CN106354921A - Allocation design method for stiffness on different position of fixed joint surface of machine - Google Patents

Allocation design method for stiffness on different position of fixed joint surface of machine Download PDF

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CN106354921A
CN106354921A CN201610740781.7A CN201610740781A CN106354921A CN 106354921 A CN106354921 A CN 106354921A CN 201610740781 A CN201610740781 A CN 201610740781A CN 106354921 A CN106354921 A CN 106354921A
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column
stiffness
design
lathe bed
faying face
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张大卫
张军傲
石光
石一光
郭悟斌
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Tianjin University
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Abstract

The invention discloses an allocation design method for stiffness on different position of fixed joint surface of machine, comprising the steps of (1) confirming every parameter of machine to be analyzed; (2) extracting all degree of freedom of bed and column of machine to be analyzed; (3) building dynamic model of bed and column system; (4) confirming the design space of variable and building equation of motion for non-damping vibration of system with multi degree of freedom; (5) constructing two-phase response surface model and conducting allocation design for the stiffness on different position of fixed joint surface of machine by using genetic algorithm iterative approximation optimum seeking technology; and (6) using finite element analysis software ANSYS to verify the optimize results. The method processes estimation and allocation design for the stiffness on different position fixed joint surface of bed and column and thus improves dynamic character of machine.

Description

A kind of Fixed Joints in Machine Tools various location stiffness parameters distribution design method
Technical field
The present invention relates to a kind of stiffness parameters planing method of bed piece column fixed combinating surface various location, specifically Say, be to be related to a kind of distribution of precision machine tool fixed combinating surface various location stiffness parameters based on response surface and genetic algorithm Method for designing.
Background technology
The dynamic property of lathe is to machine finish and working (machining) efficiency important, right in traditional Machine Tool design At each position of faying face, the process of stiffness parameters is allocated according to previous experiences, and this method is more subjective, is unfavorable for protecting Card machine dynamic performance.
Currently for various location stiffness parameters at precision machine tool fixed combinating surface distribution design still be limited to single The optimum method in position, its essence is that designer, according to design experiences, distributes the stiffness parameters at each position, then to limited Individual position carries out numerical simulation analysis calculating, then therefrom selects the stiffness parameters of optimum.This method is difficult to ensure that numerous positions The stiffness parameters put during combination are optimum to machine dynamic characteristics, and select parameter calculating needs with carrying out numerical simulation analysis simultaneously Plenty of time to be consumed is it is impossible to meet modern machine design production requirement.
It is therefore proposed that a kind of precision machine tool fixed combinating surface various location rigidity ginseng based on response surface and genetic algorithm Number distribution design method, solves design efficiency and the low problem of design accuracy, is present invention technical problem urgently to be resolved hurrily.
Content of the invention
The invention aims to overcoming deficiency of the prior art, provide a kind of based on response surface and genetic algorithm Precision machine tool fixed combinating surface various location stiffness parameters distribution design method, to positions different at lathe bed column fixed combinating surface The stiffness parameters at the place of putting are estimated and distribution design, thus improving the dynamic characteristic of lathe.
The purpose of the present invention is achieved through the following technical solutions:
A kind of Fixed Joints in Machine Tools various location stiffness parameters distribution design method, comprises the following steps:
(1) parameters of lathe to be analyzed are determined: include lathe bed column overall dimensions, faying face interface relative position Size, the mass parameter of lathe bed column and rotary inertia parameter；
(2) whole degree of freedom of bed piece column to be analyzed are extracted；
(3) set up the kinetic model of lathe bed upright post system；
(4) determine the design space of variable, set up the equation of motion of many-degrees of freedom system non-damping vibration, with bed piece Column head rank natural frequency, as design object, using the stiffness parameters of fixed combinating surface diverse location as design variable, is based on Matlab software utilizes the equation of motion of many-degrees of freedom system undamped-free vibration to obtain lathe head rank natural frequency and lathe bed The sample point of column faying face position stiffness parameter；
(5) build second-order response surface model, using genetic algorithm cyclic approximation optimization technology to Fixed Joints in Machine Tools not It is allocated designing with the stiffness parameters of position；
(6) finite element analysis software ansys is utilized to verify optimum results: Fixed Joints in Machine Tools in step (5) is different At position, the optimum allocation relational result of stiffness parameters is imparted on lathe bed column faying face, imports to finite element analysis software In ansys, and add constraint, carry out model analyses；First rank natural frequency before and after stiffness parameters distribution is contrasted, if Stiffness parameters distribution design meets requirement, then export optimum results, and terminate design process；Otherwise, re-start genetic algorithm Optimizing, till meeting design requirement.
In step (2), the vibration of lathe bed column is summarized as 12 degree of freedom, is translation and the rotation in lathe bed x direction respectively, y The translation in direction and rotation, the translation in z direction and rotation, the translation in column x direction and rotation, the translation in y direction and rotation, z The translation in direction and rotation.
In step (4) using the limit range of lathe bed column faying face rigidity as variable design space, its medial bed stand The least limit of post faying face stiffness variation is the 60% of initial faying face rigidity, and maximum limit is initial faying face rigidity 150%.
Compared with prior art, technical scheme is had the benefit that
The present invention passes through to solve the kinetics equation of exquisite system, is fixed the stiffness parameters of faying face various location With the relation of system head rank natural frequency, set up response surface model, dynamic performance is met by genetic algorithm optimizing Optimal Stiffness parameter, improve machine tooling efficiency and machining accuracy, decrease manufacturing cost, there is stronger grasping The property made, design and simulation analysis for lathe provide support.
Brief description
Fig. 1 is the overall flow figure of the inventive method；
Fig. 2 is the kinetic model schematic diagram of bed piece column；
Fig. 3-1 is the overlooking the structure diagram of bed piece column fixed combinating surface；Fig. 3-2 is that bed piece column is fixed The relative position scale diagrams of faying face.
Specific embodiment
For content of the invention, feature and effect of the present invention can be further appreciated that, hereby enumerate following examples, and coordinate accompanying drawing Describe in detail as follows, Fig. 1 is the overall flow figure of the inventive method, and the method for designing step for specific embodiment is as follows:
(1) parameters needed for precision machine tool to be analyzed are determined
Parameters needed for precision machine tool to be analyzed are respectively lathe bed column overall dimensions, faying face interface relative position Size, the mass parameter of lathe bed column and rotary inertia parameter.Lathe bed column to be analyzed and geometric parameter needed for faying face items As shown in Fig. 2 wherein faying face interface relative position a size of a3、a4、a5、c4、c6、c7、c8, column rotary inertia parameter is ix1、iy1、iz1, lathe bed rotary inertia parameter be ix2、iy2、iz2, column mass parameter is m1, lathe bed mass parameter is m2.
(2) whole degree of freedom of lathe bed column to be analyzed are extracted
For the more detailed accurate description all vibration shape of lathe bed column and the correctness for model foundation, lathe bed is stood Post vibration is summarized as 12 degree of freedom, is translation and rotation, the translation in y direction and the rotation in lathe bed x direction respectively, z direction Translation and rotation, the translation in column x direction and rotation, the translation in y direction and rotation, the translation in z direction and rotation, use qiCarry out table Show.
(3) set up the kinetic model of lathe bed upright post system
Set up machine tool structure total kinetic energy, total potential energy and Rayleigh power consumption letter using Lagrange's equation and law of conservation of energy Number.Lagrange's equation is:
d d t [ ∂ t ∂ x · i ] - ∂ t ∂ x i = q - - - ( 1 )
In formula: xiFor system generalized coordinates, q is system generalized force, and t is system total kinetic energy.
Mass of system matrix [m], stiffness matrix [k] and damping are obtained by the power consumption of system total kinetic energy, total potential energy and Rayleigh Matrix [c], study herein is the natural frequency of system free vibration, does not therefore consider Rayleigh power consumption and damping matrix.
For the lathe bed upright post system of research, q is by broad sense forceGeneralized linear damping forceAnd broad sense exciting force Q' composition it may be assumed that
q = - ∂ v ∂ x i - ∂ d ∂ x i + q ′ - - - ( 2 )
Formula (1) is brought into formula (2), obtains
d d t [ ∂ t ∂ x · i ] - ∂ t ∂ x i + ∂ v ∂ x i + ∂ d ∂ x · i = q ′ - - - ( 3 )
In formula: v is the total potential energy of system, d consumes energy for system Rayleigh.
Obtain kinetic energy and the potential energy of lathe bed column respectively, the kinetic energy of lathe bed column is added and obtains final product system total kinetic energy t, and lathe bed stands The potential energy of post is added and obtains final product system total potential energy v, is updated in formula (3), you can obtain the Lagrange's equation with regard to lathe bed column.
(4) determine the design space of variable, set up the equation of motion of many-degrees of freedom system non-damping vibration.
The distribution of lathe bed column fixed combinating surface attachment bolt assumes " concave shape ", can be seen that from Fig. 3-1 and Fig. 3-2 It is respectively provided with a stiffness parameters variable in each position, that is, every string, the position of every a line are respectively provided with variable, and setting 8 is firm altogether The variable of degree parameter.Determine variable design space when it is contemplated that faying face rigidity actual change situation, medial bed of the present invention stands Post faying face stiffness variation scope is respectively as follows: 60% that least limit is initial faying face rigidity, and maximum limit is initial combination The 150% of face rigidity, the limit range of above-mentioned faying face rigidity is each Variational Design space.
The structure choosing sample point from design space to the response surface is most important, after undesirable testing site not only affects The precision of face response surface model, or even described response surface model can be caused cannot to build, therefore theoretical next according to experimental design Determine rational sample point.In order to build described response surface model, the EXPERIMENTAL DESIGN of the present invention selects optimum Latin hypercube method Algorithm, this algorithm for design improves the uniformity of random Latin hypercube method design, makes factor more smart with the matching of response Really true, thus ensureing the approximation quality in whole design space for the approximate model building.
From Lagrange's equation determined by step (3), substitute into lathe bed column overall dimensions, faying face interface relatively The relative dimensions such as position dimension, the mass parameter of lathe bed column and rotary inertia parameter, solve power based on matlab software Learn mass matrix and the stiffness matrix of equation, set up the equation of motion of many-degrees of freedom system non-damping vibration.Many free systems are no The equation of motion of free decaying vibration is:
m { q ·· } + k { q } = 0 - - - ( 4 )
Wherein m is the mass matrix of system；K is the stiffness matrix of system；q、For the displacement of system, acceleration；
Using system head rank natural frequency as design object, many-degrees of freedom system undamped is utilized certainly based on matlab software Obtain the functional relationship of lathe head rank natural frequency and lathe bed column faying face position stiffness parameter by the equation of motion vibrating, and Extract described test sample point response value, be that response surface matching lays the foundation.
(5) build second-order response surface model, then utilize genetic algorithm cyclic approximation optimization technology to described precision machine tool The stiffness parameters of fixed combinating surface diverse location are allocated designing.
Response surface model is to represent recessive described design variable in optimization problem and institute with dominant function expression State the relation between response value.The described precision machine tool fixed combinating surface various location rigidity based on response surface and genetic algorithm Parametric distribution method for designing selects the conventional second-order response surface model with high accuracy, for the institute of n design variable State second-order response surface model can be expressed as:
y = β 0 + σ i = 1 n β i x i + σ i = 1 n σ i = 1 n β i j x i x j - - - ( 5 )
In formula: y is output variable；xiFor design variable；N is the number of design variable；β is undetermined coefficient；
The variable sample space of points of application optimum Latin hypercube method construction, comprises 8 design variables, altogether based on matlab Software solves and obtains lathe head rank natural frequency and the corresponding relation of lathe bed column faying face position stiffness parameter, sets up the response surface Model.
The stiffness parameters of described precision machine tool fixed combinating surface diverse location are allocated design using genetic algorithm, one Aspect can fully utilize the ability of searching optimum of genetic algorithm, Finding Global Optimization in fairly large solution space； On the other hand, using genetic algorithm implinit parallelism and strong robustness the features such as, the solution time of problem can be substantially reduced, carry The solution efficiency of high problem.When described genetic algorithm carries out matched design, the individual sum of iteration is selected to be 120 every time, maximum Operation algebraically be 200.
(6) finite element analysis software ansys is utilized to verify optimum results
Optimum allocation relation by the precision machine tool fixed combinating surface various location stiffness parameters obtained by genetic algorithm Result is imparted on lathe bed column faying face, imports in finite element analysis software ansys, and adds constraint, and its medial bed stands The material properties of the big part such as post are provided that elastic modelling quantity is 1.73 × 1011, and Poisson's ratio is 0.3, and density of material is 7300kg/ m3.Between lathe bed and ground by the way of supported at three point, fix the degree of freedom in three directions, carry out model analyses.To firm First rank natural frequency before and after degree parametric distribution is contrasted, if stiffness parameters distribution design meets required, output optimizes As a result, and terminate design process；Otherwise, re-start genetic algorithm optimizing, till meeting design requirement.By lathe mould The result of type model analyses proves that the distribution design method of the present invention is correctly effective, has stronger operability.
The present invention is not limited to embodiments described above.Above the description of specific embodiment is intended to describe and say Bright technical scheme, above-mentioned specific embodiment is only schematically, is not restricted.Without departing from this In the case of invention objective and scope of the claimed protection, those of ordinary skill in the art also may be used under the enlightenment of the present invention Make the concrete conversion of a lot of forms, these belong within protection scope of the present invention.

Claims (3)

1. a kind of Fixed Joints in Machine Tools various location stiffness parameters distribution design method is it is characterised in that include following walking Rapid:
(1) parameters of lathe to be analyzed are determined: include lathe bed column overall dimensions, faying face interface relative position chi The very little, mass parameter of lathe bed column and rotary inertia parameter；
(2) whole degree of freedom of bed piece column to be analyzed are extracted；
(3) set up the kinetic model of lathe bed upright post system；
(4) determine the design space of variable, set up the equation of motion of many-degrees of freedom system non-damping vibration, with bed piece column First rank natural frequency, as design object, using the stiffness parameters of fixed combinating surface diverse location as design variable, is based on Matlab software utilizes the equation of motion of many-degrees of freedom system undamped-free vibration to obtain lathe head rank natural frequency and lathe bed The sample point of column faying face position stiffness parameter；
(5) build second-order response surface model, using genetic algorithm cyclic approximation optimization technology to Fixed Joints in Machine Tools difference position The stiffness parameters put are allocated designing；
(6) finite element analysis software ansys is utilized to verify optimum results: by Fixed Joints in Machine Tools diverse location in step (5) The optimum allocation relational result of place's stiffness parameters is imparted on lathe bed column faying face, imports to finite element analysis software ansys In, and add constraint, carry out model analyses；First rank natural frequency before and after stiffness parameters distribution is contrasted, if rigidity Parametric distribution design meets requirement, then export optimum results, and terminate design process；Otherwise, re-start genetic algorithm optimizing, Till meeting design requirement.
2. a kind of Fixed Joints in Machine Tools various location stiffness parameters distribution design method according to claim 1, it is special Levy and be, in step (2), the vibration of lathe bed column is summarized as 12 degree of freedom, is translation and the rotation in lathe bed x direction respectively, y The translation in direction and rotation, the translation in z direction and rotation, the translation in column x direction and rotation, the translation in y direction and rotation, z The translation in direction and rotation.
3. a kind of Fixed Joints in Machine Tools various location stiffness parameters distribution design method according to claim 1, it is special Levy and be, in step (4) using the limit range of lathe bed column faying face rigidity as variable design space, its medial bed column The least limit of faying face stiffness variation is the 60% of initial faying face rigidity, and maximum limit is initial faying face rigidity 150%.
CN201610740781.7A 2016-08-26 2016-08-26 Allocation design method for stiffness on different position of fixed joint surface of machine Pending CN106354921A (en)

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Cited By (2)

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CN108089457A (en) * 2017-11-29 2018-05-29 北京航空航天大学 A kind of process quality control method based on online finite element simulation
CN108593249A (en) * 2018-06-01 2018-09-28 中国科学院力学研究所 A kind of Stiffness Distribution of wind tunnel experiment model support structure adjusts and its optimization method

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CN103020358A (en) * 2012-12-13 2013-04-03 天津大学 Construction method of adaptive dynamic design platform aiming at mechanical device
CN103995937A (en) * 2014-05-27 2014-08-20 天津大学 Precision machine tool mass matching design method based on response surface and genetic algorithm
CN104573201A (en) * 2014-12-23 2015-04-29 天津大学 Quality matching design method of precision machine tool

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Publication number Priority date Publication date Assignee Title
CN102052999A (en) * 2010-11-05 2011-05-11 北京工业大学 Fixed joint surface unit area dynamic property identification experiment device and identification method thereof
CN102063548A (en) * 2011-01-07 2011-05-18 西安交通大学 Method for optimally designing dynamic property of complete machine tool
CN102096749A (en) * 2011-03-22 2011-06-15 纽威数控装备（苏州）有限公司 Static and modal analysis method of numerical control machine tool with linear guide rails
CN103020358A (en) * 2012-12-13 2013-04-03 天津大学 Construction method of adaptive dynamic design platform aiming at mechanical device
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108089457A (en) * 2017-11-29 2018-05-29 北京航空航天大学 A kind of process quality control method based on online finite element simulation
CN108593249A (en) * 2018-06-01 2018-09-28 中国科学院力学研究所 A kind of Stiffness Distribution of wind tunnel experiment model support structure adjusts and its optimization method
CN108593249B (en) * 2018-06-01 2019-09-06 中国科学院力学研究所 A kind of Stiffness Distribution of wind tunnel experiment model support structure adjusts and its optimization method

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