CN104898564A - Method for reducing three-shaft linkage contour error - Google Patents

Abstract

The invention discloses a method for reducing a three-shaft linkage contour error, belongs to the field of precision efficient machining of complex curved parts, and relates to a method for reducing the three-shaft linkage contour error of a numerical control machine tool in combination with machining feed speed re-planning and contour error pre-compensation. The method comprises the steps of firstly extracting machining feed speed and ideal cutter location information from numerical control codes, and re-planning the machining feed speed of each program section in a numerical control program by using the accelerated acceleration limit and the acceleration limit of each machining feed shaft as restraint conditions; estimating a contour error value by using an accumulated chord length parametric spatial cubic spline similar desired contour method; calculating the contour error compensation quantity of each feed shaft by using a Taylor series expansion method to obtain a pre-compensated cutter location; and iteratively cycling the above processes to obtain a pre-compensated machining code, thus realizing high-quality and high-efficiency machining of complex curved parts. The method is simple and practical, and can sufficiently exert the performance of the numerical control machine tool and improve the multi-shaft linkage contour precision.

Description

A kind of method reducing three-shaft linkage profile errors

Technical field

The invention belongs to complex curved surface parts precise high-efficiency manufacture field, particularly one processing speed of feed plans that multi-shaft interlocked profile errors precompensation combines with one again, is used for reducing the method for three-shaft linkage profile errors.

Background technology

The variable curvature curved surface part with complicated face structure is widely used in high-end equipment field.Along with the continuous propelling of product process criticized by the fast development in Important Project field and high-end equipment, such crucial complex curved surface parts not only has high requirement to contour accuracy, also day by day promotes the demand of production efficiency.For improving working (machining) efficiency, current many high-grade, digitally controlled machine tools can provide larger main motion and processing feed motion speed.But, due to factors such as lathe servo feed system lagging characteristics and feed shaft mechanical inertias, adopt high speed of feed to add respectively to run axle man-hour and can produce larger following error, and then bring out continuous path and run multi-shaft interlocked profile errors under cooked mode; In addition, because complex curved surface parts adds the existence of deep camber cutter rail in man-hour and the restriction of machine tool motion performance, processing feed shaft actual motion speed does not very easily reach instruction speed value, thus exacerbates multi-shaft interlocked profile errors.When above-mentioned phenomenon can cause High-speed machining variable curvature complex parts, the performance of numerically-controlled machine cannot be not fully exerted, the contour accuracy of part cannot meet the demands.Therefore, the precise high-efficiency processing of complex curved surface parts has become an industry difficult problem.

For solving this difficult problem, the multi-shaft interlocked profile errors in high speed of feed processing gets the attention.Document " Feed speed scheduling method for parts with rapidly varied geometric feature based on drive constraint of NC machine tool ", Zhenyuan Jia etc., International Journal of Machine Tools and Manufacture, 2014, 87:73-88, the document is for the Curve Machining profile errors problem with deep camber change, a kind of subregion variable element control precision machining method is proposed, by setting up profile errors and geometric properties, relation between processing speed of feed, classifying rationally is carried out to machining area, and distribute different processing speed of feed to each subregion, achieve the processing of variable curvature curve high precision.But the method reduces profile errors by planning processing speed of feed merely, larger on the impact of working (machining) efficiency.Document " Generalized Taylor series expansion for free-form two-dimensional contour error compensation ", Feng Huo etc., International Journal of Machine Tools and Manufacture, 2012, 53:91-99, the document proposes the compensation method of a kind of popularization Taylor series expansion profile errors, by estimating the profile errors in free curve each moment in sampling period, utilize the method error of calculation offset of Taylor series expansion, compensate for profile errors, effectively improve 2-axis linkage free curve machining profile precision, but be not generalized in the middle of three-shaft linkage space curve.Similarly, document " profile of spatial curves error real-time estimation and compensation method are studied ", Xiao Xiaoping etc., Sichuan University's journal (engineering science version), 2015,47 (1): 215-222, the document utilizes transform predict servo-drive system subsequent time output valve and estimate profile errors, achieves profile of spatial curves real-time error compensation.But the method not only needs the accurate model of servo feed system, also need to change digital control system structure, increase compensator, this realizes difficulty for Highgrade integration numerically-controlled machine; In addition, the method is mainly used in compensating servo parameter and loses a profile errors brought out, and cannot reduce the multi-shaft interlocked profile errors that machine tooling feed shaft produces under continuous path operational mode.

Summary of the invention

The present invention is intended to overcome prior art defect, invent a kind of method reducing three-shaft linkage profile errors, speed of feed planning will be processed be combined with profile errors precompensation, effectively reduce three-shaft linkage profile errors when numerically-controlled machine processing feed shaft continuous path runs.

Technical scheme of the present invention is a kind of method reducing three-shaft linkage profile errors, its characteristic is, first the method is extracted in numerical control code and is processed speed of feed and desirable cutter location information, the prediction characteristic of speed of feed is processed under considering lathe continuous path operational mode, with each processing feed shaft plus acceleration limit, acceleration limiting for constraint condition, program segment processing speed of feed each in numerical control program is planned again; Secondly, utilize the actual cutter location of stable state following error model assessment, and utilize cumulative inborn parameter space cubic spline to be similar to the method expecting profile, estimate profile errors value; Utilize the method for Taylor series expansion to calculate each feed shaft profile errors compensation rate, obtain the cutter location after precompensation; Said process iterative loop, can obtain the planning aft-loaded airfoil speed of feed of whole piece cutter rail and compensate rear cutter location, thus obtaining the machining code after precompensation, realizes the high-quality and high-efficiency processing of complex curved surface parts.Overall flow is see accompanying drawing 1, and concrete steps are as follows:

1) process speed of feed to plan again

If extract in numerical control machining code i-th cutter location is R _i(Rx _i, Ry _i, Rz _i), i-th program segment directive processing speed of feed is f _i, 1≤i≤n, n is cutter location sum, consider the look-ahead algorithm of processing speed of feed under continuous path runs cooked mode, each cutter location process think processing speed of feed direction should with the desired profile trajectory tangential of this point, for avoiding the prior imformation needing machining profile mathematical model, utilize vector direction as R _ibeing similar to of place's profile traces tangential direction, therefore, the ideal processing speed of feed vector v of this point _ifor:

In formula, make in κ axle, κ=x, y, z, represent processing feed shaft X, Y, Z, then R _iplace κ axle ideal processing speed of feed component v _{κ _ i}for:

If κ axle plus acceleration limit is acceleration limiting is judge i-th program segment theoretical process time in, with constraint under, can κ axle actual processing speed of feed from v _{κ _ i-1}plus/minus speed is to v _{κ _ i}if, can not, this program segment κ axle processing speed of feed component is optimized, if the speed of feed component after optimizing is theoretical process time after optimization should be met in and with constraint under, κ axle actual processing speed of feed can from v _{κ _ i-1}plus/minus speed arrives computing method be:

Utilize and optimize aft-loaded airfoil speed of feed component synthesis processing speed of feed after calculation optimization finally, for avoiding speed big ups and downs, utilize B-spline curve method processing speed of feed to be carried out repeatedly level and smooth, the speed of feed obtained after final planning is again

2) profile errors is estimated

First, cutter rail utilizes cumulative inborn parameter space cubic spline interpolation expect machining profile between any two adjacent cutter locations, obtain R _i-1and R _ibetween approximate expectation profile traces s _ibe expressed as:

s _i＝S(u _i-1,u _i,u) (4)

Wherein, parameter u ∈ [u _i-1, u _i], u _icomputing method be:

Secondly, P is used _irepresent i-th actual cutter location, its coordinate is P _i(Px _i, Py _i, Pz _i), order a is natural number, judges:

${\&dtri;}_i\left(R_{i-a}\right)\&CenterDot;{\&dtri;}_i\left(R_{i-a-1}\right)<0---\left(6\right)$

The minimum a value meeting inequality (6) is designated as m, at matched curve s _mdistance P is found in upper utilization " dichotomy " _inearest some Q _i(Qx _i, Qy _i, Qz _i), then the profile errors vector estimated value ε at this cutter location place _i(ε _{x_i}, ε _{y_i}, ε _{z_i}) be:

$\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_{x\_i}={\mathrm{Qx}}_i-{\mathrm{Px}}_i\\ {\mathrm{\&epsiv;}}_{y\_i}={\mathrm{Qy}}_i-{\mathrm{Py}}_i\\ {\mathrm{\&epsiv;}}_{z\_i}={\mathrm{Qz}}_i-{\mathrm{Pz}}_i\end{array}\right.---\left(7\right)$

3) profile errors precompensation

First, according to again planning after processing speed of feed and stable state following error model, correspond to desirable cutter location R when estimation continuous path runs _iactual cutter location P _i(Px _i, Py _i, Pz _i), its coordinate is expressed as the function of desirable cutter location coordinate:

$\left\{\begin{array}{c}{\mathrm{Px}}_i={\mathrm{fx}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\\ {\mathrm{Py}}_i={\mathrm{fy}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\\ {\mathrm{Pz}}_i={\mathrm{fz}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\end{array}\right.---\left(8\right)$

The expression of each function is:

$\left\{\begin{array}{c}{\mathrm{fx}}_i(x,y,z)=x-\frac{f_i^s(x-{\mathrm{Px}}_{i-1})}{\mathrm{Kx}\sqrt{{(x-{\mathrm{Px}}_{i-1})}^2+{(y-{\mathrm{Py}}_{i-1})}^2+{(z-{\mathrm{Pz}}_{i-1})}^2}}\\ {\mathrm{fy}}_i(x,y,z)=y-\frac{f_i^s(y-{\mathrm{Py}}_{i-1})}{\mathrm{Ky}\sqrt{{(x-{\mathrm{Px}}_{i-1})}^2+{(y-{\mathrm{Py}}_{i-1})}^2+{(z-{\mathrm{Pz}}_{i-1})}^2}}\\ {\mathrm{fz}}_i(x,y,z)=z-\frac{f_i^s(z-{\mathrm{Pz}}_{i-1})}{\mathrm{Kz}\sqrt{{(x-{\mathrm{Px}}_{i-1})}^2+{(y-{\mathrm{Py}}_{i-1})}^2+{(z-{\mathrm{Pz}}_{i-1})}^2}}\end{array}\right.---\left(9\right)$

In formula, Kx, Ky, Kz are respectively the servo gain of X, Y, Z feed shaft control system;

Secondly, each processing feeding axial profile errors component ε is calculated _{x_i}, ε _{y_i}, ε _{z_i}; Taylor series expansion method is finally utilized to calculate each feed shaft profile errors compensation rate, if profile errors compensation rate is Δ R _i=[Δ Rx _iΔ Ry _iΔ Rz _i] ^t, then according to formula (8), actual cutter location after compensating for:

$\left\{\begin{array}{c}{\mathrm{Px}}_i^{\mathrm{com}}={\mathrm{fx}}_i({\mathrm{Rx}}_i+{\mathrm{\&Delta;x}}_i,{\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i,{\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i)\\ {\mathrm{Py}}_i^{\mathrm{com}}={\mathrm{fy}}_i({\mathrm{Rx}}_i+{\mathrm{\&Delta;x}}_i,{\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i,{\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i)\\ {\mathrm{Pz}}_i^{\mathrm{com}}={\mathrm{fz}}_i({\mathrm{Rx}}_i+{\mathrm{\&Delta;Rx}}_i,{\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i,{\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i)\end{array}\right.---\left(10\right)$

By above formula at point (Rx _i, Ry _i, Rz _i) place carries out first order Taylor series expansion and obtains:

$\left\{\begin{array}{cccc}{\mathrm{Px}}_i^{\mathrm{com}}\&ap;{\mathrm{fx}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)+\frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Rx}}_i+\frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Ry}}_i+\frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Rz}}_i\\ {\mathrm{Py}}_i^{\mathrm{com}}\&ap;{\mathrm{fy}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)+\frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Rx}}_i+\frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Ry}}_i+\frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Rz}}_i\\ {\mathrm{Pz}}_i^{\mathrm{com}}\&ap;{\mathrm{fz}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)+\frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Rx}}_i+\frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Ry}}_i+\frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& {\mathrm{\&Delta;Rz}}_i\end{array}\right.---\left(11\right)$

Compensate for realizing profile errors, κ axle actual cutter location coordinate P κ before and after compensating _i, with profile errors vector at κ axle component ε _{κ _ i}between should meet relation:

${\mathrm{P\&kappa;}}_i^{\mathrm{com}}-{\mathrm{P\&kappa;}}_i={\mathrm{\&epsiv;}}_{\mathrm{\&kappa;}\_i}---\left(12\right)$

Formula (8) and formula (12) are substituted into formula (11), and omit higher-order shear deformation and can obtain:

$\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{x\_i}\\ {\mathrm{\&epsiv;}}_{y\_i}\\ {\mathrm{\&epsiv;}}_{z\_i}\end{array}\right]=\left[\begin{array}{ccc}\frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;fx}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;fz}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\end{array}\right]\&CenterDot;\left[\begin{array}{c}{\mathrm{\&Delta;Rx}}_i\\ {\mathrm{\&Delta;Ry}}_i\\ {\mathrm{\&Delta;Rz}}_i\end{array}\right]---\left(13\right)$

Therefore, at i-th cutter location place, profile errors compensation rate Δ R _ifor:

${\mathrm{\&Delta;R}}_i=\left[\begin{array}{c}{\mathrm{\&Delta;Rx}}_i\\ {\mathrm{\&Delta;Ry}}_i\\ {\mathrm{\&Delta;Rz}}_i\end{array}\right]={\left[\begin{array}{ccc}\frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;fx}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;fz}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\end{array}\right]}^{-1}\&CenterDot;\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{x\_i}\\ {\mathrm{\&epsiv;}}_{y\_i}\\ {\mathrm{\&epsiv;}}_{z\_i}\end{array}\right]---\left(14\right)$

4) said process iterative loop, can obtain each cutter location place profile errors compensation rate, and then be compensated rear instruction cutter location for:

$\left\{\begin{array}{c}{\mathrm{Rx}}_i^{\mathrm{com}}={\mathrm{Rx}}_i+{\mathrm{\&Delta;Rx}}_i\\ {\mathrm{Ry}}_i^{\mathrm{com}}={\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i\\ {\mathrm{Rz}}_i^{\mathrm{com}}={\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i\end{array}\right.---\left(15\right)$

Utilize the processing speed of feed after planning again and the cutter location after precompensation generate numerical control machining code after compensating, process for reality.

The invention has the beneficial effects as follows: (1) takes into full account that numerically-controlled machine continuous path runs speed of feed prediction characteristic under cooked mode and feed shaft kinematics characteristic is planned processing speed of feed again, significant to giving full play to machine tool capability; (2) without the need to feed servo-system accurate model and machining profile mathematic(al) representation, profile errors precompensation can be realized by means of only machining code, highly versatile; (3) processing speed of feed is planned again and to be combined with cutter location precompensation method, to reduction space profiles error, there is important directive significance.

Accompanying drawing explanation

Fig. 1---method overall flow figure;

Fig. 2---space astroid geometric model figure;

Fig. 3---processing speed of feed is planned again, profile errors value before profile errors precompensation; Wherein, A axle represents cutter location sequence number, and B axle represents profile errors absolute value, and unit is mm

Fig. 4---processing speed of feed is planned again, profile errors value after profile errors precompensation; Wherein, A axle represents cutter location sequence number, and B axle represents profile errors absolute value, and unit is mm

Embodiment

Combination technology scheme and accompanying drawing describe the specific embodiment of the present invention in detail.

When adopting high speed of feed processed complex curved surface part, due to existence and the factor such as numerically-controlled machine dynamic perfromance, processing feed shaft mechanical inertia of variable curvature cutter rail, there will be the phenomenon that larger following error and actual processing speed of feed very easily do not reach instruction speed value, thus bring out multi-shaft interlocked profile errors, be unfavorable for the precise high-efficiency processing of variable curvature complex curved surface parts.Accordingly, for the multi-shaft interlocked profile errors in high speed of feed processing, a kind of method reducing three-shaft linkage profile errors has been invented.

The space astroid cutter rail represented for non-homogeneous B spline curve, calculates by MATLAB software and emulates, and describe the invention process process in detail, overall flow is see accompanying drawing 1.

1) as shown in Figure 1, first, utilize NX/CAM software, with constant processing speed of feed 50mm/s, the initial numerical control machining code of span astroid, the non-uniform rational B-spline parameter of space astroid is, exponent number: 3, reference mark: [(0, 0, 0), (24, 12, 10), (24, 32, 20), (48, 16, 10), (72, 20, 0), (54, 0,-20), (72,-20,-10), (48,-16, 10), (24,-32,-10), (24,-12, 5), (0, 0, 0)], weight factor: [1, 1, 1, 1, 0.7, 1, 0.7, 1, 1, 1, 1], knot vector: [0, 0, 0, 1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9, 8/9, 1, 1, 1], its geometric model is see accompanying drawing 2,

2) from generated numerical control machining code, cutter location R is extracted _iand each program segment processing speed of feed f _i, the cutter location sum n=321 obtained; Get each processing feed shaft plus acceleration limit and acceleration limiting is respectively $j_x^{\lim }=j_y^{\lim }=j_z^{\lim }=60m/s^3,a_x^{\lim }=a_y^{\lim }=a_z^{\lim }=1m/s^2,$ Utilize step 1 in technical scheme) method, consider processing speed of feed prediction characteristic, with machine tooling feed shaft acceleration, acceleration limiting for constraint, calculate each program segment processing speed of feed after planning again 1≤i≤321;

3) at i-th cutter location place, utilize formula (8) and formula (9) to calculate and correspond to theoretical cutter location R _iactual cutter location P _icoordinate; Utilize the desirable cutter location of cumulative inborn parameter space Cubic Spline Fitting, obtain approximate expectation machining profile;

4) according to technical scheme steps 2) method and formula (7) calculate P _iplace profile errors vector ε _i(ε _{x_i}, ε _{y_i}, ε _{z_i}), utilize formula (14) to calculate this dot profile error compensation amount Δ R _i, in formula, the value of each partial derivative is:

According to cutter location after formula (15) calculation compensation coordinate

5) judge whether i equals n, if not etc., utilize cutter location after compensating replace compensating front cutter location R _i(Rx _i, Ry _i, Rz _i), actual cutter location after substitution formula (8) calculation compensation coordinate make i=i+1, utilize actual cutter location after compensating replace compensating front actual cutter location P _i-1(Px _i-1, Py _i-1, Pz _i-1), return step 3), calculate next actual cutter location; Said process iterative loop, until during i=n, namely obtains whole piece cutter rail each cutter location place profile errors compensation rate and cutter location coordinate after compensating 1≤i≤321;

6) according to again planning after processing speed of feed 1≤i≤321, and cutter location after compensating 1≤i≤321, generate numerical control machining code after compensating, process for reality.Profile errors simulation result before compensating and after compensating is see accompanying drawing 3 and accompanying drawing 4, result shows, profile errors maximal value has been reduced to 0.025mm from 0.053mm, utilize three-shaft linkage space profiles error-reduction method of the present invention, effectively can reduce multi-shaft interlocked cutter rail profile errors, improve machining profile precision.

When the present invention is directed to high speed of feed lower feeding axle continuous path operation processing variable curvature complex curved surface parts, actual processing speed of feed does not very easily reach instruction speed value and the larger problem of cutter rail profile errors, invent processing speed of feed to plan again and to combine with profile errors precompensation, be used for reducing the method for three-shaft linkage profile errors, to the performance of numerically-controlled machine performance and the precise high-efficiency processing of high-performance complex curved surface parts, there is Important Project Practical significance.

Claims (1)

1. one kind is reduced the method for three-shaft linkage profile errors, its characteristic is, first the method is extracted in numerical control code and is processed speed of feed and desirable cutter location information, process speed of feed under lathe continuous path operational mode with each processing feed shaft plus acceleration limit, acceleration limiting for constraint condition, program segment processing speed of feed each in numerical control program is planned again; Secondly, utilize the actual cutter location of stable state following error model assessment, and utilize cumulative inborn parameter space cubic spline to be similar to the method expecting profile, estimate profile errors value; Utilize the method for Taylor series expansion to calculate each feed shaft profile errors compensation rate, obtain the cutter location after precompensation; Said process iterative loop, obtains the planning aft-loaded airfoil speed of feed of whole piece cutter rail and compensates rear cutter location; Thus obtain the machining code after precompensation, realize the high-quality and high-efficiency processing of complex curved surface parts; Concrete steps are as follows:

1) process speed of feed to plan again

If in numerical control machining code, i-th cutter location of extraction is R _i(Rx _i, Ry _i, Rz _i), i-th program segment directive processing speed of feed is f _i, 1≤i≤n, n is cutter location sum, and continuous path processes speed of feed under running cooked mode, wants in each cutter location process the desired profile trajectory tangential processing speed of feed direction and this point, utilizes vector direction as R _ithe approximate direction of place's profile traces tangential direction, therefore, the ideal processing speed of feed vector v of this point _ifor:

$v_i=\frac{\stackrel{\&RightArrow;}{R_{i-1}{R}_{i+1}}}{\left|\right|\stackrel{\&RightArrow;}{R_{i-1}{R}_{i+1}}\left|\right|}{f}_i---\left(1\right)$

In formula, $\left|\right|\stackrel{\&RightArrow;}{R_{i-1}{R}_{i+1}}\left|\right|=\sqrt{{({\mathrm{Rx}}_{i+1}-{\mathrm{Rx}}_{i-1})}^2+{({\mathrm{Ry}}_{i+1}-{\mathrm{Ry}}_{i-1})}^2+{({\mathrm{Rz}}_{i+1}-{\mathrm{Rz}}_{i-1})}^2};$ Make in κ axle, κ=x, y, z, represent processing feed shaft X, Y, Z, then R _iplace κ axle ideal processing speed of feed component v _{κ _ i}for:

$v_{\mathrm{\&kappa;}\_i}=\frac{f_i({\mathrm{R\&kappa;}}_{i+1}-{\mathrm{R\&kappa;}}_{i-1})}{\left|\right|\stackrel{\&RightArrow;}{R_{i-1}{R}_{i+1}}\left|\right|}---\left(2\right)$

If κ axle plus acceleration limit is acceleration limiting is judge i-th program segment theoretical process time in, with constraint under, can κ axle actual processing speed of feed from v _{κ _ i-1}plus/minus speed is to v _{κ _ i}if, can not, this program segment κ axle processing speed of feed component is optimized, if the speed of feed component after optimizing is theoretical process time after optimization should be met in and with constraint under, κ axle actual processing speed of feed can from v _{κ _ i-1}plus/minus speed arrives computing method be:

${\mathrm{\&Delta;t}}_i^p=\frac{({\mathrm{R\&kappa;}}_{i+1}-{\mathrm{R\&kappa;}}_{i-1})\left|\right|\stackrel{\&RightArrow;}{R_{i-1}{R}_i\left|\right|}}{v_{\mathrm{\&kappa;}\_i}^p\left|\right|\stackrel{\&RightArrow;}{R_{i-1}{R}_{i+1}\left|\right|}}---\left(3\right)$

Utilize and optimize aft-loaded airfoil speed of feed component synthesis processing speed of feed after calculation optimization finally, for avoiding speed big ups and downs, utilize B-spline curve method processing speed of feed to be carried out repeatedly level and smooth, the speed of feed obtained after final planning is again

2) profile errors is estimated

First, cutter rail utilizes cumulative inborn parameter space cubic spline interpolation expect machining profile between any two adjacent cutter locations, obtain R _i-1and R _ibetween approximate expectation profile traces s _ibe expressed as:

s _i＝S(u _i-1,u _i,u) (4)

Wherein, parameter u ∈ [u _i-1, u _i], u _icomputing method be:

$u_i=\left\{\begin{array}{cc}0& i=1\\ \underset{2}{\overset{i}{\mathrm{\&Sigma;}}}\left|\right|\stackrel{\&RightArrow;}{R_{i-1}{R}_i}\left|\right|& i\&GreaterEqual;2\end{array}\right.---\left(5\right)$

Secondly, P is used _irepresent i-th actual cutter location, its coordinate is P _i(Px _i, Py _i, Pz _i), order ${\&dtri;}_i\left(R_j\right)=\stackrel{\&RightArrow;}{R_i{R}_j}\&CenterDot;\stackrel{\&RightArrow;}{R_{j-1}{R}_{j+1}},$ A is natural number, judges:

${\&dtri;}_i\left(R_{i-a}\right)\&CenterDot;{\&dtri;}_i\left(R_{i-a-1}\right)<0---\left(6\right)$

The minimum a value meeting inequality (6) is designated as m, at matched curve s _mdistance P is found in upper utilization " dichotomy " _inearest some Q _i(Qx _i, Qy _i, Qz _i), then the profile errors vector estimated value ε at this cutter location place _i(ε _{x_i}, ε _{y_i}, ε _{z_i}) be:

$\left\{\begin{array}{c}{\mathrm{\&epsiv;}}_{x\_i}={\mathrm{Qx}}_i-{\mathrm{Px}}_i\\ {\mathrm{\&epsiv;}}_{y\_i}={\mathrm{Qy}}_i-{\mathrm{Py}}_i\\ {\mathrm{\&epsiv;}}_{z\_i}={\mathrm{Qz}}_i-{\mathrm{Pz}}_i\end{array}\right.---\left(7\right)$

3) profile errors precompensation

First, according to again planning after processing speed of feed and stable state following error model, correspond to desirable cutter location R when estimation continuous path runs _iactual cutter location P _i(Px _i, Py _i, Pz _i), its coordinate is expressed as the function of desirable cutter location coordinate:

$\left\{\begin{array}{c}{\mathrm{Px}}_i={\mathrm{fx}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\\ {\mathrm{Py}}_i={\mathrm{fy}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\\ {\mathrm{Pz}}_i={\mathrm{fz}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\end{array}\right.---\left(8\right)$

The expression of each function is:

$\left\{\begin{array}{c}{\mathrm{fx}}_i(x,y,z)=x-\frac{f_i^s(x-{\mathrm{Px}}_{i-1})}{\mathrm{Kx}\sqrt{{(x-{\mathrm{Px}}_{i-1})}^2{(y-{\mathrm{Py}}_{i-1})}^2+{(z-{\mathrm{Pz}}_{i-1})}^2}}\\ {\mathrm{fy}}_i(x,y,z)=y-\frac{f_i^s(y-{\mathrm{Py}}_{i-1})}{\mathrm{Ky}\sqrt{{(x-{\mathrm{Px}}_{i-1})}^2+{(y-{\mathrm{Py}}_{i-1})}^2+{(z-{\mathrm{Pz}}_{i-1})}^2}}\\ {\mathrm{fz}}_i(x,y,z)=z-\frac{f_i^s(z-{\mathrm{Pz}}_{i-1})}{\mathrm{Kz}\sqrt{{(x-{\mathrm{Px}}_{i-1})}^2+{(y-{\mathrm{Py}}_{i-1})}^2+{(z-{\mathrm{Pz}}_{i-1})}^2}}\end{array}\right.---\left(9\right)$

In formula, Kx, Ky, Kz are respectively the servo gain of X, Y, Z feed shaft control system;

Secondly, each processing feeding axial profile errors component ε is calculated _{x_i}, ε _{y_i}, ε _{z_i}; Taylor series expansion method is finally utilized to calculate each feed shaft profile errors compensation rate, if profile errors compensation rate is Δ R _i=[Δ Rx _iΔ Ry _iΔ Rz _i] ^t, then according to formula (8), actual cutter location after compensating for:

$\left\{\begin{array}{c}{\mathrm{Px}}_i^{\mathrm{com}}={\mathrm{fx}}_i({\mathrm{Rx}}_i+{\mathrm{\&Delta;Rx}}_i,{\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i,{\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i)\\ {\mathrm{Py}}_i^{\mathrm{com}}={\mathrm{fy}}_i({\mathrm{Rx}}_i+{\mathrm{\&Delta;Rx}}_i,{\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i,{\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i)\\ {\mathrm{Pz}}_i^{\mathrm{com}}={\mathrm{fz}}_i({\mathrm{Rx}}_i+{\mathrm{\&Delta;Rx}}_i,{\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i,{\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i)\end{array}\right.---\left(10\right)$

By above formula at point (Rx _i, Ry _i, Rz _i) place carries out first order Taylor series expansion and obtains:

$\left\{\begin{array}{c}{\mathrm{Px}}_i^{\mathrm{com}}\&ap;{\mathrm{fx}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)+\frac{\&PartialD;{\mathrm{fx}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}{\mathrm{\&Delta;Rx}}_i+\frac{\&PartialD;{\mathrm{fx}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}{\mathrm{\&Delta;Ry}}_i+\frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)\mathrm{\&Delta;}{\mathrm{Rz}}_i}\\ {\mathrm{Py}}_i^{\mathrm{com}}\&ap;{\mathrm{fy}}_i({\mathrm{Ry}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)+\frac{\&PartialD;{\mathrm{fy}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}{\mathrm{\&Delta;Rx}}_i+\frac{\&PartialD;{\mathrm{fy}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}{\mathrm{\&Delta;Ry}}_i+\frac{\&PartialD;{\mathrm{fz}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i){\mathrm{\&Delta;Rz}}_i}\\ {\mathrm{Pz}}_i^{\mathrm{com}}\&ap;{\mathrm{fz}}_i({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)+\frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}{\mathrm{\&Delta;Rx}}_i+\frac{\&PartialD;{\mathrm{fz}}_i}{\&PartialD;f}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\mathrm{\&Delta;}{\mathrm{Ry}}_i+\frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}{\mathrm{\&Delta;Rz}}_i\end{array}\right.---\left(11\right)$

Compensate for realizing profile errors, κ axle actual cutter location coordinate P κ before and after compensating _i, with profile errors vector at κ axle component ε _{κ _ i}between should meet relation:

${\mathrm{P\&kappa;}}_i^{\mathrm{com}}-{\mathrm{P\&kappa;}}_i={\mathrm{\&epsiv;}}_{\mathrm{\&kappa;}\_i}---\left(12\right)$

Formula (8) and formula (12) are substituted into formula (11), and omit higher-order shear deformation and can obtain:

$\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{x\_i}\\ {\mathrm{\&epsiv;}}_{y\_i}\\ {\mathrm{\&epsiv;}}_{z\_i}\end{array}\right]=\left[\begin{array}{ccc}\frac{\&PartialD;{\mathrm{fx}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{\&PartialD;{\mathrm{fx}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;z}{|}_{(R{x}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{\&PartialD;{\mathrm{fy}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{\&PartialD;{\mathrm{fy}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\end{array}\right]\&CenterDot;\left[\begin{array}{c}{\mathrm{\&Delta;Rx}}_i\\ {\mathrm{\&Delta;Ry}}_i\\ {\mathrm{\&Delta;Rz}}_i\end{array}\right]---\left(13\right)$

Therefore, at i-th cutter location place, profile errors compensation rate Δ R _ifor:

$\mathrm{\&Delta;}{R}_i=\left[\begin{array}{c}{\mathrm{\&Delta;Rx}}_i\\ {\mathrm{\&Delta;Ry}}_i\\ {\mathrm{\&Delta;Rz}}_i\end{array}\right]={\left[\begin{array}{ccc}\frac{\&PartialD;{\mathrm{fx}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{\&PartialD;{\mathrm{fx}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fx}}_i}{\&PartialD;z}{|}_{(R{x}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fy}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{\&PartialD;{\mathrm{fy}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{\&PartialD;{\mathrm{fy}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\\ \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;x}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;y}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}& \frac{{\&PartialD;\mathrm{fz}}_i}{\&PartialD;z}{|}_{({\mathrm{Rx}}_i,{\mathrm{Ry}}_i,{\mathrm{Rz}}_i)}\end{array}\right]}^{-1}\&CenterDot;\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{x\_i}\\ {\mathrm{\&epsiv;}}_{y\_i}\\ {\mathrm{\&epsiv;}}_{z\_i}\end{array}\right]---\left(14\right)$

4) said process iterative loop, can obtain each cutter location place profile errors compensation rate, and then be compensated rear instruction cutter location for:

$\left\{\begin{array}{c}{\mathrm{Px}}_i^{\mathrm{com}}={\mathrm{Rx}}_i+{\mathrm{\&Delta;Rx}}_i\\ {\mathrm{Py}}_i^{\mathrm{com}}={\mathrm{Ry}}_i+{\mathrm{\&Delta;Ry}}_i\\ {\mathrm{Pz}}_i^{\mathrm{com}}={\mathrm{Rz}}_i+{\mathrm{\&Delta;Rz}}_i\end{array}\right.---\left(15\right)$

Utilize the processing speed of feed after planning again and the cutter location after precompensation generate numerical control machining code after compensating, process for reality.