CN104714478A - Heavy double-column vertical lathe cross beam gravity deformation prediction method based on finite difference method - Google Patents

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

Heavy twin columns based on method of finite difference found car crossbeam gravity deformation Forecasting Methodology

Technical field

The present invention relates to a kind of heavy twin columns based on method of finite difference and found car crossbeam gravity deformation Forecasting Methodology.

Background technology

Heavy digital control machine tool is widely used in the major fields such as national defence, Aero-Space, the energy, boats and ships, metallurgy as processing machine tool, and the quality of its precision directly reflects with a manufacturing level of country.Due to structural factors such as the large scale of heavy double column vertical lathes self, large spans, so can cause distortion to a certain degree under self gravitation effect, and the distortion inaccuracy that this gravity causes cannot be ignored.

Crossbeam founds the core component of car as heavy twin columns, and the depth of parallelism (G5 item precision) that rail head moves work top is its most important precision index.By compensating crossbeam lower guideway processing reversible deformation curve, the G5 item precision of lathe effectively can be improved.But due to the uncontrollability of casting process, inevitably there is the various defect such as burning into sand, pore in the structural member of heavy machine tool, cause crossbeam material properties, size etc. inconsistent, the Finite Element Method making current crossbeam reversible deformation calculate employing calculates accuracy only can reach 40% ~ 50%, crossbeam need be checked through many experiments, repeated disassembled and assembled repair could meet accuracy requirement, and cost is higher and very consuming time.

Zhang Yanting obtains the elastic deformation curve of double column vertical lathes crossbeam by approximate treatment, proposes to obtain the required predeformation method adopted of rational guide rail geometric configuration, improves the precision of lathe.The method computation process is too loaded down with trivial details, and owing to adopting approximate simplified model, computational accuracy is poor.Guo Tieneng etc. utilize ANSYS to carry out finite element analysis to heavy planer-type milling machine, obtain the deflection of 25 equidistant working positions on crossbeam, drawing the endurance curves obtaining crossbeam, showing the pre-appraisal needing increase by 7% ~ 16% when predicting crossbeam endurance curves by experiment.To provide when processing lower guideway pre-estimates and lack theory support by means of only contrast finite element analysis and experimental result for the method, and wide usage is poor.King, Thomas Boyces etc. propose a kind of based on finite element analysis, combine the actual method detected simultaneously and draw crossbeam reversible deformation Processing Curve, reduce cost, improve efficiency of assembling.But method does not consider the inhomogeneity of material properties, and only crossbeam deformation induced by gravity curve is obtained by experiment, and External Force Acting curve is obtained by finite element simulation comprehensively.

In sum, theoretical calculation method process is too loaded down with trivial details, and computational accuracy is poor, but reflects crossbeam practical distortion situation by the crossbeam material properties in formula; Use finite element analysis fast and easy, computational accuracy is higher, but pretreatment process only can the material properties of definition component entirety, cannot consider the inhomogeneity of real material, not meet actual conditions, cause result of calculation and practical distortion value to differ greatly.

Summary of the invention

The object of the invention is in the inhomogenous situation of real material attribute, accurately to calculate crossbeam gravity deformation curve to solve existing finite element analysis computation method, cause the problem that result of calculation and practical distortion value differ greatly, and propose a kind of heavy twin columns based on method of finite difference and found car crossbeam gravity deformation Forecasting Methodology.

Heavy twin columns based on method of finite difference found a car crossbeam gravity deformation Forecasting Methodology, and described crossbeam gravity deformation curve computing method are realized by following steps:

Step one: the experiment of simulation practical set condition design heavy machine tool crossbeam deformation induced by gravity, obtains material heterogeneity situation sill deformation induced by gravity curve;

Step 2: utilize theory of mechanics of materials, is reduced to free beam mechanical model according to the stressing conditions of crossbeam under Gravitative Loads by crossbeam;

Step 3: crossbeam is separated into one group discrete micro-section, to the described free beam mechanical model discretize that step 2 obtains, then sets up crossbeam gravity deformation discretization model in conjunction with method of finite difference;

Step 4: heavy machine tool crossbeam deformation induced by gravity described in integrating step one is tested and crossbeam gravity deformation discretization model described in step 3, calculates the equivalent bendind rigidity of described in each discrete micro-section;

Step 5: by the practical set condition of finite element method for simulating heavy machine tool crossbeam, calculates crossbeam finite element gravity deformation curve after crossbeam and rail head being assembled;

Step 6: the described equivalent bendind rigidity utilizing step 4 to calculate, based on method of finite difference, the described crossbeam finite element gravity deformation curve that step 5 calculates is corrected, obtain final crossbeam gravity deformation curve, namely dope heavy twin columns and found car crossbeam gravity deformation degree.

Beneficial effect of the present invention is:

Heavy twin columns of the present invention found car crossbeam gravity deformation curve computing method based on method of finite difference, due to the good complementarity between theoretical calculation method and finite element method, therefore, it is possible to solve due to crossbeam material, the factors such as manufacturing process cause the inaccurate problem of Finite element analysis results, based on method of finite difference, Combining material mechanics again, deformation induced by gravity experiment obtains crossbeam gravity deformation curve computing method with Finite Element Method, the accuracy that existing employing Finite Element Method calculates crossbeam reversible deformation is brought up to 70% ~ 80% from 40% ~ 50%, by the crossbeam gravity deformation curve accurately calculated, crossbeam is made not need just can meet accuracy requirement through experiment check process, and decrease crossbeam dismounting repair number of times, reduce installation cost and installation work-hour.

Especially, the determination of gravity deformation curve is revised the theoretical bendind rigidity that finite element analysis inputs by equivalent bendind rigidity, carries out correction obtain based on method of finite difference to finite element gravity deformation simulation result.Curve after correction compares the beam deformation situation of finite element simulation curve more closing to reality.The error rate of former result of finite element and actual beam deformation is 26.86%, and the crossbeam Z-direction distortion obtained based on the crossbeam gravity deformation computing method of method of finite difference is 11.67% with the average error rate of actual beam deformation, the error amount of main machining area is 0.07mm to the maximum.Prove thus, based on the correctness of the finite element result bearing calibration of method of finite difference.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the computing method that the present invention relates to;

Fig. 2 is the crossbeam that the present invention relates to, and schematic diagram when setting up coordinate system according to its profile;

Fig. 3 is that the crossbeam gravity load that the present invention relates to bends computation model sketch; In figure, length between the free beam fulcrum that L represents 1/2; L ₁represent the length of two ends rectangular beam; L ₂represent the half of the length of stage casing rectangular beam, 2L ₂for the length of stage casing rectangular beam; A represents the length of overhanging beam; q _i, q _iIrepresent the gravity load intensity value in rectangular beam cross section, two ends and rectangular beam cross section, stage casing;

Fig. 4 is the schematic diagram of the crossbeam gravity deformation discretization model that the present invention relates to;

Fig. 5 is the crossbeam emulation constraint condition schematic diagram that the present invention determines according to crossbeam assembled condition;

Fig. 6 is the rail loads definition schematic diagram that the present invention determines according to crossbeam assembled condition;

Fig. 7 is that the crossbeam that the present invention relates to is at the gravity deformation schematic diagram of knife rest point of a knife point in Z-direction;

Fig. 8 is the crossbeam finite element gravity deformation curve that the present invention relates to;

Fig. 9 is the crossbeam actual measurement G5 item precision curve map that the present invention relates to;

Figure 10 is that the crossbeam gravity deformation curve that the present invention relates to calculates methods and results checking schematic diagram.

Embodiment

Embodiment one:

The heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and described crossbeam gravity deformation curve computing method are realized by following steps:

Step one: the experiment of simulation practical set condition design heavy machine tool crossbeam deformation induced by gravity, obtains material heterogeneity situation sill deformation induced by gravity curve;

Step 2: utilize theory of mechanics of materials, is reduced to free beam mechanical model according to the stressing conditions of crossbeam under Gravitative Loads by crossbeam;

Step 3: crossbeam is separated into one group discrete micro-section, to the described free beam mechanical model discretize that step 2 obtains, then sets up crossbeam gravity deformation discretization model in conjunction with method of finite difference;

Step 4: crossbeam gravity deformation discretization model described in heavy machine tool crossbeam deformation induced by gravity experiment described in integrating step one and step 3, calculates the equivalent bendind rigidity of described in each discrete micro-section, is used 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, calculates crossbeam finite element gravity deformation curve after crossbeam and rail head being assembled;

Step 6: the described equivalent bendind rigidity utilizing step 4 to calculate, corrects the described crossbeam finite element gravity deformation curve that step 5 calculates based on method of finite difference, obtains crossbeam gravity deformation curve final accurately.

Embodiment two:

With embodiment one unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, described in step one heavy machine tool crossbeam deformation induced by gravity experiment be specially,

Step one by one, according to crossbeam profile, using the crossbeam mid point in the surface level of crossbeam place as coordinate origin O, set up cartesian coordinate system, X-direction along beam guideway direction, and is to the right that just Y-axis is perpendicular to X-axis, and be upwards that just Z axis positive dirction meets the right-hand rule; As shown in Figure 2;

Step one two, crossbeam to be kept flat, adopt autocollimator to measure the Z-direction linearity data on flat condition sill lower guideway surface;

Step one three, again crossbeam is sidelong to stabilization, adopts level meter or autocollimator measurement to be sidelong the Z-direction linearity data on state sill lower guideway surface.

Embodiment three:

With embodiment one or two unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and described in step one, the acquisition methods of crossbeam deformation induced by gravity curve is specially:

By be sidelong described in step one three described in the Z-direction linearity and step one two that record to stabilization, crossbeam is kept flat after the difference of Z-direction linearity data that records, utilize described difference to be depicted as described crossbeam deformation induced by gravity curve.

Embodiment four:

With embodiment three unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and described in step 2, the concrete modeling method of free beam mechanical model is:

The profile of crossbeam selected one by one according to step and the working environment of machine tool beam and assembly constraint condition, crossbeam is reduced to free beam, again the self gravitation of crossbeam is put on crossbeam as uniformly distributed load, with the gravity load intensity of crossbeam, gravity size in the unit length of i.e. crossbeam represents uniformly distributed load, the stressing conditions of the computing method of the mechanics of materials to crossbeam is utilized to simplify, the crossbeam gravity load be simplified bends computation model sketch, and obtains described free beam mechanical model and be: $z^{\′\′}\left(x\right)=\frac{M\left(x\right)}{\mathrm{EI}\left(x\right)};$ In formula,

X represents the coordinate figure of crossbeam along guide rail direction;

Z (x) represents crossbeam deformation induced by gravity curve;

M (x) represents the moment of flexure suffered by crossbeam bend distortion;

E represents the elastic modulus of crossbeam material;

I (x) represents the distribution function of cross sectional moment of inertia;

So far completing the process by crossbeam being reduced to free beam, establishing the flexural deformation model under heavy double column vertical lathes crossbeam Gravitative Loads.

Embodiment five:

With embodiment one, two or four unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and described in step 3, crossbeam gravity deformation discretization model modeling method is specially:

Step 3 one, inhomogenous for material crossbeam is equidistantly divided into n section, then the coordinate x of i-th section of crossbeam _ix is met in step one by one described coordinate system _i=x ₀+ ih, i=0,1 ..., n; In formula,

H represents step-length, h=2L/n;

L represents the half of crossbeam total length;

X ₀represent the starting point coordinate of crossbeam left end;

Step 3 two, flexural deformation part for crossbeam, according to difference formula and the crossbeam deflection differential equation of second derivative, obtain material inhomogenous crossbeam gravity deformation discretization model: $\left\{\begin{array}{c}{z}_i{|}_{i=0}=z_0,z_i{|}_{i=n}=z_n,i=0,...,n\\ z_{i+1}-2z_i+z_{i-1}=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_i},i=1,...,n-1\end{array}\right.;$ In formula,

Z _irepresent the Z-direction Deformation Theory value of discrete micro-section of crossbeam, i=0,1 ..., n;

M _irepresent the moment of flexure suffered by the discrete micro-section of i of crossbeam;

(EI) _irepresent the bendind rigidity of the discrete micro-section of i of crossbeam.

Embodiment six:

With embodiment five unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and the circular of the equivalent bendind rigidity of each discrete micro-section of crossbeam described in step 4 is,

Crossbeam gravity deformation discretization model described in the Z-direction linearity data that heavy machine tool crossbeam deformation induced by gravity experiment measuring obtains according to step one two, step one three and step 3, calculating the equivalent bendind rigidity of each discrete micro-section of crossbeam is:

$\left\{\begin{array}{c}{z}_i=z_{\mathrm{ri}},i=0,..,n\\ {\left(\mathrm{Ei}\right)}_{\mathrm{vi}}=h^2\frac{M_i}{z_{i+1}-2z_i+z_{i-1}},i=1,...,n-1\end{array}\right.;$ In formula,

Z _irepresent the Z-direction deformation values of discrete micro-section of crossbeam, i=0,1 ..., n;

H represents step-length, h=2L/n;

M _irepresent the moment of flexure suffered by the discrete micro-section of i of crossbeam;

Z _rirepresent the actual measurement Z-direction linearity of the discrete micro-section of i of crossbeam in the experiment of crossbeam deformation induced by gravity;

(EI) _virepresent the equivalent bendind rigidity of the discrete micro-section of i of crossbeam;

By crossbeam deformation induced by gravity being tested moment that the crossbeam Z-direction linearity data, the free beam mechanical model that obtain calculate and step-length substitutes into above-mentioned (EI) _viexpression formula, can calculate the equivalent bendind rigidity of each discrete micro-section of crossbeam.

Embodiment seven:

With embodiment one, two, four or six unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and described in step 5, crossbeam finite element gravity deformation curve computing method are specially,

Step May Day, carry out finite-element preprocessing process:

To critical piece crossbeam, column, ram, the knife rest definition material attribute of heavy double column vertical lathes model, often kind of material properties comprises elastic modulus E, Poisson ratio ν and density of material ρ;

Analyze the constraint condition of crossbeam in practical set again: make lathe right side uprights be head tree, left column is auxiliary strut, in assembling place of head tree guide rail and crossbeam, tip iron is set to eliminate fit-up gap, together with the effect of cylinder clamp, make crossbeam at head tree place except the translational degree of freedom of Z-direction all the other 5 degree of freedom be all limited, therefore the displacement constraint in X, Y-direction is added in assembling place on the right side of crossbeam, displacement is restricted to 0mm, when crossbeam assembles at auxiliary strut place, due to the effect of Y-direction cylinder clamp, auxiliary strut and cross beam contacting surface clamp, because X-direction leaves the gap of 5 ~ 10mm, then Y-direction translation, X-direction and Z-direction rotational freedom are limited, the degree of freedom in its excess-three direction is unrestricted, the friction force that machine beam clamping device produces is not enough to support whole crossbeam, crossbeam mainly relies on leading screw to support, show that crossbeam is restricted in the degree of freedom of feed screw nut position Z-direction, therefore cylinder constraint is applied on the face of cylinder at lead screw position place, limit its axial freedom, the constraint condition of simulation leading screw,

Foundation using above-mentioned condition as the constraint condition and load that arrange finite element simulation, crossbeam constraint condition as shown in Figure 5, load is defined as overall gravity load as shown in Figure 6, arranges analog parameter, complete finite-element preprocessing process according to actual conditions in simulation software;

Step 5 two, to emulate in conjunction with actual test case, left and right two parts are divided into by crossbeam, solve crossbeam left-half at the distortion of left knife rest point of a knife point and crossbeam right half part in the distortion of right knife rest point of a knife point, obtain the crossbeam finite element gravity deformation simulation value of one group of crossbeam point of a knife point under crossbeam and blade carrier component Action of Gravity Field in Z-direction;

Step 5 three, the crossbeam finite element gravity deformation simulation value data obtained according to step 5 two, draw the Z-direction deformation curve of crossbeam gravity, obtain crossbeam finite element gravity deformation curve.

Embodiment eight:

With embodiment seven unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and described in step 6, crossbeam finite element gravity deformation curve correcting method is specially:

Step 6 one, according to the gravity deformation value of crossbeam point of a knife point in Z-direction and the relational expression of equivalent bendind rigidity:

$\left\{\begin{array}{c}{z}_i{|}_{i=0}=z_0,z_i{|}_{i=n}=z_n,i=0,...,n\\ z_{i+1}-2z_i+z_{i-1}=\frac{h^2{M}_i}{{\left(\mathrm{EI}\right)}_i},i=1,...,n-1\end{array}\right.,$

Because the material properties parameter of finite-element preprocessing process input described in step May Day is definite value, truly cannot reflect the inhomogeneity of actual crossbeam material, therefore the equivalent bendind rigidity utilizing step 4 to calculate is needed to revise the theoretical bendind rigidity that finite element analysis inputs, the inhomogeneity of the actual crossbeam material of true reflection;

Step 6 two, based on method of finite difference, according to the left side computing method of step 6 one relational expression, data processing is carried out to the crossbeam finite element gravity deformation simulation value that step 5 three obtains, obtains the finite difference fraction of finite element simulation:

$\left\{\begin{array}{c}{z}_i^s{|}_{i=0}=z_0^s,z_i^s{|}_{i=n}=z_n^s,i=0,n\\ z_{i-1}^s-2z_i^s+z_{i+1}^s=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_{\mathrm{input}}},i=1,...,n-1\end{array}\right.;$ In formula,

Z ^s _irepresent the Z-direction deformation values of each discrete micro-section of the crossbeam that finite element simulation obtains;

(EI) _inputthe theoretical bendind rigidity value of input when representing that Finite Element Correction calculates;

After the actual correction of step 6 three, completing steps six or two, each discrete micro-section of Z-direction flexural deformation value z of crossbeam ^r _imeet formula:

$\left\{\begin{array}{c}{z}_0^r=z_0^s,z_n^r=z_n^s,i=0,n\\ z_{i-1}^r-2z_i^r+z_{i+1}^r=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}}=h^2\frac{M_i}{{\left(\mathrm{Ei}\right)}_{\mathrm{input}}}\·\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{Ei}\right)}_{\mathrm{vi}}}=(z_{i-1}^s-2z_i^s+z_{i+1}^s)\·\frac{{\left(\mathrm{Ei}\right)}_{\mathrm{input}}}{{\left(\mathrm{Ei}\right)}_{\mathrm{vi}}},i=1,...,n-1\end{array}\right.,$

Step 6 four, by the theoretical bendind rigidity value (EI) of discrete for crossbeam micro-section of i _inputwith equivalent bendind rigidity (EI) _viratio as this correction factor k of discrete micro-section _i, that is: $\left\{\begin{array}{c}{k}_0=k_n=0,i=0,n\\ k_i=\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}},i=1,...,n-1\end{array}\right.,$

Step 6 five, due to method of finite difference be based on the diastrophic approximate differential equation of mechanics of materials middle cross beam, near bearing, the calculating of equivalent bendind rigidity causes correction factor excessive due to the simplification of load in computation model, do not meet actual conditions, according to the constraint condition that crossbeam assembles in head tree position, that 6 degree of freedom are all limited, auxiliary strut place Z-direction is limited, then when practical distortion and simulation calculation, the amount of deflection of crossbeam both sides constraint portions is identical with deformation extent, and namely starting condition formula is: z ^s ₀=z ^r ₀, z ^s _n=z ^r _n, k ₁=k _n-1=1, make Δ z ^r _i=z ^r _i-1-2z ^r _i+ z ^r _i+1, Δ z ^s _i=z ^s _i-1-2z ^s _i+ z ^s _i+1, then obtain heavy twin columns and found car crossbeam gravity deformation curvature correction model formation and be: $\left\{\begin{array}{c}{z}_0^r=z_0^s,z_n^r=z_n^s,i=0,n\\ {\mathrm{\Δz}}_i^r={\mathrm{\Δz}}_i^s\·k_i,i=1,..,n-1\end{array}\right..$

Embodiment eight:

With embodiment seven unlike, the heavy twin columns based on method of finite difference of present embodiment found car crossbeam gravity deformation Forecasting Methodology, and the two-part discrete micro-segment length in crossbeam left and right described in step 5 three is 460mm.

Embodiment 1:

First, the experiment of heavy double column vertical lathes crossbeam deformation induced by gravity is carried out:

Test the equivalent S-curve that obtains in conjunction with the actual processing experiential modification of this crossbeam using the crossbeam finite element analysis of interval 230mm as experiment crossbeam processing line style, utilize planer-type milling machine to process.When processing crossbeam lower guideway, crossbeam is kept flat, eliminate the impact of gravity factor on processing, after crossbeam lower guideway machines, crossbeam is sidelong, at the actual machining state of leading screw place parallels supporting simulation, and be sidelong the linearity data of stable rear measurement crossbeam lower guideway in Z-direction at crossbeam, deformation induced by gravity experiment Z-direction linearity data, as shown in table 1.

Table 1 deformation induced by gravity experiment crossbeam lower guideway Z-direction linearity data

Experimentally measurement result, after crossbeam is sidelong and is sidelong for 68 hours, the deformation values of measurement reaches steady state (SS).Crossbeam through within 68 hours, to be sidelong stable after linearity curve and the difference of crossbeam Processing Curve be the deformation induced by gravity curve of crossbeam.

The second, utilizing theory of mechanics of materials, is free beam mechanical model by the deformation induced by gravity curve of crossbeam and the model simplification of crossbeam gravity deformation:

According to crossbeam profile, the computing method of the mechanics of materials are utilized to simplify computation model, according to working environment and the assembly constraint condition of machine tool beam, crossbeam is reduced to a free beam, gravity puts on crossbeam as uniformly distributed load, with the gravity size in unit length, namely gravity load intensity represents uniformly distributed load.The crossbeam gravity load shown in Fig. 3 can be obtained and bend computation model sketch.

If this heavy machine tool crossbeam span is 9500mm, be highly 1350mm, span-depth radio is greater than 5, and application straight beam distortion line of deflection approximate differential equation calculates the Z-direction distortion of crossbeam, obtain theoretical crossbeam deformation induced by gravity curve z (x), and then obtain free beam mechanical model: consider that the reason that Finite element analysis results and practical distortion differ greatly is that crossbeam material inhomogeneity causes, can think that beam part material properties is everywhere different, therefore need the crossbeam deformation induced by gravity model under single material discrete, set up the crossbeam gravity deformation discretization model in material heterogeneity situation.

3rd, crossbeam is separated into one group discrete micro-section, then sets up crossbeam gravity deformation discretization model in conjunction with method of finite difference,

Crossbeam is equidistantly divided into n section, i.e. the coordinate x of i-th section of crossbeam _imeet: x _i=x ₀+ ih, i=0,1 ..., n, as shown in Figure 4, schematic diagram when crossbeam being separated into micro-section.

4th, in conjunction with the experiment of heavy machine tool crossbeam deformation induced by gravity and crossbeam gravity deformation discretization model, calculate the equivalent bendind rigidity of described in each discrete micro-section and characterize the real material attribute of crossbeam;

For making Finite element analysis results close to practical distortion value, need the bendind rigidity value obtaining each discrete micro-section of actual conditions sill, but this numerical value is difficult to directly record.Owing to comprising the bendind rigidity (EI) of each discrete micro-section of crossbeam in the crossbeam gravity deformation discretization model of above-mentioned foundation _i, the bendind rigidity of each discrete micro-section of crossbeam therefore can be calculated in conjunction with the deformation induced by gravity experimental data in second section and crossbeam gravity deformation discretization model.The bendind rigidity of each discrete micro-section of the crossbeam calculated utilizing the method is called the equivalent bendind rigidity (EI) of crossbeam _v.

After crossbeam gravity deformation discretization model is arranged: $\left\{\begin{array}{c}{z}_i=z_{\mathrm{ri}},i=0,..,n\\ {\left(\mathrm{Ei}\right)}_{\mathrm{vi}}=h^2\frac{M_i}{z_{i+1}-2z_i+z_{i-1}},i=1,...,n-1\end{array}\right.,$

By deformation induced by gravity being tested moment that the crossbeam Z-direction linearity data, the free beam mechanical model that obtain calculate and step-length generation such as above formula can calculate each discrete micro-section of equivalent bendind rigidity of crossbeam.Table 2 gives the result of calculation of the equivalent bendind rigidity of experiment each discrete micro-section of crossbeam.

Table 2 equivalent bendind rigidity result of calculation

To each parts definition material attribute, comprise the density p of elastic modulus E, Poisson ratio ν and material.Each parts simulation parameter information is summed up according to practical implementation, as shown in table 3.

The each component materials parameter of the heavy double column vertical lathes of table 3

5th, obtain crossbeam gravity deformation curve by the crossbeam point of a knife point Z-direction gravity deformation under simulation calculation crossbeam and knife rest effect.Crossbeam, in conjunction with actual test case, is divided into left and right two parts by emulation, and solve crossbeam left-half respectively in the distortion at right knife rest point of a knife point of the distortion of left knife rest point of a knife point and crossbeam right half part to it, crossbeam calculates the Z-direction distortion of a point of a knife point every 460mm.As Fig. 7, be point of a knife point gravity deformation in z-direction under Action of Gravity Field, obtain crossbeam finite element gravity deformation curve as shown in Figure 8.

6th, utilize equivalent bendind rigidity, based on method of finite difference, the described crossbeam finite element gravity deformation curve that step 5 calculates is corrected, each discrete micro-section of Z-direction flexural deformation value z of the crossbeam after correction ^r _imeet formula:

$\left\{\begin{array}{c}{z}_0^r=z_0^s,z_n^r=z_n^s,i=0,n\\ z_{i-1}^r-2z_i^r+z_{i+1}^r=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}}=h^2\frac{M_i}{{\left(\mathrm{Ei}\right)}_{\mathrm{input}}}\·\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{Ei}\right)}_{\mathrm{vi}}}=(z_{i-1}^s-2z_i^s+z_{i+1}^s)\·\frac{{\left(\mathrm{Ei}\right)}_{\mathrm{input}}}{{\left(\mathrm{Ei}\right)}_{\mathrm{vi}}},i=1,...,n-1\end{array}\right.,$

By the theoretical bendind rigidity value (EI) of discrete for crossbeam micro-section of i _inputwith equivalent bendind rigidity (EI) _viratio as this correction factor k of discrete micro-section _i, that is: $\left\{\begin{array}{c}{k}_0=k_n=0,i=0,n\\ k_i=\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}},i=1,...,n-1\end{array}\right.,$ Because method of finite difference is based on the diastrophic approximate differential equation of mechanics of materials middle cross beam, near bearing, the calculating of equivalent bendind rigidity causes correction factor excessive due to the simplification of load in computation model, do not meet actual conditions, according to the constraint condition that crossbeam assembles in head tree position, be that 6 degree of freedom are all limited, auxiliary strut place Z-direction is limited, then when practical distortion and simulation calculation, the amount of deflection of crossbeam both sides constraint portions is identical with deformation extent, and namely starting condition formula is: z ^s ₀=z ^r ₀, z ^s _n=z ^r _n, k ₁=k _n-1=1, make Δ z ^r _i=z ^r _i-1-2z ^r _i+ z ^r _i+1, Δ z ^s _i=z ^s _i-1-2z ^s _i+ z ^s _i+1, then obtain heavy twin columns and found the final crossbeam gravity deformation curve of car:

$\left\{\begin{array}{c}{z}_0^r=z_0^s,z_n^r=z_n^s,i=0,n\\ {\mathrm{\Δz}}_i^r={\mathrm{\Δz}}_i^s\·k_i,i=1,...,n-1\end{array}\right..$

7th, measure crossbeam G5 item precision after crossbeam is installed, test data is depicted as crossbeam actual measurement G5 item precision curve, as shown in Figure 9.Crossbeam initial manufacture curve is deducted the practical distortion curve that crossbeam G5 item precision curve is crossbeam.

Utilize the above-mentioned crossbeam gravity deformation curve computing method based on method of finite difference, obtain the crossbeam gravity deformation curve data after correcting, as shown in table 4.

Table 4 is based on the crossbeam gravity deformation curve result of calculation of method of finite difference

Crossbeam gravity deformation simulation curve, practical distortion curve and the gravity deformation curve computing method based on method of finite difference are corrected result contrast, as shown in Figure 10.Show that the curve after correction compares the beam deformation situation of finite element simulation curve more closing to reality.As calculated, the error rate of former result of finite element and actual beam deformation is 26.86%, and the crossbeam Z-direction distortion obtained based on the crossbeam gravity deformation computing method of method of finite difference is 11.67% with the average error rate of actual beam deformation, the error amount of main machining area is 0.07mm to the maximum.Demonstrate the correctness of the finite element result bearing calibration based on method of finite difference.

Claims (9)

1. the heavy twin columns based on method of finite difference found a car crossbeam gravity deformation Forecasting Methodology, it is characterized in that: described crossbeam gravity deformation curve computing method are realized by following steps:

Step one: the experiment of simulation practical set condition design heavy machine tool crossbeam deformation induced by gravity, obtains material heterogeneity situation sill deformation induced by gravity curve;

Step 2: utilize theory of mechanics of materials, is reduced to free beam mechanical model according to the stressing conditions of crossbeam under Gravitative Loads by crossbeam;

Step 3: crossbeam is separated into one group discrete micro-section, to the described free beam mechanical model discretize that step 2 obtains, then sets up crossbeam gravity deformation discretization model in conjunction with method of finite difference;

Step 4: heavy machine tool crossbeam deformation induced by gravity described in integrating step one is tested and crossbeam gravity deformation discretization model described in step 3, calculates the equivalent bendind rigidity of described in each discrete micro-section;

Step 5: by the practical set condition of finite element method for simulating heavy machine tool crossbeam, calculates crossbeam finite element gravity deformation curve after crossbeam and rail head being assembled;

Step 6: the described equivalent bendind rigidity utilizing step 4 to calculate, based on method of finite difference, the described crossbeam finite element gravity deformation curve that step 5 calculates is corrected, obtain final crossbeam gravity deformation curve, namely dope heavy twin columns and found car crossbeam gravity deformation degree.

2. found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference according to claim 1, it is characterized in that: heavy machine tool crossbeam deformation induced by gravity experiment described in step one is specially,

Step one by one, according to crossbeam profile, using the crossbeam mid point in the surface level of crossbeam place as coordinate origin O, set up cartesian coordinate system, X-direction along beam guideway direction, and is to the right that just Y-axis is perpendicular to X-axis, and be upwards that just Z axis positive dirction meets the right-hand rule;

Step one two, crossbeam to be kept flat, adopt autocollimator to measure the Z-direction linearity data on flat condition sill lower guideway surface;

Step one three, again crossbeam is sidelong to stabilization, adopts level meter or autocollimator measurement to be sidelong the Z-direction linearity data on state sill lower guideway surface.

3. according to claim 1 or 2, found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference, it is characterized in that: described in step one, the acquisition methods of crossbeam deformation induced by gravity curve is specially:

By be sidelong described in step one three described in the Z-direction linearity and step one two that record to stabilization, crossbeam is kept flat after the difference of Z-direction linearity data that records, utilize described difference to be depicted as described crossbeam deformation induced by gravity curve.

4. found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference according to claim 3, it is characterized in that: described in step 2, the concrete modeling method of free beam mechanical model is:

The profile of crossbeam selected one by one according to step and the working environment of machine tool beam and assembly constraint condition, crossbeam is reduced to free beam, again the self gravitation of crossbeam is put on crossbeam as uniformly distributed load, uniformly distributed load is represented with the gravity load intensity of crossbeam, utilize the stressing conditions of the computing method of the mechanics of materials to crossbeam to simplify, obtaining described free beam mechanical model is: $z^{\′\′}\left(x\right)=\frac{M\left(x\right)}{\mathrm{EI}\left(x\right)};$ In formula,

X represents the coordinate figure of crossbeam along guide rail direction;

Z (x) represents crossbeam deformation induced by gravity curve;

M (x) represents the moment of flexure suffered by crossbeam bend distortion;

E represents the elastic modulus of crossbeam material;

I (x) represents the distribution function of cross sectional moment of inertia.

5. according to claim 1,2 or 4, found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference, it is characterized in that: described in step 3, crossbeam gravity deformation discretization model modeling method is specially:

Step 3 one, inhomogenous for material crossbeam is equidistantly divided into n section, then the coordinate x of i-th section of crossbeam _ix is met in step one by one described coordinate system _i=x ₀+ ih, i=0,1 ..., n; In formula,

H represents step-length, h=2L/n;

L represents the half of crossbeam total length;

X ₀represent the starting point coordinate of crossbeam left end;

Step 3 two, flexural deformation part for crossbeam, according to difference formula and the crossbeam deflection differential equation of second derivative, obtain material inhomogenous crossbeam gravity deformation discretization model: $\left\{\begin{array}{c}{z}_i{|}_{i=0}=z_0,z_i{|}_{i=n}=z_n,i=0,...,n\\ z_{i+1}-{2z}_i+z_{i-1}=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_i},i=1,...,n-1\end{array}\right.;$ In formula,

Z _irepresent the Z-direction Deformation Theory value of discrete micro-section of crossbeam, i=0,1 ..., n;

M _irepresent the moment of flexure suffered by the discrete micro-section of i of crossbeam;

(EI) _irepresent the bendind rigidity of the discrete micro-section of i of crossbeam.

6. found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference according to claim 5, it is characterized in that: the circular of the equivalent bendind rigidity of each discrete micro-section of crossbeam described in step 4 is,

Crossbeam gravity deformation discretization model described in the Z-direction linearity data that heavy machine tool crossbeam deformation induced by gravity experiment measuring obtains according to step one two, step one three and step 3, calculating the equivalent bendind rigidity of each discrete micro-section of crossbeam is:

$\left\{\begin{array}{cc}{z}_i=z_{\mathrm{ri}}& i=0,...,n\\ {\left(\mathrm{EI}\right)}_{\mathrm{vi}}=h^2\frac{M_i}{z_{i+1}-{2z}_i+z_{i-1}}& i=1,...,n-1\end{array}\right.;$ In formula,

Z _irepresent the Z-direction deformation values of discrete micro-section of crossbeam, i=0,1 ..., n;

H represents step-length, h=2L/n;

M _irepresent the moment of flexure suffered by the discrete micro-section of i of crossbeam;

Z _rirepresent the actual measurement Z-direction linearity of the discrete micro-section of i of crossbeam in the experiment of crossbeam deformation induced by gravity;

(EI) _virepresent the equivalent bendind rigidity of the discrete micro-section of i of crossbeam.

7. according to claim 1,2,4 or 6, found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference, it is characterized in that: described in step 5, crossbeam finite element gravity deformation curve computing method are specially,

Step May Day, carry out finite-element preprocessing process:

To critical piece crossbeam, column, ram, the knife rest definition material attribute of heavy double column vertical lathes model, often kind of material properties comprises elastic modulus E, Poisson ratio ν and density of material ρ;

Analyze the constraint condition of crossbeam in practical set again: make lathe right side uprights be head tree, left column is auxiliary strut, in assembling place of head tree guide rail and crossbeam, tip iron is set to eliminate fit-up gap, together with the effect of cylinder clamp, make crossbeam at head tree place except the translational degree of freedom of Z-direction all the other 5 degree of freedom be all limited, therefore the displacement constraint in X, Y-direction is added in assembling place on the right side of crossbeam, displacement is restricted to 0mm, when crossbeam assembles at auxiliary strut place, due to the effect of Y-direction cylinder clamp, auxiliary strut and cross beam contacting surface clamp, because X-direction leaves the gap of 5 ~ 10mm, then Y-direction translation, X-direction and Z-direction rotational freedom are limited, the degree of freedom in its excess-three direction is unrestricted, the friction force that machine beam clamping device produces is not enough to support whole crossbeam, crossbeam mainly relies on leading screw to support, show that crossbeam is restricted in the degree of freedom of feed screw nut position Z-direction, therefore cylinder constraint is applied on the face of cylinder at lead screw position place, limit its axial freedom, the constraint condition of simulation leading screw,

Foundation using above-mentioned condition as the constraint condition and load that arrange finite element simulation, arranges analog parameter according to actual conditions, completes finite-element preprocessing process in simulation software;

Step 5 two, to emulate in conjunction with actual test case, left and right two parts are divided into by crossbeam, solve crossbeam left-half at the distortion of left knife rest point of a knife point and crossbeam right half part in the distortion of right knife rest point of a knife point, obtain the crossbeam finite element gravity deformation simulation value of one group of crossbeam point of a knife point under crossbeam and blade carrier component Action of Gravity Field in Z-direction;

Step 5 three, the crossbeam finite element gravity deformation simulation value data obtained according to step 5 two, draw the Z-direction deformation curve of crossbeam gravity, obtain crossbeam finite element gravity deformation curve.

8. found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference according to claim 7, it is characterized in that: described in step 6, crossbeam finite element gravity deformation curve correcting method is specially:

Step 6 one, according to the gravity deformation value of crossbeam point of a knife point in Z-direction and the relational expression of equivalent bendind rigidity:

$\left\{\begin{array}{c}{z}_i{|}_{i=0}=z_0,z_i{|}_{i=n}=z_n,i=0,n\\ z_{i+1}-{2z}_i+z_{i-1}=\frac{h^2{M}_i}{{\left(\mathrm{EI}\right)}_i},i=1,...,n-1\end{array}\right.,$

The equivalent bendind rigidity calculated by step 4 is revised the theoretical bendind rigidity that finite element analysis inputs, the inhomogeneity of the actual crossbeam material of true reflection;

Step 6 two, based on method of finite difference, according to the left side computing method of relational expression described in step 6 one, data processing is carried out to the crossbeam finite element gravity deformation simulation value that step 5 three obtains and completes trimming process, obtain the finite difference fraction of finite element simulation:

$\left\{\begin{array}{cc}{z}_i^s{|}_{i=0}=z_0^s,z_i^s{|}_{i=n}=z_n^s& i=0,n\\ z_{i-1}^s-{2z}_i^s+z_{i+1}^s=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}& i=1,...,n-1\end{array}\right.;$ In formula,

Z ^s _irepresent the Z-direction deformation values of each discrete micro-section of the crossbeam that finite element simulation obtains;

(EI) _inputthe theoretical bendind rigidity value of input when representing that Finite Element Correction calculates;

After the actual correction of step 6 three, completing steps six or two, each discrete micro-section of Z-direction flexural deformation value z of crossbeam ^r _imeet formula:

$\left\{\begin{array}{c}{z}_0^r=z_0^s,z_n^r=z_n^s,i=0,n\\ z_{i-1}^r-{2z}_i^r+z_{i+1}^r=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}}=h^2\frac{M_i}{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}\·\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}}=(z_{i-1}^s-{2z}_i^s+z_{i+1}^s)\·\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}},i=1,...,n-1\end{array}\right.,$

Step 6 four, by the theoretical bendind rigidity value (EI) of discrete for crossbeam micro-section of i _inputwith equivalent bendind rigidity (EI) _viratio as this correction factor k of discrete micro-section _i, that is: $\left\{\begin{array}{cc}{k}_0=k_n=0& i=0,n\\ k_i=\frac{{\left(\mathrm{EI}\right)}_{\mathrm{input}}}{{\left(\mathrm{EI}\right)}_{\mathrm{vi}}}& i=1,...,n-1\end{array}\right.,$

Satisfied 6 degree of freedom of the constraint condition that step 6 five, crossbeam assemble in head tree position are all limited, auxiliary strut place Z-direction is limited, then when practical distortion and simulation calculation, the amount of deflection of crossbeam both sides constraint portions is identical with deformation extent, and namely starting condition formula is: z ^s ₀=z ^r ₀, z ^s _n=z ^r _n, k ₁=k _n-1=1, make Δ z ^r _i=z ^r _i-1-2z ^r _i+ z ^r _i+1, Δ z ^s _i=z ^s _i-1-2z ^s _i+ z ^s _i+1, then obtain heavy twin columns and found car crossbeam gravity deformation curvature correction model formation and be: $\left\{\begin{array}{c}{z}_0^r=z_0^s,z_n^r=z_n^s,i=0,n\\ {\mathrm{\Δz}}_i^r={\mathrm{\Δz}}_i^s\·k_i,i=1,...,n-1\end{array}\right..$

9. found car crossbeam gravity deformation Forecasting Methodology based on the heavy twin columns of method of finite difference according to claim 7, it is characterized in that: the two-part discrete micro-segment length in crossbeam left and right described in step 5 three is 460mm.