CN103292654B - A kind of method calculating function size of cylindrical part - Google Patents

Abstract

A method for calculating the effective size of a cylindrical part. This method first measures and obtains the coordinates of the measuring points on the measured cylindrical surface; then gives the initial parameters of the cylinder, projects the measuring points on a plane perpendicular to the axis, and uses the inclusion The translational change of the area calculates the action size of the projection circle, so as to search for the 3 contact points of the containment area; then through the rotation change of the containment area and the change of the cylinder radius, respectively search for the fourth and fifth points in contact with the containment area Measure points; when the number of contact points is greater than or equal to 5, use 4 contact points as a combination, and further change the radius of the cylinder under the condition of maintaining 4 points of contact, and then change to 1 combination, continue to change the radius of the cylinder, and iterate successively Calculate until the criterion is met, and output the optimal value of the cylinder's effective size, cylindricity error and cylinder axis parameters. The invention can accurately calculate the optimal value of the cylinder radius and the cylindricity error satisfying the discrimination criterion of the action surface.

Description

A Method for Calculating Functional Dimensions of Cylindrical Parts

technical field

The invention relates to a method for calculating the functional dimension of a cylindrical part, which belongs to the field of precision measurement and computer application, can be used for the qualification detection of cylindrical geometric products in various situations, and provides guidance for the improvement of the part processing process and processing technology.

Background technique

Cylinder is one of the most common components in mechanical parts. Its precision has an important impact on product quality, performance and service life, and the function size of cylinder is the main technical parameter of cylindrical parts. The largest inscribed cylinder and the smallest circumscribed cylinder are collectively referred to as the active surface of the cylinder, and the radius of the largest inscribed cylinder and the smallest circumscribed cylinder are collectively referred to as the active dimension of the cylinder.

The calculation method of the maximum inscribed cylinder and the minimum circumscribed cylinder is a calculation method established based on the detection principle of the smooth cylinder ring gauge. The largest inscribed cylinder reflects the maximum matching axis that the measured hole can pass through, and the resulting cylindricity error can be regarded as the maximum gap between the measured hole and the largest matching axis; while the smallest circumscribed cylinder reflects the maximum gap between the measured axis The smallest fitting hole that can pass through, the resulting cylindricity error can be regarded as the maximum gap between the measured shaft and the smallest fitting hole.

The calculation of the action size of a cylinder is a non-differentiable complex optimization problem. At present, scholars at home and abroad mainly use traditional optimization methods, intelligent algorithms, and computational geometry methods. Due to the shortcomings of these methods such as poor calculation stability, low calculation efficiency, limited number of sampling points, and difficulty in achieving accurate solutions, it is difficult to apply the maximum inscribed cylinder method and minimum circumscribed cylinder method in actual detection. At present, the mature least square method is generally used in the market to approximate the action size of cylindrical parts.

Contents of the invention

In order to overcome the above-mentioned technical shortcomings, the object of the present invention is to provide a method for calculating the effective size of cylindrical parts. The method not only improves the accuracy of the measurement instrument for measuring the action size of the cylinder, but also has good algorithm stability and high calculation efficiency, and can be extended and applied to the calculation of the action size of the geometric body.

The present invention is a method for calculating the functional size of a cylinder part, which is used to calculate the maximum inscribed size of a cylinder, and mainly includes the following steps:

Step 1: Place the measured cylinder on the measurement platform, measure and obtain points on the surface of the cylinder in the measurement space Cartesian coordinate system , =1,2,…, n represents the number of measuring points and n is a positive integer greater than 5; all measuring points Form a point set .

Step 2: Randomly give the parameters of the cylinder, that is, the axis L direction vector of the cylinder ; Carry out the rotation transformation of the coordinate system, so that the z axis of the coordinate system is parallel to the cylinder axis L direction vector ;After the coordinate transformation, the measured point Projected on the xoy plane to get the measuring point coordinate ;all measuring points Form a point set .

Step 3: In point set , take 3 measuring points arbitrarily, and calculate the circumcenter of the triangle formed by the 3 measuring points , as the center of the circle The initial value of iteration.

Step 4: Calculate the measurement point set in sequence From each measuring point to the center of the circle distance; and record the set of measuring points coordinates from each measuring point to the center of the circle The measurement point corresponding to the minimum distance of the distance, and the contact point set of the boundary of the error tolerance area is obtained .

Step 5: Determine the set of contact points within the boundary of the error tolerance area Is there only 1 touchpoint in ;

If there is only one contact point, the contact point is a valid contact point, and the direction vector of the containment area translation at this time equal to the coordinates of the center of the circle Subtract the contact point coordinates and jump to step 8;

If the number of touch points is greater than 1, skip to the next step.

Step 6: Determine the set of contact points within the boundary of the error tolerance area Is there only 2 touchpoints in ;

If there are only 2 contact points, these 2 contact points are valid contact points, and the direction vector of the containment area translation at this time equal to the coordinates of the center of the circle Subtract the coordinates of the midpoint of the line connecting the two contact points, and skip to step 8;

If the number of touch points is greater than 2, skip to the next step.

Step 7: Calculate individual touchpoints relative center the phase angle of ,

Phase angles of all contact points form a collection ,right The elements in are sorted to get a vector , to calculate the vector 2 adjacent phase angles in Difference,

is the number of touchpoints; calculate ,if , then the acute triangle criterion is met, and skip to step 9; if ,Inquire For the corresponding two contact points, the queried two contact points are valid contact points, and the remaining contact points are invalid contact points. At this time, the direction vector of the containment area translation equal to the coordinates of the center of the circle Subtract 2 from the midpoint coordinates of the line connecting the effective contact points.

Step 8: Calculate the change of containment area in sequence to each non-contact measuring point The virtual position of the center of the circle at the time of contact ;

First calculate each non-contact measuring point separately and one of the effective contact points of the vertical median line, and then calculate the vertical median line and the center of the circle and the direction vector is The intersection point of the straight line, that is, the containment area changes to the measuring point When in contact, the virtual position of the center of the circle , all non-contact measuring points correspond to Form a collection , calculate the corresponding to each non-contact measuring point to the center distance ,all form a collection , in the collection in, remove and The corresponding elements of the opposite direction, and then query the collection The minimum value in is the translational variation of the containment area ;According to the amount of change in the containment area and the moving direction vector , calculate the coordinates of the center of the circle ; Go to step 4.

Step 9: Carry out the coordinate transformation opposite to that in step 2, restore the coordinates of the measuring point to the original value, and calculate Coordinates after coordinate transformation , which is a point on the cylinder axis L , and the cylinder axis L is is the direction vector.

Step 10: Calculate the measurement point set in sequence The distance from each measuring point to the axis L ; and record the measuring point set The minimum value of the distance from each measuring point to the axis L , and the set of measuring points corresponding to the minimum value of the recorded distance is the set of contact points on the inner boundary of the containment area , the minimum recorded distance is the radius R of the cylinder.

Step 11: Determine the set of contact points within the boundary of the containment area Whether the number of touch points in is 3;

If the number of contact points is equal to 3, the coordinate transformation of the contact points makes the z axis of the coordinate system positive and the axis of the cylinder The direction vector of In the same direction and parallel, the contact points are sorted from small to large according to their z-axis coordinates, so that , , The z -axis coordinates of the increase, at this time the direction vector of the error tolerance area rotation change equal to axis direction vector and The vector cross product; set the rotation angle initial value of ; calculate and If the dot product result is equal to 0, go to step 18, if the dot product result is not equal to 0, go to the next step;

If the number of touch points is not 3, go to step 14.

Step 12: Calculate around to rotate vector direction after angle ; Then, project the 3 contact points perpendicular to In the plane of , and calculate the center of the circumcircle of the three contact points, according to the circumcenter and Determine the axis of the rotated cylinder .

Step 13: Calculate all non-contact points to distance ,if , it means that the amount of change is insufficient, and the rotation angle becomes ;Otherwise, the change is too large, and the rest of the non-contact measurement points exceed the containment area, and the rotation angle becomes ;

judge Whether the difference between the two iteration values before and after is less than the set error allowable value; if The difference between the two iteration values before and after is less than the set error allowable value, it means that the fourth contact point is found, then the assigned to , skip to step 10; if The difference between the two iteration values before and after is not less than the set If the allowable value of error is exceeded, then go to step 12.

Step 14: Determine the set of contact points within the boundary of the containment area Whether the number of touch points in is 4;

If the number of contact points equals 4, sets the cylinder radius increment The initial value, jump to the next step;

If the number of touch points is not equal to 4, go to step 17.

Step 15: plus the current cylinder radius get , to get the cylinder after size change, its axis is , each contact point to the axis distance equal to relationship, the following formula is obtained,

in axis The direction vector of axis last point to , is the unknown quantity, and four quaternary nonlinear equations are obtained respectively, and the four unknown quantities can be solved through the nonlinear equation system, and the axis of the cylinder can be obtained .

Step 16: Calculate all non-contact points in sequence to distance , all non-contact measuring points corresponding to Form a set ,if + , it means that the amount of change is insufficient, becomes ;if + , the change is too large, and the rest of the non-contact measuring points exceed the containment area, becomes ;

judge Whether the difference between the two iteration values before and after is less than the set value Allowable value of error; if The difference between the two iteration values before and after is less than the set value Allowable value of error, indicating that the fifth contact point is found, the , The parameters assigned to the axis L respectively , , and judge whether the criterion is satisfied, if so, go to step 18, if not, go to step 10; if The difference between the two iteration values before and after is not less than the set value If the allowable value of error is exceeded, then go to step 15.

Step 17: Determine the set of contact points within the boundary of the containment area Whether the number of contact points is greater than or equal to 5;

If the number of contact points is less than 5, go to step 10;

If the number of contact points is greater than or equal to 5, take 4 of the contact point sets as a combination, and take one of the combinations as the calculation object, and determine it according to the method of tentative micro-adjustment in steps 15 and 16 ;

judge Is it less than the set Allowable value of error; if less than set Allowable error value, judge whether the criterion is met, if yes, jump to step 18, if not, change to another combination, and recalculate , re-judgment, and iterate in turn; if greater than the set Allowable value of error, will be calculated from the Assignment of parameters to the parameters of the cylinder axis L respectively , , and then skip to step 10.

Step 18: Output the parameters of the cylindricity error, the optimal value R of the radius of the cylinder, and the axis L of the cylinder.

In the above method, the steps 3 to 8 can be used alone to calculate the maximum inscribed circularity and functional size of the cross-sectional circle of the revolving body part.

Another method of calculating the active dimension of a cylinder part in the present invention is used to calculate the minimum circumscribed dimension of a cylinder, which is characterized in that it is basically the same as the calculation process of the maximum inscribed dimension, the difference lies in the way of querying the contact point and the size of the containment area Change direction, including the following steps:

Step 1: Place the measured cylinder on the measurement platform, measure and obtain points on the surface of the cylinder in the measurement space Cartesian coordinate system , =1,2,…, n represents the number of measuring points and n is a positive integer greater than 5; all measuring points Form a point set .

Step 2: Randomly give the parameters of the cylinder, that is, the axis L direction vector of the cylinder ; Carry out the rotation transformation of the coordinate system, so that the z axis of the coordinate system is parallel to the cylinder axis L direction vector ;After the coordinate transformation, the measured point Projected on the xoy plane to get the measuring point coordinate ;all measuring points Form a point set .

Step 3: In point set , take 3 measuring points arbitrarily, and calculate the circumcenter of the triangle formed by the 3 measuring points , as the center of the circle The initial value of iteration.

Step 4: Calculate the measurement point set in sequence From each measuring point to the center of the circle distance; and record the set of measuring points coordinates from each measuring point to the center of the circle The measurement point corresponding to the maximum distance of the distance, and the contact point set of the outer boundary of the error tolerance area is obtained .

Step 5: Determine the set of contact points on the outer boundary of the error tolerance area Is there only 1 touchpoint in ;

If there is only one contact point, the contact point is a valid contact point, and the direction vector of the containment area translation at this time It is equal to the coordinates of the contact point minus the coordinates of the center of the circle , jump to step 8;

If the number of touch points is greater than 1, skip to the next step.

Step 6: Determine the set of contact points on the outer boundary of the error tolerance area Is there only 2 touchpoints in ;

If there are only 2 contact points, these 2 contact points are valid contact points, and the direction vector of the containment area translation at this time It is equal to the coordinates of the midpoint of the line connecting the two contact points minus the coordinates of the center of the circle , jump to step 8;

If the number of touch points is greater than 2, skip to the next step.

Step 7: Calculate individual touchpoints relative center the phase angle of ,

Phase angles of all contact points form a collection ,right The elements in are sorted to get a vector , to calculate the vector 2 adjacent phase angles in Difference,

is the number of touchpoints; calculate ,if , then the acute triangle criterion or the diameter criterion is met, and skip to step 9; if ,Inquire For the corresponding two contact points, the queried two contact points are valid contact points, and the remaining contact points are invalid contact points. At this time, the direction vector of the containment area translation It is equal to the coordinates of the midpoint of the line between two effective contact points minus the center of the circle coordinate.

Step 8: Calculate the change of containment area in sequence to each non-contact measuring point The virtual position of the center of the circle at the time of contact ;

First calculate each non-contact measuring point separately and one of the effective contact points of the vertical median line, and then calculate the vertical median line and the center of the circle and the direction vector is The intersection point of the straight line, that is, the containment area changes to the measuring point When in contact, the virtual position of the center of the circle , all non-contact measuring points correspond to Form a set , calculate the corresponding to each non-contact measuring point to the center distance ,all form a collection , in the collection in, remove and The corresponding elements of the opposite direction, and then query the collection The minimum value in is the translational variation of the containment area ;According to the amount of change in the containment area and the moving direction vector , calculate the coordinates of the center of the circle ; Go to step 4.

Step 9: Carry out the coordinate transformation opposite to that in step 2, restore the coordinates of the measuring point to the original value, and calculate Coordinates after coordinate transformation , which is a point on the cylinder axis L , and the cylinder axis L is is the direction vector.

Step 10: Calculate the measurement point set in sequence The distance from each measuring point to the axis L ; and record the measuring point set The maximum value of the distance from each measuring point to the axis L , and the set of measuring points corresponding to the maximum recorded distance is the set of contact points on the outer boundary of the containment area , the maximum recorded distance is the radius R of the cylinder.

Step 11: Determine the set of contact points on the outer boundary of the containment area Whether the number of touch points in is 3;

If the number of contact points is equal to 3, the coordinate transformation of the contact points makes the z axis of the coordinate system positive and the axis of the cylinder The direction vector of In the same direction and parallel, the contact points are sorted from small to large according to their z-axis coordinates, so that , , The z -axis coordinates of the increase, at this time the direction vector of the error tolerance area rotation change equal to axis direction vector and The vector cross product; set the rotation angle initial value of ; calculate and If the dot product result is equal to 0, go to step 18, if the dot product result is not equal to 0, go to the next step;

If the number of touch points is not 3, go to step 14.

Step 12: Calculate around to rotate vector direction after angle ; Then, project the 3 contact points perpendicular to In the plane of , and calculate the center of the circumcircle of the three contact points, according to the circumcenter and Determine the axis of the rotated cylinder .

Step 13: Compute all non-contact points to distance ,if , it means that the amount of change is insufficient, and the rotation angle becomes ;if , the change is too large, the rest of the non-contact measuring points are beyond the containment area, the rotation angle becomes ;

judge Whether the difference between the two iteration values before and after is less than the set error allowable value; if The difference between the two iteration values before and after is less than the set error allowable value, it means that the fourth contact point is found, then the assigned to , skip to step 10; if The difference between the two iteration values before and after is not less than the set If the allowable value of error is exceeded, then go to step 12.

Step 14: Determine the set of contact points on the outer boundary of the containment area Whether the number of touch points in is 4;

If the number of contact points is equal to 4, set the cylinder radius reduction amount The initial value, jump to the next step;

If the number of touch points is not equal to 4, go to step 17.

Step 15: Subtract the current cylinder radius get , to get the cylinder after size change, its axis is , each contact point to the axis distance equal to relationship, the following formula is obtained,

in axis The direction vector of axis last point to , is the unknown quantity, and four quaternary nonlinear equations are obtained respectively, and the four unknown quantities can be solved through the nonlinear equation system, and the axis of the cylinder can be obtained .

Step 16: Calculate all non-contact points in sequence to distance , all non-contact measuring points corresponding to Form a collection ,if + , it means that the amount of change is insufficient, becomes ;if + , the change is too large, and the rest of the non-contact measuring points exceed the containment area, becomes ;

judge Whether the difference between the two iteration values before and after is less than the set value Allowable value of error; if The difference between the two iteration values before and after is less than the set value Allowable value of error, indicating that the fifth contact point is found, the , The parameters assigned to the axis L respectively , , and judge whether the criterion is satisfied, if so, go to step 18, if not, go to step 10; if The difference between the two iteration values before and after is not less than the set value If the allowable value of error is exceeded, then go to step 15.

Step 17: Determine the set of contact points on the outer boundary of the containment area Whether the number of contact points is greater than or equal to 5;

If the number of contact points is less than 5, go to step 10;

If the number of contact points is greater than or equal to 5, take 4 of the contact point sets as a combination, and take one of the combinations as the calculation object, and determine it according to the method of tentative micro-adjustment in steps 15 and 16 ;

judge Is it less than the set Allowable value of error; if less than set Allowable error value, judge whether the criterion is met, if yes, jump to step 18, if not, change to another combination, and recalculate , re-judgment, and iterate in turn; if greater than the set Allowable value of error, will be calculated from the Assignment of parameters to the parameters of the cylinder axis L respectively , , and then skip to step 10.

Step 18: Output the parameters of the cylindricity error, the optimal value R of the radius of the cylinder, and the axis L of the cylinder.

In the above method, the steps 3 to 8 can be used alone to calculate the minimum circumscribed circularity and functional size of the cross-sectional circle of the revolving body part.

In the above method, the said technical solution can calculate the straightness in any direction in space.

In the above method, the step 3 to step 8 can calculate the line-to-line parallelism error in any direction. Firstly, carry out coordinate rotation transformation so that the direction vector of the reference line is parallel to z , and at the same time, the discrete points of the measured line are rotated correspondingly. At this time, the enclosing cylinder of the measured line is projected as a circle in the xoy plane. Then step 3 to step 8 described in the above method can be applied to fit the discrete point projection of the measured line.

In the above method, the above-mentioned step 3 to step 8 can calculate the perpendicularity error between lines in any direction. First, carry out coordinate rotation transformation, so that the normal vector of the datum plane is parallel to z , and at the same time, the discrete points of the measured line are rotated correspondingly. At this time, the containing cylinder of the measured line is projected as a circle in the xoy plane. Then step 3 to step 8 described in the above method can be applied to fit the discrete point projection of the measured line.

According to the characteristics of the cylinder itself, the invention performs corresponding translational changes, rotational changes or translational changes on the containment area in the optimization direction of the cylinder radius, and finally calculates the optimal value of the cylindrical parameters and the optimal value of the cylindricity error.

The beneficial effects of the present invention are:

The calculated cylinder radius is the optimal value, the relative position of the contact point meets the criterion, the calculation stability is good, and the calculation efficiency is high.

For those skilled in the art, based on and applying the concepts disclosed in the present invention, various modifications and changes can be easily made to the solution of the present invention. It should be noted that all these modifications and changes should belong to the scope of the present invention.

Description of drawings

Fig. 1 is a flow chart of calculating the maximum inscribed radius of a cylinder according to the present invention.

Fig. 2 is a calculation effect diagram of the maximum inscribed radius of the cylinder of the present invention.

Fig. 3 is a calculation effect diagram of the minimum circumscribed radius of the cylinder of the present invention.

Detailed ways

Example 1:

A method for calculating the effective size of a cylinder part, which is used to calculate the maximum inscribed size of a cylinder, as shown in Figure 1, includes the following steps:

Step 1: Place the measured cylinder on the measurement platform, measure and obtain points on the surface of the cylinder in the measurement space Cartesian coordinate system , =1,2,…, n represents the number of measuring points and n is a positive integer greater than 5; all measuring points Form a point set .

Step 2: Randomly give the parameters of the cylinder, that is, the axis L direction vector of the cylinder ; Carry out the rotation transformation of the coordinate system, so that the z axis of the coordinate system is parallel to the cylinder axis L direction vector ;After the coordinate transformation, the measured point Projected on the xoy plane to get the measuring point coordinate ;all measuring points Form a point set .

Step 3: In point set , take 3 measuring points arbitrarily, and calculate the circumcenter of the triangle formed by the 3 measuring points , as the center of the circle The initial value of iteration.

Step 4: Calculate the measurement point set in sequence From each measuring point to the center of the circle distance; and record the set of measuring points coordinates from each measuring point to the center of the circle The measurement point corresponding to the minimum distance of the distance, and the contact point set of the boundary of the error tolerance area is obtained .

Step 5: Determine the set of contact points within the boundary of the error tolerance area Is there only 1 touchpoint in ;

If there is only one contact point, the contact point is a valid contact point, and the direction vector of the containment area translation at this time equal to the coordinates of the center of the circle Subtract the contact point coordinates and jump to step 8;

If the number of touch points is greater than 1, skip to the next step.

Step 6: Determine the set of contact points within the boundary of the error tolerance area Is there only 2 touchpoints in ;

If there are only 2 contact points, these 2 contact points are valid contact points, and the direction vector of the containment area translation at this time equal to the coordinates of the center of the circle Subtract the coordinates of the midpoint of the line connecting the two contact points, and skip to step 8;

If the number of touch points is greater than 2, skip to the next step.

Step 7: Calculate individual touchpoints relative center the phase angle of ,

Phase angles of all contact points form a set ,right The elements in are sorted to get a vector , to calculate the vector 2 adjacent phase angles in Difference,

is the number of touchpoints; calculate ,if , then the acute triangle criterion is met, and skip to step 9; if ,Inquire For the corresponding two contact points, the queried two contact points are valid contact points, and the remaining contact points are invalid contact points. At this time, the direction vector of the containment area translation equal to the coordinates of the center of the circle Subtract 2 from the midpoint coordinates of the line connecting the effective contact points.

Step 8: Calculate the change of containment area in sequence to each non-contact measuring point The virtual position of the center of the circle at the time of contact ;

First calculate each non-contact measuring point separately and one of the effective contact points of the vertical median line, and then calculate the vertical median line and the center of the circle and the direction vector is The intersection point of the straight line, that is, the containment area changes to the measuring point When in contact, the virtual position of the center of the circle , all non-contact measuring points correspond to Form a collection , calculate the corresponding to each non-contact measuring point to the center distance ,all form a collection , in the collection in, remove and The corresponding elements of the opposite direction, and then query the collection The minimum value in is the translational variation of the containment area ;According to the amount of change in the containment area and the moving direction vector , calculate the coordinates of the center of the circle ; Go to step 4.

Step 9: Carry out the coordinate transformation opposite to that in step 2, restore the coordinates of the measuring point to the original value, and calculate Coordinates after coordinate transformation , which is a point on the cylinder axis L , and the cylinder axis L is is the direction vector.

Step 10: Calculate the measurement point set in sequence The distance from each measuring point to the axis L ; and record the measuring point set The minimum value of the distance from each measuring point to the axis L , and the set of measuring points corresponding to the minimum value of the recorded distance is the set of contact points on the inner boundary of the containment area , the minimum recorded distance is the radius R of the cylinder.

Step 11: Determine the set of contact points within the boundary of the containment area Whether the number of touch points in is 3;

If the number of contact points is equal to 3, the coordinate transformation of the contact points makes the z axis of the coordinate system positive and the axis of the cylinder The direction vector of In the same direction and parallel, the contact points are sorted from small to large according to their z-axis coordinates, so that , , The z -axis coordinates of the increase, at this time the direction vector of the error tolerance area rotation change equal to axis direction vector and The vector cross product; set the rotation angle initial value of ; calculate and If the dot product result is equal to 0, go to step 18, if the dot product result is not equal to 0, go to the next step;

If the number of touch points is not 3, go to step 14.

Step 12: Calculate around to rotate vector direction after angle ; Then, project the 3 contact points perpendicular to In the plane of , and calculate the center of the circumcircle of the three contact points, according to the circumcenter and Determine the axis of the rotated cylinder .

Step 13: Calculate all non-contact points to distance ,if , it means that the amount of change is insufficient, and the rotation angle becomes ;Otherwise, the change is too large, and the rest of the non-contact measurement points exceed the containment area, and the rotation angle becomes ;

judge Whether the difference between the two iteration values before and after is less than the set error allowable value; if The difference between the two iteration values before and after is less than the set error allowable value, it means that the fourth contact point is found, then the assigned to , skip to step 10; if The difference between the two iteration values before and after is not less than the set If the allowable value of error is exceeded, then go to step 12.

Step 14: Determine the set of contact points within the boundary of the containment area Whether the number of touch points in is 4;

If the number of contact points equals 4, sets the cylinder radius increment The initial value, jump to the next step;

If the number of touch points is not equal to 4, go to step 17.

Step 15: plus the current cylinder radius get , to get the cylinder after size change, its axis is , each contact point to the axis distance equal to relationship, the following formula is obtained,

in axis The direction vector of axis last point to , is the unknown quantity, and four quaternary nonlinear equations are obtained respectively, and the four unknown quantities can be solved through the nonlinear equation system, and the axis of the cylinder can be obtained .

Step 16: Calculate all non-contact points in sequence to distance , all non-contact measuring points corresponding to Form a collection ,if + , it means that the amount of change is insufficient, becomes ;if + , the change is too large, and the rest of the non-contact measuring points exceed the containment area, becomes ;

judge Whether the difference between the two iteration values before and after is less than the set value Allowable value of error; if The difference between the two iteration values before and after is less than the set value Allowable value of error, indicating that the fifth contact point is found, the , The parameters assigned to the axis L respectively , , substituting each contact point into the following formula,

in as touch point The phase angle relative to the axis, so that each contact point corresponds to , construct the following discriminant function,

is the feasible region determined by the following set of inequalities:

In the above formula, the first constraint is the vector equation, Represents a 4-dimensional zero-column vector, the second and third constraints are numerical equations, is the number of contact points, and the judgment is the optimal solution discriminant value is equal to 0, if Equal to 0 means that the criterion is satisfied, jump to step 18, if If it is not equal to 0, it means that the judgment criterion is not satisfied, and jump to step 10; if The difference between the two iteration values before and after is not less than the set value If the allowable value of error is exceeded, then go to step 15.

Step 17: Determine the set of contact points within the boundary of the containment area Whether the number of contact points is greater than or equal to 5;

If the number of contact points is less than 5, go to step 10;

If the number of contact points is greater than or equal to 5, take 4 of the contact point sets as a combination, and take one of the combinations as the calculation object, and determine it according to the method of tentative micro-adjustment in steps 15 and 16 ;

judge Is it less than the set Allowable value of error; if less than set Allowable error value, apply the method of step 16 to judge whether the criterion is satisfied, if so, jump to step 18, if not, change a combination and recalculate , re-judgment, and iterate in turn; if greater than the set Allowable value of error, will be calculated from the Assignment of parameters to the parameters of the cylinder axis L respectively , , and then skip to step 10.

Step 18: Output the parameters of the cylindricity error, the optimal value R of the radius of the cylinder, and the axis L of the cylinder.

The validity of the calculation of the method announced by the present invention is illustrated below through an experimental example.

On the measuring platform, 24 points are obtained on the surface of the cylindrical part, and the coordinates of the measuring points are shown in Table 1.应用本发明所公布的方法，计算出最大内接圆柱的作用半径为14.99985062mm，圆柱轴线方向矢量(-0.000459923841223342,-0.000624025400837475,0.999999699531135)，圆柱轴线上一点坐标为(432.422127159553,137.332674827430,0.252514286852374)，圆柱The degree is 0.03418mm. The calculated effect is shown in Figure 2 (in the figure, * is the measuring point, O is the contact point), and the 5th, 10th, 14th, 16th and 17th measuring points are the contact points. Calculate each touchpoint separately Map, and calculate the discriminant value J of the optimal solution. After calculation, J = 1.1382e-014, which meets the discriminant criterion. The calculated cylinder action radius and cylindricity error are the optimal solution.

Table 1 The measuring point coordinates of the cylinder (unit: mm )

Measurement point number x -coordinate y- coordinate z coordinate Measurement point number x -coordinate y- coordinate z coordinate 1 447.47556 137.3431 -92.99958 13 447.48749 137.37276 -85.66769 2 440.00617 150.36197 -93.05586 14 439.98814 150.36122 -85.7225 3 424.95893 150.38625 -93.05948 15 424.97535 150.38594 -85.72581 4 417.45656 137.3433 -93.00753 16 417.4618 137.37364 -85.67423 5 425.00292 124.3788 -92.95196 17 424.98576 124.38214 -85.61846 6 439.9693 124.38485 -92.9484 18 439.98586 124.38661 -85.61504 7 439.98027 124.38204 -89.28298 19 439.99686 124.38255 -81.94842 8 424.99233 124.37691 -89.28517 20 424.96931 124.37052 -81.95173 9 417.46167 137.3578 -89.34018 twenty one 417.459 137.38801 -82.007 10 424.96768 150.38132 -89.3926 twenty two 424.96877 150.40734 -82.05929 11 439.9954 150.36113 -89.38932 twenty three 439.98606 150.37835 -82.05603 12 447.48307 137.35783 -89.33457 twenty four 447.49399 137.38793 -82.0014

Example 2:

A method for calculating the effective size of a cylindrical part, when used to calculate the minimum circumscribed size of a cylindrical body, includes the following steps:

Step 1: Place the measured cylinder on the measurement platform, measure and obtain points on the surface of the cylinder in the measurement space Cartesian coordinate system , =1,2,…, n represents the number of measuring points and n is a positive integer greater than 5; all measuring points Form a point set .

Step 2: Randomly give the parameters of the cylinder, that is, the axis L direction vector of the cylinder ; Carry out the rotation transformation of the coordinate system, so that the z axis of the coordinate system is parallel to the cylinder axis L direction vector ;After the coordinate transformation, the measured point Projected on the xoy plane to get the measuring point coordinate ;all measuring points Form a point set .

Step 3: In point set , take 3 measuring points arbitrarily, and calculate the circumcenter of the triangle formed by the 3 measuring points , as the center of the circle The initial value of iteration.

Step 4: Calculate the measurement point set in sequence From each measuring point to the center of the circle distance; and record the set of measuring points coordinates from each measuring point to the center of the circle The measurement point corresponding to the maximum distance of the distance, and the contact point set of the outer boundary of the error tolerance area is obtained .

Step 5: Determine the set of contact points on the outer boundary of the error tolerance area Is there only 1 touchpoint in ;

If there is only one contact point, the contact point is a valid contact point, and the direction vector of the containment area translation at this time It is equal to the coordinates of the contact point minus the coordinates of the center of the circle , jump to step 8;

If the number of touch points is greater than 1, skip to the next step.

Step 6: Determine the set of contact points on the outer boundary of the error tolerance area Is there only 2 touchpoints in ;

If there are only 2 contact points, these 2 contact points are valid contact points, and the direction vector of the containment area translation at this time It is equal to the coordinates of the midpoint of the line connecting the two contact points minus the coordinates of the center of the circle , jump to step 8;

If the number of touch points is greater than 2, skip to the next step.

Step 7: Calculate individual touchpoints relative center the phase angle of ,

Phase angles of all contact points form a set ,right The elements in are sorted to get a vector , to calculate the vector 2 adjacent phase angles in Difference,

is the number of touchpoints; calculate ,if , then the acute triangle criterion or the diameter criterion is met, and skip to step 9; if ,Inquire For the corresponding two contact points, the queried two contact points are valid contact points, and the remaining contact points are invalid contact points. At this time, the direction vector of the containment area translation It is equal to the coordinates of the midpoint of the line between two effective contact points minus the center of the circle coordinate.

Step 8: Sequentially calculate the containment area changes to each non-contact measuring point The virtual position of the center of the circle at the time of contact ;

First calculate each non-contact measuring point separately and one of the effective contact points of the vertical median line, and then calculate the vertical median line and the center of the circle and the direction vector is The intersection point of the straight line, that is, the containment area changes to the measuring point When in contact, the virtual position of the center of the circle , all non-contact measuring points correspond to Form a set , calculate the corresponding to each non-contact measuring point to the center distance ,all form a collection , in the collection in, remove and The corresponding elements of the opposite direction, and then query the collection The minimum value in is the translational variation of the containment area ;According to the amount of change in the containment area and the moving direction vector , calculate the coordinates of the center of the circle ; Go to step 4.

Step 9: Carry out the coordinate transformation opposite to that in step 2, restore the coordinates of the measuring point to the original value, and calculate Coordinates after coordinate transformation , which is a point on the cylinder axis L , and the cylinder axis L is is the direction vector.

Step 10: Calculate the measurement point set in sequence The distance from each measuring point to the axis L ; and record the measuring point set The maximum value of the distance from each measuring point to the axis L , and the set of measuring points corresponding to the maximum recorded distance is the set of contact points on the outer boundary of the containment area , the maximum recorded distance is the radius R of the cylinder.

Step 11: Determine the set of contact points on the outer boundary of the containment area Whether the number of touch points in is 3;

If the number of contact points is equal to 3, the coordinate transformation of the contact points makes the z axis of the coordinate system positive and the axis of the cylinder The direction vector of In the same direction and parallel, the contact points are sorted from small to large according to their z-axis coordinates, so that , , The z -axis coordinates of the increase, at this time the direction vector of the error tolerance area rotation change equal to axis direction vector and The vector cross product; set the rotation angle initial value of ; calculate and If the dot product result is equal to 0, go to step 18, if the dot product result is not equal to 0, go to the next step;

If the number of touch points is not 3, go to step 14.

Step 12: Calculate around to rotate vector direction after angle ; Then, project the 3 contact points perpendicular to In the plane of , and calculate the center of the circumcircle of the three contact points, according to the circumcenter and Determine the axis of the rotated cylinder .

Step 13: Compute all non-contact points to distance ,if , it means that the amount of change is insufficient, and the rotation angle becomes ;if , the change is too large, the rest of the non-contact measuring points are beyond the containment area, the rotation angle becomes ;

judge Whether the difference between the two iteration values before and after is less than the set error allowable value; if The difference between the two iteration values before and after is less than the set error allowable value, it means that the fourth contact point is found, then the assigned to , skip to step 10; if The difference between the two iteration values before and after is not less than the set If the allowable value of error is exceeded, then go to step 12.

Step 14: Determine the set of contact points on the outer boundary of the containment area Whether the number of touch points in is 4;

If the number of contact points is equal to 4, set the cylinder radius reduction amount The initial value, jump to the next step;

If the number of touch points is not equal to 4, go to step 17.

Step 15: Subtract the current cylinder radius get , to get the cylinder after size change, its axis is , each contact point to the axis distance equal to relationship, the following formula is obtained,

in axis The direction vector of axis last point to , is the unknown quantity, and four quaternary nonlinear equations are obtained respectively, and the four unknown quantities can be solved through the nonlinear equation system, and the axis of the cylinder can be obtained .

Step 16: Calculate all non-contact points in sequence to distance , all non-contact measuring points corresponding to Form a set ,if + , it means that the amount of change is insufficient, becomes ;if + , the change is too large, and the rest of the non-contact measuring points exceed the containment area, becomes ;

judge Whether the difference between the two iteration values before and after is less than the set value Allowable value of error; if The difference between the two iteration values before and after is less than the set value Allowable value of error, indicating that the fifth contact point is found, the , The parameters assigned to the axis L respectively , , and apply the method of step 16 in Embodiment 1 to judge whether the criterion is satisfied, if it is satisfied, then jump to step 18, if it does not meet the criterion, jump to step 10; if The difference between the two iteration values before and after is not less than the set value If the allowable value of error is exceeded, then go to step 15.

Step 17: Determine the set of contact points on the outer boundary of the containment area Whether the number of contact points is greater than or equal to 5;

If the number of contact points is less than 5, go to step 10;

If the number of contact points is greater than or equal to 5, take 4 of the contact point sets as a combination, and take one of the combinations as the calculation object, and determine it according to the method of tentative micro-adjustment in steps 15 and 16 ;

judge Is it less than the set Allowable value of error; if less than set Allowable value of error, apply the method of step 16 in embodiment 1, judge whether to meet the criterion of discrimination, if satisfied then jump to step 18, if not satisfy the criterion of discrimination, change 1 combination, recalculate , re-judgment, and iterate in turn; if greater than the set Allowable value of error, will be calculated from the Assignment of parameters to the parameters of the cylinder axis L respectively , , and then skip to step 10.

Step 18: Output the parameters of the cylindricity error, the optimal value R of the radius of the cylinder, and the axis L of the cylinder.

The validity of the calculation of the method announced by the present invention is illustrated below through an experimental example.

On the measuring platform, 24 points are obtained on the surface of the cylindrical part, and the coordinates of the measuring points are shown in Table 2.应用本发明所公布的方法，计算出最大内接圆柱的作用半径为11.9990887mm，圆柱轴线方向矢量(0.00111825745503225,0.000306176357337651,0.999999327877925)，圆柱轴线上一点坐标为(404.550573605996,126.630909902755,0.0446863090043053)，圆柱度为0.01475mm. The calculated effect is shown in attached drawing 3 (in the figure, * is the measuring point, ☆ is the contact point), and the 1st, 5th, 14th, 19th and 20th measuring points are the contact points. Calculate each touchpoint separately Map, and calculate the discriminant value J of the optimal solution. After calculating J = 2.5931e-014, it meets the discriminant criterion, and the calculated cylinder action radius and cylindricity error are the optimal solution.

Table 2 Measuring point coordinates of the cylinder (unit: mm )

Measurement point number x -coordinate y- coordinate z coordinate Measurement point number x -coordinate y- coordinate z coordinate 1 416.50196 126.62207 -42.61907 13 416.50921 126.6223 -35.28499 2 410.49696 137.01158 -42.60984 14 410.50862 137.01277 -35.27656 3 398.50797 136.99947 -42.59217 15 398.51415 137.00824 -35.25898 4 392.51838 126.62312 -42.58308 16 392.51911 126.62285 -35.24976 5 398.49642 116.23034 -42.59151 17 398.50985 116.23174 -35.25818 6 410.49805 116.22964 -42.60937 18 410.50947 116.22875 -35.27604 7 410.50638 116.22778 -38.94272 19 410.51541 116.2301 -31.6094 8 398.50449 116.23247 -38.92521 20 398.51512 116.23001 -31.59186 9 392.52266 126.62223 -38.91647 twenty one 392.51775 126.62182 -31.58326 10 398.50907 137.00335 -38.9252 twenty two 398.51751 137.0105 -31.59181 11 410.50058 137.01238 -38.94329 twenty three 410.51169 137.01117 -31.60976 12 416.50494 126.62223 -38.95278 twenty four 416.51224 126.62176 -31.61957

Claims (2)

1. calculate a method for function size of cylindrical part, connecing size for calculating cylindrical most imperial palace, it is characterized in that, comprise the steps:

Step 1: be placed on measuring table by tested cylinder, measures and obtains the point on periphery in measurement space rectangular coordinate system , =1,2 ..., nrepresent measure-point amount and nfor being greater than the positive integer of 5; All measuring points form measuring point collection ;

Step 2: the parameter providing cylinder at random, the i.e. axis of cylinder ldirection vector ; Carry out the rotational transform of coordinate system, make coordinate system zaxle is parallel to cylinder axis ldirection vector ; After coordinate transform, by measuring point be projected in xoyin plane, obtain measuring point coordinate ; All measuring points form measuring point collection ;

Step 3: at point set in, arbitrarily take out 3 measuring points, and calculate 3 measuring points and form leg-of-mutton circumcenter , as the center of circle iteration initial value;

Step 4: calculate measuring point collection successively in each measuring point to the center of circle distance; And record measuring point collection in each measuring point to central coordinate of circle measuring point corresponding to the minor increment of distance, obtains the contact point set of error containment region inner boundary ;

Step 5: the contact point set of error in judgement containment region inner boundary in whether only have 1 contact point;

If only have 1 contact point, then this contact point is the direction vector of effective contact point, now containment region translation equal central coordinate of circle deduct contact point coordinate, jump to step 8;

If contact point quantity is greater than 1, then jump to next step;

Step 6: the contact point set of error in judgement containment region inner boundary in whether only have 2 contact points;

If only have 2 contact points, then these 2 contact points are the direction vector of effective contact point, now containment region translation equal central coordinate of circle deduct the middle point coordinate of 2 contact point lines, jump to step 8;

If contact point quantity is greater than 2, then jump to next step;

Step 7: calculate each contact point the relative center of circle phasing degree ,

The phasing degree had point of contact form set , right in element sort, obtain vector , compute vector in adjacent 2 phasing degree difference,

for the quantity of contact point; Calculate if, , then meet oxygon criterion, jump to step 9; If , inquiry 2 corresponding contact points, 2 the effective contact points of contact point inquired, all the other contact points are the direction vector of invalid contact point, now containment region translation equal central coordinate of circle deduct the middle point coordinate of 2 effective contact point lines;

Step 8: calculate containment region successively and vary to and each noncontact measuring point center of circle virtual location during contact ;

First each noncontact measuring point is calculated respectively with the vertical centering control separated time of one of them effective contact point, then calculate vertical centering control separated time and cross the center of circle and direction vector is the intersection point of straight line, be containment region and vary to and this measuring point during contact, the virtual location in the center of circle , all noncontact measuring points are corresponding composition set , calculate each noncontact measuring point corresponding to the center of circle distance , all form set , in set in, reject with incorgruous corresponding element, then query set in minimum value, be the translation variation of containment region ; According to containment region variation and moving direction vector , calculate the coordinate in the center of circle ; Forward step 4 to;

Step 9: carry out the coordinate transform with contrary in step 2, measuring point coordinate reverts to original value, calculates coordinate after coordinate transform , to be on cylinder axis L a bit, cylinder axis L with for direction vector;

Step 10: calculate measuring point collection successively in each measuring point to axis ldistance; And record measuring point collection in each measuring point to axis lthe minimum value of distance, test points set corresponding to institute's recording distance minimum value is the contact point set of containment region inner boundary , the minimum value of institute's recording distance is the radius of cylinder r;

Step 11: the contact point set judging containment region inner boundary whether the quantity of middle contact point is 3;

If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out, makes coordinate system zaxle forward and cylinder axis direction vector in the same way and parallel, butt contact carries out ascending sequence by its z-axis coordinate, makes , , 's zaxial coordinate increases progressively, and now error containment region rotates the direction vector of variation equal axis direction vector with vector multiplication cross; Arrange and rotate variation angle initial value; Calculate with dot product, if dot product result equals 0, jump to step 18, if dot product result is not equal to 0, jump to next step;

If the quantity of contact point is not 3, jump to step 14;

Step 12: calculate around rotate direction vector after angle ; Then, 3 contact points are projected in perpendicular to plane in, and calculate the center of circle of the circumscribed circle of 3 contact points, according to circumcenter with determine the axis of postrotational cylinder ;

Step 13: calculate all noncontacts point and arrive distance if, , then represent that variation is not enough, the anglec of rotation become ; Otherwise change excessive, all the other noncontact measuring points exceed containment region, the anglec of rotation become ;

Judge whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If before and after the difference of iterative value of twice be less than setting error permissible value, then illustrate and find the 4th contact point, then will assignment is given , jump to step 10; If before and after the difference of iterative value of twice be not less than setting error permissible value, then jump to step 12;

Step 14: the contact point set judging containment region inner boundary whether the quantity of middle contact point is 4;

If the quantity of contact point equals 4, setting cylindrical radius recruitment initial value, jump to next step;

If the quantity of contact point is not equal to 4, then jump to step 17;

Step 15: add current cylindrical radius obtain , obtain cylinder after dimensional variations, its axis is , according to 4 contact points to axis distance equal relation, with axis direction vector, axis upper is some unknown quantity, obtains 4 quaternary nonlinear equations respectively, can be obtained the axis of cylinder by Nonlinear System of Equations direction vector, axis on a bit;

Step 16: calculate all noncontacts point successively and arrive distance , all noncontact measuring points are corresponding composition set if, + , then represent that variation is not enough, become ; If + , then change excessive, all the other noncontact measuring points exceed containment region, become ;

Judge before and after the difference of iterative value of 2 times whether be less than setting error permissible value; If before and after the difference of iterative value of 2 times be less than setting error permissible value, illustrates and finds the 5th contact point, will direction vector, axis upper some difference assignment is to axis lparameter , , and judge whether to meet criterion, if meet, jump to step 18, if do not meet criterion, jump to step 10; If before and after the difference of iterative value of 2 times be not less than setting error permissible value, then jump to step 15;

Step 17: the contact point set judging containment region inner boundary whether the quantity of middle contact point is more than or equal to 5;

If the quantity of contact point is less than 5, jump to step 10;

If the quantity of contact point is more than or equal to 5, with in contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, according in step 15,16 exploratory trace adjustment method determine ;

Judge whether to be less than setting error permissible value; If be less than setting error permissible value, judges whether to meet criterion, if met, jumps to step 18, if do not meet criterion, changes 1 combination, recalculate , re-start judgement, iteration is gone down successively; If be greater than setting error permissible value, by what calculate parameter assignment respectively give cylinder axis lparameter , , then jump to step 10;

Step 18: the optimal value exporting deviation from cylindrical form, cylindrical radius rand cylinder axis lparameter.

2. calculate a method for function size of cylindrical part, for calculating cylindrical minimum external size, it is characterized in that, comprise the steps:

Step 1: be placed on measuring table by tested cylinder, measures and obtains the point on periphery in measurement space rectangular coordinate system , =1,2 ..., nrepresent measure-point amount and nfor being greater than the positive integer of 5; All measuring points form measuring point collection ;

Step 2: the parameter providing cylinder at random, the i.e. axis of cylinder ldirection vector ; Carry out the rotational transform of coordinate system, make coordinate system zaxle is parallel to cylinder axis ldirection vector ; After coordinate transform, by measuring point be projected in xoyin plane, obtain measuring point coordinate ; All measuring points form measuring point collection ;

Step 3: at point set in, arbitrarily take out 3 measuring points, and calculate 3 measuring points and form leg-of-mutton circumcenter , as the center of circle iteration initial value;

Step 4: calculate measuring point collection successively in each measuring point to the center of circle distance; And record measuring point collection in each measuring point to central coordinate of circle measuring point corresponding to the ultimate range of distance, obtains the contact point set that error contains area outer ;

Step 5: the contact point set of error in judgement containment region outer boundary in whether only have 1 contact point;

If only have 1 contact point, then this contact point is the direction vector of effective contact point, now containment region translation equal contact point coordinate and deduct central coordinate of circle , jump to step 8;

If contact point quantity is greater than 1, then jump to next step;

Step 6: the contact point set of error in judgement containment region outer boundary in whether only have 2 contact points;

If only have 2 contact points, then these 2 contact points are the direction vector of effective contact point, now containment region translation the middle point coordinate equaling 2 contact point lines deducts central coordinate of circle , jump to step 8;

If contact point quantity is greater than 2, then jump to next step;

Step 7: calculate each contact point the relative center of circle phasing degree ,

The phasing degree had point of contact form set , right in element sort, obtain vector , compute vector in adjacent 2 phasing degree difference,

for the quantity of contact point; Calculate if, , then meet oxygon criterion or diameter criterion, jump to step 9; If , inquiry 2 corresponding contact points, 2 the effective contact points of contact point inquired, all the other contact points are the direction vector of invalid contact point, now containment region translation the middle point coordinate equaling 2 effective contact point lines deducts the center of circle coordinate;

Step 8: calculate containment region successively and vary to and each noncontact measuring point center of circle virtual location during contact ;

First each noncontact measuring point is calculated respectively with the vertical centering control separated time of one of them effective contact point, then calculate vertical centering control separated time and cross the center of circle and direction vector is the intersection point of straight line, be containment region and vary to and this measuring point during contact, the virtual location in the center of circle , all noncontact measuring points are corresponding composition set , calculate each noncontact measuring point corresponding to the center of circle distance , all form set , in set in, reject with incorgruous corresponding element, then query set in minimum value, be the translation variation of containment region ; According to containment region variation and moving direction vector , calculate the coordinate in the center of circle ; Forward step 4 to;

Step 9: carry out the coordinate transform with contrary in step 2, measuring point coordinate reverts to original value, calculates coordinate after coordinate transform , be cylinder axis lon a bit, cylinder axis lwith for direction vector;

Step 10: calculate measuring point collection successively in each measuring point to axis ldistance; And record measuring point collection in each measuring point to axis lthe maximal value of distance, test points set corresponding to institute's recording distance maximal value is the contact point set of containment region outer boundary , the maximal value of institute's recording distance is the radius of cylinder r;

Step 11: the contact point set judging containment region outer boundary whether the quantity of middle contact point is 3;

If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out, makes coordinate system zaxle forward and cylinder axis direction vector in the same way and parallel, butt contact carries out ascending sequence by its z-axis coordinate, makes , , 's zaxial coordinate increases progressively, and now error containment region rotates the direction vector of variation equal axis direction vector with vector multiplication cross; Arrange and rotate variation angle initial value; Calculate with dot product, if dot product result equals 0, jump to step 18, if dot product result is not equal to 0, jump to next step;

If the quantity of contact point is not 3, jump to step 14;

Step 12: calculate around rotate direction vector after angle ; Then, 3 contact points are projected in perpendicular to plane in, and calculate the center of circle of the circumscribed circle of 3 contact points, according to circumcenter with determine the axis of postrotational cylinder ;

Step 13: calculate all noncontact measuring points and arrive distance if, , then represent that variation is not enough, the anglec of rotation become ; If , change excessive, all the other noncontact measuring points exceed containment region, the anglec of rotation become ;

Judge whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If before and after the difference of iterative value of twice be less than setting error permissible value, then illustrate and find the 4th contact point, then will assignment is given , jump to step 10; If before and after the difference of iterative value of twice be not less than setting error permissible value, then jump to step 12;

Step 14: the contact point set judging containment region outer boundary whether the quantity of middle contact point is 4;

If the quantity of contact point equals 4, setting cylindrical radius decrease initial value, jump to next step;

If the quantity of contact point is not equal to 4, then jump to step 17;

Step 15: add current cylindrical radius obtain , obtain cylinder after dimensional variations, its axis is , according to 4 contact points to axis distance equal relation, with axis direction vector, axis upper is some unknown quantity, obtains 4 quaternary nonlinear equations respectively, can be obtained the axis of cylinder by Nonlinear System of Equations direction vector, axis on a bit;

Step 16: calculate all noncontacts point successively and arrive distance , all noncontact measuring points are corresponding composition set if, + , then represent that variation is not enough, become ; If + , then change excessive, all the other noncontact measuring points exceed containment region, become ;

Judge before and after the difference of iterative value of 2 times whether be less than setting error permissible value; If before and after the difference of iterative value of 2 times be less than setting error permissible value, illustrates and finds the 5th contact point, will direction vector, axis upper some difference assignment is to axis lparameter , , and judge whether to meet criterion, if meet, jump to step 18, if do not meet criterion, jump to step 10; If before and after the difference of iterative value of 2 times be not less than setting error permissible value, then jump to step 15;

Step 17: the contact point set judging containment region outer boundary whether the quantity of middle contact point is more than or equal to 5;

If the quantity of contact point is less than 5, jump to step 10;

If the quantity of contact point is more than or equal to 5, with in contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, according in step 15,16 exploratory trace adjustment method determine ;

Judge whether to be less than setting error permissible value; If be less than setting error permissible value, judges whether to meet criterion, if met, jumps to step 18, if do not meet criterion, changes 1 combination, recalculate , re-start judgement, iteration is gone down successively; If be greater than setting error permissible value, by what calculate parameter assignment respectively give cylinder axis lparameter , , then jump to step 10;

Step 18: the optimal value exporting deviation from cylindrical form, cylindrical radius rand cylinder axis lparameter.