CN112765740B - Method for determining buffering effect of hanging basket type buffering device in design stage - Google Patents

Method for determining buffering effect of hanging basket type buffering device in design stage Download PDF

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CN112765740B
CN112765740B CN202011630097.6A CN202011630097A CN112765740B CN 112765740 B CN112765740 B CN 112765740B CN 202011630097 A CN202011630097 A CN 202011630097A CN 112765740 B CN112765740 B CN 112765740B
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buffer device
type buffer
basket type
precision instrument
basket
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CN112765740A (en
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杨功碧
张江源
涂勇强
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Xiamen Huayuan Jiahang Technology Co ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00—Springs
    • F16F1/36—Springs made of rubber or other material having high internal friction, e.g. thermoplastic elastomers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/02—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
    • F16F15/04—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means
    • F16F15/08—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means with rubber springs ; with springs made of rubber and metal
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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Abstract

The invention discloses a method for determining the buffering effect of a hanging basket type buffering device in a design stage, which comprises the following steps: s1, constructing a six-way stiffness damping model of each rubber shock absorber and defining physical parameters; s2, constructing an inertial coordinate system, an inertial navigation coordinate system and a vibration damper coordinate system, and defining the relation among the coordinate systems; s3, defining physical parameters, kinematic parameters, external excitation and buffering effects of the system; s4, constructing a six-degree-of-freedom kinetic equation of the hanging basket type buffer device; s5, calculating the maximum value of the three-way acceleration of the precise instrument according to external impact, and obtaining the three-way buffering effect of the basket type buffering base; the method is simple and convenient to calculate, easy to operate, high in result accuracy and reliability, free of manufacturing an actual device and complex tests, capable of determining the buffering effect of the basket type buffering device in a design stage, shortening the design period of the basket type buffering device and reducing the test risk of the basket type buffering device.

Description

Method for determining buffering effect of hanging basket type buffering device in design stage
Technical Field
The invention relates to the technical field of hanging basket type buffer devices, in particular to a method for determining the buffer effect of a hanging basket type buffer device in a design stage.
Background
The precision instrument needs a good use environment to exert the maximum precision, but in actual use, the precision instrument mounted on the military carrier is often threatened by large impact far exceeding the working bearing capacity of the precision instrument, and in order to avoid the precision reduction or damage of the precision instrument caused by the large impact, the precision instrument needs to be designed and provided with a buffer device to attenuate the influence of the large impact on the precision instrument. In consideration of the requirement of damping large impact and the limitation of space volume, the patent CN202485550U disclosed by the utility model provides a damping device for damping large impact for a precision instrument. While the basket buffer device provided by the publication CN202485550U has been widely used in precision instruments for military carriers.
With the deep advancement of the reliability design requirements of precision instruments, the determination of the buffering effect of the basket type buffering device is an important assessment work for confirming the reliable work of the precision instruments in a large-impact environment. At present, a test method is mainly adopted to determine the buffering effect of the hanging basket type buffering device, and the specific method comprises the following steps: after the basket type buffering base is designed and manufactured, the basket type buffering base is installed on the impact table, the precision instrument is installed on the basket type buffering base, acceleration sensors are respectively attached to the table top of the impact table and the precision instrument, the impact table is controlled to impact the basket type buffering base greatly, and the buffering effect of the basket type buffering device is obtained by collecting acceleration sensor signals on the table top of the impact table and the precision instrument. The test method can reflect the buffering effect of the basket type buffering base more objectively and truly, but has obvious disadvantages: the cycle is long, and if improperly designed, the basket type buffer device and even the precise instrument will be damaged. Therefore, in order to shorten the period and reduce the risk of the test, the determination of the cushioning effect of the basket cushioning device must be performed at the design stage.
Disclosure of Invention
The invention aims to provide a method for determining the buffering effect of a hanging basket type buffering device in the design stage by solving the technical problems.
For this purpose, the technical scheme of the invention is as follows:
A method for determining the buffering effect of a basket type buffering device in a design stage comprises the following steps:
S1, constructing a six-way rigidity damping model of each rubber shock absorber, and defining physical parameters of the six-way rigidity damping model of the rubber shock absorber, wherein the physical parameters comprise rigidity and damping in three linear directions and rigidity and damping in three torsion directions of the six-way rigidity damping model;
s2, constructing an inertial coordinate system, a precise instrument coordinate system and a vibration damper coordinate system, and defining the relation among the coordinate systems;
S3, defining physical parameters of the system, wherein the physical parameters comprise the combined weight of the precision instrument and the basket type buffer device bracket, and the combination of the precision instrument and the basket type buffer device bracket is relative to a coordinate system of the precision instrument The basket-type buffer device is relative to a precision instrument coordinate system/>Damping matrix of (c), and basket buffer device relative to precision instrument coordinate systemIs a stiffness matrix of (2); defining kinematic parameters, including a displacement component of the precision instrument relative to the basket type buffer device base and a rotation angle component of the precision instrument relative to the basket type buffer device base; defining external stimulus consisting of components of external motion input; the method is characterized in that impact based on the outside is generally transmitted to a basket type buffer device through linear motion to define a buffer effect, wherein the buffer effect in the x direction is a ratio of the maximum acceleration of an x-direction precise instrument to the maximum value of external x-direction linear acceleration, the buffer effect in the y direction is a ratio of the maximum acceleration of the y-direction precise instrument to the maximum value of external y-direction linear acceleration, and the buffer effect in the z direction is a ratio of the maximum acceleration of a z-direction precise instrument to the maximum value of external z-direction linear acceleration;
s4, constructing a six-degree-of-freedom dynamics equation of the basket type buffer device based on the system physical parameters, the system kinematic parameters and the external excitation defined in the step S3;
S5, calculating the maximum value of the three-way acceleration of the precision instrument according to external impact, and obtaining the x-direction buffer effect of the basket type buffer base, the y-direction buffer effect of the basket type buffer base and the z-direction buffer effect of the basket type buffer base.
Further, the specific implementation steps of the step S1 are as follows:
S101, taking the gravity center of a single rubber shock absorber as an origin, defining the normal direction of the front end surface of a rubber shock absorber base as a forward axial direction, defining the normal direction of the right end surface of the rubber shock absorber base as a right axial direction, and defining the normal direction of the top surface of the rubber shock absorber as an upward axial direction; the three axes of the nth rubber damper coordinate system are: forward axis J nRn, right axis J nPn, and radial axis J nSn, n=1, 2,3,4;
s102, defining three linear directions of rigidity of a six-direction rigidity damping model of the rubber shock absorber to be right-direction rigidity k pn, forward-direction rigidity k rn and upward-direction rigidity k sn respectively; the damping in three linear directions are right-direction damping c pn, forward-direction damping c rn and upward-direction damping c sn respectively; the rigidity in the three torsion directions are right-handed rigidity k λn, forward-handed rigidity k ξn and upward-handed rigidity k υn respectively; the three torsional directional damping are respectively right-handed damping c λn, forward-handed damping c ξn and upward-handed damping c υn;
s103, representing various parameters of a six-directional stiffness damping model of the rubber shock absorber in a matrix form:
The linear stiffness matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the linear damping matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the torsional stiffness matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the torsional damping matrix defining the six-way stiffness damping model of the rubber shock absorber is:
further, the specific implementation steps of step S2 are as follows:
S201, constructing an inertial coordinate system, a precise instrument coordinate system and a vibration damper coordinate system: constructing an inertial coordinate system O-XYZ, wherein O coincides with the mass center of the precise instrument under the static state, OY faces to the right front of the precise instrument, OZ faces upwards perpendicular to the precise instrument, OX is obtained by right hand rule, and the characteristic of the inertial coordinate system O-XYZ is static relative to the ground, namely, is consistent with the initial state all the time; construction of a precision instrument coordinate System Its static precision instrument coordinate system/>Coincident with inertial coordinate system O-XYZ, and/>Fixedly connected with a precise instrument, and a coordinate system/>, of the precise instrumentIs characterized by moving along with the movement of a precision instrument; constructing a damper coordinate system: constructing a damper coordinate system J n-PnRnSn for each damper; wherein n is the position number of the damper, J n is the damping center of the n-th damper, J nRn faces to the right front of the n-th damper, J nSn is vertical to the n-th damper and J nPn is obtained by right hand rule, n=1, 2,3,4;
s202, defining the relation between an inertial coordinate system and a vibration damper coordinate system:
setting any vector to be p n in the damper coordinate system J n-PnRnSn of the nth damper and x in the inertial coordinate system O-XYZ, the conversion relationship between x and p n is:
x＝An·pn+rn，
Where r n is the displacement vector of O relative to J n, which is determined by:
rn＝[rxn ryn rzn]T，
wherein r xn is the projection of the displacement vector of the O point relative to J n in the O-XYZ direction; r yn is the projection of the displacement vector of the O point relative to J n in the OY direction at O-XYZ; r zn is the projection of the displacement vector of the O point relative to J n in the OZ direction at O-XYZ;
A n is the orthogonal transformation matrix of J n-PnRnSn and O-XYZ, which is determined by the rotation angle of each coordinate axis between O-XYZ and J n-PnRnSn:
Where α n,βn and γ n are three components of the rotational Euler angle of O-XYZ relative to J n-PnRnSn: gamma n is the angle of rotation of O-XYZ about J nSn for the first step in the rotation euler angle of J n-PnRnSn, beta n is the angle of rotation of O-XYZ about J nRn for the second step in the rotation euler angle of J n-PnRnSn, and alpha n is the angle of rotation of O-XYZ about J nPn for the third step in the rotation euler angle of J n-PnRnSn.
Further, the specific implementation steps of step S3 are as follows:
s301, defining system physical parameters, including:
defining the combined weight of a precision instrument and a basket type buffer device bracket as m;
Defining a combination of a precision instrument and a basket buffer support relative to a precision instrument coordinate system The moment of inertia of (2) is: /(I)
Wherein,Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>The component on the axis of the shaft,Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>A component on the axis;
definition and basket type buffer device relative to precision instrument coordinate system Damping matrix/>And stiffness matrixThe method comprises the following steps of:
The displacement components of the precision instrument relative to the cradle type buffer device base are x, y and z; wherein x is the center of a coordinate system of the precise instrument Projection on OX of displacement relative to inertial frame center O, y being precision instrument frame center/>Projection of displacement on OY relative to inertial coordinate system center O, z is precision instrument coordinate system center/>Projection of the displacement on OZ with respect to the inertial coordinate system center O; the rotation angle components of the precision instrument relative to the cradle type buffer device base are theta, phi and phi; wherein θ is the central coordinate axis/>, of the precision instrument coordinate systemRelative to the rotation angle on the inertial coordinate system axis OX, phi is the center coordinate axis/>, of the precision instrument coordinate systemWith respect to the rotation angle on the inertial coordinate system axis OY, ψ is the precision instrument coordinate system center axis/>With respect to the rotation angle on the inertial coordinate axis OZ. Therefore, the basket buffer device is relative to the precision instrument coordinate system/>Damping matrix/>The meaning of each symbol in (a) is: c xx is the damping force of the basket type buffer device in the x direction generated by the x direction displacement of the precision instrument; c xy is the damping force of the basket type buffer device in the x direction generated by the displacement of the precise instrument in the y direction; c xz is the damping force of the basket type buffer device in the x direction generated by the z direction displacement of the precision instrument; c xθ is the damping force of the basket type buffer device in the x direction generated by the theta direction rotation of the precision instrument; c xφ is the damping force of the basket type buffer device in the x direction generated by the phi-direction rotation of the precision instrument; c xψ is the damping force of the basket type buffer device in the x direction generated by the rotation of the psi direction of the precision instrument; c yx is the damping force of the basket type buffer device in the y direction generated by the x-direction displacement of the precision instrument; c yy is the damping force of the basket type buffer device in the y direction generated by the displacement of the precise instrument in the y direction; c yz is the damping force of the basket type buffer device in the y direction generated by the z direction displacement of the precision instrument; c yθ is the damping force of the basket type buffer device in the y direction generated by the theta direction rotation of the precision instrument; c yφ is the damping force of the basket type buffer device in the y direction generated by the phi-direction rotation of the precision instrument; c yψ is the damping force of the basket type buffer device in the y direction generated by the rotation of the psi direction of the precision instrument; c zx is the damping force of the basket type buffer device in the z direction generated by the x direction displacement of the precision instrument; c zy is the damping force of the basket type buffer device in the z direction generated by the displacement of the precise instrument in the y direction; c zz is the damping force of the basket type buffer device in the z direction generated by the z direction displacement of the precision instrument; c zθ is the damping force of the basket type buffer device in the z direction generated by the theta direction rotation of the precision instrument; c zφ is the damping force of the basket type buffer device in the z direction generated by the phi-direction rotation of the precision instrument; c zψ is the damping force of the basket type buffer device in the z direction generated by the rotation of the psi direction of the precision instrument; c θx is damping moment in theta direction generated by x-direction displacement of the basket type buffer device; c θy is damping moment in theta direction generated by y-direction displacement of the basket type buffer device; c θz is damping moment in theta direction generated by z-direction displacement of the basket type buffer device; c θθ is damping moment in the theta direction generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; c θφ is damping moment in theta direction generated by rotation of the basket type buffer device in phi direction of the precision instrument; c θψ is damping moment in the theta direction generated by rotation of the basket type buffer device in the phi direction of the precision instrument; c φx is the damping moment in phi direction generated by x-direction displacement of the basket type buffer device; c φy is the damping moment in phi direction generated by y-direction displacement of the basket type buffer device by the precision instrument; c φz is the damping moment in phi direction generated by z-direction displacement of the basket type buffer device by the precision instrument; c φθ is the damping moment in phi direction generated by the rotation of the basket type buffer device in theta direction of the precision instrument; c φφ is the damping moment in the phi direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; c φψ is the damping moment in phi direction generated by the rotation of the basket type buffer device in phi direction of the precision instrument; c ψx is the damping moment of the basket type buffer device in the psi direction generated by the x-direction displacement of the precision instrument; c ψy is the damping moment of the basket type buffer device in the psi direction generated by the y-direction displacement of the precision instrument; c ψz is the damping moment of the basket type buffer device in the psi direction generated by the z-direction displacement of the precision instrument; c ψθ is the damping moment of the basket type buffer device in the phi direction generated by the theta direction rotation of the precision instrument; c ψφ is the damping moment of the basket type buffer device in the phi direction generated by the rotation of the precision instrument in the phi direction; c ψψ is the damping moment of the basket type buffer device in the psi direction generated by the rotation of the precision instrument in the psi direction;
similarly, the basket type buffer device is relative to a coordinate system of a precise instrument Stiffness matrix/>The meaning of each symbol in (a) is: k xx is the spring force of the basket type buffer device in the x direction generated by the x direction displacement of the precision instrument; k xy is the spring force of the basket type buffer device in the x direction generated by the displacement of the precise instrument in the y direction; k xz is the spring force of the basket type buffer device in the x direction generated by the z direction displacement of the precision instrument; k xθ is the spring force of the basket type buffer device in the x direction generated by the theta direction rotation of the precision instrument; k xφ is the spring force of the basket type buffer device in the x direction generated by the phi-direction rotation of the precision instrument; k xψ is the spring force of the basket type buffer device in the x direction generated by the rotation of the psi direction of the precision instrument; k yx is the spring force of the basket type buffer device in the y direction generated by the displacement of the precision instrument in the x direction; k yy is the spring force of the basket type buffer device in the y direction generated by the displacement of the precise instrument in the y direction; k yz is the spring force of the basket type buffer device in the y direction generated by the z direction displacement of the precision instrument; k yθ is the spring force of the basket type buffer device in the y direction generated by the theta direction rotation of the precision instrument; k yφ is the spring force of the basket type buffer device in the y direction generated by the phi-direction rotation of the precision instrument; k yψ is the spring force of the basket type buffer device in the y direction generated by the rotation of the psi direction of the precision instrument; k zx is the spring force of the basket type buffer device in the z direction generated by the displacement of the precision instrument in the x direction; k zy is the spring force of the basket type buffer device in the z direction generated by the displacement of the precision instrument in the y direction; k zz is the spring force of the basket type buffer device in the z direction generated by the z direction displacement of the precision instrument; k zθ is the spring force of the basket type buffer device in the z direction generated by the theta direction rotation of the precision instrument; k zφ is the spring force of the basket type buffer device in the z direction generated by the phi-direction rotation of the precision instrument; k zψ is the spring force of the basket type buffer device in the z direction generated by the rotation of the psi direction of the precision instrument; k θx is the spring moment in the theta direction generated by x-direction displacement of the precision instrument of the basket type buffer device; k θy is the spring moment in the theta direction generated by the displacement of the basket type buffer device in the y direction of the precision instrument; k θz is the spring moment in the theta direction generated by z-direction displacement of the precision instrument of the basket type buffer device; k θθ is a spring moment in the theta direction generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; k θφ is the spring moment in the theta direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k θψ is the spring moment in the theta direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k φx is the phi-direction spring moment generated by x-direction displacement of the basket type buffer device by the precision instrument; k φy is the phi-direction spring moment generated by the y-direction displacement of the basket type buffer device by the precision instrument; k φz is the phi-direction spring moment generated by z-direction displacement of the basket type buffer device by the precision instrument; k φθ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; k φφ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k φψ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k ψx is the spring moment of the cradle type buffer device in the psi direction generated by the x-direction displacement of the precision instrument; k ψy is the spring moment of the basket type buffer device in the psi direction generated by the y-direction displacement of the precision instrument; k ψz is the spring moment of the basket type buffer device in the psi direction generated by the z-direction displacement of the precision instrument; k ψθ is the spring moment of the cradle type buffer device in the phi direction generated by the theta direction rotation of the precision instrument; k ψφ is the spring moment of the basket type buffer device in the phi direction generated by the rotation of the precision instrument in the phi direction; k ψψ is a spring moment in the psi direction generated by rotation of the basket type buffer device in the psi direction of the precision instrument;
S302, defining system kinematics parameters, including:
defining displacement components of the precision instrument relative to a cradle type buffer device base as x, y and z; wherein x is the center of a coordinate system of the precise instrument Projection on OX of displacement relative to inertial frame center O, y being precision instrument frame center/>Projection of displacement on OY relative to inertial coordinate system center O, z is precision instrument coordinate system center/>Projection of the displacement on OZ with respect to the inertial coordinate system center O;
Defining the rotation angle components of the precision instrument relative to the cradle type buffer device base as theta, phi and phi; wherein θ is the central coordinate axis of the precise instrument coordinate system Relative to the rotation angle on the inertial coordinate system axis OX, phi is the center coordinate axis/>, of the precision instrument coordinate systemWith respect to the rotation angle on the inertial coordinate system axis OY, ψ is the precise instrument coordinate system center coordinate axisRotation angle on the coordinate axis OZ with respect to the inertial coordinate system;
S303, defining that external excitation consists of external motion input components including u, v, w, alpha, beta and gamma, wherein u is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OX, v is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OY, and w is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OZ; alpha is the component of rotation of the basket buffer mount relative to the inertial frame on OX, beta is the component of rotation of the basket buffer mount relative to the inertial frame on OY, and gamma is the component of rotation of the basket buffer mount relative to the inertial frame on OZ;
s304, defining a buffering effect according to the system kinematics parameters and external excitation:
The impact based on the outside is generally transmitted to the basket type buffer device through linear motion, and the buffer effect of the basket type buffer device is defined to be divided into x-direction buffer effect, y-direction buffer effect and z-direction buffer effect; the following are provided:
The x-direction buffering effect is the ratio of the maximum acceleration of the x-direction precision instrument to the maximum value of the external x-direction linear acceleration, namely:
the y-direction buffering effect is the ratio of the maximum acceleration of the y-direction precise instrument to the maximum value of the external y-direction linear acceleration, namely:
the z-direction buffering effect is the ratio of the maximum acceleration of the z-direction precise instrument to the maximum value of the external z-direction linear acceleration, namely:
further, the specific implementation steps of step S4 are as follows:
s401, determining a six-degree-of-freedom kinetic equation of the basket type buffer device based on the system physical parameters, the system kinematic parameters and the external excitation defined in the step S3, wherein the six-degree-of-freedom kinetic equation is as follows:
S402, simplifying a kinetic equation of the basket type buffer device into a block matrix form:
wherein M is a mass blocking matrix of a combination of the precision instrument and the basket type buffer device bracket, The moment of inertia block matrix is the combination of a precision instrument and a basket type buffer device bracket, X is a displacement block matrix of the precision instrument relative to the basket type buffer device bottom plate in three directions of X, y and z, theta is a rotation block matrix of the precision instrument relative to the basket type buffer device bottom plate in three directions of theta, phi and phi, C xx is a damping force block matrix of the basket type buffer device generated by displacement of the precision instrument in three directions of X, y and z, C xθ is a damping force block matrix of the basket type buffer device generated by rotation of the precision instrument in three directions of theta, phi and phi in three directions of X, y and z, C θx is a damping moment block matrix of the basket type buffer device generated by displacement of the precision instrument in three directions of X, y and phi in three directions of phi, C θθ is a damping moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by rotation of the precision instrument, K xx is a spring force block matrix of the basket type buffer device in the three directions of X, y and z generated by displacement of the precision instrument, K xθ is a spring force block matrix of the basket type buffer device in the three directions of X, y and z generated by rotation of the precision instrument, K θx is a spring moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by displacement of the precision instrument, K θθ is a spring moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by rotation of the precision instrument, the spring moment block matrix in three directions of phi is a displacement block matrix in three directions of x, y and z of external excitation, and alpha is a rotation block matrix in three directions of theta, phi and phi of external excitation.
Further, the specific implementation steps of step S5 are as follows:
s501, according to the definition of the step S3 and coordinate conversion, obtaining:
In the above two formulas, C xxn＝[An][Cpn][An]T, Kxxn＝[An][Kpn][An]T；
S502, bringing the various calculated above and the external excitation defined in the step S304 into a dynamic equation, and solving a differential equation by a run-Kutta method to obtain the three-way acceleration of the precise instrument;
S503, according to the maximum value of the three-way acceleration of the precision instrument determined in the step S502, obtaining the x-direction buffer effect of the basket type buffer base, the y-direction buffer effect of the basket type buffer base and the z-direction buffer effect of the basket type buffer base.
Compared with the prior art, the method for determining the buffering effect of the basket type buffering device in the design stage is simple and convenient to calculate, easy to operate, high in result accuracy and reliability, free of manufacturing an actual device and complex tests, capable of determining the buffering effect of the basket type buffering device in the design stage, shortened in design period of the basket type buffering device and reduced in test risk of the basket type buffering device.
Drawings
FIG. 1 is a schematic diagram of a basket buffer system of the present invention;
FIG. 2 is a flow chart of a method of determining the buffering effect of a basket buffering device according to the present invention;
FIG. 3 (a) is a front view of a rubber damper in the basket type buffering apparatus of the present invention;
FIG. 3 (b) is a top view of the rubber damper in the basket buffer of the present invention;
FIG. 3 (c) is a three-dimensional view of a rubber damper in the basket type damper according to the present invention;
FIG. 4 is a six-way stiffness damping model of a rubber shock absorber in a basket buffer of the present invention;
FIG. 5 is a coordinate system definition of the basket buffer of the present invention;
FIG. 6 is a graph showing the x-direction acceleration of the precision instrument under x-direction impact determined by the method of determining the cushioning effect of the basket type cushioning device in the design stage according to the embodiment of the present invention;
FIG. 7 is a view showing the y-acceleration of the precision instrument under y-impact determined by the method of determining the cushioning effect of the basket type cushioning device at the design stage according to the embodiment of the present invention;
FIG. 8 is a z-acceleration of the precision instrument under z-impact determined by the method of determining the cushioning effect of the basket type cushioning device at the design stage according to an embodiment of the present invention.
Detailed Description
The invention will now be further described with reference to the accompanying drawings and specific examples, which are in no way limiting.
As shown in fig. 1, the basket buffer system includes a precision instrument 1, a basket buffer bracket 2, a rubber damper 3, a rubber damper stay 4, and a basket buffer floor 5; wherein, the configuration of hanging flower basket buffer device support 2 and rubber shock absorber pillar 4 coincides the focus of precision instrument 1 and the shock absorber array center that four rubber shock absorbers 3 constitute, reduces the motion coupling that strikes to the precision instrument. The large impact is transmitted to the basket type buffer device from the mounting surface through the basket type buffer device bottom plate 5, the shock absorber array formed by the four rubber shock absorbers 3 attenuates the impact through the deformation of the shock absorbers, finally, the impact reaching the basket type buffer device bracket 2 and the precision instrument 1 is far smaller than the impact input on the basket type buffer device bottom plate 5, and finally, the use precision of the precision instrument 1 is improved.
The buffering effect of the basket type buffering device is an important evaluation index for reliable operation of the precision instrument in a large impact environment. Since external impact is generally transferred to the basket type buffering device through a linear motion, the buffering effect is divided into: an x-direction buffer effect, a y-direction buffer effect, and a z-direction buffer effect. The x-direction buffering effect is defined as the ratio of the maximum acceleration of the x-direction precise instrument to the maximum value of the external x-direction linear acceleration, the y-direction buffering effect is defined as the ratio of the maximum acceleration of the y-direction precise instrument to the maximum value of the external y-direction linear acceleration, and the z-direction buffering effect is defined as the ratio of the maximum acceleration of the z-direction precise instrument to the maximum value of the external z-direction linear acceleration.
The prior art mainly adopts a test method to determine the buffering effect of the hanging basket type buffering device, and the specific method comprises the following steps: after the basket type buffer base is designed and manufactured, the basket type buffer base is arranged on an impact table, a precision instrument is arranged on the basket type buffer base, acceleration sensors are respectively attached to an impact table surface and the precision instrument in the x direction, the y direction and the z direction, the impact table is respectively controlled to give large impact to the basket type buffer base in the x direction, the y direction and the z direction, acceleration sensor signals in the same direction as the impact direction on the impact table surface and the precision instrument are collected, and the ratio of the maximum value of the acceleration sensor signals in the same direction as the impact direction on the precision instrument to the maximum value of the acceleration sensor in the same direction as the impact direction on the impact table surface is the buffer effect of the basket type buffer device in the same direction as the impact direction. The test method can reflect the buffering effect of the basket type buffering base more objectively and truly, but has obvious disadvantages: the cycle is long, and if improperly designed, the basket type buffer device and even the precise instrument will be damaged. Therefore, in order to shorten the period and reduce the risk of the test, the determination of the buffering effect of the basket type buffering device must be performed in the design stage; in summary, the method for determining the buffering effect of the basket type buffering device in the design stage solves the problems in the prior art, shortens the design period of the basket type buffering device and reduces the test risk of the basket type buffering device.
As shown in fig. 2, the method for determining the buffering effect of the basket type buffering device in the design stage of the present application is implemented as follows:
s1, constructing a six-way rigidity damping model of each rubber shock absorber, and defining physical parameters of the six-way rigidity damping model of the rubber shock absorber; in particular, the method comprises the steps of,
S101, constructing a six-way rigidity damping model for each rubber shock absorber;
Specifically, as shown in fig. 3 (a), 3 (b) and 3 (c), the center of gravity of the single rubber damper is taken as the origin, the normal direction of the front end surface of the rubber damper base is defined as the forward axis direction, the normal direction of the right end surface of the rubber damper base is defined as the right axis direction, and the normal direction of the top surface of the rubber damper is defined as the upward axis direction; correspondingly, the three axes of the nth rubber damper coordinate system are respectively: forward axis J nRn, right axis J nPn, and radial axis J nSn, n=1, 2,3,4;
s102, defining physical parameters of a six-directional stiffness damping model of the rubber shock absorber;
Specifically, as shown in fig. 4, the rigidities in the three linear directions of the six-directional rigidity damping model of the rubber shock absorber are right-directional rigidity k pn, forward-directional rigidity k rn, and upward-directional rigidity k sn, respectively; the damping in three linear directions are right-direction damping c pn, forward-direction damping c rn and upward-direction damping c sn respectively; the rigidity in the three torsion directions are right-handed rigidity k λn, forward-handed rigidity k ξn and upward-handed rigidity k υn respectively; the three torsional directional damping are respectively right-handed damping c λn, forward-handed damping c ξn and upward-handed damping c υn;
s103, for facilitating simplification of a system dynamics equation, six-direction rigidity damping model parameters of the rubber shock absorber are expressed in a matrix form; based on this, the first and second light sources,
The linear stiffness matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the linear damping matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the torsional stiffness matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the torsional damping matrix defining the six-way stiffness damping model of the rubber shock absorber is:
In the present embodiment, the linear stiffness matrices of the six-way stiffness damping models of the four rubber shock absorbers are all equal, The linear damping matrixes of six-direction stiffness damping models of the four rubber vibration absorbers are equal, and the linear damping matrixes of the six-direction stiffness damping models of the four rubber vibration absorbers are equal in weight percentTorsional rigidity matrixes of six-direction rigidity damping models of four rubber vibration absorbers are equal, and the torsional rigidity matrixes of the six-direction rigidity damping models of the four rubber vibration absorbers are equal in weight percentThe torsional damping matrixes of the six-directional stiffness damping models of the four rubber shock absorbers are equal,
S2, constructing an inertial coordinate system, a precise instrument coordinate system and a vibration damper coordinate system, and defining the relation among the coordinate systems:
s201, as shown in FIG. 5, constructing an inertial coordinate system, a precision instrument coordinate system and a vibration damper coordinate system; in particular, the method comprises the steps of,
Constructing an inertial coordinate system O-XYZ, wherein O coincides with the mass center of the precise instrument under the static state, OY faces to the right front of the precise instrument, OZ faces upwards perpendicular to the precise instrument, OX is obtained by right hand rule, and the characteristic of the inertial coordinate system O-XYZ is static relative to the ground, namely, is consistent with the initial state all the time;
Construction of a precision instrument coordinate System Its static precision instrument coordinate system/>Coincident with inertial coordinate system O-XYZ, and/>Fixedly connected with a precise instrument, and a coordinate system/>, of the precise instrumentIs characterized by moving along with the movement of a precision instrument;
Constructing a damper coordinate system: constructing a damper coordinate system J n-PnRnSn for each damper; wherein n is the position number of the damper, J n is the damping center of the n-th damper, J nRn faces to the right front of the n-th damper, J nSn is vertical to the n-th damper and J nPn is obtained by right hand rule, n=1, 2,3,4; wherein the damper coordinate system J n-PnRnSn is characterized as moving with damper movement;
s202, defining the relation between an inertial coordinate system and a vibration damper coordinate system:
setting any vector to be p n in the damper coordinate system J n-PnRnSn of the nth damper and x in the inertial coordinate system O-XYZ, the conversion relationship between x and p n is:
x＝An·pn+rn，
Where r n is the displacement vector of O relative to J n, which is determined by:
rn＝[rxn ryn rzn]T，
wherein r xn is the projection of the displacement vector of the O point relative to J n in the O-XYZ direction; r yn is the projection of the displacement vector of the O point relative to J n in the OY direction at O-XYZ; r zn is the projection of the displacement vector of the O point relative to J n in the OZ direction at O-XYZ;
A n is the orthogonal transformation matrix of J n-PnRnSn and O-XYZ, which is determined by the rotation angle of each coordinate axis between O-XYZ and J n-PnRnSn:
Where α n,βn and γ n are three components of the rotational Euler angle of O-XYZ relative to J n-PnRnSn: gamma n is the angle of rotation of O-XYZ about J nSn in the first step of rotation of Euler angle relative to J n-PnRnSn, beta n is the angle of rotation of O-XYZ about J nRn in the second step of rotation of Euler angle relative to J n-PnRnSn, alpha n is the angle of rotation of O-XYZ about J nPn in the third step of rotation of Euler angle relative to J n-PnRnSn;
specifically, in the present embodiment:
r1＝[208 233 0]Tmm;r2＝[-178 233 0]Tmm;r3＝[-178 -203 0]Tmm;r4＝[208 -203 0]Tmm;
α1＝α2＝α3＝α4＝0;β1＝β2＝β3＝β4＝0;γ1＝γ2＝γ3＝γ4＝0;
According to the following:
And (3) calculating to obtain:
S3, defining system physical parameters, kinematic parameters, external excitation and buffering effects:
S301, defining system physical parameters, including: combined weight of precision instrument and basket buffer support, combination of precision instrument and basket buffer support relative to precision instrument coordinate system The basket-type buffer device is relative to a precision instrument coordinate system/>Damping matrix of (2), and basket buffer device relative to precision instrument coordinate system/>Is a stiffness matrix of (2);
In particular, the method comprises the steps of,
(1) Defining the combined weight of a precision instrument and a basket type buffer device bracket as m;
(2) Defining a combination of a precision instrument and a basket buffer support relative to a precision instrument coordinate system The moment of inertia of (2) is: /(I)
Wherein,Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>The component on the axis of the shaft,Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>A component on the axis;
Specifically, in this embodiment: m=20 Kg;
(3) Definition and basket type buffer device relative to precision instrument coordinate system Damping matrix/>And stiffness matrix/>The method comprises the following steps of:
The displacement components of the precision instrument relative to the cradle type buffer device base are x, y and z; wherein x is the center of a coordinate system of the precise instrument Projection on OX of displacement relative to inertial frame center O, y being precision instrument frame center/>Projection of displacement on OY relative to inertial coordinate system center O, z is precision instrument coordinate system center/>Projection of the displacement on OZ with respect to the inertial coordinate system center O; the rotation angle components of the precision instrument relative to the cradle type buffer device base are theta, phi and phi; wherein θ is the central coordinate axis/>, of the precision instrument coordinate systemRelative to the rotation angle on the inertial coordinate system axis OX, phi is the center coordinate axis/>, of the precision instrument coordinate systemWith respect to the rotation angle on the inertial coordinate system axis OY, ψ is the precision instrument coordinate system center axis/>With respect to the rotation angle on the inertial coordinate axis OZ. Therefore, the basket buffer device is relative to the precision instrument coordinate system/>Damping matrix/>The meaning of each symbol in (a) is: c xx is the damping force of the basket type buffer device in the x direction generated by the x direction displacement of the precision instrument; c xy is the damping force of the basket type buffer device in the x direction generated by the displacement of the precise instrument in the y direction; c xz is the damping force of the basket type buffer device in the x direction generated by the z direction displacement of the precision instrument; c xθ is the damping force of the basket type buffer device in the x direction generated by the theta direction rotation of the precision instrument; c xφ is the damping force of the basket type buffer device in the x direction generated by the phi-direction rotation of the precision instrument; c xψ is the damping force of the basket type buffer device in the x direction generated by the rotation of the psi direction of the precision instrument; c yx is the damping force of the basket type buffer device in the y direction generated by the x-direction displacement of the precision instrument; c yy is the damping force of the basket type buffer device in the y direction generated by the displacement of the precise instrument in the y direction; c yz is the damping force of the basket type buffer device in the y direction generated by the z direction displacement of the precision instrument; c yθ is the damping force of the basket type buffer device in the y direction generated by the theta direction rotation of the precision instrument; c yφ is the damping force of the basket type buffer device in the y direction generated by the phi-direction rotation of the precision instrument; c yψ is the damping force of the basket type buffer device in the y direction generated by the rotation of the psi direction of the precision instrument; c zx is the damping force of the basket type buffer device in the z direction generated by the x direction displacement of the precision instrument; c zy is the damping force of the basket type buffer device in the z direction generated by the displacement of the precise instrument in the y direction; c zz is the damping force of the basket type buffer device in the z direction generated by the z direction displacement of the precision instrument; c zθ is the damping force of the basket type buffer device in the z direction generated by the theta direction rotation of the precision instrument; c zφ is the damping force of the basket type buffer device in the z direction generated by the phi-direction rotation of the precision instrument; c zψ is the damping force of the basket type buffer device in the z direction generated by the rotation of the psi direction of the precision instrument; c θx is damping moment in theta direction generated by x-direction displacement of the basket type buffer device; c θy is damping moment in theta direction generated by y-direction displacement of the basket type buffer device; c θz is damping moment in theta direction generated by z-direction displacement of the basket type buffer device; c θθ is damping moment in the theta direction generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; c θφ is damping moment in theta direction generated by rotation of the basket type buffer device in phi direction of the precision instrument; c θψ is damping moment in the theta direction generated by rotation of the basket type buffer device in the phi direction of the precision instrument; c φx is the damping moment in phi direction generated by x-direction displacement of the basket type buffer device; c φy is the damping moment in phi direction generated by y-direction displacement of the basket type buffer device by the precision instrument; c φz is the damping moment in phi direction generated by z-direction displacement of the basket type buffer device by the precision instrument; c φθ is the damping moment in phi direction generated by the rotation of the basket type buffer device in theta direction of the precision instrument; c φφ is the damping moment in the phi direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; c φψ is the damping moment in phi direction generated by the rotation of the basket type buffer device in phi direction of the precision instrument; c ψx is the damping moment of the basket type buffer device in the psi direction generated by the x-direction displacement of the precision instrument; c ψy is the damping moment of the basket type buffer device in the psi direction generated by the y-direction displacement of the precision instrument; c ψz is the damping moment of the basket type buffer device in the psi direction generated by the z-direction displacement of the precision instrument; c ψθ is the damping moment of the basket type buffer device in the phi direction generated by the theta direction rotation of the precision instrument; c ψφ is the damping moment of the basket type buffer device in the phi direction generated by the rotation of the precision instrument in the phi direction; c ψψ is the damping moment of the basket type buffer device in the psi direction generated by the rotation of the precision instrument in the psi direction;
similarly, the basket type buffer device is relative to a coordinate system of a precise instrument Stiffness matrix/>The meaning of each symbol in (a) is: k xx is the spring force of the basket type buffer device in the x direction generated by the x direction displacement of the precision instrument; k xy is the spring force of the basket type buffer device in the x direction generated by the displacement of the precise instrument in the y direction; k xz is the spring force of the basket type buffer device in the x direction generated by the z direction displacement of the precision instrument; k xθ is the spring force of the basket type buffer device in the x direction generated by the theta direction rotation of the precision instrument; k xφ is the spring force of the basket type buffer device in the x direction generated by the phi-direction rotation of the precision instrument; k xψ is the spring force of the basket type buffer device in the x direction generated by the rotation of the psi direction of the precision instrument; k yx is the spring force of the basket type buffer device in the y direction generated by the displacement of the precision instrument in the x direction; k yy is the spring force of the basket type buffer device in the y direction generated by the displacement of the precise instrument in the y direction; k yz is the spring force of the basket type buffer device in the y direction generated by the z direction displacement of the precision instrument; k yθ is the spring force of the basket type buffer device in the y direction generated by the theta direction rotation of the precision instrument; k yφ is the spring force of the basket type buffer device in the y direction generated by the phi-direction rotation of the precision instrument; k yψ is the spring force of the basket type buffer device in the y direction generated by the rotation of the psi direction of the precision instrument; k zx is the spring force of the basket type buffer device in the z direction generated by the displacement of the precision instrument in the x direction; k zy is the spring force of the basket type buffer device in the z direction generated by the displacement of the precision instrument in the y direction; k zz is the spring force of the basket type buffer device in the z direction generated by the z direction displacement of the precision instrument; k zθ is the spring force of the basket type buffer device in the z direction generated by the theta direction rotation of the precision instrument; k zφ is the spring force of the basket type buffer device in the z direction generated by the phi-direction rotation of the precision instrument; k zψ is the spring force of the basket type buffer device in the z direction generated by the rotation of the psi direction of the precision instrument; k θx is the spring moment in the theta direction generated by x-direction displacement of the precision instrument of the basket type buffer device; k θy is the spring moment in the theta direction generated by the displacement of the basket type buffer device in the y direction of the precision instrument; k θz is the spring moment in the theta direction generated by z-direction displacement of the precision instrument of the basket type buffer device; k θθ is a spring moment in the theta direction generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; k θφ is the spring moment in the theta direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k θψ is the spring moment in the theta direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k φx is the phi-direction spring moment generated by x-direction displacement of the basket type buffer device by the precision instrument; k φy is the phi-direction spring moment generated by the y-direction displacement of the basket type buffer device by the precision instrument; k φz is the phi-direction spring moment generated by z-direction displacement of the basket type buffer device by the precision instrument; k φθ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; k φφ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k φψ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k ψx is the spring moment of the cradle type buffer device in the psi direction generated by the x-direction displacement of the precision instrument; k ψy is the spring moment of the basket type buffer device in the psi direction generated by the y-direction displacement of the precision instrument; k ψz is the spring moment of the basket type buffer device in the psi direction generated by the z-direction displacement of the precision instrument; k ψθ is the spring moment of the cradle type buffer device in the phi direction generated by the theta direction rotation of the precision instrument; k ψφ is the spring moment of the basket type buffer device in the phi direction generated by the rotation of the precision instrument in the phi direction; k ψψ is a spring moment in the psi direction generated by rotation of the basket type buffer device in the psi direction of the precision instrument;
S302, defining system kinematics parameters, including:
(1) Defining displacement components of the precision instrument relative to a cradle type buffer device base as x, y and z; wherein x is the center of a coordinate system of the precise instrument Projection of displacement on OX relative to inertial frame center O, y being the precision instrument frame centerProjection of displacement on OY relative to inertial coordinate system center O, z is precision instrument coordinate system center/>Projection of the displacement on OZ with respect to the inertial coordinate system center O;
(2) Defining the rotation angle components of the precision instrument relative to the cradle type buffer device base as theta, phi and phi; wherein θ is the central coordinate axis of the precise instrument coordinate system Relative to the rotation angle on the inertial coordinate system axis OX, phi is the center coordinate axis/>, of the precision instrument coordinate systemWith respect to the rotation angle on the inertial coordinate system axis OY, ψ is the precision instrument coordinate system center axis/>Rotation angle on the coordinate axis OZ with respect to the inertial coordinate system;
s303, defining external excitation:
Defining external excitation to be composed of external motion input components u, v, w, alpha, beta and gamma, wherein u is the projection of the displacement of the basket buffer device base relative to an inertial coordinate system on OX, v is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OY, and w is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OZ; alpha is the component of rotation of the basket buffer mount relative to the inertial frame on OX, beta is the component of rotation of the basket buffer mount relative to the inertial frame on OY, and gamma is the component of rotation of the basket buffer mount relative to the inertial frame on OZ;
s304, defining a buffering effect according to the system kinematics parameters and external excitation:
impact based on the outside is generally transferred to the basket type buffer device through linear motion, the buffer effect is divided into x-direction, y-direction and z-direction buffer effects, and the x-direction, y-direction and z-direction buffer effects of the basket type buffer device are defined as follows:
The x-direction buffering effect is the ratio of the maximum acceleration of the x-direction precision instrument to the maximum value of the external x-direction linear acceleration, namely:
the y-direction buffering effect is the ratio of the maximum acceleration of the y-direction precise instrument to the maximum value of the external y-direction linear acceleration, namely: />
the z-direction buffering effect is the ratio of the maximum acceleration of the z-direction precise instrument to the maximum value of the external z-direction linear acceleration, namely:
specifically, in this embodiment, according to the design requirement of the user, in order to obtain the x-direction buffering effect, the external input in the x-direction is made to be a half sine wave impact with an amplitude of 200g and a period of 10ms, and the external input in the other directions is made to be 0, namely:
according to the design requirement of a user, in order to obtain the y-direction buffering effect, the y-direction external input is half sine wave impact with the amplitude of 200g and the period of 10ms, and the other directions of external input are 0, namely:
According to the design requirement of a user, in order to obtain a z-direction buffering effect, the external input in the z direction is half sine wave impact with the amplitude of 200g and the period of 10ms, and the external input in the other directions is 0, namely:
In the above three formulas, g=9.8 m/s 2, t=10 ms;
s4, constructing and simplifying a kinetic equation of the hanging basket type buffer device:
Based on the system physical parameters, the system kinematic parameters and the external excitation defined in the step S3, determining a six-degree-of-freedom kinetic equation of the basket type buffer device as follows:
In order to simplify the kinetic equation of the basket type buffer device, the above formula is divided into a block matrix form:
Substituting each block matrix in the above formula by a simplified matrix symbol to obtain:
wherein M is a mass blocking matrix of a combination of the precision instrument and the basket type buffer device bracket, The moment of inertia block matrix is the combination of a precision instrument and a basket type buffer device bracket, X is a displacement block matrix of the precision instrument relative to the basket type buffer device bottom plate in three directions of X, y and z, theta is a rotation block matrix of the precision instrument relative to the basket type buffer device bottom plate in three directions of theta, phi and phi, C xx is a damping force block matrix of the basket type buffer device generated by displacement of the precision instrument in three directions of X, y and z, C xθ is a damping force block matrix of the basket type buffer device generated by rotation of the precision instrument in three directions of theta, phi and phi in three directions of X, y and z, C θx is a damping moment block matrix of the basket type buffer device generated by displacement of the precision instrument in three directions of X, y and phi in three directions of phi, C θθ is a damping moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by rotation of the precision instrument, K xx is a spring force block matrix of the basket type buffer device in the three directions of X, y and z generated by displacement of the precision instrument, K xθ is a spring force block matrix of the basket type buffer device in the three directions of X, y and z generated by rotation of the precision instrument, K θx is a spring moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by displacement of the precision instrument, K θθ is a spring moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by rotation of the precision instrument, the spring moment block matrix in three directions of phi is a displacement block matrix in three directions of x, y and z of external excitation, and alpha is a rotation block matrix in three directions of theta, phi and phi of external excitation.
S5, calculating to obtain the maximum value of the three-way acceleration of the precise instrument and the buffering effect according to external impact:
In the dynamic equation of the basket buffer device in step S4, X and Θ are the quantities to be solved, M and I O are known physical parameters of the system, and U and α are known external inputs, so that the dynamic equation of the basket buffer device needs to be solved by calculating C xx、Cxθ、Cθx、Cθθ、Kxx、Kxθ、Kθx and K θθ;
According to the definition and coordinate conversion of the step S3, the following steps are obtained:
In the above two formulas, C xxn＝[An][Cpn][An]T, Kxxn＝[An][Kpn][An]T；
Specifically, in the present embodiment, it is calculated by:
The various calculated above are carried into a dynamic equation, and the external excitation defined in the step S304 is carried into the dynamic equation at the same time, and a differential equation is solved by a run-Kutta method, so that the three-way acceleration and buffering effect of the precise instrument can be obtained; in particular, the method comprises the steps of,
As shown in fig. 6, under the x-direction impact, the maximum acceleration of the precision instrument in the x-direction is: 68g, the x-direction buffering effect of the basket type buffering base is as follows:
as shown in fig. 7, under the impact in the y direction, the maximum acceleration in the y direction of the precision instrument is: 72g, so the y-direction buffering effect of the basket type buffering base is as follows:
As shown in fig. 8, under z-direction impact, the maximum acceleration of the precision instrument in the z-direction is: 53g, so the z-direction buffering effect of the basket type buffering base is as follows:
In order to verify the reliability of the method for determining the buffering effect of the hanging basket type buffering device in the design stage, the three-way buffering effect of the hanging basket type buffering device obtained by adopting the existing test method is compared with the three-way buffering effect of the hanging basket type buffering device determined by the method. Referring to fig. 1, a basket style buffer base is designed and manufactured. And then installing the basket type buffer base on the impact table, installing the precision instrument on the basket type buffer base, attaching acceleration sensors on the table surface of the impact table and the precision instrument in the x direction, the y direction and the z direction respectively, controlling the impact table to impact the basket type buffer base greatly in the x direction, the y direction and the z direction respectively, collecting acceleration sensor signals in the same direction as the impact direction on the table surface of the impact table and the precision instrument, and acquiring the buffer effect of the basket type buffer device in the corresponding direction, wherein the ratio of the maximum value of the acceleration sensor signals in the same direction as the impact direction on the precision instrument to the maximum value of the acceleration sensor in the same direction as the impact direction on the table surface of the impact table. The results of comparing the three-way buffering effect of the basket type buffering base obtained by the existing test method with the three-way buffering effect of the basket type buffering base determined by the method of the present application are shown in Table 1. As can be seen from table 1, the maximum difference between the three-way buffering effect of the basket type buffering base obtained by the method and the three-way buffering effect of the basket type buffering base obtained by the existing test method is only 1%, and the accuracy and the reliability of the method provided by the application are verified.
TABLE 1
/>

Claims (6)

1. The method for determining the buffering effect of the basket type buffering device in the design stage is characterized by comprising the following steps of:
S1, constructing a six-way rigidity damping model of each rubber shock absorber, and defining physical parameters of the six-way rigidity damping model of the rubber shock absorber, wherein the physical parameters comprise rigidity and damping in three linear directions and rigidity and damping in three torsion directions of the six-way rigidity damping model;
s2, constructing an inertial coordinate system, a precise instrument coordinate system and a vibration damper coordinate system, and defining the relation among the coordinate systems;
S3, defining physical parameters of the system, wherein the physical parameters comprise the combined weight of the precision instrument and the basket type buffer device bracket, and the combination of the precision instrument and the basket type buffer device bracket is relative to a coordinate system of the precision instrument The basket-type buffer device is relative to a precision instrument coordinate system/>Damping matrix of (c), and basket buffer device relative to precision instrument coordinate systemIs a stiffness matrix of (2); defining kinematic parameters, including a displacement component of the precision instrument relative to the basket type buffer device base and a rotation angle component of the precision instrument relative to the basket type buffer device base; defining external stimulus consisting of components of external motion input; the method comprises the steps that impact based on the outside world is transmitted to a basket type buffer device through linear motion to define a buffer effect, wherein the buffer effect in the x direction is a ratio of the maximum acceleration of an x-direction precise instrument to the maximum value of external x-direction linear acceleration, the buffer effect in the y direction is a ratio of the maximum acceleration of the y-direction precise instrument to the maximum value of external y-direction linear acceleration, and the buffer effect in the z direction is a ratio of the maximum acceleration of a z-direction precise instrument to the maximum value of external z-direction linear acceleration;
s4, constructing a six-degree-of-freedom dynamics equation of the basket type buffer device based on the system physical parameters, the system kinematic parameters and the external excitation defined in the step S3;
S5, calculating the maximum value of the three-way acceleration of the precision instrument according to external impact, and obtaining the x-direction buffer effect of the basket type buffer base, the y-direction buffer effect of the basket type buffer base and the z-direction buffer effect of the basket type buffer base.
2. The method for determining the buffering effect of a basket buffer device in a design phase according to claim 1, wherein the specific implementation step of step S1 is as follows:
S101, taking the gravity center of a single rubber shock absorber as an origin, defining the normal direction of the front end surface of a rubber shock absorber base as a forward axial direction, defining the normal direction of the right end surface of the rubber shock absorber base as a right axial direction, and defining the normal direction of the top surface of the rubber shock absorber as an upward axial direction; the three axes of the nth rubber damper coordinate system are: forward axis J nRn, right axis J nPn, and radial axis J nSn, n=1, 2,3,4;
s102, defining three linear directions of rigidity of a six-direction rigidity damping model of the rubber shock absorber to be right-direction rigidity k pn, forward-direction rigidity k rn and upward-direction rigidity k sn respectively; the damping in three linear directions are right-direction damping c pn, forward-direction damping c rn and upward-direction damping c sn respectively; the rigidity in the three torsion directions are right-handed rigidity k λn, forward-handed rigidity k ξn and upward-handed rigidity k υn respectively; the three torsional directional damping are respectively right-handed damping c λn, forward-handed damping c ξn and upward-handed damping c υn;
s103, representing various parameters of a six-directional stiffness damping model of the rubber shock absorber in a matrix form:
The linear stiffness matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the linear damping matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the torsional stiffness matrix defining the six-way stiffness damping model of the rubber shock absorber is:
the torsional damping matrix defining the six-way stiffness damping model of the rubber shock absorber is:
3. The method for determining the buffering effect of a basket buffer device in the design phase according to claim 2, wherein the specific implementation step of step S2 is as follows:
S201, constructing an inertial coordinate system, a precise instrument coordinate system and a vibration damper coordinate system: constructing an inertial coordinate system O-XYZ, wherein O coincides with the mass center of the precise instrument under the static state, OY faces to the right front of the precise instrument, OZ faces upwards perpendicular to the precise instrument, OX is obtained by right hand rule, and the characteristic of the inertial coordinate system O-XYZ is static relative to the ground, namely, is consistent with the initial state all the time; construction of a precision instrument coordinate System Its static precision instrument coordinate system/>Coincident with inertial coordinate system O-XYZ, and/>Fixedly connected with a precise instrument, and a coordinate system/>, of the precise instrumentIs characterized by moving along with the movement of a precision instrument; constructing a damper coordinate system: constructing a damper coordinate system J n-PnRnSn for each damper; wherein n is the position number of the damper, J n is the damping center of the n-th damper, J nRn faces to the right front of the n-th damper, J nSn is vertical to the n-th damper and J nPn is obtained by right hand rule, n=1, 2,3,4;
s202, defining the relation between an inertial coordinate system and a vibration damper coordinate system:
setting any vector to be p n in the damper coordinate system J n-PnRnSn of the nth damper and x in the inertial coordinate system O-XYZ, the conversion relationship between x and p n is:
x＝An·pn+rn，
Where r n is the displacement vector of O relative to J n, which is determined by:
rn＝[rxn ryn rzn]T，
wherein r xn is the projection of the displacement vector of the O point relative to J n in the O-XYZ direction; r yn is the projection of the displacement vector of the O point relative to J n in the OY direction at O-XYZ; r zn is the projection of the displacement vector of the O point relative to J n in the OZ direction at O-XYZ;
A n is the orthogonal transformation matrix of J n-PnRnSn and O-XYZ, which is determined by the rotation angle of each coordinate axis between O-XYZ and J n-PnRnSn:
Where α n,βn and γ n are three components of the rotational Euler angle of O-XYZ relative to J n-PnRnSn: gamma n is the angle of rotation of O-XYZ about J nSn for the first step in the rotation euler angle of J n-PnRnSn, beta n is the angle of rotation of O-XYZ about J nRn for the second step in the rotation euler angle of J n-PnRnSn, and alpha n is the angle of rotation of O-XYZ about J nPn for the third step in the rotation euler angle of J n-PnRnSn.
4. A method for determining a buffering effect of a basket buffer according to claim 3, wherein the step S3 is specifically implemented as follows:
s301, defining system physical parameters, including:
defining the combined weight of a precision instrument and a basket type buffer device bracket as m;
Defining a combination of a precision instrument and a basket buffer support relative to a precision instrument coordinate system The moment of inertia of (2) is: /(I)
Wherein,Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>The component on the axis of the shaft,Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>Component on axis,/>Relative to the shaft/>, for a combination of precision instruments and basket buffer supportsThe moment of inertia of/>A component on the axis;
definition and basket type buffer device relative to precision instrument coordinate system Damping matrix/>And stiffness matrix/>The method comprises the following steps of:
The displacement components of the precision instrument relative to the cradle type buffer device base are x, y and z; wherein x is the center of a coordinate system of the precise instrument Projection on OX of displacement relative to inertial frame center O, y being precision instrument frame center/>Projection of displacement on OY relative to inertial coordinate system center O, z is precision instrument coordinate system center/>Projection of the displacement on OZ with respect to the inertial coordinate system center O; the rotation angle components of the precision instrument relative to the cradle type buffer device base are theta, phi and phi; wherein θ is the central coordinate axis/>, of the precision instrument coordinate systemRelative to the rotation angle on the inertial coordinate system axis OX, phi is the center coordinate axis/>, of the precision instrument coordinate systemWith respect to the rotation angle on the inertial coordinate system axis OY, ψ is the precision instrument coordinate system center axis/>Rotation angle on the coordinate axis OZ with respect to the inertial coordinate system; therefore, the basket buffer device is relative to the precision instrument coordinate system/>Damping matrix/>The meaning of each symbol in (a) is: c xx is the damping force of the basket type buffer device in the x direction generated by the x direction displacement of the precision instrument; c xy is the damping force of the basket type buffer device in the x direction generated by the displacement of the precise instrument in the y direction; c xz is the damping force of the basket type buffer device in the x direction generated by the z direction displacement of the precision instrument; c xθ is the damping force of the basket type buffer device in the x direction generated by the theta direction rotation of the precision instrument; c xφ is the damping force of the basket type buffer device in the x direction generated by the phi-direction rotation of the precision instrument; c xψ is the damping force of the basket type buffer device in the x direction generated by the rotation of the psi direction of the precision instrument; c yx is the damping force of the basket type buffer device in the y direction generated by the x-direction displacement of the precision instrument; c yy is the damping force of the basket type buffer device in the y direction generated by the displacement of the precise instrument in the y direction; c yz is the damping force of the basket type buffer device in the y direction generated by the z direction displacement of the precision instrument; c yθ is the damping force of the basket type buffer device in the y direction generated by the theta direction rotation of the precision instrument; c yφ is the damping force of the basket type buffer device in the y direction generated by the phi-direction rotation of the precision instrument; c yψ is the damping force of the basket type buffer device in the y direction generated by the rotation of the psi direction of the precision instrument; c zx is the damping force of the basket type buffer device in the z direction generated by the x direction displacement of the precision instrument; c zy is the damping force of the basket type buffer device in the z direction generated by the displacement of the precise instrument in the y direction; c zz is the damping force of the basket type buffer device in the z direction generated by the z direction displacement of the precision instrument; c zθ is the damping force of the basket type buffer device in the z direction generated by the theta direction rotation of the precision instrument; c zφ is the damping force of the basket type buffer device in the z direction generated by the phi-direction rotation of the precision instrument; c zψ is the damping force of the basket type buffer device in the z direction generated by the rotation of the psi direction of the precision instrument; c θx is damping moment in theta direction generated by x-direction displacement of the basket type buffer device; c θy is damping moment in theta direction generated by y-direction displacement of the basket type buffer device; c θz is damping moment in theta direction generated by z-direction displacement of the basket type buffer device; c θθ is damping moment in the theta direction generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; c θφ is damping moment in theta direction generated by rotation of the basket type buffer device in phi direction of the precision instrument; c θψ is damping moment in the theta direction generated by rotation of the basket type buffer device in the phi direction of the precision instrument; c φx is the damping moment in phi direction generated by x-direction displacement of the basket type buffer device; c φy is the damping moment in phi direction generated by y-direction displacement of the basket type buffer device by the precision instrument; c φz is the damping moment in phi direction generated by z-direction displacement of the basket type buffer device by the precision instrument; c φθ is the damping moment in phi direction generated by the rotation of the basket type buffer device in theta direction of the precision instrument; c φφ is the damping moment in the phi direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; c φψ is the damping moment in phi direction generated by the rotation of the basket type buffer device in phi direction of the precision instrument; c ψx is the damping moment of the basket type buffer device in the psi direction generated by the x-direction displacement of the precision instrument; c ψy is the damping moment of the basket type buffer device in the psi direction generated by the y-direction displacement of the precision instrument; c ψz is the damping moment of the basket type buffer device in the psi direction generated by the z-direction displacement of the precision instrument; c ψθ is the damping moment of the basket type buffer device in the phi direction generated by the theta direction rotation of the precision instrument; c ψφ is the damping moment of the basket type buffer device in the phi direction generated by the rotation of the precision instrument in the phi direction; c ψψ is the damping moment of the basket type buffer device in the psi direction generated by the rotation of the precision instrument in the psi direction;
similarly, the basket type buffer device is relative to a coordinate system of a precise instrument The meaning of each symbol in the stiffness matrix K O is: k xx is the spring force of the basket type buffer device in the x direction generated by the x direction displacement of the precision instrument; k xy is the spring force of the basket type buffer device in the x direction generated by the displacement of the precise instrument in the y direction; k xz is the spring force of the basket type buffer device in the x direction generated by the z direction displacement of the precision instrument; k xθ is the spring force of the basket type buffer device in the x direction generated by the theta direction rotation of the precision instrument; k xφ is the spring force of the basket type buffer device in the x direction generated by the phi-direction rotation of the precision instrument; k xψ is the spring force of the basket type buffer device in the x direction generated by the rotation of the psi direction of the precision instrument; k yx is the spring force of the basket type buffer device in the y direction generated by the displacement of the precision instrument in the x direction; k yy is the spring force of the basket type buffer device in the y direction generated by the displacement of the precise instrument in the y direction; k yz is the spring force of the basket type buffer device in the y direction generated by the z direction displacement of the precision instrument; k yθ is the spring force of the basket type buffer device in the y direction generated by the theta direction rotation of the precision instrument; k yφ is the spring force of the basket type buffer device in the y direction generated by the phi-direction rotation of the precision instrument; k yψ is the spring force of the basket type buffer device in the y direction generated by the rotation of the psi direction of the precision instrument; k zx is the spring force of the basket type buffer device in the z direction generated by the displacement of the precision instrument in the x direction; k zy is the spring force of the basket type buffer device in the z direction generated by the displacement of the precision instrument in the y direction; k zz is the spring force of the basket type buffer device in the z direction generated by the z direction displacement of the precision instrument; k zθ is the spring force of the basket type buffer device in the z direction generated by the theta direction rotation of the precision instrument; k zφ is the spring force of the basket type buffer device in the z direction generated by the phi-direction rotation of the precision instrument; k zψ is the spring force of the basket type buffer device in the z direction generated by the rotation of the psi direction of the precision instrument; k θx is the spring moment in the theta direction generated by x-direction displacement of the precision instrument of the basket type buffer device; k θy is the spring moment in the theta direction generated by the displacement of the basket type buffer device in the y direction of the precision instrument; k θz is the spring moment in the theta direction generated by z-direction displacement of the precision instrument of the basket type buffer device; k θθ is a spring moment in the theta direction generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; k θφ is the spring moment in the theta direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k θψ is the spring moment in the theta direction generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k φx is the phi-direction spring moment generated by x-direction displacement of the basket type buffer device by the precision instrument; k φy is the phi-direction spring moment generated by the y-direction displacement of the basket type buffer device by the precision instrument; k φz is the phi-direction spring moment generated by z-direction displacement of the basket type buffer device by the precision instrument; k φθ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the theta direction of the precision instrument; k φφ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k φψ is the phi-direction spring moment generated by the rotation of the basket type buffer device in the phi direction of the precision instrument; k ψx is the spring moment of the cradle type buffer device in the psi direction generated by the x-direction displacement of the precision instrument; k ψy is the spring moment of the basket type buffer device in the psi direction generated by the y-direction displacement of the precision instrument; k ψz is the spring moment of the basket type buffer device in the psi direction generated by the z-direction displacement of the precision instrument; k ψθ is the spring moment of the cradle type buffer device in the phi direction generated by the theta direction rotation of the precision instrument; k ψφ is the spring moment of the basket type buffer device in the phi direction generated by the rotation of the precision instrument in the phi direction; k ψψ is a spring moment in the psi direction generated by rotation of the basket type buffer device in the psi direction of the precision instrument;
S302, defining system kinematics parameters, including:
defining displacement components of the precision instrument relative to a cradle type buffer device base as x, y and z; wherein x is the center of a coordinate system of the precise instrument Projection on OX of displacement relative to inertial frame center O, y being precision instrument frame center/>Projection of displacement on OY relative to inertial coordinate system center O, z is precision instrument coordinate system center/>Projection of the displacement on OZ with respect to the inertial coordinate system center O;
Defining the rotation angle components of the precision instrument relative to the cradle type buffer device base as theta, phi and phi; wherein θ is the central coordinate axis of the precise instrument coordinate system Relative to the rotation angle on the inertial coordinate system axis OX, phi is the center coordinate axis/>, of the precision instrument coordinate systemWith respect to the rotation angle on the inertial coordinate system axis OY, ψ is the precision instrument coordinate system center axis/>Rotation angle on the coordinate axis OZ with respect to the inertial coordinate system;
S303, defining that external excitation consists of external motion input components including u, v, w, alpha, beta and gamma, wherein u is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OX, v is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OY, and w is the projection of the displacement of the basket buffer device base relative to the inertial coordinate system on OZ; alpha is the component of rotation of the basket buffer mount relative to the inertial frame on OX, beta is the component of rotation of the basket buffer mount relative to the inertial frame on OY, and gamma is the component of rotation of the basket buffer mount relative to the inertial frame on OZ;
s304, defining a buffering effect according to the system kinematics parameters and external excitation:
based on the impact of the outside, the impact is transmitted to the basket type buffer device through linear motion, and the buffer effect of the basket type buffer device is defined to be divided into x-direction buffer effect, y-direction buffer effect and z-direction buffer effect; the following are provided:
The x-direction buffering effect is the ratio of the maximum acceleration of the x-direction precision instrument to the maximum value of the external x-direction linear acceleration, namely:
the y-direction buffering effect is the ratio of the maximum acceleration of the y-direction precise instrument to the maximum value of the external y-direction linear acceleration, namely:
the z-direction buffering effect is the ratio of the maximum acceleration of the z-direction precise instrument to the maximum value of the external z-direction linear acceleration, namely:
5. The method for determining the buffering effect of a basket buffer device in the design phase of claim 4, wherein the step S4 is specifically implemented as follows:
s401, determining a six-degree-of-freedom kinetic equation of the basket type buffer device based on the system physical parameters, the system kinematic parameters and the external excitation defined in the step S3, wherein the six-degree-of-freedom kinetic equation is as follows:
S402, simplifying a kinetic equation of the basket type buffer device into a block matrix form:
wherein M is a mass blocking matrix of a combination of the precision instrument and the basket type buffer device bracket, The moment of inertia block matrix is the combination of a precision instrument and a basket type buffer device bracket, X is a displacement block matrix of the precision instrument relative to the basket type buffer device bottom plate in three directions of X, y and z, theta is a rotation block matrix of the precision instrument relative to the basket type buffer device bottom plate in three directions of theta, phi and phi, C xx is a damping force block matrix of the basket type buffer device generated by displacement of the precision instrument in three directions of X, y and z, C xθ is a damping force block matrix of the basket type buffer device generated by rotation of the precision instrument in three directions of theta, phi and phi in three directions of X, y and z, C θx is a damping moment block matrix of the basket type buffer device generated by displacement of the precision instrument in three directions of X, y and phi in three directions of phi, C θθ is a damping moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by rotation of the precision instrument, K xx is a spring force block matrix of the basket type buffer device in the three directions of X, y and z generated by displacement of the precision instrument, K xθ is a spring force block matrix of the basket type buffer device in the three directions of X, y and z generated by rotation of the precision instrument, K θx is a spring moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by displacement of the precision instrument, K θθ is a spring moment block matrix of the basket type buffer device in the three directions of theta, phi and phi generated by rotation of the precision instrument, the spring moment block matrix in three directions of phi is a displacement block matrix in three directions of x, y and z of external excitation, and alpha is a rotation block matrix in three directions of theta, phi and phi of external excitation.
6. The method for determining the buffering effect of a basket buffer device in the design phase according to claim 5, wherein the specific implementation step of step S5 is:
s501, according to the definition of the step S3 and coordinate conversion, obtaining:
In the above two formulas, C xxn＝[An][Cpn][An]T, Kxxn＝[An][Kpn][An]T；
S502, bringing the various calculated above and the external excitation defined in the step S304 into a dynamic equation, and solving a differential equation by a run-Kutta method to obtain the three-way acceleration of the precise instrument;
S503, according to the maximum value of the three-way acceleration of the precision instrument determined in the step S502, obtaining the x-direction buffer effect of the basket type buffer base, the y-direction buffer effect of the basket type buffer base and the z-direction buffer effect of the basket type buffer base.
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