CN101653921A - Error compensation method of numerical control grinding contour of camshaft - Google Patents

Abstract

The invention discloses an error compensation method of numerical control grinding contour of a camshaft, comprising the following steps: a. performing offline measurement on the contour line of a processed cam sheet by multiple trail cut processing to obtain practical contour line data for respectively lifting; b. calculating the lifting error value of one circle of the whole cam sheet by comparing theory lift and actual measurement lift data, analyzing the lift error, and predicting the error; c. building a virtual lift table, and performing secondary fairing processing to the virtual lift;d. adopting a post-processed virtual lift table to replace an original lift table, and performing numerical control processing of the camshaft which has the same type with a trail cut camshaft under the same technological condition. Based on the above steps, the invention programs and develops the error analysis and compensation processing software of numerical control grinding contour error of acamshaft and realizes the intelligent and automatic application of a technical method; the lift error value of the whole contour line of the processed cam sheet is integrally reduced, molded line precision is obviously improved, no burn or waveness exists on the surface of the contour, surface quality is favorable, and error compensation effect is obvious.

Description

Error compensation method of numerical control grinding contour of camshaft

Technical field

The present invention relates to a kind of error compensating method, particularly relate to the profile errors compensation method in a kind of camshaft numerical control grinding process.

Background technology

Camshaft is one of engine major part, be used to control the air inlet and the exhaust of engine, its molded lines precision is extremely crucial to the influence of engine performance, and the crudy of camshaft and working (machining) efficiency directly have influence on the quality and the developing of automobile industry of automobile product.Machining accuracy is that Camshaft Grinding is processed one of most important technical indicator, and the method that improves machining accuracy mainly contains: error prevents and error compensation.Error prevents it is to realize high accuracy processing by improving lathe hardware precision, and this method cost height is uneconomical, and machining accuracy acquires a certain degree, and the back is just very difficult improves again.And error compensation is by whole process being carried out analysis and modeling, and in system, add a kind of new initial error artificially and remove to reduce, offset original initial error, this method is economical and practical, has great importance at high-precision working research of modern times and in using.

Influencing the THE CAM PROFILE ERROR factor has a lot, controls order of accuarcy of parameter, environment temperature, positional servosystem characteristic and control accuracy and profiling modeling or the like comprising machine tool mechanical precision, control system.In existing THE CAM PROFILE ERROR Compensation Research, mainly contain two kinds of approach: the one, implement compensation at the individual error influence factor, by systematic parameter, rationally being provided with of parameter of axle control are improved the cam contour precision.Because the actual cam contour that processes is a result of various factor comprehensive action, so have very big limitation at the method for individual error influence factor modeling; Two are based on the multi-body system kinematical theory, set up the Mathematical Modeling of each moving component of lathe, the constraint equation of derivation precise motion and parameter, and finally generate accurate digital control instruction, improve the cam ground precision with this, this method is also just launched Compensation Research at most of error effect factor, can't comprehensively consider the combined influence of various errors, and amount of calculation is bigger, is difficult for promoting.As seen, there is the imperfection part in the technology of existing THE CAM PROFILE ERROR compensation, has influenced its application in reality processing.

Summary of the invention

Technical problem to be solved by this invention provides a kind of can the analysis under specific process conditions, various errors are to the combined influence of camshaft numerical control grinding machining accuracy, the reflection error is comprehensive, can effectively improve the error compensation method of numerical control grinding contour of camshaft of camshaft profile precision.

In order to solve the problems of the technologies described above, error compensation method of numerical control grinding contour of camshaft provided by the invention, may further comprise the steps: a. is that molded lines carries out off-line measurement by repeatedly trial cut processing to processing back cam bit outline line, obtains real contour line data one lift; B. by theoretical lift of contrast and actual measurement lift size of data, find the solution the lift range error value in whole one week of cam bit, analyze lift range error, predicated error; C makes up virtual lift table and virtual lift is carried out the secondary fairing processing; D. adopt the virtual lift table through post processing to replace original lift table, carry out under the same process condition, the digital control processing with the camshaft of this trial cut camshaft same model is characterized in that:

(1), trial cut processing

Before cam bit carried out the trial cut in-process measurement, earlier camshaft is cleaned up, and as far as possible workpiece is placed a bit of time and measured again, during measurement, each cam bit done repeatedly measure, obtain many group actual measurement lift data; Calculate the lift range error value of several groups of data through formula (a), observe the conversion trend of several grouping errors; If the variation tendency of several grouping errors reaches unanimity on the whole substantially, illustrate that the camshaft detected state is more stable, this moment, detected TP also compared accurately;

e＝h _S-h _L (a)

In the formula: the e-lift range error

h _S-actual measurement lift

h _L-theoretical lift

Through m trial cut processing, each cam bit will produce m group actual measurement lift and lift range error; Repeatedly the arithmetic mean value x of trial cut lift range error is as trial cut gained lift range error, and destabilizing factor influences in the trial cut processing to reduce, shown in formula (b):

$(\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="A2009100443260014H1.png,A2009100443260015H1.png"\; state="\{\{state\}\}">e</figure-callout>}}_1},\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A2009100443260014H1.png"\; state="\{\{state\}\}">e</figure-callout>}}_2},\&CenterDot;\&CenterDot;\&CenterDot;,\stackrel{\&OverBar;}{e_n})=(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{i1},\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{\mathrm{in}})---\left(b\right)$

The total number of n-lift data in the formula

e _n-Di n corner lift range error value

M-trial cut number of times

-m time trial cut, the arithmetic mean of instantaneous value of n data

(2), analyze the lift range error rule, obtain predicated error

At first will realize the identification for error rule section, specific practice is: set an error threshold, this threshold size is decided on the concrete error amount of trial cut processing gained, usually between 0.01～0.04mm; When the lift range error value of continuous a plurality of corners when setting threshold value, this section just becomes preliminary election rule section, because the rule fragment position of selecting in advance is different in size, distance between section and section hour, two sections preliminary election rule sections are combined into one section, so that the transition more fairing of the error amount that dopes between section and section; Secondly to processings that carry out curve fitting of whole group lift data, finding the overall trend of lift range error, the processing that carries out curve fitting of employing least square method multinomial:

If about corner x _kWith lift range error y _kOne group of data,

(x _k，y _k)x＝1，2，3，...，m (c)

Parameter a ₀, a ₁, a ₂..., a _n(n＜m) makes multinomial p (x)=a ₀+ a ₁X+...+a _nx _nSatisfy

Then claim p (x)=a ₀+ a ₁X+...+a _nx _nN least square fitting multinomial for data (1.1);

By first order necessary condition, make S reach a of minimum of a value ₀, a ₁, a ₂..., a _nShould satisfy the necessary bar of single order

$\frac{\&PartialD;S}{\&PartialD;a_j}=0,$ j＝0，1，2，...，n (e)

Directly calculate

${\mathrm{\&Sigma;}}_{i=0}^n\left({\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{i+j}\right)a_i-{\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x_k}^j=0$ j＝0，1，2，...，n (f)

The normal equation group, its corresponding coefficient matrix is

$\left[\begin{array}{ccccc}m& {\mathrm{\&Sigma;}}_{k=1}^m{x}_k& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^n& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k\\ {\mathrm{\&Sigma;}}_{k=1}^m{x}_k& {\mathrm{\&Sigma;}}_{k=1}^m{x_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A2009100443260014H1.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{n+1}& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x}_k\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;\\ {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^n& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{n+1}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{2n}& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x_k}^n\end{array}\right]---\left(g\right)$

Least square problem finally can be summed up as finds the solution the normal equation group, by Gaussian elimination method the normal equation group is dissolved the last triangulated linear Algebraic Equation set of separating for together in the solver, and a is found the solution in back substitution then ₀, a ₁, a ₂..., a _n, obtain polynomial fitting

p(x)＝a ₀+a ₁x+...+a _nx _n (h)

With corner x _k(k=1,2,3 ..., m) inverse iteration is gone into formula (h) and can be found the solution and obtain lift range error value new after match, and this error has reflected that all mismachining tolerance influence factors influence rule and size to cam bit under the current state;

For avoiding occurring the be beyond expression phenomenon of initial data trend of process of fitting treatment gained curve, the present invention adopts the method for segment processing, the whole profile section is divided into three sections or four sections uniformly carries out match; Be the error of avoiding the high order match to be brought, the order of process of fitting treatment should be between 3～6 usually;

(3) make up virtual lift table and virtual lift carried out the secondary fairing processing

The lift range error value that obtains by abovementioned steps can reflect the steady state error of process system, promptly can be used as under the same process condition prediction error value that produces with the camshaft processing back of this trial cut camshaft same model;

Lift range error based on analyzing and processing obtains can obtain virtual lift table through formula (i),

S _x(i)＝S _l(i)-α□E(i) (i)

In the formula: S _x(i)-an i virtual lift range value

S _l(i)-an i theoretical lift range value

E (i)-i prediction error value

α-penalty coefficient

Add a proportionality coefficient before predicted value, generally, this ratio is taken between 0.5～0.8;

The method of taking to reduce repeatedly error is to eliminate the influence of residual error behind the single compensation;

In the method for secondary light along same employing least square polynomial fit processing in the process, handle compensating the back data, secondary light is suitable to be exactly that the junction, front and back of fairing compensator section is so that the lift range error data realize single order, Second Order Continuous in essence, adopt interactive processing method, search out the head and the tail point that needs the fairing section by single order, the second dervative figure that observes the lift data, utilize the least square polynomial fit method that this section is handled, and with the Rule of judgment of the error amount before and after handling as the fairing success; Adopt the least square method multinomial that virtual lift table is carried out the secondary fairing processing, it is suitable that the saltus step data are made local light, and with the error amount before and after handling as the feasible Rule of judgment of fairing, the process errors maximum is less than 0.010mm;

(4) adopt virtual lift table to replace original lift table, carry out under the same process condition, with the digital control processing of the camshaft of this trial cut camshaft same model through post processing.

Based on above step, by programming development error analysis of camshaft numerical control grinding and compensation deals software, realized intellectuality, the automation application of technical method.

The present invention takes artificially to introduce the error compensation principle that the influence of process system steady state error was offset or reduced to error, by the TP after relatively cam pitch curve and trial cut are processed, the rule of all errors of system to cam processing influence found out in analysis, make up virtual lift table according to rule classification and size, be follow-up cam ground processing and implementation precompensation.By adopting above-mentioned error compensating method, the lift range error value integral body of the cam bit whole profile section that processes reduces, and the molded lines precision is improved significantly.Burn and percent ripple do not appear in contour surface simultaneously, and surface quality is better.The error compensation effect is very remarkable.

Description of drawings

The automatic identification program flow chart of Fig. 1 error rule section;

Fig. 2 analyzes automatically and merges short spacing section flow chart;

Fig. 3 error analysis compensation deals overall flow figure;

Fig. 4 trial cut gained cam bit lift range error figure;

Fig. 5 trial cut lift range error and predicated error comparison diagram;

Processing effect comparison diagram before and after Fig. 6 error compensation.

The specific embodiment

The invention will be further described below in conjunction with the drawings and specific embodiments.

Embodiment 1:

(1) trial cut processing

Before cam bit carried out the trial cut in-process measurement, earlier camshaft is cleaned up, and as far as possible workpiece is placed a bit of time and measured again.During measurement, each cam bit is done repeatedly measurement, obtain many group actual measurement lift data.Calculate the lift range error value of several groups of data through formula (a), observe the conversion trend of several grouping errors.If the variation tendency of several grouping errors reaches unanimity on the whole substantially, illustrate that the camshaft detected state is more stable, this moment, detected TP also compared accurately.

e＝h _S-h _L (a)

In the formula: the e-lift range error

h _S-actual measurement lift

h _L-theoretical lift

Through m trial cut processing, each cam bit will produce m group actual measurement lift and lift range error.Repeatedly the arithmetic mean value x of trial cut lift range error is as trial cut gained lift range error, to reduce destabilizing factor influence in the trial cut processing, shown in formula (b).

$(\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="A2009100443260014H1.png,A2009100443260015H1.png"\; state="\{\{state\}\}">e</figure-callout>}}_1},\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A2009100443260014H1.png"\; state="\{\{state\}\}">e</figure-callout>}}_2},\&CenterDot;\&CenterDot;\&CenterDot;,\stackrel{\&OverBar;}{e_n})=(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{i1},\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{\mathrm{in}})---\left(b\right)$

The total number of n-lift data in the formula

e _n-Di n corner lift range error value

M-trial cut number of times

-m time trial cut, the arithmetic mean of instantaneous value of n data

(2) analyze the lift range error rule, obtain predicated error

In the Camshaft Grinding processing, be that the less lift section of error amount does not need precompensation again, prevent that error from strengthening having degree of precision.Therefore, when analytical error, it is bigger only to need to analyze mismachining tolerance, and the apparent in view section of error rule, and promptly so-called rule section is with the grinding accuracy of effective raising camshaft.

At first to realize identification, adopt the method for software programming to finish automatically among the present invention for error rule section.Specific practice is: set an error threshold, this threshold size is decided on the concrete error amount of trial cut processing gained, usually between 0.01～0.04mm.When the lift range error value of continuous a plurality of corners when setting threshold value, this section just becomes preliminary election rule section, because the rule fragment position of selecting in advance is different in size, distance between section and section hour, two sections preliminary election rule sections are combined into one section, so that the transition more fairing of the error amount that dopes between section and section.The program flow diagram that automatic identification of rule section and short spacing section merge is shown in accompanying drawing 1,2.

Secondly to the processing that carries out curve fitting of whole group lift data, to find the overall trend of lift range error.

The curve match has two kinds of methods usually: it is bigger that (1) data exist measure error or data to comprise error ratio, if require all points of the curve negotiating of asking, will make curve keep all measure errors, this is not desirable.But wish to obtain an approximate smooth curve, and can reflect the general trend of test data, make not fluctuation of curve as far as possible, generally adopt the least square method fitting of a polynomial.(2) allow all set points of curve negotiating, this method is applicable to does not have the match of the curve of approximation of measure error, and it can use the interpolation method approximate solution, generally adopts Cubic Spline Functions Fitting.Usually beat greatlyyer because of the camshaft lift range error, the present invention adopts the processing that carries out curve fitting of least square method multinomial.

If about corner x _kWith lift range error y _kOne group of data,

(x _k，y _k)x＝1，2，3，...，m (c)

Parameter a ₀, a ₁, a ₂..., a _n(n＜m) makes multinomial p (x)=a ₀+ a ₁X+...+a _nx _nSatisfy

Then claim p (x)=a ₀+ a ₁X+...+a _nx _nN least square fitting multinomial for data (1.1).

By first order necessary condition, make S reach a of minimum of a value ₀, a ₁, a ₂..., a _nShould satisfy the necessary bar of single order

$\frac{\&PartialD;S}{\&PartialD;a_j}=0,$ j＝0，1，2，...，n (e)

Directly calculate

${\mathrm{\&Sigma;}}_{i=0}^n\left({\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{i+j}\right)a_i-{\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x_k}^j=0$ j＝0，1，2，...，n (f)

The normal equation group, its corresponding coefficient matrix is

$\left[\begin{array}{ccccc}m& {\mathrm{\&Sigma;}}_{k=1}^m{x}_k& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^n& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k\\ {\mathrm{\&Sigma;}}_{k=1}^m{x}_k& {\mathrm{\&Sigma;}}_{k=1}^m{x_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A2009100443260014H1.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{n+1}& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x}_k\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;\\ {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^n& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{n+1}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{2n}& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x_k}^n\end{array}\right]---\left(g\right)$

Least square problem finally can be summed up as finds the solution the normal equation group.By Gaussian elimination method the normal equation group is dissolved the last triangulated linear Algebraic Equation set of separating for together in the solver, a is found the solution in back substitution then ₀, a ₁, a ₂..., a _n, obtain polynomial fitting

p(x)＝a ₀+a ₁x+...+a _nx _n (h)

With corner x _k(k=1,2,3 ..., m) inverse iteration is gone into formula (h) and can be found the solution and obtain lift range error value new after match, and this error has reflected that all mismachining tolerance influence factors influence rule and size to cam bit under the current state.

For avoiding occurring the be beyond expression phenomenon of initial data trend of process of fitting treatment gained curve, the present invention adopts the method for segment processing, the whole profile section is divided into three sections or four sections uniformly carries out match.Be the error of avoiding the high order match to be brought, the order of process of fitting treatment should be between 3～6 usually.

(3) set up virtual lift table and post processing.

The lift range error value that obtains by abovementioned steps can reflect the steady state error of process system, promptly can be used as under the same process condition prediction error value that produces with the camshaft processing back of this trial cut camshaft same model.

Lift range error based on analyzing and processing obtains can obtain virtual lift table through formula (i).

S _x(i)＝S _l(i)-α□E(i)

(i)

In the formula: S _x(i)-an i virtual lift range value

S _l(i)-an i theoretical lift range value

E (i)-i prediction error value

α-penalty coefficient

Because destabilizing factor is to the interference of subsequent parts processing in the method divergence of analyses and prediction error amount, the processing, the error amount that causes doping can not be accomplished absolute stablizing, so add a proportionality coefficient before predicted value, generally, this ratio is taken between 0.5～0.8.

The method of taking to reduce repeatedly error is to eliminate the influence of residual error behind the single compensation.If the stability of a system better can strengthen penalty coefficient and reduce to compensate number of times, on the contrary,, can reduce penalty coefficient if the stability of a system is not high, repeatedly compensation comes the approximation theory value.

Cam lift through precompensation is the error prediction value that oppositely superposeed on the basis of original theory lift, so the lift behind the precompensation decreases on whole fairness, thereby cause the speed of process medium sand wheel carrier and acceleration saltus step more violent, strengthen cam face percent ripple and faceted pebble so on the contrary, reduced surface quality.For can be with the adding in the original theory lift of error amount success of prediction, can reduce the influence that the change because of original lift causes surface quality again, it is suitable to carry out secondary light to the lift after the compensation.Because the lift of this moment has comprised the predicted value of error, thus in the process of fairing,, just prediction error value may be reduced if the change amount of lift data is excessive, thus the effect and the precision of influence compensation.

Based on this principle, along the same method that adopts least square polynomial fit to handle in the process, handle compensating the back data in secondary light.Secondary light is suitable to be exactly that the junction, front and back of fairing compensator section is so that the lift range error data realize single order, Second Order Continuous in essence.For reliability and the convenience that improves fairing, adopt interactive processing method, search out the head and the tail point that needs the fairing section by single order, the second dervative figure that observes the lift data, utilize the least square polynomial fit method that this section is handled, and with the Rule of judgment of the error amount before and after handling as the fairing success.Adopt the least square method multinomial that virtual lift table is carried out the secondary fairing processing, it is suitable that the saltus step data are made local light, and with the error amount before and after handling as the feasible Rule of judgment of fairing, the process errors maximum is less than 0.010mm.

(4) adopt virtual lift table to replace original lift table, carry out under the same process condition, with the digital control processing of the camshaft of this trial cut camshaft same model through post processing.

The overall flow of implementation process as shown in Figure 3.

Embodiment 2:

(1) lift range error is obtained in trial cut processing

Present embodiment carries out the trial cut processing of certain camshaft part on a total control camshaft grinding machine, it is 0.020mm that the maximum of this part allows lift range error.Because of the fully debugging preheating of process before processing of this grinding machine, running status is stable, so trial cut gets final product for 1 time.The lift range error that obtains as shown in Figure 4, this camshaft maximum lift error is 99 ° of corners, error amount is-0.021mm not satisfy required precision

(2) analyze the lift range error rule, obtain predicated error

By error analysis software the lift range error curve is analyzed, realized identification, merging, and the lift range error curve is carried out the least square method fitting of a polynomial for the rule section.Step-up error rule section identification threshold value is 0.01mm in the present embodiment, adopts the processing that carries out curve fitting of 4 rank multinomials, and is more obvious because of the lift range error curve law, need not the mode that adopts piecewise fitting to handle, and the disposable match of full lift section is finished.The prediction error value that obtains after the curve match as shown in Figure 5.

(3) make up virtual lift table and post processing

Make up virtual lift table, penalty coefficient α=0.7 according to formula (i).The grinding carriage accelerating curve that calculates by this virtual lift table is 160 ° at corner and locates to take place saltus step, so need carry out secondary light along post processing to virtual lift table.Judge that via error analysis software the short head and the tail point of fairing for 127 ° and 160 ° of corners, carries out 3 rank multinomial least square fittings to this section.

(4) adopt virtual lift table to instruct processing

The virtual lift table that adopts present embodiment to make up carries out this camshaft numerical control grinding processing under the same process condition, and contrast as shown in Figure 6 before and after its processing effect compensation.As can be seen from the figure this camshaft maximum lift error place is behind the error precompensation before the compensation, and the lift range error value has dropped to-0.007mm, and simultaneously, cam bit maximum lift error is reduced to 0.011mm, satisfies process requirements.As seen through the error analysis compensation, the cam global error is reduced, and contour accuracy is improved significantly.

In the above-described embodiments; only the present invention has been carried out exemplary description; the scope of the inventive concept that the present invention is total is limited in claim and the equivalent thereof; those skilled in the art can design various embodiments according to different actual needs under the situation of the scope and spirit that do not break away from the present invention and protected.

Claims (6)

1, a kind of error compensation method of numerical control grinding contour of camshaft may further comprise the steps: a. is that molded lines carries out off-line measurement by repeatedly trial cut processing to processing back cam bit outline line, obtains real contour line data--lift; B. by theoretical lift of contrast and actual measurement lift size of data, find the solution the lift range error value in whole one week of cam bit, analyze lift range error, predicated error; C makes up virtual lift table and virtual lift is carried out the secondary fairing processing; D. adopt the virtual lift table through post processing to replace original lift table, carry out under the same process condition, the digital control processing with the camshaft of this trial cut camshaft same model is characterized in that:

(1), trial cut processing

Before cam bit carried out the trial cut in-process measurement, earlier camshaft is cleaned up, and as far as possible workpiece is placed a bit of time and measured again, during measurement, each cam bit done repeatedly measure, obtain many group actual measurement lift data; Calculate the lift range error value of several groups of data through formula (a), observe the conversion trend of several grouping errors; If the variation tendency of several grouping errors reaches unanimity on the whole substantially, illustrate that the camshaft detected state is more stable, this moment, detected TP also compared accurately;

e＝h _S-h _L (a)

In the formula: the e-lift range error

h _S-actual measurement lift

h _L-theoretical lift

Through m trial cut processing, each cam bit will produce m group actual measurement lift and lift range error; Repeatedly the arithmetic mean value x of trial cut lift range error is as trial cut gained lift range error, and destabilizing factor influences in the trial cut processing to reduce, shown in formula (b):

$(\stackrel{\&OverBar;}{e_1},\stackrel{\&OverBar;}{e_2},...,\stackrel{\&OverBar;}{e_n})=(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{i1},\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{i2},...,\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{e}_{\mathrm{in}})---\left(b\right)$

The total number of n-lift data in the formula

e _n-Di n corner lift range error value

M-trial cut number of times

-m time trial cut, the arithmetic mean of instantaneous value of n data

(2), analyze the lift range error rule, obtain predicated error

At first will realize the identification for error rule section, specific practice is: set an error threshold, this threshold size is decided on the concrete error amount of trial cut processing gained, usually between 0.01～0.04mm; When the lift range error value of continuous a plurality of corners when setting threshold value, this section just becomes preliminary election rule section, because the rule fragment position of selecting in advance is different in size, distance between section and section hour, two sections preliminary election rule sections are combined into one section, so that the transition more fairing of the error amount that dopes between section and section; Secondly to processings that carry out curve fitting of whole group lift data, finding the overall trend of lift range error, the processing that carries out curve fitting of employing least square method multinomial:

If about corner x _kWith lift range error y _kOne group of data,

(x _k，y _k)x＝1，2，3，...，m (c)

Parameter a ₀, a ₁, a ₂..., a _n(n＜m) makes multinomial p (x)=a ₀+ a ₁X+...+a _nx _nSatisfy

Then claim p (x)=a ₀+ a ₁X+...+a _nx _nN least square fitting multinomial for data (1.1); By first order necessary condition, make S reach a of minimum of a value ₀, a ₁, a ₂..., a _nShould satisfy the necessary bar of single order

$\frac{\&PartialD;S}{\&PartialD;a_j}=0,$ j＝0，1，2，...，n (e)

Directly calculate

${\mathrm{\&Sigma;}}_{i=0}^n\left({\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{i+j}\right)a_i-{\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x_k}^j=0$ j＝0，1，2，...，n (f)

The normal equation group, its corresponding coefficient matrix is

$\left[\begin{array}{ccccc}m& {\mathrm{\&Sigma;}}_{k=1}^m{x}_k& ...& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^n& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k\\ {\mathrm{\&Sigma;}}_{k=1}^m{x}_k& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^2& ...& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{n+1}& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x}_k\\ .& .& & .& .\\ .& .& ...& .& .\\ .& .& & .& .\\ {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^n& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{n+1}& ...& {\mathrm{\&Sigma;}}_{k=1}^m{x_k}^{2n}& {\mathrm{\&Sigma;}}_{k=1}^m{y}_k{x_k}^n\end{array}\right]---\left(g\right)$

Least square problem finally can be summed up as finds the solution the normal equation group, by Gaussian elimination method the normal equation group is dissolved the last triangulated linear Algebraic Equation set of separating for together in the solver, and a is found the solution in back substitution then ₀, a ₁, a ₂..., a _n, obtain polynomial fitting

p(x)＝a ₀+a ₁x+...+a _nx _n (h)

With corner x _k(k=1,2,3 ..., m) inverse iteration is gone into formula (h) and can be found the solution and obtain lift range error value new after match, and this error has reflected that all mismachining tolerance influence factors influence rule and size to cam bit under the current state;

(3) make up virtual lift table and virtual lift carried out the secondary fairing processing

The lift range error value that obtains by abovementioned steps can reflect the steady state error of process system, promptly can be used as under the same process condition prediction error value that produces with the camshaft processing back of this trial cut camshaft same model;

Lift range error based on analyzing and processing obtains can obtain virtual lift table through formula (i),

S _x(i)＝S _l(i)-α□E(i)

(i)

In the formula: S _x(x)-an i virtual lift range value

S _l(i)-an i theoretical lift range value

E (i)-i prediction error value

α-penalty coefficient

Add a proportionality coefficient before predicted value, generally, this ratio is taken between 0.5～0.8;

The method of taking to reduce repeatedly error is to eliminate the influence of residual error behind the single compensation;

In the method for secondary light along same employing least square polynomial fit processing in the process, handle compensating the back data, secondary light is suitable to be exactly that the junction, front and back of fairing compensator section is so that the lift range error data realize single order, Second Order Continuous in essence, adopt interactive processing method, search out the head and the tail point that needs the fairing section by single order, the second dervative figure that observes the lift data, utilize the least square polynomial fit method that this section is handled, and with the Rule of judgment of the error amount before and after handling as the fairing success;

(4) adopt virtual lift table to replace original lift table, carry out under the same process condition, with the digital control processing of the camshaft of this trial cut camshaft same model through post processing.

2, error compensation method of numerical control grinding contour of camshaft according to claim 1 is characterized in that: in step a, cam bit trial cut number of times is decided on the lathe stable state.

3, error compensation method of numerical control grinding contour of camshaft according to claim 1 and 2 is characterized in that: in above-mentioned steps (2), adopt the method for segment processing, the whole profile section is divided into three sections or four sections uniformly carries out match; Be the error of avoiding the high order match to be brought, the order of process of fitting treatment should be between 3～6 usually.

4, error compensation method of numerical control grinding contour of camshaft according to claim 3, it is characterized in that: the phenomenon of initial data trend if the disposable process of fitting treatment gained of appearance full section lift range error data curve is beyond expression, adopt the method for segment processing, the whole profile section is divided into three sections or four sections uniformly carries out match.

5, error compensation method of numerical control grinding contour of camshaft according to claim 1 and 2, it is characterized in that: in the step (3): adopt the least square method multinomial that virtual lift table is carried out the secondary fairing processing, it is suitable that the saltus step data are made local light, and with the error amount before and after handling as the feasible Rule of judgment of fairing, the process errors maximum is less than 0.010mm.

6, error compensation method of numerical control grinding contour of camshaft according to claim 1 and 2, it is characterized in that: making up virtual lift table in step (3) is under the same process condition, at with the camshaft of this trial cut camshaft same model, oppositely the prediction error value of proportionality coefficient is multiply by in stack on the basis of original theory lift.

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