CN105740485A - Motion simulation method and system of mechanical system mechanics - Google Patents

Abstract

The invention provides a motion simulation method and system of a mechanical system mechanics. The method comprises the following steps: firstly setting a condition for establishing a mechanics equation, and then acquiring a Jacobian matrix required for establishing the mechanics equation according to the set condition, and then establishing the mechanics equation, using a position of each object as to-be-solved unknown number of the mechanics equation; and finally solving the mechanics equation to acquire the position of each object at each moment, and constructing a mechanical system animated image according to the position information of each object at each moment, and displaying the mechanical system animated image. Through the adoption of the method provided by the invention, the motion of the mechanical system mechanics can be simulated and the mechanical system can be conveniently and fast designed.

Description

The movement simulating method of a kind of mechanical system mechanics and system

Technical field

The invention belongs to mechanics and field of mechanical technique, be specifically related to movement simulating method and the system of a kind of mechanical system mechanics.

Background technology

From the 70-80 age in 20th century, traditional CAD/CAE/CAM technology initially enters the practical stage, they are primarily upon product component quality and performance, by adopting software or the instrument of structural design, project analysis and manufacture process control, to reach design and to manufacture the purpose of high-quality parts.Specifically, traditional cad technique, based on 3D solid geometric modeling technology, supports detailed construction design and the morphological analysis of product component.Traditional CAE technology refers mainly to application finite element software, completes the functional analysis problem such as the structural analysis of product component, heat analysis, vibration characteristics.Traditional CAM technology is intended to the manufacturability improving product component, it is provided that the aspects such as lathe, robot, casting process, punching course, forging processing are better controlled.In in the past few decades, traditional CAD/CAE/CAM technology is widely used at main industrial circle (automobile, aviation, universal machine, mechano-electronic etc.), and achieves huge effect.With auto industry, in 5 years of 1995-1999, component failure rate reduces 40%, accompanies with it, is the corresponding reduction of product development and manufacturing cost.

The Kinematic Simulation Technology of mechanical system mechanics is as a kind of Virtual Prototype Technique and CAD/CAE/CAM technology, to the design/analysis/manufacture of system, to improve product total quality and performance and to reduce exploitation and manufacturing cost, the quality and the performance that improve parts produce well effect.

The product of Current Domestic is mainly still fixed against experiment and experience, for using emulation mode to be designed or fewer, currently, the theme becoming machinery manufacturing industry development safe and stable, energy-conservation, for better manufacture, it is very important for carrying out dynamics simulation for system, and this contributes to being designed for engineering goods and revising, and then carries out production and sales.Domestic for dynamic-simulation method urgent need independent development capability.How to carry out the exploitation of own emulation mode, and it is put into industrial quarters carry out learning and develop, be a current research emphasis, and be badly in need of the important step developed.

Summary of the invention

It is an object of the invention to propose movement simulating method and the system of a kind of mechanical system mechanics, it is possible to the motion of mechanical system mechanics is emulated and designs mechanical system quickly and easily.

In order to solve above-mentioned technical problem, the present invention provides the movement simulating method of a kind of mechanical system mechanics, comprises the following steps:

First, set the condition setting up kinetics equation, including

(1) set the material parameter (elastic modelling quantity, density etc.) of each object in mechanical system, dimensional parameters (length, width, highly) and initial position parameters；

(2) selecting in mechanical system the connected mode between each object to set up mechanical system model, connected mode includes rotating hinge, mobile hinge, fixed joint etc.；

(3) external force that given mechanical system model is subject to；

(4) time of mechanical system mechanical analysis and the time step calculated are set as required.

Then, obtain the Jacobian matrix set up required for kinetics equation according to the condition of aforementioned setting, then build kinetics equation, using the position of each object as kinetics equation unknown number to be solved；

Finally, kinetics equation is solved, it is thus achieved that in mechanical system, each object is in the position of each moment (i.e. each step-length)；Build mechanical system animated image according to each object at the positional information in each moment and show.So allowing user have one to recognize clearly, it is judged that whether this design meets the needs of oneself, user can Amending design as required.

The present invention provides the dynamic simulation system of a kind of mechanical system mechanics, comprises with lower module:

Model parameter input module, for inputting the dimensional parameters of each object of mechanical system, the initial position parameters of material parameter and each object；

Connected mode chosen module, for the connected mode needed between each object selected in the multiple connected mode prestored；

External force input module, the external force value suffered by input model；

Calculating time and material calculation input module, for inputting the time that machinery mechanics of system is analyzed, and the time step calculated；

Dynamics analysis module, is used for carrying out dynamic analysis, and it includes kinetics equation and builds submodule and calculating sub module；Kinetics equation builds submodule for setting up the parameter such as the Jacobian matrix required for kinetics equation, external force battle array according to the parameter of model parameter input module, connected mode chosen module, the input of external force input module or setting, then the mechanical equation of mechanical system motion is built, using the position of each object as unknown number to be solved；Calculating sub module is for solving the mechanical equation of mechanical system motion, it is thus achieved that the position in each moment (i.e. time step) of each object in mechanical system motion；

Display module, for the position according to object each in etching system time each, it is shown that the image frame of mechanical system.

Compared with prior art, it has the great advantage that the present invention, the invention provides input element, calculates link and result display function, all sidedly mechanical system can be carried out dynamics simulation emulation；The function of the present invention belongs to advanced level at home, well fills the domestic gaps.

Accompanying drawing explanation

Fig. 1 is each object position coordinates schematic diagram in mechanical system.

Fig. 2 is after using the rotating shaft of the inventive method and system emulation to drive slide block movement under force, at the emulating image in six moment.

Fig. 3 is that the slide block using the inventive method and system emulation drives what rotate axle to move back and forth in process under the effect of power, at the emulating image in six moment.

Detailed description of the invention

As it is shown in figure 1, the position of each object can be represented by the position of barycenter in mechanical system, and the position of barycenter can be represented by the direction of the position coordinates of barycenter and barycenter.The present invention using the position of each object as kinetics equation unknown number to be solved；In such mechanical system, the unknown number of i-th object just can be defined as: qⁱ=[xy θ]^T, wherein, the locative coordinate of x and y, the direction of θ object.The unknown number of so whole mechanical system can be defined as: q=[q¹q²…q^N]^T, wherein qⁱFor the unknown number of i-th object,_NFor the number of object in system, T is transposition operative symbol.In mechanical system, the connected mode between each object can be represented by the constraint equation shown in such as formula (1):

$C(q,t)=\left[\begin{array}{c}{C}^1(q,t)\\ C^2(q,t)\\ .\\ .\\ .\\ C^S(q,t)\end{array}\right]=0---\left(1\right)$

In formula (1), C¹(q t) represents first constraint equation, C^S(q t) represents the S constraint equation t express time (i.e. step-length).

If time t is sought first derivative by wushu (1), it is possible to obtain the constraint of velocity equation as shown in formula (1),

$C_q\stackrel{\·}{q}+C_t=0---\left(2\right)$

In formula (2),For speed, C_qFor the Jacobian matrix of constraint equation, $C_t=\left[\begin{array}{c}\frac{\∂C^1}{\∂t}\\ \frac{\∂C^2}{\∂t}\\ .\\ .\\ .\\ \frac{\∂C^S}{\∂t}\end{array}\right]$ For the right item of constraint of velocity equation, time derivation is obtained by it by constraint equation.

Again to formula (1) derivation once, it is possible to obtain the constrained equations of acceleration as shown in formula (3),

$C_q\stackrel{\·\·}{q}-\mathrm{\γ}=0---\left(3\right)$

In formula (3),For acceleration, γ is the right item of constrained equations of acceleration.

In concrete calculating, it is not required to above-mentioned equation to calculate Jacobian matrix C_qRight-hand vector C with speed, constrained equations of acceleration_tAnd γ, the present invention directly utilizes the constraint equation direct-assembling Jacobian matrix C adjoining object_q, assembling process is:

If i-th and j object are connected (kth constraint equation) by kth hinge, the coefficient Jacobian matrix of its constraint of velocity equation is respectivelyWithIts speed, constrained equations of acceleration right-hand vector respectivelyWithThenRow k i-th corresponding to the system restriction equation Jacobian matrix of block form arranges,Corresponding to the row k jth row of the system restriction equation Jacobian matrix of block form, and other element of row k is all 0, namely shown in Jacobian matrix such as formula (4),

$C_q=\begin{array}{c}\left[\begin{array}{ccccc}...& ...& ...& ...& ...\\ 0& C_{q^i}^k& 0& C_{q^j}^k& 0\\ ...& ...& ...& ...& ...\end{array}\right]\end{array}---\left(4\right)$

WithProcessing mode similar, be respectively filled in the C of block form_tRow k with γ.

If the constraint equation of this system is: C (q, t)=0, then shown in the mechanical equation of mechanical system motion such as formula (5),

$\left\{\begin{array}{c}M\stackrel{\·\·}{q}+C_q^T\mathrm{\χ}=Q_e\\ C(q,t)=0\end{array}\right.---\left(5\right)$

In formula (5),For Mass matrix； $Q=\left[\begin{array}{c}{Q}_e^1\\ Q_e^2\\ .\\ .\\ .\\ Q_e^N\end{array}\right]$ For external force battle array, χ is Lagrange multiplier, wherein,

$M^1=\left[\begin{array}{ccc}{m}_1& 0& 0\\ 0& m_1& 0\\ 0& 0& \frac{m_1{l}_1^2}{12}\end{array}\right],M^2=\left[\begin{array}{ccc}{m}_2& 0& 0\\ 0& m_2& 0\\ 0& 0& \frac{m_2{l}_2^2}{12}\end{array}\right]...M^N=\left[\begin{array}{ccc}{m}_N& 0& 0\\ 0& m_N& 0\\ 0& 0& \frac{m_N{l}_N^2}{12}\end{array}\right]$

M in formula₁,m₂…m_NFor object 1,2 ... the quality of N, l₁,l₂,l_NFor object 1,2 ... the length of N.

$Q_e^1=\left[\begin{array}{c}{\left(Q_e^1\right)}_x\\ {\left(Q_e^1\right)}_y\\ {\left(Q_e^1\right)}_{\mathrm{\θ}}\end{array}\right]$ For external force suffered on object 1, whereinRepresent external force suffered by object x direction,Represent external force suffered by object y direction,Represent external force suffered by object rotation direction. $Q_e^2=\left[\begin{array}{c}{\left(Q_e^2\right)}_x\\ {\left(Q_e^2\right)}_y\\ {\left(Q_e^2\right)}_{\mathrm{\θ}}\end{array}\right]$ For external force suffered on object 2,Represent object x direction, y direction, external force suffered by rotation direction respectively ...For external force suffered on object N.If not by external force, Q on object_eIt is 0.

Equation (5) comprises one group of differential equation and one group of algebraic equation, is called differential/algebraic equations group.The present invention uses the method that contracts that equation (5) is solved.

The thought of the method that contracts is to utilize the generalized coordinates of suitable algorithms selection independence, and finds independent generalized coordinates and the relation of dependent coordinate, equation is converted to the pure differential equation about independent coordinate and is integrated.

In solution procedure, first position coordinates is write as block form $q={\left[\begin{array}{cc}{q}_d^T& q_i^T\end{array}\right]}^T,$ Wherein q_dIndependent coordinate vector, q is tieed up for S_iDependent coordinate vector is tieed up for 3N-S.Such constraint of velocity equation (2) and constrained equations of acceleration (3) can be corresponding write as the block form as shown in formula (6):

$\begin{array}{cc}{C}_{q_d}{\stackrel{\·}{q}}_d+C_{q_i}{\stackrel{\·}{q}}_i=-C_t& C_{q_d}{\stackrel{\·\·}{q}}_d+C_{q_i}{\stackrel{\·\·}{q}}_i=\mathrm{\γ}---\left(6\right)\end{array}$

It is Line independent between constraint equation, therefore always can choose suitable dependent coordinate vector q_dMake matrixIt is nonsingular, therefore has the relation shown in formula (7),

$\begin{array}{cc}{\stackrel{\·}{q}}_d=C_{\mathrm{di}}{\stackrel{\·}{q}}_i-C_{q_d}^{-1}{C}_t& {\stackrel{\·\·}{q}}_d=C_{\mathrm{di}}{\stackrel{\·\·}{q}}_i+C_{q_d}^{-1}\mathrm{\γ}---\left(7\right)\end{array}$

Formula (7) is updated in the mechanical equation (5) of mechanical system motion, it is possible to equation (5) abbreviation is become shown in formula (8),

$\stackrel{\‾}{M}{\stackrel{\·\·}{q}}_d={\stackrel{\‾}{Q}}_d---\left(8\right)$

In formula (8),For the Mass matrix after abbreviation,For independent coordinate q_dSecond dervative,For the external force battle array after abbreviation.Equation (8) can solve either directly through numerical integration and obtain, and so can be obtained by q_dNamely the position of independent coordinate is then according to the relation between dependent coordinate and independent coordinateIt is iterated obtaining the position q of not independent coordinate_i.Thus can calculate and obtain the position q in each moment of each object in system.

By the result of obtained position q, for a certain moment: figure is drawn.Owing to each object is rectangle, calculate the position obtaining each four summits of object respectively.Then be linked in sequence summit, just obtains the figure of each object.Thus obtain the figure of etching system time this.Then the figure of etching system when we can obtain each in the whole calculating time.Then according to the figure of etching system time each, we can form animation, thus can have the figure of the process animation of system motion.

Claims (5)

1. the movement simulating method of a mechanical system mechanics, it is characterised in that comprise the following steps:

First, set the condition setting up kinetics equation, including:

Set the connected mode between each object in the material parameter of each object in mechanical system, dimensional parameters and initial position parameters, selection mechanical system, set up mechanical system model；

The external force that given mechanical system model is subject to；

Set the time of mechanical system mechanical analysis and the time step calculated as required；

Then, obtain the Jacobian matrix set up required for kinetics equation according to the condition of aforementioned setting, then build kinetics equation, using the position of each object as kinetics equation unknown number to be solved；

Finally, kinetics equation is solved, it is thus achieved that in mechanical system, each object is in the position in each moment；Build mechanical system animated image according to each object at the positional information in each moment and show.

2. the movement simulating method of mechanical system mechanics as claimed in claim 1, it is characterised in that shown in described Jacobian matrix such as formula (1),

$C_q=\left[\begin{array}{ccccc}...& ...& ...& ...& ...\\ 0& C_{q^i}^k& 0& C_{q^j}^k& 0\\ ...& ...& ...& ...& ...\end{array}\right]---\left(1\right)$

In formula (1),WithRepresent i-th object and j object coefficient Jacobian matrix by kth hinge constraint of velocity equation time connected, q respectivelyⁱFor the unknown number of i-th object, q^jUnknown number for jth object.

3. the movement simulating method of mechanical system mechanics as claimed in claim 1, it is characterised in that shown in described mechanical equation such as formula (2),

$\left\{\begin{array}{c}M\stackrel{\·\·}{q}+C_q^T\mathrm{\χ}=Q_e\\ C(q,t)=0\end{array}\right.---\left(2\right)$

In formula (2),For acceleration,For Mass matrix； $Q_e=\left[\begin{array}{c}{Q}_e^1\\ Q_e^2\\ .\\ .\\ .\\ Q_e^N\end{array}\right]$ For external force battle array, χ is Lagrange multiplier, wherein,

$M^1=\left[\begin{array}{ccc}{m}_1& 0& 0\\ 0& m_1& 0\\ 0& 0& \frac{m_1{l}_1^2}{12}\end{array}\right],M^2=\left[\begin{array}{ccc}{m}_2& 0& 0\\ 0& m_2& 0\\ 0& 0& \frac{m_2{l}_2^2}{12}\end{array}\right]...M^N=\left[\begin{array}{ccc}{m}_N& 0& 0\\ 0& m_N& 0\\ 0& 0& \frac{m_N{l}_N^2}{12}\end{array}\right]$

M in formula₁,m₂…m_NFor object 1,2 ... the quality of N, l₁,l₂,l_NFor object 1,2 ... the length of N；

$Q_e^N=\left[\begin{array}{c}{\left(Q_e^N\right)}_x\\ {\left(Q_e^N\right)}_y\\ {\left(Q_e^N\right)}_{\mathrm{\θ}}\end{array}\right]$ For external force suffered on object N, whereinRepresent external force suffered by object x direction,Represent external force suffered by object y direction,Represent external force suffered by object rotation direction；

(q, t)=0 is the constraint equation of system to C.

4. the movement simulating method of mechanical system mechanics as claimed in claim 3, it is characterised in that use the method that contracts that mechanical equation is solved.

5. the dynamic simulation system of a mechanical system mechanics, it is characterised in that comprise with lower module:

Model parameter input module, for inputting the dimensional parameters of each object of mechanical system, the initial position parameters of material parameter and each object；

Connected mode chosen module, for the connected mode needed between each object selected in the multiple connected mode prestored；

External force input module, the external force value suffered by input model；

Calculating time and material calculation input module, for inputting the time that machinery mechanics of system is analyzed, and the time step calculated；

Dynamics analysis module, is used for carrying out dynamic analysis, and it includes kinetics equation and builds submodule and calculating sub module；Kinetics equation builds submodule for building the mechanical equation of mechanical system motion, using the position of each object as unknown number to be solved；Calculating sub module is for solving the mechanical equation of mechanical system motion, it is thus achieved that the position in each moment of each object in mechanical system motion；

Display module, for the position according to object each in etching system time each, it is shown that the image frame of mechanical system.