CN102004822A - Modality-based frequency analysis method for space six-freedom-degree parallel motion system - Google Patents

Abstract

The invention provides a modality-based frequency analysis method for a space six-freedom-degree parallel motion system. The invention is realized by comprising the following steps of: creating a modality equation of a parallel motion system according to a second-order vibration differential equation of the space docking six-freedom-degree parallel motion system; constructing an equation system matrix; decomposing the system matrix by utilizing a numerical analysis method; calculating the low-order modality set of the six-freedom-degree parallel motion system and a corresponding characteristic frequency; and analyzing the low-order modality frequency of the space six-freedom-degree parallel motion system. The invention breaks through the traditional method based on physical space analysis and design, can be applied to the design and the analysis of all space six-freedom-degree parallel motion systems to ensure that the designed mechanism satisfies the requirement on a designed bandwidth, provides effective basis for changing the system modality, provides a new method and concept for more effective six-freedom-degree structural design and optimization and has important significance for practical application and theoretical analysis of a project.

Description

Space six-freedom parallel kinematic system frequency analysis method based on mode

(1) technical field

The present invention relates to mechanical technique, is a kind of space six-freedom parallel kinematic system frequency analysis method based on mode specifically.

(2) background technology

Space articulation mechanism six-freedom parallel kinematic system adopts hydraulically powered typical Stewart platform form, be with the different of parallel kinematic system of present existence, space articulation parallel kinematic system requirements kinematic system has super large space ability, overlength supporting leg impulse stroke and high system's frequency range.At present, the Stewart platform that satisfies the index request of space articulation kinematic system does not still have precedent at home, and also only the U.S. and Russia have the type docking mechanism kinematic system in the world.The parallel kinematic system works frequency range of this large-scale over-long supporting leg form can reach 10Hz, and current hydraulic-driven parallel kinematic simulation system frequency range 3-5Hz only, and work space is little.Require and the big parallel kinematic system of work space for high frequency range, ignore its structure and can't satisfy the actual techniques index with the system that driving mode will cause designing.Design the parallel kinematic structure that satisfies space articulation mechanism kinematic performance requirement, must carry out frequency-response analysis system.

(3) summary of the invention

The object of the present invention is to provide a kind of space six-freedom parallel kinematic system frequency analysis method based on mode.

The object of the present invention is achieved like this: according to the second order oscillatory differential equation of space articulation six-freedom parallel kinematic system, set up the modal equations of parallel kinematic system, the equationof structure system matrix, adopt numerical analysis method that system matrix is decomposed, calculate the lower mode collection and the characteristic of correspondence frequency thereof of six-freedom parallel kinematic system, analyze the lower mode frequency of space six-freedom parallel kinematic system; Space six-freedom parallel kinematic system works near the meta usually, and its lower mode frequency analysis mainly concentrates on meta on engineering is used, and this moment the second order model of vibration of parallel kinematic system is represented with following form:

$M\stackrel{\·\·}{x}\left(t\right)+C\stackrel{\·}{x}\left(t\right)+\mathrm{Kx}\left(t\right)=f\left(t\right)$

M is the wide mass matrix of n * n in the formula; C is n * n broad sense damping matrix; K is n * n broad sense Stiffness Matrix; F (t) is the outside input stimulus of system;

Be analytic system meta model frequency, damping term and external drive item are removed, so, obtain undamped second order vibration equation, suppose that its model frequency is ω _n, Mode Shape is ψ, then obtains space six-freedom parallel kinematic system modal equations,

(K-ω _nM)ψ＝0

The structure matrix of coefficients, matrix of coefficients equals the matrix product of the contrary and n dimension broad sense Stiffness Matrix of n * n dimension generalized mass battle array, adopt methods of numerical then, characteristic value decomposition, svd calculate mode and its characteristic of correspondence frequency of the needs investigation of space six-freedom parallel kinematic system, try to achieve the corresponding model frequency of system according to characteristic frequency, reflect according to the model frequency of analyzing whether designed system meets the demands.

A kind of space six-freedom parallel kinematic system frequency analysis method based on mode of the present invention is broken through the method for tradition based on physical space analysis and design, has especially overcome the universal method based on the design of single channel equivalent frequency.The present invention can be applied in the design and analysis of the six-freedom parallel system that has living space, make the mechanism of design satisfy the requirement of design frequency range, for a change system mode provides effective foundation, for more effective six degree of freedom structural design provides new method and thinking with optimizing, for engineering practical application and theoretical analysis, all significant.

(4) description of drawings

Fig. 1 is a space articulation mechanism six-freedom parallel kinematic system structural representation.

(5) embodiment

The invention will be further described for example below in conjunction with accompanying drawing.

Embodiment 1: in conjunction with Fig. 1, a kind of space six-freedom parallel kinematic system frequency analysis method of the present invention based on mode, second order oscillatory differential equation according to space articulation six-freedom parallel kinematic system, set up the modal equations of parallel kinematic system, the equationof structure system matrix, adopt numerical analysis method that system matrix is decomposed, calculate the lower mode collection and the characteristic of correspondence frequency thereof of six-freedom parallel kinematic system, analyze the lower mode frequency of space six-freedom parallel kinematic system; Space six-freedom parallel kinematic system works near the meta usually, and its lower mode frequency analysis mainly concentrates on meta on engineering is used, and this moment the second order model of vibration of parallel kinematic system is represented with following form:

$M\stackrel{\·\·}{x}\left(t\right)+C\stackrel{\·}{x}\left(t\right)+\mathrm{Kx}\left(t\right)=f\left(t\right)$

M is the wide mass matrix of n * n in the formula; C is n * n broad sense damping matrix; K is n * n broad sense Stiffness Matrix; F (t) is the outside input stimulus of system;

Be analytic system meta model frequency, damping term and external drive item are removed, so, obtain undamped second order vibration equation, suppose that its model frequency is ω _n, Mode Shape is ψ, then obtains space six-freedom parallel kinematic system modal equations,

(K-ω _nM)ψ＝0

The structure matrix of coefficients, matrix of coefficients equals the matrix product of the contrary and n dimension broad sense Stiffness Matrix of n * n dimension generalized mass battle array, adopt methods of numerical then, characteristic value decomposition, svd calculate mode and its characteristic of correspondence frequency of the needs investigation of space six-freedom parallel kinematic system, try to achieve the corresponding model frequency of system according to characteristic frequency, reflect according to the model frequency of analyzing whether designed system meets the demands.

Embodiment 2: a kind of space six-freedom parallel kinematic system frequency analysis method of the present invention based on mode, parallel kinematic system of described space articulation mechanism by motion platform (1), go up and connect hinge (2), hydraulic-driven supporting leg (3), connect hinge (4) and fixed base platform (5) down and form.It is 4.0m that meta props up leg length, stroke 1.850m.Last hinge garden diameter 3.0m, following hinge garden diameter 7.3m.Platform and load gross mass are 563Kg.At the space six-freedom parallel kinematic system under this structure, when keeping its meta in the second order oscillatory differential equation 6 * 6 of the broad sense Stiffness Matrix dimension Stiffness Matrix and 6 * 6 the dimension mass matrixes, then generalized mass matrix and Stiffness Matrix are:

$M=\left[\begin{array}{cccccc}1839& 0& 0& 0& 428.9& 0\\ 0& 1839& 0& -428.9& 0& 0\\ 0& 0& 1638& 0& 0& 0\\ 0& -428.9& 0& 1470& 0& 0\\ 428.9& 0& 0& 0& 1470& 0\\ 0& 0& 0& 0& 0& 2708\end{array}\right]$

$K=\left[\begin{array}{cccccc}4.341\×{10}^7& 0& 0& 0& -7.085\×{10}^6& 0\\ 0& 4.341\×{10}^7& 0& 7.085\×{10}^6& 0& 0\\ 0& 0& 9.286\×{10}^7& 0& 0& 0\\ 0& 7.085\×{10}^6& 0& 8.379\×{10}^7& 0& 0\\ -7.085\×{10}^6& 0& 0& 0& 8.379\×{10}^7& 0\\ 0& 0& 0& 0& 0& 1.545\×{10}^8\end{array}\right]$

Damping term in the equation and external drive item are removed, construct its matrix of coefficients by space six-freedom parallel kinematic system ground modal equations, this 6 * 6 maintains matrix number and is:

$D=\left[\begin{array}{cccccc}2.653\×{10}^4& 0& 0& 0& -1.839\×{10}^4& 0\\ 0& 2.653\×{10}^4& 0& 1.839\×{10}^4& 0& 0\\ 0& 0& 5.668\×{10}^4& 0& 0& 0\\ 0& 1.256\×{10}^4& 0& 6.235\×{10}^4& 0& 0\\ -1.256\×{10}^4& 0& 0& 0& 6.235\×{10}^4& 0\\ 0& 0& 0& 0& 0& 5.707\×{10}^4\end{array}\right]$

Adopt the method for numerical value, the factor arrays that is obtained by modal equations is carried out characteristic value decomposition, obtained the modal matrix and the characteristic frequency vector of this parallel institution.

$U=\left[\begin{array}{cccccc}0.3793& 0& 0& 0& 0& -0.9253\\ 0& -0.3793& 0& 0& -0.9253& 0\\ 0& 0& 0& -1& 0& 0\\ 0& -0.9253& 0& 0& 0.3793& 0\\ -0.9253& 0& 0& 0& 0& -0.3793\\ 0& 0& -1& 0& 0& 0\end{array}\right]$

$E_{\mathrm{freq}}=\left[\begin{array}{c}682808.8\\ 682808.8\\ 57070.11\\ 56678.48\\ 20866.53\\ 20866.53\end{array}\right]$

The model frequency of the space articulation mechanism six-freedom parallel kinematic system that can try to achieve by the characteristic frequency that calculates, this model frequency is expressed as:

${\mathrm{\ω}}_n=\left[\begin{array}{c}41.6\\ 41.6\\ 38.0\\ 37.9\\ 23\\ 23\end{array}\right]$

Six-freedom parallel system of space articulation mechanism to this structure carries out model frequency identification experiment, obtain its corresponding to the minimum model frequency of hydraulic pressure rigidity, this frequency is about 22Hz, and the first rank model frequency that identification obtains is close with the second rank model frequency, its mode mainly is mapped in X and Y translation direction, the 3rd rank mode is mapped in the heave direction, and fourth, fifth rank mode mainly is mapped in inclination and pitch orientation, and the 6th rank mode mainly is mapped in yaw direction.The consistance of test findings and analysis result of the present invention has well illustrated feasibility and the space six degree of freedom model frequency that proposes of the present invention validity of analyzing thought in engineering reality of the present invention.

Claims (1)

1. space six-freedom parallel kinematic system frequency analysis method based on mode, it is characterized in that: according to the second order oscillatory differential equation of space articulation six-freedom parallel kinematic system, set up the modal equations of parallel kinematic system, the equationof structure system matrix, adopt numerical analysis method that system matrix is decomposed, calculate the lower mode collection and the characteristic of correspondence frequency thereof of six-freedom parallel kinematic system, analyze the lower mode frequency of space six-freedom parallel kinematic system; Space six-freedom parallel kinematic system works near the meta usually, and its lower mode frequency analysis mainly concentrates on meta on engineering is used, and this moment the second order model of vibration of parallel kinematic system is represented with following form:

$M\stackrel{\·\·}{x}\left(t\right)+C\stackrel{\·}{x}\left(t\right)+\mathrm{Kx}\left(t\right)=f\left(t\right)$

M is the wide mass matrix of n * n in the formula; C is n * n broad sense damping matrix; K is n * n broad sense Stiffness Matrix; F (t) is the outside input stimulus of system;

Be analytic system meta model frequency, damping term and external drive item are removed, so, obtain undamped second order vibration equation, suppose that its model frequency is ω _n, Mode Shape is ψ, then obtains space six-freedom parallel kinematic system modal equations,

(K-ω _nM)ψ＝0

The structure matrix of coefficients, matrix of coefficients equals the matrix product of the contrary and n dimension broad sense Stiffness Matrix of n * n dimension generalized mass battle array, adopt methods of numerical then, characteristic value decomposition, svd calculate mode and its characteristic of correspondence frequency of the needs investigation of space six-freedom parallel kinematic system, try to achieve the corresponding model frequency of system according to characteristic frequency, reflect according to the model frequency of analyzing whether designed system meets the demands.

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