importing in software.

(3) as revised the parameter value of engine and wheel box, also can in interface, revise.

(4) click and synthesize, quality, barycenter and moment of inertia after can being synthesized.

Embodiments of the invention:

Embodiment 1:

The present invention utilizes the definition of inertia, employing matrix form is derived, have succinctly, feature intuitively, its conclusion has extremely simple and clear form, be easy to utilize computerese to solve, the present invention seeks to overcome the shortcoming of experimental method and large scale business software synthetic method, can serve more efficiently, more easily dynamic analysis and the optimization of powertrain system of automobile;

As shown in Figure 3, for achieving the above object, the synthetic method of inertia of the present invention relates to following three ultimate principles: first, the definition that utilizes inertia is expressed with the matrix form inertia matrix under different coordinates of having derived, second, utilize the mathematical method in linear algebra, moment of inertia matrix is carried out to similarity transformation, the moment of inertia matrix obtaining under new coordinate system is expressed, the 3rd, under the same coordinate system, utilize superposition principle that the quality of two rigid bodies, barycenter and moment of inertia are synthesized, concrete technical scheme is as follows:

Step 1, 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 engine and wheel box and coordinate system thereof as shown in Figure 2, 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;

Step 2, 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:

$J=\left(\begin{array}{ccc}{J}_{\mathrm{xx}}& -J_{\mathrm{xy}}& -J_{\mathrm{xz}}\\ -J_{\mathrm{xy}}& J_{\mathrm{yy}}& -J_{\mathrm{yz}}\\ -J_{\mathrm{xz}}& -J_{\mathrm{yz}}& J_{\mathrm{zz}}\end{array}\right)---\left(1\right)$

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:

${\tilde{R}}_i^{c_1}=\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)---\left(2\right)$

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

$\begin{array}{c}J=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i\left(\begin{array}{ccc}{y_i}^2+{z_i}^2& -x_i{y}_i& -x_i{z}_i\\ -x_i{y}_i& {x_i}^2+{z_i}^2& -y_i{z}_i\\ -x_i{z}_i& -y_i{z}_i& {x_i}^2+{y_i}^2\end{array}\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)}^T\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{c_1}\right)}^T{\tilde{R}}_i^{c_1}\end{array}---\left(3\right)$

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:

$R_i^{b_1}=A^{b_1{c}_1}{R}_i^{c_1}=A{R}_i^{c_1}---\left(5\right)$

${\tilde{R}}_i^{b_1}=A^{b_1{c}_1}{\tilde{R}}_i^{c_1}{A}^{c_1{b}_1}=A{\tilde{R}}_i^{c_1}{A}^T---\left(6\right)$

${\left({\tilde{R}}_i^{b_1}\right)}^T={\left(A\right|{\tilde{R}}_i^{c_1}{A}^T)}^T=A{\left({\tilde{R}}_i^{c_1}\right)}^T{A}^T---\left(7\right)$

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

$J_{b_1}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_{i}A{\left({\tilde{R}}_i^{C_1}\right)}^T{A}^{T}A{\tilde{R}}_i^{c_1}{A}^T=A\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{c_1}\right)}^T{\tilde{R}}_i^{c_1}\right)A^T={\mathrm{AJA}}^T---\left(8\right)$

By Fig. 1, there is vector correlation:

$\stackrel{\→}{{\mathrm{cR}}_i}=\stackrel{\→}{{\mathrm{cb}}_1}+-{\stackrel{\→}{b_{1}R}}_i--\left(9\right)$

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

${\tilde{R}}_i^c={\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1}---\left(10\right)$

$\begin{array}{c}{J}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^c\right)}^T{\tilde{R}}_i^c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{({\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1})}^T({\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1})\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i({\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}+{\left({\tilde{R}}_i^{b_1}\right)}^T{\widetilde{\mathrm{cb}}}_1+{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1})\end{array}---\left(11\right)$

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

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}={\widetilde{\mathrm{cb}}}_1^T\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\tilde{R}}_i^{b_1}=0_{3\×3}---\left(12\right)$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{b_1}\right)}^T{\widetilde{\mathrm{cb}}}_1=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}\right)}^T={\left({\widetilde{\mathrm{cb}}}_1^T\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\tilde{R}}_i^{b_1}\right)}^T=0_{3\×3}---\left(13\right)$

Obtain:

$J_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i({\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1})---\left(14\right)$

Consider for constant vector, for normal matrix, note:

$J_{{\mathrm{cb}}_1}={m\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1---\left(15\right)$

Therefore:

$J_c={\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i+J_{b_1}=m{\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\mathrm{AJA}}^T=J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T---\left(16\right)$

In like manner, can derive wheel box at c-x ^ry ^rz ^rinertia matrix under coordinate system:

$J_c^{\′}=J_{{\mathrm{cb}}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T---\left(17\right)$

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;

$J_c^a=J_c+J_c^{\′}=J_{{\mathrm{cb}}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T---\left(18\right).$

The conclusion formula (18) that adopts matrix form to derive has extremely simple and clear form, can greatly facilitate the realization of computerese, therefore, also needs according to the conclusion of deriving, and adopts following step complete the input of inertia parameter and synthesize;

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

The present invention and traditional experimental technique and large scale business software synthetic method have three remarkable advantages,

One, without the model of setting up rigid body, as long as their relevant parameters of input can carry out the synthetic of quality, barycenter and moment of inertia;

Two, synthetic method adopts matrix form to derive, and has obtained very simple and clear conclusion, is convenient to the realization of computer program, efficient and applicability is strong;

Three, adopt Microsoft Excel reading out data mode, revise simple, easy to use, reliablely, can use for layman.The present invention has now utilized computerese to be developed to moment of inertia composite software, and it is that the dynamic analysis of powertrain system of automobile and the decoupling zero optimization of suspension system are dealt with the work in earlier stage.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any modifications of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.

Claims (4)

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 $J_c^a=J_c+J_c^{\′}=J_{c{b}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T,$ 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 $J_c^a=J_c+J_c^{\′}=J_{c{b}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T,$ Utilize computerese to work out corresponding program and calculate synthetic result.

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:

$J=\left(\begin{array}{ccc}{J}_{\mathrm{xx}}& -J_{\mathrm{xy}}& -J_{\mathrm{xz}}\\ -J_{\mathrm{xy}}& J_{\mathrm{yy}}& -J_{\mathrm{yz}}\\ -J_{\mathrm{xz}}& -J_{\mathrm{yz}}& J_{\mathrm{zz}}\end{array}\right)---\left(1\right)$

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:

${\tilde{R}}_i^{c_1}=\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)---\left(2\right)$

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

$\begin{array}{c}J=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i\left(\begin{array}{ccc}{y_i}^2+{z_i}^2& -x_i{y}_i& -x_i{z}_i\\ -x_i{y}_i& {x_i}^2+{z_i}^2& -y_i{z}_i\\ -x_i{z}_i& -y_i{z}_i& {x_i}^2+{y_i}^2\end{array}\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)}^T\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{c_1}\right)}^T{\tilde{R}}_i^{c_1}\end{array}---\left(3\right)$

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:

$R_i^{b_1}=A^{b_1{c}_1}{R}_i^{c_1}=A{R}_i^{c_1}---\left(5\right)$

${\tilde{R}}_i^{b_1}=A^{b_1{c}_1}{\tilde{R}}_i^{c_1}{A}^{c_1{b}_1}=A{\tilde{R}}_i^{c_1}{A}^T---\left(6\right)$

${\left({\tilde{R}}_i^{b_1}\right)}^T={\left(A\right|{\tilde{R}}_i^{c_1}{A}^T)}^T=A{\left({\tilde{R}}_i^{c_1}\right)}^T{A}^T---\left(7\right)$

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

$J_{b_1}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_{i}A{\left({\tilde{R}}_i^{C_1}\right)}^T{A}^{T}A{\tilde{R}}_i^{c_1}{A}^T=A\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{c_1}\right)}^T{\tilde{R}}_i^{c_1}\right)A^T={\mathrm{AJA}}^T---\left(8\right)$

There is vector correlation:

$\stackrel{\→}{{\mathrm{cR}}_i}=\stackrel{\→}{{\mathrm{cb}}_1}+-{\stackrel{\→}{b_{1}R}}_i--\left(9\right)$

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

${\tilde{R}}_i^c={\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1}---\left(10\right)$

$\begin{array}{c}{J}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^c\right)}^T{\tilde{R}}_i^c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{({\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1})}^T({\widetilde{\mathrm{cb}}}_1+{\tilde{R}}_i^{b_1})\\ =\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i({\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}+{\left({\tilde{R}}_i^{b_1}\right)}^T{\widetilde{\mathrm{cb}}}_1+{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1})\end{array}---\left(11\right)$

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

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}={\widetilde{\mathrm{cb}}}_1^T\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\tilde{R}}_i^{b_1}=0_{3\×3}---\left(12\right)$

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\tilde{R}}_i^{b_1}\right)}^T{\widetilde{\mathrm{cb}}}_1=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\left({\widetilde{\mathrm{cb}}}_1^T{\tilde{R}}_i^{b_1}\right)}^T={\left({\widetilde{\mathrm{cb}}}_1^T\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i{\tilde{R}}_i^{b_1}\right)}^T=0_{3\×3}---\left(13\right)$

Obtain:

$J_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i({\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\left({\tilde{R}}_i^{b_1}\right)}^T{\tilde{R}}_i^{b_1})---\left(14\right)$

Consider for constant vector, for normal matrix, note:

$J_{{\mathrm{cb}}_1}={m\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1---\left(15\right)$

Therefore:

$J_c={\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{m}_i+J_{b_1}=m{\widetilde{\mathrm{cb}}}_1^T{\widetilde{\mathrm{cb}}}_1+{\mathrm{AJA}}^T=J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T$

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

$J_c^{\′}=J_{{\mathrm{cb}}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T---\left(17\right)$

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;

$J_c^a=J_c+J_c^{\′}=J_{{\mathrm{cb}}_2}^{\′}+A^{\′}{J}^{\′}{\left(A^{\′}\right)}^T+J_{{\mathrm{cb}}_1}+{\mathrm{AJA}}^T---\left(18\right).$

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.