CN105701285B - A kind of high-speed main spindle rotating accuracy assessment method based on heuritic approach - Google Patents
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Abstract
The present invention provides a kind of high-speed main spindle rotating accuracy assessment method based on heuritic approach constructs objective function firstly, establishing the mathematical model of the high-speed main spindle rotating accuracy evaluation of method of minimun zone according to Cross Criterion；Secondly, the speed of random initializtion population, position, temperature etc., and the individual adaptation degree and global optimum of population are calculated, and then calculate the adaptation value of each ideal adaptation angle value under Current Temperatures；Again, linear search is carried out using the summing function of adaptation value as sub-goal, the substitution value of global optimum is found from all ideal adaptation angle value, the speed of each individual and position in Population Regeneration；Finally, carrying out moving back warm operation if not up to preset maximum number of iterations, continue iteration, the optimal solution until obtaining method of minimun zone evaluation function.The evaluation problem of high-speed main spindle rotating accuracy is converted to non-linear unconstrained optimization problem by the present invention, and is solved using heuritic approach to it, has degree of precision and good robustness.
Description
Technical Field
The invention relates to the technical field of high-speed spindle rotation precision evaluation, in particular to a heuristic algorithm-based high-speed spindle rotation precision evaluation method.
Background
The high-speed spindle rotation error is a main factor influencing the machining precision of the machine tool, and the high-speed spindle rotation precision is a main index for evaluating the dynamic performance of the machine tool. As the rotation precision of the high-speed spindle has great influence on the service performance and service life of the machine tool and the quality of machined parts, a large amount of research is carried out on the evaluation method by domestic and foreign scholars in recent decades.
The evaluation of the spindle rotation accuracy can generally be performed by a roundness error evaluation method. Currently, the main methods for roundness evaluation are: least squares circle method (LSC), maximum inscribed circle Method (MIC), minimum circumscribed circle Method (MCC), minimum zone circle Method (MZC), and chebyshev fitting method. The evaluation result of the minimum area circle method is minimum, the accuracy is highest, but the measurement accuracy is affected by local optimization easily when the traditional roundness error evaluation method is used for solving.
Disclosure of Invention
The invention aims to overcome the problems in the prior art, provides a heuristic algorithm-based high-speed spindle rotation precision evaluation method with high precision and good robustness for realizing accurate evaluation of the high-speed spindle rotation precision, simultaneously considers the problems of local and global search, and avoids the problem of local optimization when solving an objective function.
The technical scheme of the invention is as follows: a heuristic algorithm-based high-speed spindle rotation precision evaluation method comprises the following steps:
1. a heuristic algorithm-based high-speed spindle rotation precision evaluation method is characterized by comprising the following steps:
step one, establishing a high-speed spindle rotation precision evaluation model based on a minimum area circle method according to a cross criterion, and determining a nonlinear optimization objective function as follows:
ψ＝max{R1,R2...Rm}-min{R1,R2...Rm}
where psi is the objective function and,the distance from the measured point to the center of the circle, i is 1,m, m is the number of measuring points on the measured contour, (a)i,bi) Determining for least area circle methodThe coordinates of the centers of the two concentric circles,
(xxi,yyi) Any measuring point on the measured profile;
step two, regarding all points on the detected contour as a population, and randomly initializing the position x of the populationiVelocity vi(i＝1,2...m)；
Step three, calculating the fitness value of each individual according to the objective function, and storing the fitness value in piThen, an optimal value is selected from all the individual fitness values to serve as an initial value of global optimization, and the initial value is stored in pgPerforming the following steps;
step four, setting the initial value of the temperature and adopting a formula t0＝ψ(pg) /ln5, and determining each p at the current temperature according to the following formulaiThe adaptation value of (c):
wherein, Tpit (p)i) I.e. corresponding piCorresponding adaptation value, tiIs the current temperature;
step five, taking the summation function of the adaptive values as a sub-objective function, and performing one-dimensional search on the summation function to find the optimal value of the objective function;
step six, obtaining a global optimal value p according to the result of the step fivegSubstitute value ofWherein [ αn,βn]For the interval of the optimal value in the step five, taking (α)n+βn) 2 is an approximate value of the optimal value, thereby updating the speed and the position of the particles;
step seven, the iteration times are increased by i to i +1, and whether the maximum iteration times are reached is judged, namely whether i is less than MiterIf yes, turning to the step eight, otherwise, stopping searching and outputting a result;
step eight, performing temperature reduction operation ti+1＝λ·tiAnd turning to the third step.
The fifth step specifically comprises the following steps:
1) selecting an initial interval (α) by using a summation function of the adaptation values as a sub-target function, i.e., phi ═ sum (tfit)1,β1) And setting the precision to epsilon (epsilon > 0), calculating the value of n so that Fn≥(β1-α1) E,/epsilon, let F0＝F1Calculate ζ as 11＝α1+(Fn-2/Fn)·(β1-α1)，μ1＝α1+(Fn-1/Fn)·(β1-α1) Wherein F isnIs a Fibonacci sequence;
2) determine phi (zeta)k)＞φ(μk) If true, set the parameters to αk+1＝ζk，βk+1＝βk，ζk+1＝μk，μk+1＝αk+1+(Fn-k-1/Fn-k)·(βk+1-αk+1) Otherwise, set the parameters to αk+1＝αk，βk+1＝μk，μk+1＝ζk，ζk+1＝αk+1+(Fn-k-2/Fn-k)·(βk+1-αk+1)；
3) Judging whether k is n-2, if yes, αn＝ζn-1,βn＝βn-1(ii) a Otherwise, k equals k +1, go to step 2).
The updating of the particle speed and position in the above step six is realized by the following formula:
vi+1＝ω·(vi+c1·r1·(pi-xi)+c2·r2·(p'g-xi))
xi+1＝xi+vi+1
wherein,is a velocity compression factor, vi+1And xi+1Are respectively provided withVelocity and position of the i +1 th generation particle, c1Is a self-cognitive learning factor, c2Social cognitive learning factor, r1、r2To comply withUniformly distributed random number, p'gIs a substitute value for the global optimum value.
The invention has the beneficial effects that: the invention provides a high-speed spindle rotation precision evaluation method based on a heuristic algorithm, establishes a minimum area circle method error calculation model based on the heuristic algorithm, and can quickly and accurately calculate the rotation error value of a high-speed spindle.
The invention has the following advantages:
1. a heuristic search algorithm is applied to a minimum area circle method to carry out high-speed spindle rotation precision evaluation, and in the calculation and search, the search direction and the search step length do not need to be determined, so that the complexity of the evaluation method is reduced.
2. The improved Fibonacci sequence is used for linking the individual adaptive value with the global optimum, so that the evaluation result is prevented from falling into the local optimum, and the generation of nonlinear errors in the evaluation process is reduced.
3. Compared with the accepted excellent evaluation method, the method has high precision and good robustness for both roundness evaluation and spindle gyration precision evaluation.
For a more clear understanding of the present invention, reference is now made to the following detailed description taken in conjunction with the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of the method of the present invention;
FIG. 2 is a flow chart of the steps of the method of the present invention;
FIG. 3 is a graph comparing the results of the method of the present invention with those of the conventional method.
Detailed Description
Referring to fig. 1 and 2 (wherein, capital Y in fig. 2 is an abbreviation of YES, which represents the case that the condition is satisfied, and capital N is an abbreviation of NO, which represents the case that the condition is not satisfied), the invention provides a high-speed spindle revolution precision evaluation method based on a heuristic algorithm, comprising the following steps:
step one, establishing a high-speed spindle rotation precision evaluation model based on a minimum area circle method according to a cross criterion, and determining a nonlinear optimization objective function as follows:
ψ＝max{R1,R2...Rm}-min{R1,R2...Rm}
where psi is the objective function and,the distance from the measured point to the center of the circle, i is 1,m, m is the number of measuring points on the measured contour, (a)i,bi) The coordinates of the centers of two concentric circles determined for the minimum area circle method,
(xxi,yyi) Any measuring point on the measured profile;
step two, regarding all points on the detected contour as a population, and randomly initializing the position x of the populationiVelocity vi(i＝1,2...m)；
Step three, calculating the fitness value of each individual according to the objective function, and storing the fitness value in piThen, an optimal value is selected from all the individual fitness values to serve as an initial value of global optimization, and the initial value is stored in pgPerforming the following steps;
step four, setting the initial value of the temperature and adopting a formula t0＝ψ(pg) /ln5, and determining each p at the current temperature according to the following formulaiThe adaptation value of (c):
wherein, Tpit (p)i) I.e. corresponding piCorresponding adaptation value, tiIs the current temperature;
step five, taking the summation function of the adaptive values as a sub-objective function, and performing one-dimensional search on the summation function to find the optimal value of the objective function;
the method specifically comprises the following steps:
1) selecting an initial interval (α) by using a summation function of the adaptation values as a sub-target function, i.e., phi ═ sum (tfit)1,β1) And setting the precision to epsilon (epsilon > 0), calculating the value of n so that Fn≥(β1-α1) E,/epsilon, let F0＝F1Calculate ζ as 11＝α1+(Fn-2/Fn)·(β1-α1)，μ1＝α1+(Fn-1/Fn)·(β1-α1) Wherein F isnIs a Fibonacci sequence;
2) determine phi (zeta)k)＞φ(μk) If true, set the parameters to αk+1＝ζk，βk+1＝βk，ζk+1＝μk，μk+1＝αk+1+(Fn-k-1/Fn-k)·(βk+1-αk+1) Otherwise, set the parameters to αk+1＝αk，βk+1＝μk，μk+1＝ζk，ζk+1＝αk+1+(Fn-k-2/Fn-k)·(βk+1-αk+1)；
3) Judging whether k is n-2, if yes, αn＝ζn-1,βn＝βn-1(ii) a Otherwise, k equals k +1, go to step 2).
Step six, obtaining a global optimal value p according to the result of the step fivegSubstitute value ofAnd thereby update the velocity and position of the particles;
wherein the updating of the particle velocity and position is achieved by:
vi+1＝ω·(vi+c1·r1·(pi-xi)+c2·r2·(p'g-xi))
xi+1＝xi+vi+1
wherein,is a velocity compression factor, vi+1And xi+1Are respectively provided withVelocity and position of the i +1 th generation particle, c1Is a self-cognitive learning factor, c2Social cognitive learning factor, r1、r2To comply withUniformly distributed random number, p'gIs a substitute value for the global optimum value.
Step seven, the iteration times are increased by i to i +1, and whether the maximum iteration times are reached is judged, namely whether i is less than MiterIf yes, turning to the step eight, otherwise, stopping searching and outputting a result;
step eight, performing temperature reduction operation ti+1＝λ·tiAnd turning to the third step.
The invention applies a heuristic search algorithm to the minimum area circle method, combines global search and local search, and uses the improved Fibonacci number series to link local and global, thereby avoiding the result falling into local optimum, having faster convergence speed and higher solving precision.
The effectiveness and stability of the invention are verified by the following specific examples:
table 1 shows the roundness evaluation data extracted from an SCI article, which is compared with the results obtained by the method of the article, by performing the roundness evaluation on the set of data according to the present invention, as shown in table 2; table 2 shows the results of the CMM, the improved PSO, and the evaluation of the circularity error by the heuristic search algorithm, which can be compared with the known excellent method to fully verify the reliability of the present invention.
TABLE 1 raw data for roundness error measurement
TABLE 2 CMM, improved PSO, heuristic search algorithm roundness error evaluation result comparison
FIG. 3 shows a set of operation data of a high-speed spindle collected by a sensor, which are evaluated for rotation accuracy by applying the present invention and a conventional method, respectively, (a) is the method of the present invention, which obtains center coordinates (1.6107,1.6516) and a final error value (f)MZC1The center coordinates obtained by the general method (1.5504,1.6379) are (3.7589), (b) and the final error value obtained is fMZC23.7673. The quantitative comparison can intuitively show that the method has higher accuracy when being applied to the evaluation of the rotation accuracy of the high-speed spindle.
In summary, the invention provides a high-speed spindle rotation precision evaluation method based on a heuristic algorithm, establishes a minimum area circle method error calculation model based on the heuristic algorithm, and can quickly and accurately calculate the rotation error value of the high-speed spindle.
The invention has the following advantages:
1. a heuristic search algorithm is applied to a minimum area circle method to carry out high-speed spindle rotation precision evaluation, and in the calculation and search, the search direction and the search step length do not need to be determined, so that the complexity of the evaluation method is reduced.
2. The improved Fibonacci sequence is used for linking the individual adaptive value with the global optimum, so that the evaluation result is prevented from falling into the local optimum, and the generation of nonlinear errors in the evaluation process is reduced.
3. Compared with the accepted excellent evaluation method, the method has high precision and good robustness for both roundness evaluation and spindle gyration precision evaluation.
The components, processes and letters that are not described in detail in the present embodiment represent common components, common means and common general knowledge in the industry, and are not described here. The above examples are merely illustrative of the present invention and should not be construed as limiting the scope of the invention, which is intended to be covered by the claims and any design similar or equivalent to the scope of the invention.
Claims (3)
1. A heuristic algorithm-based high-speed spindle rotation precision evaluation method is characterized by comprising the following steps:
step one, establishing a high-speed spindle rotation precision evaluation model based on a minimum area circle method according to a cross criterion, and determining a nonlinear optimization objective function as follows:
ψ＝max{R1,R2...Rm}-min{R1,R2...Rm}
where psi is the objective function and,the distance from a measured point to the center of a circle is 1,2.. m, and m is the number of the measured points on the measured contour, (a)i,bi) The coordinates of the centers of two concentric circles determined by the circle of least area method, (xx)i,yyi) Any measuring point on the measured profile;
step two, regarding all points on the detected contour as a population, and randomly initializing the position x of the populationiVelocity viWherein i is 1,2.. m;
step three, calculating the fitness value of each individual according to the objective function, and storing the fitness value in piThen, an optimal value is selected from all the individual fitness values to serve as an initial value of global optimization, and the initial value is stored in pgPerforming the following steps;
step four, setting the initial value of the temperature and adopting a formula t0＝ψ(pg) /ln5, and determining each p at the current temperature according to the following formulaiThe adaptation value of (c):
wherein, Tpit (p)i) I.e. corresponding piCorresponding adaptation value, tiIs the current temperature;
step five, taking the summation function of the adaptive values as a sub-objective function, and performing one-dimensional search on the summation function to find the optimal value of the objective function;
step six, obtaining a global optimal value p according to the result of the step fivegSubstitute value ofWherein [ αn,βn]For the interval of the optimal value in the step five, taking (α)n+βn) 2 is an approximate value of the optimal value, thereby updating the speed and the position of the particles;
step seven, increasing the iteration times j to j +1, and judging whether the maximum iteration times is reached, namely whether j is more than MiterIf yes, turning to the step eight, otherwise, stopping searching and outputting a result;
step eight, performing temperature reduction operation ti+1＝λ·tiAnd turning to the third step.
2. A heuristic-based high-speed spindle revolution accuracy assessment method as claimed in claim 1, characterized in that: the fifth step specifically comprises the following steps:
1) selecting an initial interval (α) by using a summation function of the adaptation values as a sub-target function, i.e., phi ═ sum (tfit)1,β1) And setting the precision to epsilon, where epsilon > 0, and calculating the value of n so that F isn≥(β1-α1) E,/epsilon, let F0＝F1Calculate ζ as 11＝α1+(Fn-2/Fn)·(β1-α1)，μ1＝α1+(Fn-1/Fn)·(β1-α1) Wherein F isnIs a Fibonacci sequence;
2) determine phi (zeta)k)＞φ(μk) If true, set the parameters to αk+1＝ζk，βk+1＝βk，ζk+1＝μk，μk+1＝αk+1+(Fn-k-1/Fn-k)·(βk+1-αk+1) Otherwise, set the parameters to αk+1＝αk，βk+1＝μk，μk+1＝ζk，ζk+1＝αk+1+(Fn-k-2/Fn-k)·(βk+1-αk+1)；
3) Judging whether k is n-2, if yes, αn＝ζn-1,βn＝βn-1(ii) a Otherwise, k equals k +1, go to step 2).
3. A heuristic-based high-speed spindle revolution accuracy assessment method as claimed in claim 1, characterized in that: wherein the updating of the particle speed and position in the sixth step is realized by the following formula:
vi+1＝ω·(vi+c1·r1·(pi-xi)+c2·r2·(p′g-xi))
xi+1＝xi+vi+1
wherein,is a velocity compression factor, vi+1And xi+1Respectively the velocity and position of the (i + 1) th generation particle, c1Is a self-cognitive learning factor, c2Social cognitive learning factor, r1、r2To obey uniformly distributed random numbers, pg' is a substitute value for the global optimum.
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Non-Patent Citations (3)
| Title |
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| An Online Spindle Rotation Error Measurement System Based on Improved Three Point Method;Yun Zhang 等;《The Ninth International Conference on Electronic Measurement&Instruments》;20091231;第651-656页 |
| 主轴回转运动精度的计算机视觉测量系统;关芳芳 等;《机械设计与制造工程》;20140830;第43卷(第8期);第50-53页 |
| 基于遗传算法的主轴回转误差评价方法;高慧中 等;《组合机床与自动化加工技术》;20121231(第12期);第19-22页 |
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