CN103235553B - Method for automatically compensating numerical control machining size error based on fractional order - Google Patents
Method for automatically compensating numerical control machining size error based on fractional order Download PDFInfo
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Abstract
The invention discloses a method for automatically compensating a numerical control machining size error based on a fractional order. The method comprises the following steps of performing machining, and measuring the size of a machined workpiece to obtain actual machining size data; comparing expected size data with the actual size data to solve a size error, and analyzing the error to identify a system order; calculating the amount of error compensation to be applied before the machining of the next workpiece according to the system order and a size error generated during the machining of the previous workpiece by adopting an iterative learning control law; and correcting a numerical control machining program for the workpiece by using the amount of error compensation before the machining of the next workpiece, and performing numerical control machining on the next workpiece by adopting the corrected numerical control machining program. The size error is automatically compensated by programming and developing numerical control machining size error compensation processing software based on the steps. The size error of the machined workpiece is integrally reduced, the machining accuracy is improved, the qualified rate of the workpiece is remarkably increased, and the remarkable error compensation effect is achieved.
Description
Technical field
The present invention relates to a kind of error compensating method, particularly relate to a kind of digital control processing scale error automatic compensating method based on fractional order.
Background technology
Machining precision is one of most important technical indicator of digital control processing, and the method improving machining precision mainly contains: error preventive treatment and error compensation method.Error preventive treatment is eliminated by Design and manufacture approach or reduces possible error source, meets requirement on machining accuracy by improving Machine Manufacture precision.In a lot of application scenario, the physical restriction of machine tool accuracy can not merely be overcome by Design and manufacture.And after exceeding certain precision, it is very high for attempting to reach more high-precision economic cost by reconditioner bed structure.Error compensation method is a kind of software engineering, and a kind of compensation rate of artificial generation goes to offset the current initial error being called problem, is a kind of means of not only effective but also economic raising machine finish, one of important technology pillar having become modern precision digital control processing.
Affect a lot of because have of workpiece size precision in NC Machining Process, manufacture comprising numerically-controlled machine itself and assemble defect, tool dimension error, machine spindle servo-drive system characteristic etc. that force deformation that thermal deformation that lathe temperature variation causes, machine cut power cause, tool wear cause.In existing digital control processing scale error Compensation Research, mainly contain two kinds of approach: one is for certain or certain the several factor detection causing error, modeling, predicated error, and online or off-line is implemented to compensate.But this mode is only for specific numerical control processing environment, and model lacks dirigibility, can not contain all factors causing error, and detect loaded down with trivial details, calculated amount is comparatively large, not easily promotes; Two is regular linear compensations, according to processing technology and equipment situation, determines that is often processed the compensation rate needing after certain hour to implement.Because the actual scale error processed presents non-linear behavior, can not compensate scale error because accidentalia causes by this way, can not effectively suppress causing the non-linear factor of scale error.Visible, there is imperfection part in existing Error Compensation Technology, have impact on its reality processing in application.
Summary of the invention
Technical matters to be solved by this invention is to provide a kind of error auto compensatng method, to consider in digital-control processing system various factors to the impact of numerical control (NC) Machining Accuracy, no longer error source is detected, modeling, but from causing the result of error, by the measurement to mismachining tolerance, error analysis, identification system exponent number, need the error compensation amount applied before adopting suitable iterative learning control law to calculate next work pieces process, and then error compensation is carried out to the processing of next workpiece.This method, based on fractional order iterative learning thought, utilizes actual measurement workpiece size data identification systematic education, adopts suitable iterative learning control law, automatically provide error compensation amount, improve numerical control (NC) Machining Accuracy stability, rate of reducing the number of rejects and seconds.
For solving the problems of the technologies described above, the digital control processing scale error compensation method based on fractional order provided by the invention, realizes mainly through following steps:
Step 1: by repeatedly processing, carries out off-line measurement to the workpiece size after processing, obtains actual processing dimension data;
Step 2: by contrast desired size data and actual measurement dimensional data size, solve scale error, analytical error, identification system exponent number;
Step 3: the scale error produced according to the systematic education determined in step 2 and last workpiece, needs the error compensation amount applied before adopting suitable iterative learning control law to calculate next work pieces process;
Step 4: with the nc program of error compensation amount correction workpiece before next work pieces process, adopts nc program after revising, carries out the digital control processing of next workpiece.
Actually described in step 1 add man-hour, different desired size can be set, carry out organizing processing more; Workpiece opposite side size is measured, obtains many group actual measurement dimensional datas; Calculate the scale error value of these group data through formula (a), observe the variation tendency of scale error; The variation tendency of a few packet size error is non-linear non-monotonic increase on the whole;
e＝Dime-D （a）
In formula: e---scale error
Dime---desired size
D---actual measurement size
Carry out the processing of m workpiece under the desired size of each setting, obtain m actual measurement size and scale error; The arithmetic mean of m workpiece size error as average error, in this, as the parameter of systematic education identification, as shown in formula (b):
In formula: E (e)---the average error of m workpiece
M---the number of one group of actual measurement workpiece
E
i---the scale error of i-th workpiece
Analytical error described in step 2, identification system exponent number; Here system is the closed-loop system formed through workpiece size self-operated measuring unit, with Closed-loop Nc System unlike, closed loop is not now position ring, neither speed ring, but a compensatory control ring comprising the workpiece size of feed system, frock and tool system; The identification process of systematic education is the process of an iterative learning, as shown in formula (c); Systematic education identification be out integer then system be integer rank, identification be out decimal then system be fractional order; Finally, identification systematic education is out defined as α; α is systematic education and the exponent number of iterative learning control law; The compensation rate that iterative learning control law can be adopted in the identification process of exponent number to determine, carries out the calculating of workpiece size, completes an identification process with this; The condition completing identification is: E (e
n)≤ε, wherein E (e
n) be the N time iteration after the average error of one group of workpiece, ε is minimum positive number;
α
l+1＝α
l+Τ·E(e
l),Τ＞0 （c）
In formula: α
l+1---the systematic education determined during (l+1) secondary identification process
α
l---the systematic education determined during the l time identification process
E (e
l)---the average error of one group of workpiece after the l time iteration
Τ---constant coefficient
Described in step 3, arrange suitable error threshold according to workpiece size accuracy requirement, what scale error exceeded threshold value carries out error compensation, and the symbol of error compensation amount is contrary with the symbol of error; Adopt suitable iterative learning control law error of calculation compensation rate, adopt the calculating of the D-type iterative learning control law amount of compensating here, as shown in formula (d), in formula (d), penalty coefficient is as shown in formula (e);
C
k+1(s)＝Γ
k+1(s)·E
k(s) （d）
Γ(s)＝kp·s
α/(1+t·s
alpha),0＜α＜alpha≤1,kp＞0,t＞0 （e）
In formula: C
k+1(s)---the compensation rate of (k+1) individual workpiece, employing be frequency-domain representation
Γ
k+1(s)---the penalty coefficient of (k+1) individual workpiece, employing be frequency-domain representation
Γ (s)---penalty coefficient, employing be frequency-domain representation
E
kthe scale error of (s)---a kth workpiece, employing be frequency-domain representation
Kp---constant coefficient
α---systematic education
alpha——α＜alpha≤1
T---time constant
S---Laplace transform variable
In order to the disorder preventing excessive compensation rate from bringing system, guarantee lathe job security, introduce compensation rate amplitude C
maxamplitude limit is carried out to error compensation amount; If C
k+1be greater than C
max, then C is made
k+1=C
max; If C
k+1be less than-C
max, then C is made
k+1=-C
max;
Described in step 4, obtain the compensation rate of next workpiece according to preceding step, compensation rate is in the correction of next work pieces process advance row nc program accordingly, under same process condition, carry out digital control processing.
Based on above step, by programming development digital control processing scale error compensation deals software, realize scale error auto-compensation.
The invention has the beneficial effects as follows, by adopting above-mentioned error compensating method, the scale error entirety of the workpiece processed reduces, and machining precision improves, and workpiece qualification rate significantly improves, error compensation successful.
Accompanying drawing explanation
Fig. 1 digital control processing scale error bucking-out system structural drawing.
Fig. 2 digital control processing scale error compensates process flow diagram.
Embodiment
Below in conjunction with accompanying drawing and embodiment, the invention will be further described.
Step 1 is specific as follows: measure workpiece opposite side size, obtains actual measurement dimensional data; Calculate the scale error value of these group data through formula (a), observe the variation tendency of scale error; The variation tendency of scale error is non-linear non-monotonic increase on the whole;
e(k)＝Dime-D(k) （a）
In formula: e (k)---a kth workpiece size error
Dime---desired size
D (k)---a kth workpiece actual measurement size
Calculate the parameter of arithmetic mean as systematic education identification of one group of workpiece size error, as shown in formula (b).Solve the scale error mean value of one group of processing work, this parameter is the parameter of systematic education identification is also the index whether identification completes.
In formula: E (e)---the average error of m workpiece
M---the number of one group of actual measurement workpiece
E
i---the scale error of i-th workpiece
Step 2 is specific as follows: analytical error, identification system exponent number; Here system is the closed-loop system formed through workpiece size self-operated measuring unit, with Closed-loop Nc System unlike, closed loop is not now position ring, neither speed ring, but the compensatory control ring of a workpiece size.As shown in Figure 1, system input is scale error, exports compensation rate through iterative learning strategy, before next workpiece is processed, revise nc program, and final system exports workpiece physical size.The identification process of systematic education is the process of an iterative learning, as shown in formula (c); Identification can from integer 1, with 0.01 for saltus step interval, systematic education identification be out integer then system be integer rank, identification be out decimal then system be fractional order; Finally, identification systematic education is out defined as α; α is systematic education and the exponent number of iterative learning control law; The compensation rate that iterative learning control law can be adopted in the identification process of exponent number to determine, carries out the calculating of workpiece size, completes an identification process with this.
α
l+1＝α
l+Τ·E(e
l),Τ＞0 （c）
In formula: α
l+1---the systematic education determined during (l+1) secondary identification process
α
l---the systematic education determined during the l time identification process
E (e
l)---the average error of one group of workpiece after the l time iteration
Τ---constant coefficient
Here the initial value α of exponent number is got
0=1, namely think that system is 1 rank system, upgrade systematic education according to the average error after iterative compensation according to formula (c), re-start iterative compensation, the average error after more each iterative compensation, to E (e
n)≤ε (E (e
n) be the N time iteration after the average error of one group of workpiece, ε is minimum positive number) complete the identification of exponent number.Last identification result is in table 1.
| α | alpha | kp | Average error |
| 0.6 | 0.95 | 12 | 0.00022724 |
| 0.61 | 0.95 | 12 | 0.00017521 |
| 0.62 | 0.95 | 12 | 0.00012672 |
| 0.63 | 0.95 | 12 | 0.000081884 |
| 0.64 | 0.95 | 12 | 0.000042254 |
Table 1
Step 3 is specific as follows: adopt suitable iterative learning control law error of calculation compensation rate; Arrange suitable error threshold according to workpiece size accuracy requirement, super going beyond the scope carries out error compensation; The symbol of error compensation amount is contrary with the symbol of error; Adopt the calculating of the D-type iterative learning control law amount of compensating, as shown in formula (d), in formula (d), penalty coefficient is as shown in formula (e);
C
k+1(s)＝Γ
k+1(s)·E
k(s) （d）
Γ(s)＝kp·s
α/(1+t·s
alpha),0＜α＜alpha≤1,kp＞0,t＞0 （e）
In formula: C
k+1(s)---the compensation rate of (k+1) individual workpiece, employing be frequency-domain representation
Γ
k+1(s)---the penalty coefficient of (k+1) individual workpiece, employing be frequency-domain representation
E
kthe scale error of (s)---a kth workpiece, employing be frequency-domain representation
Γ (s)---penalty coefficient, employing be frequency-domain representation
Kp---constant coefficient
α---systematic education
Alpha---α < alpha≤1, gets 0.95 here
T---time constant, very little, generally get 0.00001
S---Laplace transform variable
In order to the disorder preventing excessive compensation rate from bringing system, guarantee lathe job security, introduce compensation rate amplitude C
maxamplitude limit is carried out to error compensation amount; If C
k+1be greater than C
max, then C is made
k+1=C
max; If C
k+1be less than-C
max, then C is made
k+1=-C
max.
Step 4 is specific as follows: the compensation rate obtaining next workpiece according to preceding step, and compensation rate is in the correction of next work pieces process advance row nc program accordingly, under same process condition, carry out digital control processing.
The overall flow figure of implementation process as shown in Figure 2.
By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.
Claims (7)
1., based on a digital control processing scale error automatic compensating method for fractional order, it is characterized in that, its step is as follows:
Step (1): process, carries out on-position measure to the workpiece size after processing, obtains actual processing dimension data;
Step (2): by contrast desired size data and actual measurement dimensional data size, solve scale error, by repeatedly processing and error measure, analytical error, identification system exponent number;
Step (3): according to the scale error produced when systematic education and last work pieces process, needs the error compensation amount applied before adopting iterative learning control law to calculate next work pieces process;
Step (4): with the nc program of error compensation amount correction workpiece before next work pieces process, adopt revised nc program, carry out the digital control processing of next workpiece;
In described step (2), described identification system exponent number, system is the closed-loop system formed through workpiece size self-operated measuring unit, and described closed loop is the compensatory control ring of the workpiece size comprising feed system, frock and tool system; The process of the identification of systematic education, as shown in formula (c); Finally, identification systematic education is out defined as α, and α is systematic education and the exponent number of iterative learning control law; The compensation rate adopting iterative learning control law to determine in the identification process of exponent number, carries out the calculating of workpiece size, completes an identification process with this; The condition completing identification is: E (e
n)≤ε, wherein E (e
n) be the N time iteration after the average error of one group of workpiece, ε is minimum positive number;
α
l+1＝α
l+Τ·E(e
l),Τ＞0 (c)
In formula: α
l+1---the systematic education determined during (l+1) secondary identification process
α
l---the systematic education determined during the l time identification process
E (e
l)---the average error of one group of workpiece after the l time iteration
Τ---constant coefficient.
2., as claimed in claim 1 based on the digital control processing scale error automatic compensating method of fractional order, it is characterized in that, in described step (1), before measuring, set different desired size, carry out organizing processing more.
3. as claimed in claim 1 based on the digital control processing scale error automatic compensating method of fractional order, it is characterized in that, in described step (1), on-position measure is carried out to the size after work pieces process, obtain many group actual measurement dimensional datas.
4. as claimed in claim 1 based on the digital control processing scale error automatic compensating method of fractional order, it is characterized in that, in described step (2), solve the scale error value of these group data through formula (a), analyze the change of scale error; The variation tendency of many packet sizes error is non-linear non-monotonic,
e＝Dime-D (a)
In formula: e---scale error
Dime---desired size
D---actual measurement size
Carry out the processing of m workpiece under the desired size of each setting, obtain m actual measurement size and scale error; The arithmetic mean of m workpiece size error as average error, in this, as the parameter of systematic education identification, as shown in formula (b):
In formula: E (e)---the average error of m workpiece
M---the number of one group of actual measurement workpiece
E
i---the scale error of i-th workpiece.
5. as claimed in claim 1 based on the digital control processing scale error automatic compensating method of fractional order, it is characterized in that, in described step (3), according to workpiece size accuracy requirement step-up error threshold value, scale error exceeds error threshold and carries out error compensation, the symbol of error compensation amount is contrary with the symbol of error, adopts iterative learning control law error of calculation compensation rate.
6. as claimed in claim 5 based on the digital control processing scale error automatic compensating method of fractional order, it is characterized in that, described error of calculation compensation rate adopts the calculating of the D-type iterative learning control law amount of compensating, as shown in formula (d), in formula (d), penalty coefficient is as shown in formula (e);
C
k+1(s)＝Γ
k+1(s)·E
k(s) (d)
Γ(s)＝kp·s
α/(1+t·s
alpha),0＜α＜alpha≤1,kp＞0,t＞0 (e)
In formula: C
k+1(s)---the compensation rate of (k+1) individual workpiece, employing be frequency-domain representation
Γ
k+1(s)---the penalty coefficient of (k+1) individual workpiece, employing be frequency-domain representation
E
kthe scale error of (s)---a kth workpiece, employing be frequency-domain representation
Γ (s)---penalty coefficient, employing be frequency-domain representation
Kp---constant coefficient
α---systematic education
alpha——α＜alpha≤1
T---time constant
S---Laplace transform variable
Introduce compensation rate amplitude C
maxamplitude limit is carried out to error compensation amount; If C
k+1be greater than C
max, then C is made
k+1=C
max; If C
k+1be less than-C
max, then C is made
k+1=-C
max.
7., as claimed in claim 1 based on the digital control processing scale error automatic compensating method of fractional order, it is characterized in that, described identification from integer 1, with 0.01 for saltus step interval.
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