CN109506613A - One kind being based on the depth of parallelism assessment method of maximum material requirement (MMR) cylinder - Google Patents

Abstract

The invention belongs to the field of precision measurement and computer application, and in particular relates to a digital evaluation method for the parallelism of a cylinder based on a maximum entity requirement (MMR). Is it possible to use this method to evaluate its parallelism tolerance, and then measure the measurement point data of the actual measured cylinder and the actual reference cylinder through a three-coordinate measuring machine, and judge whether the dimensional errors of the actual measured cylinder and the actual reference cylinder are qualified or not? , and then fit the measurement point data of the actual reference cylinder, and perform coordinate transformation on the measurement point data of the actual reference cylinder and the actual measured cylinder, then calculate the limit equivalent diameter of the actual measured cylinder, and finally pass the measured cylinder. The relevant tolerance requirements are used to determine the eligibility of the parallelism error of the part.

Description

A Method for Evaluating Parallelism of Cylinders Based on Maximum Solid Requirement (MMR)

technical field

The invention belongs to the field of precision metrology and computer application, and in particular relates to a digital evaluation method for the parallelism of a cylinder based on a maximum entity requirement (MMR), which can be used for the parallelism tolerance of the axis of the cylinder to be measured and the parallelism of the reference cylinder when the MMR is simultaneously applied to the product. Evaluation of accuracy error compliance.

Background technique

Parallelism error is a key parameter that reflects the machining quality of parts, which directly affects the assembly success rate and working life of the product. Evaluating the parallelism error of parts quickly and effectively has important practical significance for improving the success rate of assembly of parts and saving the cost of product inspection. Geometric tolerances and dimensional tolerances can be linked together by tolerance principles. Different tolerance principles can meet different usage requirements. For example, the maximum entity requirement reflects the assemblability of parts.

The national standard GB/T16671-2009 gives some constraints when MMR is used for the parallelism tolerance of the reference cylinder axis and its corresponding reference cylinder. The constraints are as follows: 1. Both the measured cylinder and the reference cylinder are in the maximum solid state; 2. . The local dimensions of the measured cylinder and the reference cylinder should be between their respective maximum limit size and minimum limit size; 3. The existence direction of the axis of the measured cylinder in the maximum solid state and the axis of the reference cylinder in the maximum solid state The relationship between.

Therefore, in order to detect the eligibility of the above-mentioned parallelism of parts between the maximum limit size and the minimum limit size (there are many methods for evaluating the eligibility of dimensional errors, which are mature and do not belong to the scope of the present invention), the national standard GB/T1958 -2004 gives a method for checking the eligibility of the above-mentioned parallelism tolerance of the cylinder under test using a comprehensive physical gauge with high precision and a certain size. However, physical gauges with high precision and a certain size have disadvantages such as high production cost and limited measurement (a gauge of a specific size can only measure a specific part).

When the parallelism tolerance of the axis of the measured cylinder has MMR, but the reference cylinder does not have MMR, the method to check whether the parallelism tolerance of the measured cylinder is qualified, in the field of precision measurement and computer applications, the actual measured cylinder can be obtained through a three-coordinate measuring machine. and the set of measuring points on the actual datum cylinder, and then fit the measuring points on the actual datum cylinder to an ideal datum cylinder, and then calculate the parallelism error of the axis of the actual measured cylinder relative to the axis of its datum cylinder, and judge the actual measured point. Check whether the parallelism of the cylinder meets the requirements. However, there is no effective mathematical evaluation method to check the parallelism tolerance of the measured cylinder and its eligibility of the parallelism tolerance when MMR is simultaneously applied to the reference cylinder.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a parallelism evaluation method based on the maximum entity requirement (MMR), which can realize the parallelism tolerance of the axis of the measured cylinder and the parallelism of the product when the reference cylinder adopts MMR at the same time. In addition, the method can be extended to the qualification evaluation of the orientation error of the parts when the orientation tolerance of other measured elements and their reference elements are MMR.

In order to solve the above-mentioned problems, the present invention is achieved through the following solutions:

Step 1: Determine if the part is suitable for this evaluation method. Obtain the key information of the reference cylinder A and the measured cylinder B respectively from the part drawings; if the parallelism tolerance of the measured cylinder B and its corresponding reference cylinder are MMR, and the shape tolerance of the reference cylinder A is also MMR, then transfer to Step 2.

The key information of the datum cylinder A has the following contents: the nominal diameter d ₁ of the datum cylinder, the upper deviation and the lower deviation of the datum cylinder are es ₁ and ei ₁ respectively; the shape tolerance is MMR, and the shape tolerance is T ₁ ; Length L ₁ of cylinder A.

The key information of the tested cylinder B has the following contents: the nominal diameter d ₂ of the tested cylinder; the upper and lower deviations of the tested cylinder are es ₂ and ei ₂ respectively; the parallelism tolerance T ₂ ; the parallelism tolerance and its corresponding benchmarks both use MMR.

Step 2: Determine whether the size error of the actual reference cylinder A and the size error of the actual measured cylinder B are both qualified. First, use a three-coordinate measuring machine to obtain the measuring point data sets on the contours of the actual reference cylinder A and the actual measured cylinder B , and then determine whether the dimensional errors of the actual reference cylinder A and the actual measured cylinder B are qualified at the same time. If the dimensional errors are all qualified, go to step 3, otherwise terminate the evaluation method.

Step 3: Fit the fitting cylinder A ₁ of the actual datum cylinder A through calculation, establish a local coordinate system on the fitting cylinder A ₁ , and compare the actual datum cylinder A measured by the three-coordinate measuring machine with the actual measured cylinder. Coordinate transformation is performed on the coordinate value of the measuring point of B to obtain the coordinate value of the measuring point of the actual reference cylinder A and the actual measured cylinder B in the local coordinate system.

Step 4: Take the spatial position variation q _A of the actual reference cylinder A relative to its largest entity effective cylinder A ₂ as the design variable, take the variation range of q _A as the constraint condition of the objective function, and use the actual measured cylinder B in different The diameter d _B,n = f ( q _A ) of the smallest circumscribed cylinder with orientation constraints at the spatial position is optimized as the objective function, and the limit equivalent dimension d B of the actual measured cylinder B is obtained by solving the constrained objective optimization problem _{, min} , among them, the smallest circumscribed cylinder with orientation constraint of the actual measured cylinder B : when the actual reference cylinder A is within its maximum solid effective cylinder A ₂ , take the axis parallel to the maximum solid effective cylinder A ₂ as the axis, and the energy The maximum ideal accommodating cylinder that contains the actual measured cylinder B ; the limit equivalent diameter d _B,min of the actual measured cylinder B : in the process of changing the spatial position of the actual reference cylinder A relative to its largest solid effective cylinder A ₂ , by fitting The diameter of the smallest of all resulting smallest circumscribed cylinders with orientation constraints.

Step 5: Judging the eligibility of the parallelism error of the actual measured hole B by comparing the maximum actual size d _B of the measured cylinder B and the limit equivalent diameter d _{B, min} of the measured cylinder B.

In order to make the present invention easy to operate, and taking into account the influence of shape tolerance on the total error of the parts, the present invention is embodied as:

Step 1: Determine if the part is suitable for this evaluation method. Obtain the key information of the reference cylinder A and the measured cylinder B respectively from the part drawings; if the parallelism tolerance of the measured cylinder B and its corresponding reference cylinder are MMR, and the shape tolerance of the reference cylinder A is also MMR, then transfer to Step 2.

The key information of the datum cylinder A has the following contents: the nominal diameter d ₁ of the datum cylinder, the upper deviation and the lower deviation of the datum cylinder are es ₁ and ei ₁ respectively; the shape tolerance is MMR, and the shape tolerance is T ₁ ; Length L ₁ of cylinder A.

The key information of the tested cylinder B has the following contents: the nominal diameter d ₂ of the tested cylinder; the upper and lower deviations of the tested cylinder are es ₂ and ei ₂ respectively; the parallelism tolerance T ₂ ; the parallelism tolerance and their corresponding benchmarks are marked MMR.

Step 2: Determine whether the size error of the actual reference cylinder A and the size error of the actual measured cylinder B are both qualified. First, use a three _- coordinate measuring machine to obtain the measuring point sets on the contours _of the actual reference cylinder A and the actual measured cylinder B , respectively . _,m,0 , y _A,m,0 , z _A,m,0 )}, where m is the serial number of the measuring point on the actual reference cylinder profile, m =1, 2, … , M , M is a positive integer; The measuring point set of the actual measured cylinder B { g _B,n,0 ( x _B,n,0 , y _B,n,0 , z _B,n,0 )}, where n is the The serial number of the measuring point, n = 1, 2, … , N , where N is a positive integer.

Then determine whether the dimensional errors of the actual reference cylinder A and the actual measured cylinder B are qualified at the same time. If the dimensional errors of both are qualified, go to step 3, otherwise terminate the evaluation method.

Step 3: In order to facilitate the calculation and reduce the complexity of subsequent calculations, it is necessary to roughly move the geometric center of the actual reference cylinder to the coordinate origin of the local coordinate system, that is, formula 1: g _A,m1 = g _A,m,0 - ( g _A,max + g _A,min )/2. g _A,max , g _A,min are the coordinates of the farthest point and the nearest point from the coordinate origin in the actual reference cylinder contour measuring points, respectively. With the movement of the actual datum cylinder, the coordinate value of the measuring point of the actual measured cylinder changes accordingly, and the coordinate value after the change is Formula 2: g _B,n,1 = g _B,n,0 - ( g _{A, max} + g _A,min )/2. Then, the smallest circumscribed cylinder A ₁ of the actual reference cylinder is obtained by fitting, and the axis of the smallest circumscribed cylinder A ₁ is moved to the z -axis of the local coordinate system.

Then compute objective optimization problem 1:

st.

The optimal solution ( x _1,min , y _1,min , μ _1,min , ν _1,min ) is obtained, and the smallest circumscribed cylinder A ₁ of the actual reference cylinder A is obtained.

Substitute the measuring point set { g _A,m,1 ( x _A,m,1 , y _A,m,1 , z _A,m,1 )} on the outline of the actual reference cylinder into the following formula for coordinate transformation, m =1 , 2 , … , M ;

The set of measuring points { g _A,m ( x _A,m , y _A,m , z _A,m )} on the contour of the actual reference cylinder after transformation can be obtained.

Substitute the measuring point set { g _B,n,1 ( x _B,n,1 , y _B,n,1 , z _B,n,1 )} on the actual measured cylindrical contour into the following formula to perform coordinate transformation, n = 1 , 2 , … , N ;

The set of measuring points { g _B,n ( x _B,n , y _B,n , z _B,n )} on the actual measured cylindrical contour after transformation can be obtained.

Step 4: First, through formula 3: d _A = d ₁ + es ₁ + T ₁ , obtain the diameter d _A of the largest solid effective cylinder A ₂ of the reference cylinder A ;

Then, solve objective optimization problem 2:

st.

Solve the limit equivalent diameter d _B,min =min d _B,n of the actual measured cylinder B.

Step 5: Calculate the diameter d _B of the largest solid effective cylinder B ₂ of the measured hole B by formula 4: d _B = d ₂ + es ₂ + T ₂ .

If the limit equivalent diameter of the tested cylinder B d _B,min ≤ d _B , it can be determined that the parallelism error of the actual measured cylinder is qualified, otherwise the parallelism error of the actual measured cylinder is unqualified.

In the present invention, the objective optimization problem 1 and the objective optimization problem 2 need to be solved. These two objective optimization problems have the following two identical characteristics: the objective function value will not drop significantly near the optimal solution; Give multiple feasible initial solutions. According to the characteristics of the above-mentioned objective optimization problem, the present invention provides a genetic algorithm to solve the objective optimization problem 1 and the objective optimization problem 2. The specific steps of the algorithm are as follows:

Step 11: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S , the length of each individual R , the maximum evolutionary generation K , the crossover probability W , and the mutation probability C .

Step 12: Define N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , … , P _S,q,r ), the value of each individual and the feasible solution in the objective optimization problem ( x ₁ , x ₂ , … , x _r ) has a one-to-one correspondence, and P _{S, q, r} and x _r have the same value range; q =1, 2, … , N _S ; r = 1, 2, … , R ; the set consisting of all individuals is { P _{S, q} }.

Step 13: According to a uniform distribution, randomly obtain N _S individuals P _S,q within the value range of P _S,q,r ; n =1, ... , N _S ; r =1, 2, ... , R .

Taking the value of P _{S, q, r} as the value of x _r in the above objective optimization problem, calculate its objective function value f _q = f ( x ₁ , x ₂ , …, x _r ); q =1, 2, … , N _S ; r =1, 2, … , R .

Record the optimal objective function value f _min =min f _q at this time, and record the optimal solution P _S,min , q =1, 2, … , N _S corresponding to the global optimal objective function value.

Step 14: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 15 and Step 16 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., N _S .

Step 15: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, … , R . Equation 6: P _S,k,i = P _S,k,i (1- W )+ P _S,l,j W ; P _S,k,j = P _S,k,j (1- W )+ P _S,l,i W , where W is a random number in the interval [0,1].

Step 16: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower and upper bounds of the value range of P _S,h,t respectively; k is the current iteration number; K is the maximum evolution number; C is a random number in the [0,1] interval.

Step 17: After Step 15 and Step 16, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , N _S ; r =1, 2, … , R .

Step 18: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra K , stop the iteration, and output the optimal solution P _S,min of the objective optimization problem and its corresponding objective function value f _min , otherwise the population { P _{S, q} } is used as the initial population for the next evolution, and jumps to step 14 to continue the optimization.

In order to increase the operability of this method, the initial parameters of the aforementioned genetic algorithm can be set as follows: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, The mutation probability C is 0.1.

In order to make the calculation of the present invention more efficient, the following algorithm can be used to solve and calculate the target optimization problem 1 in the present invention:

Step 21: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S , the length R of each individual, the maximum evolutionary generation K , the crossover probability W , and the mutation probability C .

Step 22: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , N _S ; the set consisting of all individuals is { P _S,q }.

Step 23: According to uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q =1, . . . , N _S .

Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _{A, q} ; q =1, 2, … , N _S ;

Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value.

Step 24: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., N _S .

Step 25: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4. Equation 6: P _S,k,i = P _S,k,i (1- W )+ P _S,l,j W ; P _S,k,j = P _S,k,j (1- W )+ P _S,l,i W , where W is a random number in the interval [0,1].

Step 26: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower and upper bounds of the value range of P _S,h,t respectively; k is the current iteration number; K is the maximum evolution number; C is a random number in the [0,1] interval.

Step 27: After Step 25 and Step 26, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4.

Step 28: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₁ , y ₁ , α ₁ , β ₁ ) = P _S,min and its corresponding The objective function value d _A,min =min( d _A,q,max ), otherwise the population at this time { P _{S, q} } is used as the initial population of the next evolution, and jump to step 24 to continue the optimization.

In order to make the calculation of the present invention more efficient, the following algorithm can be used to solve and calculate the target optimization problem 2 in the present invention:

Step 31: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S , the length R of each individual, the maximum evolutionary generation K , the crossover probability W , and the mutation probability C .

Step 32: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 2 The solutions in ( x ₀ , y ₀ , dα , dβ ) correspond one-to-one, q =1, 2, … , N _S ; the set composed of all individuals is { P _S,q }.

Step 33: According to a uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q =1, . . . , N _S .

Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₀ , y ₀ , dα , dβ in the above objective optimization problem 2, respectively value, and calculate its corresponding objective function value d _B,q ; q =1, 2, … , N _S ;

Record the optimal objective function value d _B,min =min( d _B,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value.

Step 34: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 35 and Step 36 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., N _S .

Step 35: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4. Equation 6: P _S,k,i = P _S,k,i (1- W )+ P _S,l,j W ; P _S,k,j = P _S,k,j (1- W )+ P _S,l,i W , where W is a random number in the interval [0,1].

Step 36: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower and upper bounds of the value range of P _S,h,t respectively; k is the current iteration number; K is the maximum evolution number; C is a random number in the [0,1] interval.

Step 37: After Step 35 and Step 36, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4.

Step 38: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₀ , y ₀ , dα , dβ ) = P _S,min and its corresponding target The function value d _B,min =min( d _B,q,min ), otherwise, the population { P _S,q } at this time is used as the initial population of the next evolution, and jump to step 34 to continue the optimization.

Description of drawings

Figure 1 is a flow chart of the basic method of the present invention.

Fig. 2 is the basic flow chart of the genetic algorithm for solving the target optimization problem in the present invention.

Figure 3. Parts design diagram of the experimental object.

Detailed ways

Experiment implementation example:

Step 1: Determine if the part is suitable for this evaluation method. Obtain the key information of the reference cylinder A and the measured cylinder B respectively from the part drawings; if the parallelism tolerance of the measured cylinder B and its corresponding reference cylinder are MMR, and the shape tolerance of the reference cylinder A is also MMR, then transfer to Step 2.

The key information of the datum cylinder A has the following contents: the nominal diameter d ₁ of the datum cylinder, the upper deviation and the lower deviation of the datum cylinder are es ₁ and ei ₁ respectively; the shape tolerance is MMR, and the shape tolerance is T ₁ ; Length L ₁ of cylinder A.

The key information of the tested cylinder B has the following contents: the nominal diameter d ₂ of the tested cylinder; the upper and lower deviations of the tested cylinder are es ₂ and ei ₂ respectively; the parallelism tolerance T ₂ ; the parallelism tolerance and their corresponding benchmarks are marked MMR.

Step 2: Determine whether the size error of the actual reference cylinder A and the size error of the actual measured cylinder B are both qualified. First, use a three _- coordinate measuring machine to obtain the measuring point sets on the contours _of the actual reference cylinder A and the actual measured cylinder B , respectively . _,m,0 , y _A,m,0 , z _A,m,0 )}, where n is the serial number of the measuring point on the actual reference cylinder profile, m =1, 2, … , M , M is a positive integer; The measuring point set of the actual measured cylinder B { g _B,n,0 ( x _B,n,0 , y _B,n,0 , z _B,n,0 )}, where n is the The serial number of the measuring point, n = 1, 2, … , N , where N is a positive integer.

Then determine whether the dimensional errors of the actual reference cylinder A and the actual measured cylinder B are qualified at the same time. If the dimensional errors of both are qualified, go to step 3, otherwise terminate the evaluation method.

Step 3: In order to facilitate the calculation and reduce the complexity of subsequent calculations, it is necessary to roughly move the geometric center of the actual reference cylinder to the coordinate origin of the local coordinate system, that is, formula 1: g _A,m1 = g _A,m,0 - ( g _A,max + g _A,min )/2. g _A,max , g _A,min are the coordinates of the farthest point and the nearest point from the coordinate origin in the actual reference cylinder contour measuring points, respectively. With the movement of the actual datum cylinder, the coordinate value of the measuring point of the actual measured cylinder changes accordingly, and the coordinate value after the change is Formula 2: g _B,n,1 = g _B,n,0 - ( g _{A, max} + g _A,min )/2. Then, the smallest circumscribed cylinder A ₁ of the actual reference cylinder is obtained by fitting, and the axis of the smallest circumscribed cylinder A ₁ is moved to the z -axis of the local coordinate system.

Then compute objective optimization problem 1:

st.

Step 21: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is is 0.1.

Step 22: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , 20; the set composed of all individuals is { P _S,q }.

Step 23: According to uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q = 1, . . . , 20.

Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _A,q ; q =1, 2, … , 20;

Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value.

Step 24: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., 20.

Step 25: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4. Equation 6: P _S,k,i = P _S,k,i (1-0.6)+ P _S,l,j 0.6; P _S,k,j = P _S,k,j (1-0.6)+ P _S,l,i 0.6, where W is a random number in the interval [0,1].

Step 26: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower bound and upper bound of the value range of P _{S, h, t} respectively; k is the current iteration number; C is a random number in the [0,1] interval.

Step 27: After Step 25 and Step 26, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4.

Step 28: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₁ , y ₁ , α ₁ , β ₁ ) = P _S,min and its corresponding The objective function value d _A,min =min( d _A,q,max ), otherwise the population at this time { P _{S, q} } is used as the initial population of the next evolution, and jump to step 24 to continue the optimization.

The optimal solution ( x _1,min , y _1,min , μ _1,min , ν _1,min ) is obtained, and the diameter d _A,min= min d _A of the smallest circumscribed cylinder A ₁ of the actual reference cylinder A is obtained at this time _,m , m =1 , 2 , … , M .

Substitute the measuring point set { g _A,m,1 ( x _A,m,1 , y _A,m,1 , z _A,m,1 )} on the outline of the actual reference cylinder into the following formula for coordinate transformation, m =1 , 2 , … , M ;

The set of measuring points { g _A,m ( x _A,m , y _A,m , z _A,m )} on the contour of the actual reference cylinder after transformation can be obtained.

Substitute the measuring point set { g _B,n,1 ( x _B,n,1 , y _B,n,1 , z _B,n,1 )} on the actual measured cylindrical contour into the following formula to perform coordinate transformation, n = 1 , 2 , … , N ;

The set of measuring points { g _B,n ( x _B,n , y _B,n , z _B,n )} on the actual measured cylindrical contour after transformation can be obtained.

Step 4: First, through formula 3: d _A = d ₁ + es ₁ + T ₁ , obtain the diameter d _A of the largest solid effective cylinder A ₂ of the reference cylinder A ;

Then, solve objective optimization problem 2:

st.

Step 31: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is is 0.1.

Step 32: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , 20; the set composed of all individuals is { P _S,q }.

Step 33: According to a uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q = 1, . . . , 20.

Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _A,q ; q =1, 2, … , 20;

Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value.

Step 34: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., 20.

Step 35: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4. Equation 6: P _S,k,i = P _S,k,i (1-0.6)+ P _S,l,j 0.6; P _S,k,j = P _S,k,j (1-0.6)+ P _S,l,i 0.6, where W is a random number in the interval [0,1].

Step 36: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower bound and upper bound of the value range of P _{S, h, t} respectively; k is the current iteration number; C is a random number in the [0,1] interval.

Step 37: After Step 35 and Step 36, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4.

Step 38: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₀ , y ₀ , dα , dβ ) = P _S,min and its corresponding target The function value d _B,min =min( d _B,q,min ), otherwise the population { P _S,q } at this time is used as the initial population of the next evolution, and jumps to step 34 to continue the optimization.

Solve the actual measured cylinderBThe limiting equivalent diameter ofd _B,min =mind _B,n , then the optimal solution is (x _0,min ,y _0,min , dα _min ,dβ _min ).

Step 5: Through formula 4: d _B = d ₂ + es ₂ + T ₂ , calculate the diameter d _B of the largest solid effective cylinder B ₂ of the tested cylinder B.

If the limit equivalent diameter of the tested cylinder B d _B,min ≤ d _B , it can be judged that the parallelism error of the actual measured cylinder is qualified, otherwise the parallelism error of the actual measured cylinder is unqualified.

test subject:

The measured cylinder has both dimensional tolerance and directional tolerance, and the parallelism tolerance of the axis of the measured cylinder and its datum have maximum entity requirements. The reference cylinder has both dimensional tolerance and shape tolerance, and the shape tolerance has the maximum entity requirement. The qualification of the parallelism error of the part is evaluated as follows:

Step 1: Obtain the key information of the reference cylinder A and the measured cylinder B (the unit of length is millimeters, and the unit of angle is radians) from the parts drawing shown in Figure 3.

The key information of the datum cylinder A includes the following parts: the nominal diameter of the datum cylinder d ₁ =64, the upper and lower deviations of the datum cylinder are es ₁ =0, ei ₁ =-0.019 respectively; the shape tolerance is applied MMR, The shape tolerance is T ₁ =0.1; the length of the reference cylinder A is L ₁ =36.

The key information of the tested cylinder B has the following contents: the nominal diameter of the tested cylinder d ₂ =30; the upper and lower deviations of the tested cylinder are es ₂ =0, ei ₂ =-0.013 respectively; parallelism Tolerance T ₂ =0.01; both the parallelism tolerance and its corresponding datum use MMR.

The parallelism tolerance of the measured cylinder B and its corresponding reference cylinder are MMR, and the shape tolerance of the reference cylinder A is also MMR, then go to step 2.

Step 2: Use a three-coordinate measuring machine to obtain the measuring point datasets on the contours of the actual reference cylinder A and the actual measured cylinder B , respectively, and their measuring point datasets are shown in Table 1:

On the contour of the actual datum cylinder A , 6 layers of measuring point data with the same spacing are measured, and each layer of measuring points contains 8 evenly distributed measuring points. A total of 48 measuring points are measured on the contour of the actual datum cylinder A. These 48 measuring points are The measuring point data set composed of measuring points is { p _{A, m} }, where m is the serial number of the measuring point on the actual reference hole, m = 1, 2, … , 48; 6 is measured on the actual measured cylinder B profile The measuring point data with the same spacing between layers, and each layer of measuring points contains 8 evenly distributed measuring points, a total of 48 measuring points are measured on the actual measured cylinder B contour, and the measuring point data set composed of these 48 measuring points is { p _{B, n} }, where n is the serial number of the measuring point on the contour of the actual measured cylinder B , n = 1, 2, … , 48.

Fitting the measuring points p _{A, n} of each layer of the actual datum cylinder A respectively to obtain a fitting circle, a total of 6 fitting circles, the diameters of these 6 fitting circles are 63.983, 63.987, 63.985, 63.993, 63.997, 63.991 , the diameter of each layer of fitting circle is between the minimum limit size and the maximum limit size of the actual reference cylinder A , so it is judged that the size error of the actual reference cylinder A is qualified; p _{B, m} respectively perform the fitting operation to obtain a fitted circle, a total of 6 fitted circles, the diameters of the 6 fitted circles are 29.989, 29.992, 29.988, 29.996, 29.994, 29.997, respectively. The diameters are between the minimum limit size and the maximum limit size of the actual measured cylinder B , so it can be determined that the size error of the actual measured cylinder B is qualified; since both the actual reference cylinder A and the actual measured cylinder B have qualified size errors, Then you can go to step 3.

Step 3: In order to facilitate the calculation and reduce the complexity of subsequent calculations, it is necessary to roughly move the geometric center of the actual reference cylinder to the coordinate origin of the local coordinate system, that is, formula 1: g _A,m1 = g _A,m,0 - ( g _A,max + g _A,min )/2. g _A,max , g _A,min are the coordinates of the farthest point and the nearest point from the coordinate origin in the actual reference cylinder contour measuring points, respectively. With the movement of the actual datum cylinder, the coordinate value of the measuring point of the actual measured cylinder changes accordingly, and the coordinate value after the change is Formula 2: g _B,n,1 = g _B,n,0 - ( g _{A, max} + g _A,min )/2. Then, the smallest circumscribed cylinder A ₁ of the actual reference cylinder is obtained by fitting, and the axis of the smallest circumscribed cylinder A ₁ is moved to the z -axis of the local coordinate system.

Then compute objective optimization problem 1:

st.

Step 21: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is is 0.1.

Step 22: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , 20; the set composed of all individuals is { P _S,q }.

Step 23: According to uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q = 1, . . . , 20.

Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _A,q ; q =1, 2, … , 20;

Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value.

Step 24: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., 20.

Step 25: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4. Equation 6: P _S,k,i = P _S,k,i (1-0.6)+ P _S,l,j 0.6; P _S,k,j = P _S,k,j (1-0.6)+ P _S,l,i 0.6, where W is a random number in the interval [0,1].

Step 26: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower bound and upper bound of the value range of P _{S, h, t} respectively; k is the current iteration number; C is a random number in the [0,1] interval.

Step 27: After Step 25 and Step 26, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4.

Step 28: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₁ , y ₁ , α ₁ , β ₁ ) = P _S,min and its corresponding The objective function value d _A,min =min( d _A,q,max ), otherwise the population at this time { P _{S, q} } is used as the initial population of the next evolution, and jump to step 24 to continue the optimization.

The optimal solution is obtained ( x _1,min , y _1,min , μ _1,min , ν _1,min )= (-0.3315, 0.5641, 0.0206, 0.0141), and the minimum circumscribed cylinder A of the actual reference cylinder A is obtained at this time The diameter of ₁ is d _A,min = 63.995.

Substitute the measuring point set { g _A,m,1 ( x _A,m,1 , y _A,m,1 , z _A,m,1 )} on the outline of the actual reference cylinder into the following formula for coordinate transformation, m =1 , 2 , … , M ;

The set of measuring points { g _A,m ( x _A,m , y _A,m , z _A,m )} on the contour of the actual reference cylinder after transformation can be obtained.

Substitute the measuring point set { g _B,n,1 ( x _B,n,1 , y _B,n,1 , z _B,n,1 )} on the actual measured cylindrical contour into the following formula to perform coordinate transformation, n = 1 , 2 , … , N ;

The set of measuring points { g _B,n ( x _B,n , y _B,n , z _B,n )} on the actual measured cylindrical contour after transformation can be obtained.

Step 4: First, through formula 3: d _A = d ₁ + es ₁ + T ₁ =64+0+0.1=64.1, obtain the diameter d _A of the largest solid effective cylinder A ₂ of the reference cylinder A ; then, solve the objective optimization problem 2:

st.

Step 31: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is is 0.1.

Step 32: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , 20; the set composed of all individuals is { P _S,q }.

Step 33: According to a uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q = 1, . . . , 20.

Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _A,q ; q =1, 2, … , 20;

Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value.

Step 34: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26 . The probability that the individual P _S,q is selected is Equation 5:

,

q = 1, 2, ..., 20.

Step 35: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4. Equation 6: P _S,k,i = P _S,k,i (1-0.6)+ P _S,l,j 0.6; P _S,k,j = P _S,k,j (1-0.6)+ P _S,l,i 0.6, where W is a random number in the interval [0,1].

Step 36: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7:

Among them, P _min and P _max are the lower bound and upper bound of the value range of P _{S, h, t} respectively; k is the current iteration number; C is a random number in the [0,1] interval.

Step 37: After Step 35 and Step 36, a new population { P _{S, q} } is formed. _Substitute ( x _{1 ,} x _{2 ,} . _

If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4.

Step 38: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₀ , y ₀ , dα , dβ ) = P _S,min and its corresponding target The function value d _B,min =min( d _B,q,min ), otherwise, the population { P _S,q } at this time is used as the initial population of the next evolution, and jump to step 34 to continue the optimization.

The limit equivalent diameter d _B,min = 29.993 of the actual measured cylinder B is obtained, and the optimal solution is (0.116, 0.089, 0.012, -0.008).

Step 5: Through formula 4: d _B = d ₂ + es ₂ + T ₂ =30+0+0.01=30.01, calculate the diameter d _B of the largest solid effective cylinder B ₂ of the tested cylinder B.

Since the limit equivalent diameter of the measured cylinder B is d _B,min = 29.993≤d _B =30.01, the parallelism error of the actual measured cylinder can be judged to be qualified.

Table 1 Data set of the reference cylinder and the measuring point of the measured cylinder

Claims (7)

1. A method for evaluating parallelism based on maximum entity requirement (MMR) cylinder, characterized in that the specific steps are as follows: Step 1: Determine whether the part is suitable for this evaluation method: Obtain the key information of the reference cylinder A and the measured cylinder B from the part drawings; if the parallelism tolerance of the measured cylinder B and its corresponding reference cylinder are MMR, and the benchmark The shape tolerance of cylinder A also adopts MMR, then go to step 2; The key information of the datum cylinder A has the following contents: the nominal diameter d ₁ of the datum cylinder, the upper deviation and the lower deviation of the datum cylinder are es ₁ and ei ₁ respectively; the shape tolerance is MMR, and the shape tolerance is T ₁ ; the length L ₁ of the cylinder A ; The key information of the tested cylinder B has the following contents: the nominal diameter d ₂ of the tested cylinder; the upper and lower deviations of the tested cylinder are es ₂ and ei ₂ respectively; the parallelism tolerance T ₂ ; the parallelism tolerance and its corresponding benchmarks use MMR; Step 2: Determine whether the dimensional error of the actual datum cylinder A and the dimensional error of the actual measured cylinder B are qualified at the same time: First, use a three-coordinate measuring machine to obtain the measuring point data sets on the contours of the actual datum cylinder A and the actual measured cylinder B respectively. , and then determine whether the dimensional errors of the actual reference cylinder A and the actual measured cylinder B are both qualified at the same time. If the dimensional errors of both are qualified, go to step 3, otherwise terminate the evaluation method; Step 3: Fit the fitting cylinder A ₁ of the actual datum cylinder A through calculation, establish a local coordinate system on the fitting cylinder A ₁ , and compare the actual datum cylinder A measured by the three-coordinate measuring machine with the actual measured cylinder. Coordinate transformation is performed on the coordinate value of the measuring point of B to obtain the coordinate value of the actual reference cylinder A and the measuring point of the actual measured cylinder B in the local coordinate system; Step 4: Take the spatial position variation q _A of the actual reference cylinder A relative to its largest entity effective cylinder A ₂ as the design variable, take the variation range of q _A as the constraint condition of the objective function, and use the actual measured cylinder B in different The diameter d _B,n = f ( q _A ) of the smallest circumscribed cylinder with orientation constraints at the spatial position is optimized as the objective function, and the limit equivalent dimension d B of the actual measured cylinder B is obtained by solving the constrained objective optimization problem _{, min} , among them, the smallest circumscribed cylinder with orientation constraint of the actual measured cylinder B : when the actual reference cylinder A is within its maximum solid effective cylinder A ₂ , take the axis parallel to the maximum solid effective cylinder A ₂ as the axis, and the energy The maximum ideal accommodating cylinder that contains the actual measured cylinder B ; the limit equivalent diameter d _B,min of the actual measured cylinder B : in the process of changing the spatial position of the actual reference cylinder A relative to its largest solid effective cylinder A ₂ , by fitting The diameter of the smallest of all the resulting smallest circumscribed cylinders with orientation constraints; Step 5: Judging the eligibility of the parallelism error of the actual measured hole B by comparing the maximum actual size d _B of the measured cylinder B and the limit equivalent diameter d _{B, min} of the measured cylinder B. 2. A method for evaluating parallelism based on a maximum entity requirement (MMR) cylinder according to claim 1, characterized in that: The data of the coordinate values of the measuring points on the outline of the actual reference cylinder A and the actual measured cylinder B described in step 2 are measured by a three-coordinate measuring machine in the space rectangular coordinate system, and these measuring point sets are the actual reference cylinder A respectively. The set of measuring points { g _A,m,0 ( x _A,m,0 , y _A,m,0 , z _A,m,0 )}, where m is the serial number of the measuring point on the actual datum cylinder profile, m =1, 2, … , M , M is a positive integer; the actual measuring point set of the measured cylinder B { g _B,n,0 ( x _B,n,0 , y _B,n,0 , z _{B,n, 0} )}, where n is the serial number of the measuring point on the actual measured cylindrical contour, n =1, 2, … , N , N is a positive integer. 3. A method for evaluating the parallelism of a cylinder based on maximum entity requirements (MMR) according to claim 2, wherein: Step 1: Determine whether the part is suitable for this evaluation method: Obtain the key information of the reference cylinder A and the measured cylinder B from the part drawings; if the parallelism tolerance of the measured cylinder B and its corresponding reference cylinder are MMR, and the benchmark The shape tolerance of cylinder A also adopts MMR, then go to step 2; The key information of the datum cylinder A has the following contents: the nominal diameter d ₁ of the datum cylinder, the upper deviation and the lower deviation of the datum cylinder are es ₁ and ei ₁ respectively; the shape tolerance is MMR, and the shape tolerance is T ₁ ; the length L ₁ of the cylinder A ; The key information of the tested cylinder B has the following contents: the nominal diameter d ₂ of the tested cylinder; the upper and lower deviations of the tested cylinder are es ₂ and ei ₂ respectively; the parallelism tolerance T ₂ ; the parallelism tolerance and their corresponding benchmarks are marked with MM; Step 2: Determine the actual datum cylinderAThe dimensional error of the actual measured cylinderBWhether the dimensional error of the test is qualified at the same time: first use a three-coordinate measuring machine to obtain the actual reference cylinder respectivelyAand the actual measured cylinderBThe set of measuring points on the contour of , which are the actual datum cylinderAset of measuring points {g _A,m,0 (x _A,m,0 ,y _A,m,0 ,z _A,m,0 )},in,nis the serial number of the measuring point on the actual datum cylinder profile,m=1, 2, … ,M,Mis a positive integer; the actual measured holeBset of measuring points {g _B,n,0 (x _B,n,0 , y _B,n,0 ,z _B,n,0 )},in,nis the serial number of the measuring point on the actual measured cylindrical contour,n=1, 2, … ,N,Nis a positive integer; Then determine whether the dimensional errors of the actual reference cylinder A and the actual measured cylinder B are both qualified at the same time. If the dimensional errors of both are qualified, go to step 3, otherwise terminate the evaluation method; Step 3: In order to facilitate the calculation and reduce the complexity of subsequent calculations, it is necessary to roughly move the geometric center of the actual reference cylinder to the coordinate origin of the local coordinate system, that is, formula 1: g _A,m1 = g _A,m,0 - ( g _A,max + g _A,min )/2; g _A,max , g _A,min are the coordinates of the farthest point and the nearest point in the measuring point of the actual datum cylinder profile respectively; with the movement of the actual datum cylinder, the coordinate value of the measuring point of the actual cylinder to be measured will occur correspondingly. change, the coordinate value after the change is formula 2: g _B,n,1 = g _B,n,0 - ( g _A,max + g _A,min )/2; then, the actual reference cylinder is obtained by fitting Minimum circumscribed cylinder A ₁ , and move the axis of the minimum circumscribed cylinder A ₁ to the z -axis of the local coordinate system; Then compute objective optimization problem 1: st. The optimal solution ( x _1,min , y _1,min , μ _1,min , ν _1,min ) is obtained, and the minimum circumscribed cylinder A ₁ of the actual reference cylinder A is obtained at this time; Substitute the measuring point set { g _A,m,1 ( x _A,m,1 , y _A,m,1 , z _A,m,1 )} on the outline of the actual reference cylinder into the following formula for coordinate transformation, m =1 , 2 , … , M ; The measuring point set { g _A,m ( x _A,m , y _A,m , z _A,m )} on the contour of the actual datum cylinder after transformation can be obtained; Substitute the measuring point set { g _B,n,1 ( x _B,n,1 , y _B,n,1 , z _B,n,1 )} on the actual measured cylindrical contour into the following formula to perform coordinate transformation, n = 1 , 2 , … , N ; The measuring point set { g _B,n ( x _B,n , y _B,n , z _B,n )} on the actual measured cylindrical contour after transformation can be obtained; Step 4: First, through formula 3: d _A = d ₁ + es ₁ + T ₁ , obtain the diameter d _A of the largest solid effective cylinder A ₂ of the reference cylinder A ; Then, solve objective optimization problem 2: st. Solve the limit equivalent diameter d _B,min =min d _B,n of the actual measured cylinder B ; Step 5: Calculate the diameter d _B of the largest solid effective cylinder B ₂ of the measured hole B by formula 4: d _B = d ₂ + es ₂ + T ₂ ; If the limit equivalent diameter of the tested cylinder B d _B,min ≤ d _B , it can be determined that the parallelism error of the actual measured cylinder is qualified, otherwise the parallelism error of the actual measured cylinder is unqualified. 4. A method for evaluating parallelism based on a maximum entity requirement (MMR) cylinder according to claim 3, characterized in that: The steps for solving the constrained objective optimization problem are as follows: Step 11: Initialize the parameters of the population first. These parameters have the following contents: the size of the population N _S , the length R of each individual, the maximum evolutionary algebra K , the crossover probability W , and the mutation probability C ; Step 12: Define N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , … , P _S,q,r ), the value of each individual and the feasible solution in the objective optimization problem ( x ₁ , x ₂ , … , x _r ) has a one-to-one correspondence, and P _{S, q, r} and x _r have the same value range; q =1, 2, … , N _S ; r = 1, 2, … , R ; the set composed of all individuals is { P _{S, q} }; Step 13: According to uniform distribution, randomly obtain N _S individuals P _S,q within the value range of P _S,q,r ; n =1, . . . , N _S ; r =1, 2, . . , R ; Taking the value of P _S,q,r as the value of x _r in the above objective optimization problem, calculate its objective function value f _q = f ( x ₁ , x ₂ , … , x _r ); q =1, 2, … , N _S ; r =1, 2, … , R ; Record the optimal objective function value f _min =min f _q at this time, and record the optimal solution P _S,min , q =1, 2, … , N _S corresponding to the global optimal objective function value; Step 14: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 15 and Step 16; the probability of individual P _{S, q} being selected is formula 5: , q = 1, 2, ..., N _S ; Step 15: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1,2, … , R ; Equation 6: P _S,k,i = P _S,k,i (1- W )+ P _S,l,j W ; P _S,k,j = P _S,k,j (1- W )+ P _S,l,i W , where W is a random number in the interval [0,1]; Step 16: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7: Among them, P _min and P _max are the lower and upper bounds of the value range of P _S,h,t respectively; k is the current iteration number; K is the maximum evolution number; C is a random number in the [0,1] interval; Step 17: After Step 15 and Step 16, a new population { P _{S, q} } is formed; _Substitute ( x _{1 ,} x _{2 ,} . _ If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , N _S ; r =1, 2, … , R ; Step 18: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra K , stop the iteration, and output the optimal solution P _S,min of the objective optimization problem and its corresponding objective function value f _min , otherwise the population { P _{S, q} } is used as the initial population for the next evolution, and jumps to step 14 to continue the optimization. 5. A method for evaluating parallelism based on a maximum entity requirement (MMR) cylinder according to claim 4, characterized in that: The initial parameters of the genetic algorithm are set as follows: the population size N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is 0.1. 6. A method for evaluating the parallelism of a cylinder based on maximum physical requirements (MMR) according to claim 4, wherein: The solution to objective optimization problem 1 is as follows: Step 21: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is is 0.1; Step 22: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , 20; the set composed of all individuals is { P _S,q }; Step 23: According to uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q =1, . . . , 20; Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _A,q ; q =1, 2, … , 20; Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value; Step 24: randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26; The probability that the individual P _S,q is selected is Equation 5: , q = 1, 2, ..., 20; Step 25: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1, 2, 3, 4; Equation 6: P _S,k,i = P _S,k,i (1-0.6)+ P _S,l,j 0.6; P _S,k,j = P _S,k,j (1-0.6)+ P _S,l,i 0.6, where W is a random number in the interval [0,1]; Step 26: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7: Among them, P _min and P _max are the lower and upper bounds of the value range of P _{S, h, t} respectively; k is the current iteration number; C is a random number in the interval [0,1]; Step 27: After Step 25 and Step 26, a new population { P _{S, q} } is formed; _Substitute ( x _{1 ,} x _{2 ,} . _ If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4; Step 28: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₁ , y ₁ , α ₁ , β ₁ ) = P _S,min and its corresponding The objective function value d _A,min =min( d _A,q,max ), otherwise the population at this time { P _{S, q} } is used as the initial population of the next evolution, and jump to step 24 to continue the optimization. 7. A method for evaluating parallelism based on a maximum entity requirement (MMR) cylinder according to claim 4, characterized in that: The solution to objective optimization problem 2 is as follows: Step 31: First initialize the parameters of the population. These parameters have the following contents: the size of the population N _S is 20, the length R of each individual is 4, the maximum evolutionary generation K is 200, the crossover probability W is 0.6, and the mutation probability C is is 0.1; Step 32: Set N _S individuals P _S,q ( P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 ), whose value is the same as the target optimization problem 1 The solutions in ( x ₁ , y ₁ , α ₁ , β ₁ ) correspond to, q =1, 2, … , 20; the set composed of all individuals is { P _S,q }; Step 33: According to a uniform distribution, randomly obtain N _S values within the value range of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 to generate N _S individuals P _S,q ; q =1, . . . , 20; Take the values of P _S,q,1 , P _S,q,2 , P _S,q,3 , P _S,q,4 as the independent variables x ₁ , y ₁ , α ₁ , β in the above objective optimization problem 1, respectively ₁ , and calculate its corresponding objective function value d _A,q ; q =1, 2, … , 20; Record the optimal objective function value d _A,min =min( d _A,q,min ) at this time, and record the optimal solution P _S,min corresponding to the optimal function value; Step 34: Randomly select individuals from the above-mentioned population { P _{S, q} } with a certain probability for the operations of Step 25 and Step 26. The probability of individual P _{S, q} being selected is formula 5: , q = 1, 2, ..., 20; Step 35: Randomly select two individuals P _S,k and P _S,l from the population { P _S,q }, and compare the i -th element P _S,k,i in the individual P _S ,k with the individual P _S, The jth element P _{S,l,j in} l is crossed according to formula 6, where k, l =1, 2, … , N _S ; i, j =1,2, 3, 4; formula 6: P _S,k,i = P _S,k,i (1-0.6)+ P _S,l,j 0.6; P _S,k,j = P _S,k,j (1-0.6)+ P _{S,l, i} 0.6, where W is a random number in the interval [0,1]; Step 36: Randomly select an individual P _S,h from the population { P _S,q }, and perform mutation operation on the t -th element in P _S,h according to formula 7, formula 7: Among them, P _min and P _max are the lower and upper bounds of the value range of P _{S, h, t} respectively; k is the current iteration number; C is a random number in the [0,1] interval; Step 37: After Step 35 and Step 36, a new population { P _{S, q} } is formed; _Substitute ( x _{1 ,} x _{2 ,} . _ If f _min ≥ f _q , update the optimal solution to P _S,min = P _S,q , and update the corresponding optimal value of the objective function f _min = f _q ; q =1,2, … , 20; r =1, 2, … , 4; Step 38: If the evolutionary algebra of the genetic algorithm is greater than the maximum evolutionary algebra of 200, stop the iteration, and output the optimal solution of the target optimization problem ( x ₀ , y ₀ , dα , dβ ) = P _S,min and its corresponding target The function value d _B,min =min( d _B,q,min ), otherwise the population { P _S,q } at this time is used as the initial population of the next evolution, and jumps to step 34 to continue the optimization.