CN104714478B - Heavy double-column vertical lathe cross beam gravity deformation prediction method based on finite difference method - Google Patents

Heavy double-column vertical lathe cross beam gravity deformation prediction method based on finite difference method Download PDF

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CN104714478B
CN104714478B CN201410853151.1A CN201410853151A CN104714478B CN 104714478 B CN104714478 B CN 104714478B CN 201410853151 A CN201410853151 A CN 201410853151A CN 104714478 B CN104714478 B CN 104714478B
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gravity deformation
curve
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CN104714478A (en
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韩振宇
邵忠喜
王瀚
富宏亚
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Harbin Institute of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/401—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for measuring, e.g. calibration and initialisation, measuring workpiece for machining purposes
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q1/00—Members which are comprised in the general build-up of a form of machine, particularly relatively large fixed members
    • B23Q1/01—Frames, beds, pillars or like members; Arrangement of ways
    • B23Q1/015—Frames, beds, pillars

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Abstract

The invention relates to a heavy double-column vertical lathe cross beam gravity deformation prediction method based on a finite difference method. Due to the fact that an existing finite element analysis computing method cannot accurately calculate a cross beam gravity deformation curve on the condition that actual materials have not uniform attributes, the calculation result much differs from an actual deformation value. The heavy double-column vertical lathe cross beam gravity deformation prediction method based on the finite difference method comprises the steps that actual assembling conditions are simulated to design a heavy machine tool cross beam self-weight deformation experiment to obtain a self-weight deformation curve. By means of the material mechanical theory, a cross beam is simplified into a simply supported beam mechanical model and then made into micro segments through discretization, and a cross beam gravity deformation discretization model is built on the basis of the finite difference method; the equivalent weight bending rigidity of each discrete micro segment is calculated; the cross beam finite element gravity deformation curve is calculated; the equivalent weight bending rigidity is utilized for correcting the cross beam finite element gravity deformation curve on the basis of the finite difference method to obtain a final cross beam gravity deformation curve. The heavy double-column vertical lathe cross beam gravity deformation prediction method is applied to heavy double-column vertical lath cross beam gravity deformation curve calculation.

Description

The vertical car crossbeam gravity deformation Forecasting Methodology of heavy twin columns based on finite difference calculus
Technical field
The present invention relates to a kind of vertical car crossbeam gravity deformation Forecasting Methodology of heavy twin columns based on finite difference calculus.
Background technology
Heavy digital control machine tool is widely used in the emphasis such as national defence, Aero-Space, the energy, ship, metallurgy as processing machine tool Field, the quality of its precision is directly reflected with a manufacturing level of country.Due to heavy double column vertical lathes itself The structural factors such as large scale, large span, so a certain degree of deformation can be caused under self gravitation effect, and the gravity causes Distortion inaccuracy cannot ignore.
Crossbeam founds the core component of car, the depth of parallelism (G5 essence of the rail head movement to work top as heavy twin columns Degree) it is its most important precision index.Compensated by processing reversible deformation curve to crossbeam lower guideway, lathe can be effectively improved G5 precision.But due to the uncontrollability of casting process, inevitably there is burning into sand, stomata etc. in the structural member of heavy machine tool Various defects, cause crossbeam material properties, size etc. inconsistent, current crossbeam reversible deformation is calculated the finite element method meter for using Calculate accuracy to be only capable of reaching 40%~50%, crossbeam need to be checked by many experiments, repeated disassembled and assembled repair could meet precision will Ask, it is relatively costly and very time-consuming.
Zhang Yanting obtains the elastic deformation curve of double column vertical lathes crossbeam by approximate calculation, proposes to obtain and reasonably leads The predeformation method used needed for rail geometry, improves the precision of lathe.The method calculating process is excessively cumbersome, and due to Using approximate simplified model, computational accuracy is poor.Guo Tieneng etc. carries out finite element analysis using ANSYS to heavy planer-type milling machine, 25 deflections of equidistant operating position on crossbeam are obtained, drafting obtains the endurance curves of crossbeam, is shown experimentally that pre- The pre- appraisal of increase by 7%~16% is needed when surveying crossbeam endurance curves.The method is only tied by contrasting finite element analysis with experiment Pre- appraisal when fruit provides processing lower guideway lacks theory support, and wide usage is poor.King, Thomas Boyce etc. proposes a kind of based on finite element Analysis, crossbeam reversible deformation Processing Curve is drawn in combination with actually detected method, reduces cost, improves efficiency of assembling. But method does not consider the inhomogeneity of material properties comprehensively, only crossbeam deformation induced by gravity curve is obtained by testing, and external force is acted on Curve is obtained by finite element simulation.
In sum, theoretical calculation method process is excessively cumbersome, and computational accuracy is poor, but can pass through the beam section in formula Material attribute reflects crossbeam practical distortion situation；Using finite element analysis fast and easy, computational accuracy is higher, but pretreatment process It is only capable of the overall material properties of definition component, it is impossible to consider the inhomogeneity of real material, do not meet actual conditions, causes to calculate Result differs greatly with practical distortion value.
The content of the invention
Cannot be uneven in real material attribute the invention aims to solve existing finite element analysis computation method The accurate problem for calculating crossbeam gravity deformation curve, causing result of calculation to be differed greatly with practical distortion value in the case of one, and carry Go out a kind of vertical car crossbeam gravity deformation Forecasting Methodology of heavy twin columns based on finite difference calculus.
A kind of vertical car crossbeam gravity deformation Forecasting Methodology of heavy twin columns based on finite difference calculus, the crossbeam gravity deformation Curve computational methods are realized by following steps：
Step one：The deformation induced by gravity experiment of simulation practical set condition design heavy machine tool crossbeam, obtains material heterogeneity feelings Condition sill deformation induced by gravity curve；
Step 2：Using theory of mechanics of materials, crossbeam is reduced to letter according to stressing conditions of the crossbeam under Gravitative Loads Strutbeam mechanical model；
Step 3：Crossbeam is separated into one group discrete micro- section, the simply supported beam mechanical model obtained to step 2 is discrete Change, crossbeam gravity deformation discretization model is set up in conjunction with finite difference calculus；
Step 4：The experiment of heavy machine tool crossbeam deformation induced by gravity and crossbeam gravity described in step 3 become with reference to described in step one Shape discretization model, calculates each described discrete micro- section of equivalent bending rigidity；
Step 5：By the practical set condition of finite element method for simulating heavy machine tool crossbeam, by crossbeam and rail head Crossbeam finite element gravity deformation curve is calculated after assembling；
Step 6：The equivalent bending rigidity being calculated using step 4, based on finite difference calculus to step 5 meter The crossbeam finite element gravity deformation curve for obtaining is corrected, and obtains final crossbeam gravity deformation curve, that is, predict Go out the vertical car crossbeam gravity deformation degree of heavy twin columns.
Beneficial effects of the present invention are：
Heavy twin columns of the invention found car crossbeam gravity deformation curve computational methods based on finite difference calculus, due to reason By the good complementarity between computational methods and finite element method, therefore, it is possible to solve due to crossbeam material, manufacturing process Cause the inaccurate problem of Finite element analysis results etc. factor, based on finite difference calculus, in conjunction with the mechanics of materials, deformation induced by gravity reality Test and obtain crossbeam gravity deformation curve computational methods with finite element method, existing use finite element method is calculated into crossbeam reversible deformation Accuracy bring up to 70%~80% from 40%~50%, by the crossbeam gravity deformation curve being accurately calculated, make horizontal stroke Beam needs not move through experiment check process and just disclosure satisfy that required precision, and reduces crossbeam dismounting repair number of times, reduces and installs Cost and installation work-hour.
Especially, the determination of gravity deformation curve is the theoretical bending resistance being input into finite element analysis by equivalent bending rigidity Rigidity is modified, and finite element gravity deformation simulation result is corrected based on finite difference calculus is obtained.Curve after correction Compared to finite element simulation curve closer to actual beam deformation situation.The mistake of former result of finite element and actual beam deformation Rate is 26.86%, and the crossbeam Z-direction deformation that the crossbeam gravity deformation computational methods for being based on finite difference calculus are obtained is horizontal with actual The average error rate of beam deformation is 11.67%, and the error amount of main machining area is 0.07mm to the maximum.Thus prove, based on having Limit the correctness of the finite element result bearing calibration of calculus of finite differences.
Brief description of the drawings
Fig. 1 is the flow chart of computational methods of the present invention；
Fig. 2 is crossbeam of the present invention, and schematic diagram when setting up coordinate system according to its profile；
Fig. 3 is that crossbeam gravitational load of the present invention bends computation model sketch；In figure, L represents 1/2 simply supported beam branch Length between point；L1Represent the length of two ends rectangular beam；L2Represent the half of the length of stage casing rectangular beam, 2L2It is stage casing rectangular beam Length；A represents the length of overhanging beam；qI, qIIRepresent the gravitational load collection of two ends rectangle beam section and stage casing rectangle beam section Angle value；
Fig. 4 is the schematic diagram of crossbeam gravity deformation discretization model of the present invention；
Fig. 5 is that the present invention emulates constraints schematic diagram according to the crossbeam that crossbeam assembled condition determines；
Fig. 6 is that the present invention defines schematic diagram according to the rail loads that crossbeam assembled condition determines；
Fig. 7 be crossbeam of the present invention knife rest point of a knife point Z-direction gravity deformation schematic diagram；
Fig. 8 is crossbeam finite element gravity deformation curve of the present invention；
Fig. 9 is that crossbeam of the present invention surveys G5 precision curve map；
Figure 10 is crossbeam gravity deformation curve computational methods result verification schematic diagram of the present invention.
Specific embodiment
Specific embodiment one：
The vertical car crossbeam gravity deformation Forecasting Methodology of the heavy twin columns based on finite difference calculus of present embodiment, the crossbeam Gravity deformation curve computational methods are realized by following steps：
Step one：The deformation induced by gravity experiment of simulation practical set condition design heavy machine tool crossbeam, obtains material heterogeneity feelings Condition sill deformation induced by gravity curve；
Step 2：Using theory of mechanics of materials, crossbeam is reduced to letter according to stressing conditions of the crossbeam under Gravitative Loads Strutbeam mechanical model；
Step 3：Crossbeam is separated into one group discrete micro- section, the simply supported beam mechanical model obtained to step 2 is discrete Change, crossbeam gravity deformation discretization model is set up in conjunction with finite difference calculus；
Step 4：The experiment of heavy machine tool crossbeam deformation induced by gravity and crossbeam gravity described in step 3 become with reference to described in step one Shape discretization model, calculates each described discrete micro- section of equivalent bending rigidity, for characterizing the attribute of crossbeam real material；
Step 5：By the practical set condition of finite element method for simulating heavy machine tool crossbeam, by crossbeam and rail head Crossbeam finite element gravity deformation curve is calculated after assembling；
Step 6：The equivalent bending rigidity being calculated using step 4, based on finite difference calculus to step 5 meter The crossbeam finite element gravity deformation curve for obtaining is corrected, and obtains accurately final crossbeam gravity deformation curve.
Specific embodiment two：
From unlike specific embodiment one, the heavy twin columns based on finite difference calculus of present embodiment found car crossbeam Gravity deformation Forecasting Methodology, described in step one heavy machine tool crossbeam deformation induced by gravity experiment specifically,
Step one by one, according to crossbeam profile, using crossbeam crossbeam midpoint in the horizontal plane as coordinate origin O, build Vertical cartesian coordinate system, X-direction is to the right that just, Y-axis is upwards that just Z axis are just perpendicular to X-axis along beam guideway direction Direction meets the right-hand rule；As shown in Figure 2；
Step one two, crossbeam is kept flat, using the Z-direction straight line on autocollimator measurement flat condition sill lower guideway surface Degrees of data；
Step one three, crossbeam side put to stabilization again, put under state using level meter or autocollimator measurement side The Z-direction straight line degrees of data on crossbeam lower guideway surface.
Specific embodiment three：
From unlike specific embodiment one or two, the heavy twin columns based on finite difference calculus of present embodiment found car Crossbeam gravity deformation Forecasting Methodology, the acquisition methods of crossbeam deformation induced by gravity curve are specially described in step one：
Side described in step one three is put crossbeam described in the Z-direction straight line degrees of data and step one two measured to stabilization The Z-direction straight line degrees of data measured after keeping flat makes the difference, and obtains difference, and it is bent to be depicted as described crossbeam deformation induced by gravity using the difference Line.
Specific embodiment four：
From unlike specific embodiment three, the heavy twin columns based on finite difference calculus of present embodiment found car crossbeam Gravity deformation Forecasting Methodology, the specific modeling method of simply supported beam mechanical model described in step 2 is：
The profile of the crossbeam selected one by one according to step and the working environment of machine tool beam and assembly constraint condition, by horizontal stroke Beam is reduced to simply supported beam, then the self gravitation of crossbeam is put on into crossbeam as uniform load, with the gravitational load intensity of crossbeam, Gravity size i.e. in the unit length of crossbeam represents uniform load, using the computational methods of the mechanics of materials to the stress of crossbeam Situation is simplified, the crossbeam gravitational load bending computation model sketch being simplified, and obtains the simply supported beam mechanical model For：In formula,
X represents coordinate value of the crossbeam along guide rail direction；
Z (x) represents crossbeam deformation induced by gravity curve；
M (x) represents the suffered moment of flexure of crossbeam bend deformation；
E represents the elastic modelling quantity of crossbeam material；
I (x) represents the distribution function of cross sectional moment of inertia；
So far the process by the way that crossbeam to be reduced to simply supported beam is completed, heavy double column vertical lathes crossbeam from recast is established Flexural deformation model under.
Specific embodiment five：
From unlike specific embodiment one, two or four, the heavy twin columns based on finite difference calculus of present embodiment Vertical car crossbeam gravity deformation Forecasting Methodology, crossbeam gravity deformation discretization model modeling method is specially described in step 3：
Step 3 one, the inhomogenous crossbeam of material is equidistantly divided into n sections, then i-th section of coordinate x of crossbeamiIn step X is met in coordinate system described ini=x0+ ih, i=0,1 ..., n；In formula,
H represents step-length, h=2L/n；
L represents the half of crossbeam total length；
x0Represent the starting point coordinate of crossbeam left end；
Step 3 two, the flexural deformation part for crossbeam, the difference formula and crossbeam line of deflection according to second dervative are micro- Divide equation, obtain the inhomogenous crossbeam gravity deformation discretization model of material： In formula,
ziRepresent the Z-direction deformation values of discrete micro- section of crossbeam, i=0,1 ..., n；
MiRepresent the moment of flexure suffered by the discrete micro- section of i of crossbeam；
(EI)iRepresent the bending rigidity of the discrete micro- section of i of crossbeam.
Specific embodiment six：
From unlike specific embodiment five, the heavy twin columns based on finite difference calculus of present embodiment found car crossbeam Gravity deformation Forecasting Methodology, the circular of the equivalent bending rigidity of each discrete micro- section of crossbeam described in step 4 is,
The Z-direction linearity that the heavy machine tool crossbeam deformation induced by gravity experiment measurement according to step one two, step one three is obtained Crossbeam gravity deformation discretization model described in data and step 3, calculate each discrete micro- section of crossbeam equivalent bending rigidity be：
In formula,
ziRepresent the Z-direction deformation values of discrete micro- section of crossbeam, i=0,1 ..., n；
H represents step-length, h=2L/n；
MiRepresent the moment of flexure suffered by the discrete micro- section of i of crossbeam；
zriRepresent actual measurement Z-direction linearitys of the discrete micro- section of i of crossbeam in the experiment of crossbeam deformation induced by gravity；
(EI)viRepresent the equivalent bending rigidity of the discrete micro- section of i of crossbeam；
It is calculated by the way that crossbeam deformation induced by gravity is tested into the crossbeam Z-direction straight line degrees of data for obtaining, simply supported beam mechanical model Moment and step-length substitute into above-mentioned (EI)viExpression formula, you can calculate the equivalent bending rigidity of each discrete micro- section of crossbeam.
Specific embodiment seven：
From unlike specific embodiment one, two, four or six, the heavy type based on finite difference calculus of present embodiment is double The vertical car crossbeam gravity deformation Forecasting Methodology of post, crossbeam finite element gravity deformation curve computational methods described in step 5 specifically,
Step 5 one, carry out finite-element preprocessing process：
Critical piece crossbeam, column, ram to heavy double column vertical lathes model, knife rest definition material attribute, it is every kind of Material properties include elastic modulus E, Poisson's ratio ν and density of material ρ；
Constraints of the crossbeam in practical set is analyzed again：Lathe right side uprights are made for head tree, left column is auxiliary Column, sets tip iron to eliminate fit-up gap at the assembling of head tree guide rail and crossbeam, together with the effect of cylinder clamp, Remaining 5 free degree is limited in addition to the translational degree of freedom of Z-direction at head tree to make crossbeam, therefore at assembling on the right side of crossbeam Displacement constraint in addition X, Y-direction, displacement is limited to 0mm；When crossbeam is assembled at auxiliary strut, due to Y-direction oil cylinder folder The effect of tight device, auxiliary strut is clamped with cross beam contacting surface, and the gap of 5~10mm is left due to X-direction, then Y-direction translation, X-direction is limited with Z-direction rotational freedom, and the free degree in its excess-three direction is unrestricted, what machine beam clamping device was produced Frictional force is not enough to support whole crossbeam, and crossbeam relies primarily on leading screw supporting, shows freedom of the crossbeam in feed screw nut position Z-direction Degree is restricted, therefore applies cylinder constraint on the face of cylinder at lead screw position, limits its axial freedom, simulation leading screw Constraints；
Using above-mentioned condition as set finite element simulation constraints and load foundation, crossbeam constraints such as Fig. 5 Shown, load is defined as global gravitational load as shown in fig. 6, setting analog parameter according to actual conditions in simulation software, Complete finite-element preprocessing process；
Step 5 two, emulated with reference to actual test situation, will crossbeam be divided into left and right two parts, solve crossbeam left half Part, in the deformation of right knife rest point of a knife point, obtains crossbeam and blade carrier component in the deformation of left knife rest point of a knife point and crossbeam right half part The crossbeam finite element gravity deformation simulation value of one group of crossbeam point of a knife point under Action of Gravity Field in Z-direction；
Step 5 three, the crossbeam finite element gravity deformation obtained according to step 5 two emulate Value Data, draw crossbeam gravity Z-direction deformation curve, obtain crossbeam finite element gravity deformation curve.
Specific embodiment eight：
From unlike specific embodiment seven, the heavy twin columns based on finite difference calculus of present embodiment found car crossbeam Gravity deformation Forecasting Methodology, crossbeam finite element gravity deformation curve correcting method is specially described in step 6：
Step 6 one, according to crossbeam point of a knife point in the gravity deformation value of Z-direction and the relational expression of equivalent bending rigidity：
Because the material properties parameter of finite-element preprocessing process input described in step 5 one is definite value, it is impossible to true reflection The inhomogeneity of actual crossbeam material, it is therefore desirable to which the equivalent bending rigidity being calculated using step 4 is defeated to finite element analysis The theoretical bending rigidity for entering is modified, the inhomogeneity of the true actual crossbeam material of reflection；
Step 6 two, the crossbeam finite element gravity deformation simulation value obtained to step 5 three based on finite difference calculus are according to step The left side computational methods of rapid 61 relational expression carry out data processing, obtain the finite difference fraction of finite element simulation：
In formula,
zs iRepresent the Z-direction deformation values of each discrete micro- section of the crossbeam that finite element simulation is obtained；
(EI)inputThe theoretical bending rigidity value being input into when representing that Finite Element Correction is calculated；
After step 6 three, the actual correction of completion step 6 two, each discrete micro- section of Z-direction flexural deformation value z of crossbeamr iMeet Formula：
Step 6 four, the theoretical bending rigidity value (EI) by the discrete micro- section of i of crossbeaminputWith equivalent bending rigidity (EI)vi's Ratio is used as discrete micro- section of the correction factor ki, i.e.,：
Step 6 five, it is the approximate differential equation based on mechanics of materials middle cross beam flexural deformation, branch due to finite difference calculus The calculating of the neighbouring equivalent bending rigidity of seat causes correction factor excessive due to the simplification of load in computation model, does not meet actual feelings Condition, is that 6 frees degree are limited according to the constraints that crossbeam is assembled in head tree position, and Z-direction is limited at auxiliary strut System, then when practical distortion is with simulation calculation, the amount of deflection of crossbeam both sides constraint portions is identical with deformation extent, i.e. primary condition formula For：zs 0=zr 0、zs n=zr n, k1=kn-1=1, make Δ zr i=zr i-1-2zr i+zr i+1, Δ zs i=zs i-1-2zs i+zs i+1, then obtain Heavy twin columns found car crossbeam gravity deformation curvature correction model formation：
Specific embodiment eight：
From unlike specific embodiment seven, the heavy twin columns based on finite difference calculus of present embodiment found car crossbeam Gravity deformation Forecasting Methodology, the two-part discrete micro- segment length of crossbeam or so described in step 5 three is 460mm.
Embodiment 1：
First, heavy double column vertical lathes crossbeam deformation induced by gravity experiment is carried out：
Test the equivalence that the crossbeam finite element analysis to be spaced 230mm is obtained with reference to the reality processing experiential modification of the crossbeam S-curve is processed as experiment crossbeam processing line style using planer-type milling machine.Crossbeam is put down when crossbeam lower guideway is processed Put, eliminate influence of the gravity factor to processing, crossbeam side is put, supported with parallels at leading screw by crossbeam lower guideway after machining Simulation reality processing state, and straight line degrees of data of the crossbeam lower guideway in Z-direction, deformation induced by gravity reality are measured after stabilization is put in crossbeam side Z-direction straight line degrees of data is tested, as shown in table 1.
The deformation induced by gravity of table 1 tests crossbeam lower guideway Z-direction straight line degrees of data
According to experimental measurements, crossbeam side is put after 68 hours sides put, and the deformation values of measurement reach stable state.Crossbeam is passed through Cross 68 hours sides and put the deformation induced by gravity curve of the difference as crossbeam of linearity curve and crossbeam Processing Curve after stabilization.
Second, it is that the model simplification of crossbeam gravity deformation is letter by the deformation induced by gravity curve of crossbeam using theory of mechanics of materials Strutbeam mechanical model：
According to crossbeam profile, the computational methods using the mechanics of materials simplify to computation model, according to machine tool beam Working environment and assembly constraint condition, a simply supported beam is reduced to by crossbeam, and gravity puts on crossbeam as uniform load, with unit Gravity size in length, i.e. gravitational load intensity represent uniform load.Can obtain the crossbeam gravitational load bending shown in Fig. 3 Computation model sketch.
Highly it is 1350mm if the heavy machine tool crossbeam span is 9500mm, span-depth radio is more than 5, is scratched using straight beam deformation The curve approximation differential equation calculates the Z-direction deformation of crossbeam, obtains crossbeam deformation induced by gravity curve z (x) of theory, and then obtain freely-supported Beam mechanical model：Consider that the reason for Finite element analysis results differ greatly with practical distortion is crossbeam material What inhomogeneity was caused, it is believed that beam part material properties everywhere are different, therefore the crossbeam under single material need to be conducted oneself with dignity Distorted pattern is discrete, the crossbeam gravity deformation discretization model set up in the case of material heterogeneity.
3rd, crossbeam is separated into one group discrete micro- section, set up crossbeam gravity deformation discretization in conjunction with finite difference calculus Model,
Crossbeam is equidistantly divided into the coordinate x of section crossbeam of n sections, i.e., i-thiMeet：xi=x0+ ih, i=0,1 ..., n, such as Shown in Fig. 4, schematic diagram when crossbeam is separated into micro- section.
4th, with reference to the experiment of heavy machine tool crossbeam deformation induced by gravity and crossbeam gravity deformation discretization model, calculate each Described discrete micro- section of equivalent bending rigidity and the real material attribute of sign crossbeam；
To make Finite element analysis results close to practical distortion value, it is necessary to obtain the anti-of each discrete micro- section of actual conditions sill Curved rigidity value, but the numerical value is difficult to directly measure.Due to including crossbeam in the crossbeam gravity deformation discretization model of above-mentioned foundation Each discrete micro- section of bending rigidity (EI)i, therefore the deformation induced by gravity experimental data and crossbeam gravity deformation in second section can be combined Discretization model calculates the bending rigidity of each discrete micro- section of crossbeam.Each discrete micro- section of the crossbeam that will be calculated using the method Bending rigidity is referred to as the equivalent bending rigidity (EI) of crossbeamv。
After crossbeam gravity deformation discretization model is arranged：
The crossbeam Z-direction straight line degrees of data that obtains is tested by by deformation induced by gravity, that simply supported beam mechanical model is calculated is curved Square value and step-length generation such as above formula can calculate each discrete micro- section of equivalent bending rigidity of crossbeam.It is each discrete that table 2 gives experiment crossbeam The result of calculation of micro- section of equivalent bending rigidity.
The equivalent bending rigidity result of calculation of table 2
To each part definition material attribute, including elastic modulus E, Poisson's ratio ν and material density p.According to engineering reality Using each part simulation parameter information is summed up, as shown in table 3.
Each component materials parameter of heavy double column vertical lathes of table 3
5th, the crossbeam point of a knife point Z-direction gravity deformation under being acted on by simulation calculation crossbeam and knife rest obtains crossbeam gravity Deformation curve.Emulation combines actual test situation, and crossbeam is divided into left and right two parts, solves crossbeam left-half respectively to it and exists , in the deformation of right knife rest point of a knife point, crossbeam calculates a knife every 460mm for the deformation of left knife rest point of a knife point and crossbeam right half part The Z-direction deformation of cusp.It is point of a knife point gravity deformation in z-direction under Action of Gravity Field such as Fig. 7, obtains crossbeam as shown in Figure 8 Finite element gravity deformation curve.
6th, using equivalent bending rigidity, based on the crossbeam finite element that finite difference calculus is calculated to step 5 Gravity deformation curve is corrected, each discrete micro- section of Z-direction flexural deformation value z of the crossbeam after correctionr iMeet formula：
By the theoretical bending rigidity value (EI) of the discrete micro- section of i of crossbeaminputWith equivalent bending rigidity (EI)viRatio conduct Discrete micro- section of the correction factor ki, i.e.,：Because finite difference calculus is based on material power The calculating of equivalent bending rigidity near the approximate differential equation of middle cross beam flexural deformation, bearing is learned due to load in computation model Simplification causes correction factor excessive, does not meet actual conditions, is 6 according to the constraints that crossbeam is assembled in head tree position The free degree is limited, and Z-direction is limited at auxiliary strut, then when practical distortion is with simulation calculation, crossbeam both sides constraint portions Amount of deflection it is identical with deformation extent, i.e. primary condition formula is：zs 0=zr 0、zs n=zr n, k1=kn-1=1, make Δ zr i=zr i-1- 2zr i+zr i+1, Δ zs i=zs i-1-2zs i+zs i+1, then the final crossbeam gravity deformation curve of the vertical car of heavy twin columns is obtained：
7th, G5 precision of crossbeam is measured after crossbeam is installed, test data is depicted as into crossbeam surveys G5 precision curve, As shown in Figure 9.Crossbeam initial manufacture curve is subtracted the practical distortion curve of crossbeam G5 precision curve as crossbeam.
Using the above-mentioned crossbeam gravity deformation curve computational methods based on finite difference calculus, the crossbeam gravity after being corrected Deformation curve data, as shown in table 4.
Table 4 is based on the crossbeam gravity deformation curve result of calculation of finite difference calculus
Crossbeam gravity deformation simulation curve, practical distortion curve and gravity deformation curve based on finite difference calculus are calculated Method correction result is contrasted, as shown in Figure 10.Draw the curve after correction compared to finite element simulation curve closer to reality Beam deformation situation.It is computed, former result of finite element is 26.86% with the error rate of actual beam deformation, and is based on The crossbeam Z-direction that the crossbeam gravity deformation computational methods of finite difference calculus are obtained deforms 11.67%, the error amount of main machining area is 0.07mm to the maximum.Demonstrate the finite element result correction based on finite difference calculus The correctness of method.

Claims (9)

1. a kind of heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology, it is characterised in that：The horizontal stroke Beam gravity deformation curve computational methods are realized by following steps：
Step one：Simulation practical set condition design heavy machine tool crossbeam deformation induced by gravity experiment, in the case of obtaining material heterogeneity Crossbeam deformation induced by gravity curve；
Step 2：Using theory of mechanics of materials, crossbeam is reduced to simply supported beam according to stressing conditions of the crossbeam under Gravitative Loads Mechanical model；
Step 3：Crossbeam is separated into one group discrete micro- section, the simply supported beam mechanical model discretization obtained to step 2, then Crossbeam gravity deformation discretization model is set up with reference to finite difference calculus；
Step 4：With reference to described in step one heavy machine tool crossbeam deformation induced by gravity experiment and crossbeam gravity deformation described in step 3 from Dispersion model, calculates each described discrete micro- section of equivalent bending rigidity；
Step 5：By the practical set condition of finite element method for simulating heavy machine tool crossbeam, crossbeam and rail head are assembled Crossbeam finite element gravity deformation curve is calculated afterwards；
Step 6：The equivalent bending rigidity being calculated using step 4, is calculated based on finite difference calculus to step 5 To the crossbeam finite element gravity deformation curve be corrected, obtain final crossbeam gravity deformation curve, that is, predict weight The vertical car crossbeam gravity deformation degree of type twin columns.
2. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 1, and it is special Levy and be：Heavy machine tool crossbeam deformation induced by gravity experiment described in step one is specially：
Step one by one, according to crossbeam profile, using crossbeam crossbeam midpoint in the horizontal plane as coordinate origin O, set up flute Karr coordinate system, X-direction is to the right that just, Y-axis is upwards just Z axis positive direction perpendicular to X-axis along beam guideway direction Meet the right-hand rule；
Step one two, crossbeam is kept flat, using the Z-direction straight line number of degrees on autocollimator measurement flat condition sill lower guideway surface According to；
Step one three, crossbeam side put to stabilization again, state sill is put using level meter or autocollimator measurement side The Z-direction straight line degrees of data on lower guideway surface.
3. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 2, and it is special Levy and be：The acquisition methods of crossbeam deformation induced by gravity curve are specially described in step one：
Side described in step one three is put the Z-direction straight line degrees of data measured to stabilization to keep flat crossbeam with described in step one two The Z-direction straight line degrees of data for measuring afterwards is poor, obtains difference, and described crossbeam deformation induced by gravity curve is depicted as using the difference.
4. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 3, and it is special Levy and be：The specific modeling method of simply supported beam mechanical model described in step 2 is：
The profile of the crossbeam selected one by one according to step and the working environment of machine tool beam and assembly constraint condition, by crossbeam letter Simply supported beam is turned to, then the self gravitation of crossbeam is put on into crossbeam as uniform load, table is come with the gravitational load intensity of crossbeam Show uniform load, the computational methods using the mechanics of materials simplify to the stressing conditions of crossbeam, obtain the simply supported beam mechanics Model is：In formula,
X represents coordinate value of the crossbeam along guide rail direction；
Z (x) represents crossbeam deformation induced by gravity curve；
M (x) represents the suffered moment of flexure of crossbeam bend deformation；
E represents the elastic modelling quantity of crossbeam material；
I (x) represents the distribution function of cross sectional moment of inertia.
5. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 2 or 4, its It is characterised by：Crossbeam gravity deformation discretization model modeling method is specially described in step 3：
Step 3 one, the inhomogenous crossbeam of material is equidistantly divided into n sections, then i-th section of coordinate x of crossbeamiIt is described one by one in step X is met in coordinate systemi=x0+ ih, i=0,1 ..., n；In formula,
H represents step-length, h=2L/n；
L represents the half of crossbeam total length；
x0Represent the starting point coordinate of crossbeam left end；
Step 3 two, the flexural deformation part for crossbeam, difference formula and crossbeam line of deflection differential side according to second dervative Journey, obtains the inhomogenous crossbeam gravity deformation discretization model of material： In formula,
ziRepresent the Z-direction deformation values of discrete micro- section of crossbeam, i=0,1 ..., n；
MiRepresent the moment of flexure suffered by the discrete micro- section of i of crossbeam；
(EI)iRepresent the bending rigidity of the discrete micro- section of i of crossbeam.
6. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 5, and it is special Levy and be：The circular of the equivalent bending rigidity of each discrete micro- section of crossbeam described in step 4 is：
The Z-direction straight line degrees of data that the heavy machine tool crossbeam deformation induced by gravity experiment measurement according to step one two, step one three is obtained And crossbeam gravity deformation discretization model described in step 3, calculate each discrete micro- section of crossbeam equivalent bending rigidity be：
In formula,
ziRepresent the Z-direction deformation values of discrete micro- section of crossbeam, i=0,1 ..., n；
H represents step-length, h=2L/n；
MiRepresent the moment of flexure suffered by the discrete micro- section of i of crossbeam；
zriRepresent actual measurement Z-direction linearitys of the discrete micro- section of i of crossbeam in the experiment of crossbeam deformation induced by gravity；
(EI)viRepresent the equivalent bending rigidity of the discrete micro- section of i of crossbeam.
7. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation prediction side according to claim 1,2,4 or 6 Method, it is characterised in that：Crossbeam finite element gravity deformation curve computational methods are specially described in step 5：
Step 5 one, carry out finite-element preprocessing process：
Critical piece crossbeam, column, ram to heavy double column vertical lathes model, knife rest definition material attribute, every kind of material Attribute includes elastic modulus E, Poisson's ratio ν and density of material ρ；
Constraints of the crossbeam in practical set is analyzed again：Make lathe right side uprights for head tree, left column is auxiliary strut, Tip iron is set at the assembling of head tree guide rail and crossbeam to eliminate fit-up gap, together with the effect of cylinder clamp, makes horizontal stroke Remaining 5 free degree is limited beam in addition to the translational degree of freedom of Z-direction at head tree, therefore is added at assembling on the right side of crossbeam Displacement constraint in X, Y-direction, displacement is limited to 0mm；When crossbeam is assembled at auxiliary strut, filled because Y-direction oil cylinder is clamped The effect put, auxiliary strut is clamped with cross beam contacting surface, the gap of 5~10mm is left due to X-direction, then Y-direction translation, X side Limited to Z-direction rotational freedom, the free degree in its excess-three direction is unrestricted, the friction that machine beam clamping device is produced Power is not enough to support whole crossbeam, and crossbeam relies primarily on leading screw supporting, shows that crossbeam is received in the free degree of feed screw nut position Z-direction To limitation, therefore apply cylinder constraint on the face of cylinder at lead screw position, limit its axial freedom, simulate the constraint of leading screw Condition；
Using above-mentioned condition as the constraints for setting finite element simulation and the foundation of load, according to actual conditions in simulation software In setting analog parameter, complete finite-element preprocessing process；
Step 5 two, emulated with reference to actual test situation, will crossbeam be divided into left and right two parts, solve crossbeam left-half In the deformation of left knife rest point of a knife point and crossbeam right half part in the deformation of right knife rest point of a knife point, crossbeam and blade carrier component gravity are obtained Effect under one group of crossbeam point of a knife point Z-direction crossbeam finite element gravity deformation simulation value；
Step 5 three, the crossbeam finite element gravity deformation obtained according to step 5 two emulate Value Data, draw the Z-direction of crossbeam gravity Deformation curve, obtains crossbeam finite element gravity deformation curve.
8. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 7, and it is special Levy and be：Crossbeam finite element gravity deformation curve correcting method is specially described in step 6：
Step 6 one, according to crossbeam point of a knife point in the gravity deformation value of Z-direction and the relational expression of equivalent bending rigidity：
z i | i = 0 = z 0 , z i | i = n = z n , i = 0 , n z i + 1 - 2 z i + z i - 1 = h 2 M i ( E I ) i , i = 1 , ... , n - 1 ,
The equivalent bending rigidity being calculated with step 4 is modified to the theoretical bending rigidity that finite element analysis is input into, truly The inhomogeneity of the actual crossbeam material of reflection；
Step 6 two, the crossbeam finite element gravity deformation simulation value obtained to step 5 three based on finite difference calculus are according to step 6 The left side computational methods of relational expression described in carry out data processing and complete trimming process, obtain the finite difference of finite element simulation Formula：
In formula,
zs iRepresent the Z-direction deformation values of each discrete micro- section of the crossbeam that finite element simulation is obtained；
(EI)inputThe theoretical bending rigidity value being input into when representing that Finite Element Correction is calculated；
After step 6 three, the actual correction of completion step 6 two, each discrete micro- section of Z-direction flexural deformation value z of crossbeamr iMeet formula：
z 0 r = z 0 s , z n r = z n s , i = 0 , n z i - 1 r - 2 z i r + z i + 1 r = h 2 M i ( E I ) v i = h 2 M i ( E I ) i n p u t · ( E I ) i n p u t ( R I ) v i = ( z i - 1 s - 2 z i s + z i + 1 s ) · ( E I ) i n p u t ( E I ) v i , i = 1 , ... , n - 1 ,
Step 6 four, the theoretical bending rigidity value (EI) by the discrete micro- section of i of crossbeaminputWith equivalent bending rigidity (EI)viRatio As discrete micro- section of the correction factor ki, i.e.,：
The constraints that step 6 five, crossbeam is assembled in head tree position meet 6 frees degree limited, Z at auxiliary strut Direction is limited, then when practical distortion is with simulation calculation, the amount of deflection of crossbeam both sides constraint portions is identical with deformation extent, i.e., initially Condition formula is：zs 0=zr 0、zs n=zr n, k1=kn-1=1, make Δ zr i=zr i-1-2zr i+zr i+1, Δ zs i=zs i-1-2zs i+ zs i+1, then obtaining the vertical car crossbeam gravity deformation curvature correction model formation of heavy twin columns is：
9. the heavy twin columns based on finite difference calculus found car crossbeam gravity deformation Forecasting Methodology according to claim 7, and it is special Levy and be：The two-part discrete micro- segment length of crossbeam or so described in step 5 three is 460mm.
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