CN114995281B - Optimal tool position planning method and device for non-expandable straight line curved surface - Google Patents

Abstract

A method and device for optimal tool position planning for non-developable ruled surfaces based on the equal bow height error method is suitable for side milling of non-developable ruled surfaces. The method first determines the parametric equation of the ruled surface to be processed, and derives the curvature of the upper and lower directrixes on the ruled surface at the current tool position. Secondly, the initial processing step corresponding to the upper and lower directrixes is calculated according to the curvature and the bow height tolerance, and the bow height error is checked. The processing step is further iteratively adjusted to maximize it within the bow height tolerance. Finally, the tool positions of the upper and lower directrixes under their respective processing steps are compared to obtain the tool position under the optimal processing step within the bow height tolerance. The entire tool path trajectory is traversed to complete the optimal tool position planning for non-developable ruled surfaces based on the equal bow height error method. The invention uses the upper and lower directrixes of the non-developable ruled surface as constraints to obtain the optimal tool position planning within the bow height tolerance. The bow height error is uniform and consistent, the number of tool position points is small, and the overall processing quality and processing efficiency are improved.

Description

Optimal tool position planning method and device for non-developable ruled surfaces

Technical Field

The present invention belongs to the field of mechanical processing technology, and the present invention relates to a method and a device for optimal tool position planning of a non-developable ruled surface, which is of great significance for achieving high-quality and high-efficiency processing of complex non-developable ruled surfaces.

Background technique

Nowadays, with the development of aerospace, transportation and other fields, the demand for high-quality high-end equipment is becoming more and more urgent. Precision complex curved surface parts widely used in this field are subject to higher requirements in terms of processing efficiency, forming accuracy and yield rate. Non-developable ruled surfaces are typical features of such complex parts, which are generally processed by multi-axis linkage CNC machine tools. Multi-axis linkage CNC machining requires the support of automatic programming technology. Tool path planning methods are the core technology of automatic programming, and their quality determines the processing quality and efficiency of the surface.

The main difference between the various existing tool path trajectory planning algorithms is the different methods for determining the processing step length, which mainly affects the bow height error. Due to the curvature of non-developable ruled surfaces changing at different positions, when a fixed processing step length is used as the tool path trajectory for surface approximation, in order to ensure the processing accuracy requirements, the same tool step length results in too many tool position points; if the number of tool position points is reduced, the actual maximum bow height error range within a processing step length at the position with excessive curvature will be greater than the bow height tolerance. Therefore, the existing tool path trajectory planning algorithms cannot handle the balance between the overall processing quality and processing efficiency of the parts.

Summary of the invention

Based on the analysis of the changing curvature of non-developable ruled surfaces and the optimal step length within the bow height tolerance, the present invention takes the upper and lower directrixes of the non-developable ruled surfaces as constraints, and proposes an optimal tool position planning method for ruled surfaces based on the equal bow height error method. The bow height errors of discrete steps along the tool path trajectory of the ruled surface are uniformed, the number of tool position points is minimized within the bow height tolerance requirement, and the overall processing quality and efficiency are improved.

The present invention is achieved through the following technical solutions.

An optimal tool position planning method for a non-developable ruled surface, comprising:

Step S1, obtaining corresponding cubic B-spline curve parameter equations according to respective control points of upper and lower directrixes of the non-developable ruled surface, thereby determining a parameter expression of the non-developable ruled surface represented by upper and lower directrixes;

Step S2, respectively calculating the curvature of the upper and lower directrixes at the current tool position;

Step S3, calculating the corresponding initial processing step lengths according to the curvatures of the upper and lower directrixes at the current tool position and the bow height tolerance, wherein the curvature at the current tool position is used as the curvature between the next tool position obtained according to the initial processing step length and the current tool position;

Step S4, calculating the actual maximum bow height error of the upper and lower alignments under the initial processing step length;

Step S5, respectively checking the actual maximum bow height errors of the upper and lower alignments, and iteratively adjusting the initial processing step lengths of each to maximize the actual maximum bow height error within the bow height tolerance, thereby obtaining the maximum processing step lengths of the upper and lower alignments;

Step S6, comparing the tool positions of the upper and lower alignments at their respective maximum processing step lengths, and the position closer to the current tool position is the tool position at the current optimal processing step length based on the equal bow height error;

Step S7, traverse the entire tool path trajectory to obtain the tool positions under all optimal processing steps, so as to obtain the optimal tool position planning position for the non-developable ruled surface based on the equal bow height error method.

Optionally, in step S1, the corresponding cubic B-spline curve parameter equations are obtained according to the respective control points of the upper and lower directrixes of the non-developable ruled surface, so as to determine the parameter expression of the non-developable ruled surface represented by the upper and lower directrixes, including:

1) Multiple cubic B-spline curves are determined by multiple control points of the upper and lower directrixes, where each cubic B-spline curve is determined by multiple continuous control points. Any cubic B-spline curve is expressed as:

P _j (t) = [x _j (t) y _j (t)] = UM _j Q _j

Wherein, P _j (t) is the cubic B-spline curve equation, t is the curve parameter, j represents the number of segments of the spline curve, U represents the parameter matrix, M _j represents the coefficient matrix and is related to the weights defined by the curve control points, Q _j represents the control point matrix, x _j (t) is the component of the spline curve on the x-axis, and y _j (t) is the component of the spline curve on the y-axis;

2) solving the multiple segments of cubic B-spline curves corresponding to the upper and lower directrixes, and respectively forming the upper directrix C ₁ (u) and the lower directrix C ₂ (u) according to the respective cubic B-spline curves;

3) Establish the parametric expression of non-developable ruled surfaces using upper and lower directrixes

P(u,v)＝(1-v)C ₁ (u)+vC ₂ (u)(0≤v≤1)

Among them, u and v are surface parameters, u controls the corresponding positions of the upper and lower directrixes, and v controls the position of the points on the straight generatrix.

Optionally, in step S2, respectively calculating the curvatures of the upper and lower directrixes at the current tool position includes:

Step S21, construct the parametric equations of the upper and lower directrixes as follows:

Among them, _a1x , _b1x , _c1x , _d1x , _{a1y , b1y, c1y, d1y, a2x, b2x, c2x, d2x, a2y , b2y , c2y , d2y are polynomial coefficients of} the parametric equation and are known quantities;

Step S22, the curvature formulas of the upper and lower directrixes are respectively

Step S23, respectively substitute the parameters u corresponding to the contact point positions of the upper and lower guidelines at the current tool position to obtain the upper curvature ρ ₁ (u _1i ) at the current tool position and the lower curvature ρ ₂ (u _2i ) at the current tool position, where u _1i represents the surface parameters of the upper guideline at the current tool position, and u _2i represents the surface parameters of the lower guideline at the current tool position.

Optionally, in step S3, the corresponding initial processing step lengths are calculated according to the curvature and bow height tolerance of the upper and lower directrixes at the current tool position, including:

Among them, ΔL ₁ is the initial machining step length of the upper reference line at the current tool position;

ΔL ₂ is the initial machining step length of the lower guideline at the current tool position;

ρ ₁ is the curvature of the upper directrix at the current tool position;

ρ ₂ is the curvature of the lower guideline at the current tool position;

e is the allowable error of bow height.

Optionally, in step S4, the calculating of the actual maximum bow height error of the upper and lower alignments under the initial processing step length includes:

Step S41, the upper guideline initial parameter interval is Let _ua = _u1i ,

Step S42, let u _I =u _a +(1-λ)(u _b -u _a ), u _II =u _a +λ(u _b -u _a ), λ is the interval compression coefficient, and calculate the bow height error at point C ₁ (u _I ):

And the bow height error at point C ₁ (u _II ):

Wherein, V _I , V _II , and V _L are vectors, V _I =C ₁ (u _1i )C ₁ (u _I ), V _II =C ₁ (u _1i )C ₁ (u _II ),

Step S43, if ε _I > ε _II , then set u _b = u _II ; otherwise, set u _a = u _I ;

Step S44, judging whether |ε _I -ε _II |＜Δε holds, where Δε is the iteration accuracy. If so, outputting the actual maximum bow height error ε ₁ =(ε _I +ε _II )/2 of the upper alignment line under the initial processing step, and the corresponding maximum bow height error point parameter u ₁ =(u _I +u _II )/2; otherwise, returning to step S42;

Step S45, using the method of steps S41 to S44 to obtain the actual maximum bow height error ε ₂ of the lower alignment line under the initial processing step length and the corresponding parameter u ₂ ;

Step S46, define function ε=f(u _a ,u _b ) as the maximum bow height error function, then

Optionally, in step S5, the actual maximum bow height errors of the upper and lower alignments are respectively checked, and the initial processing step lengths of the respective alignments are iteratively adjusted so that the actual maximum bow height error is maximized within the bow height tolerance, including:

Step S51, the upper guideline initial parameter interval is Determine whether the actual maximum bow height error ε ₁ of the upper alignment under the initial processing step satisfies:

e-Δe≤ε ₁ ≤e

Among them, e is the bow height tolerance, Δe is the error accuracy;

Among them, the upper and lower guideline contact points at the current tool position are C ₁ (u _1i ) and C ₂ (u _2i ), and the corresponding points of the upper and lower guidelines at their respective initial processing steps are ΔL ₁ and ΔL ₂ are the initial processing steps of the upper and lower alignments, respectively.

If so, output the surface parameters of the corresponding points If not, proceed as follows:

(1) If ε ₁ ＞e, then execute

a1) Let _ua = u _1i ,

b1) Find the midpoint of the parameter interval [u _a ,u _b ] Calculate f(u _1i ,u _m );

c1) If f(u _1i ,u _m )＞e, let u _b =u _m ; otherwise, let u _a =u _m ;

d1) Determine whether f(u _1i , _um ) satisfies e-Δe≤f(u _1i , _um )≤e. If so, output parameter u _1i+1 = _um ; if not, go to step b1);

(2) If ε ₁ ＜e-Δe, then execute

a2) Order Where η is the upper interval coefficient;

b2) Find the midpoint of the parameter interval [u _a ,u _b ] Calculate f(u _1i ,u _m );

c2) If f(u _1i ,u _m )＞e, let u _b =u _m ; otherwise, let u _a =u _m ;

d2) Determine whether f(u _1i , _um ) satisfies e-Δe≤f(u _1i , _um )≤e. If so, output parameter u _1i+1 = _um ; if not, go to step b2);

That is, the corresponding point parameter u _1i+1 of the upper alignment line under the maximum processing step length within the bow height tolerance is obtained;

The same method as step S51 is used to obtain the corresponding point parameter u _2i+1 of the lower alignment line at the maximum processing step length within the bow height tolerance.

Optionally, in step S6, the tool positions of the upper and lower alignments under the respective maximum processing step lengths are compared, and the position closer to the current tool position is the tool position under the optimal processing step length based on the equal bow height error, including:

The current tool position is u _i, and the corresponding contact point parameter of the upper reference line is u _1i . The current tool position is u _i , and the corresponding contact point parameter of the lower reference line is u _2i . The tool position of the upper reference line at the maximum processing step length is The corresponding upper guideline contact point parameter is u _1i+1 , and the tool position of the upper guideline at the maximum processing step length is The corresponding lower guideline cutting contact point parameter is u′ _2i+1 , where u′ _2i+1 is the lower guideline cutting contact point parameter corresponding to the tool position based on the upper guideline cutting contact point parameter u _1i+1 ;

Tool position of lower guideline at maximum machining step length The corresponding upper guideline contact point parameter is u′ _1i+1 , and the tool position of the lower guideline at the maximum machining step length is The corresponding lower guideline cutting contact point parameter is u _2i+1 , where u′ _1i+1 is the upper guideline cutting contact point parameter corresponding to the tool position based on the lower guideline cutting contact point parameter u _2i+1 ;

Determine whether it meets the following requirements:

u′ _2i+1 ＜u _2i+1

If so, the tool position under the optimal machining step is If not, then

Optionally, in step S1, 13 cubic B-spline curves are determined by 16 control points of the upper directrix, and 13 cubic B-spline curves are determined by 16 control points of the lower directrix, wherein each cubic B-spline curve is determined by four continuous control points, wherein the 16 control points and the M _j matrix are given by the international standard "Inspection Conditions for Machining Centers".

U＝[1 tt ² t ³ ]，

Among them, q _j,x , q _j+1,x , q _j+2,x , and q _j+3,x represent four consecutive control points on the x-axis, and q _j,y , q _j+1,y , q _j+2,y , and q _j+3,y represent four consecutive control points on the y-axis.

Optionally, in step S41, the upper guideline initial parameter interval is Let _ua = _u1i , Previously, it also included:

The upper and lower guideline contact points at the current tool position are C ₁ (u _1i ) and C ₂ (u _2i ), respectively, and the following equations are solved:

Get the corresponding point of the upper alignment at its initial processing step

and the corresponding point of the lower guideline at its initial processing step

The present invention also provides an electronic device, including a processor and a memory, wherein an optimal tool position planning program for non-developable ruled surfaces is stored in the memory, and when the optimal tool position planning program for non-developable ruled surfaces is executed by the processor, the optimal tool position planning method for non-developable ruled surfaces as described above is completed.

Compared with the prior art, the present invention has the following advantages and outstanding technical effects: the present invention takes the upper and lower directrixes of the non-developable ruled surface as constraints, adopts a method of accurately searching for the maximum processing step length within a range and selecting the best one to determine the next tool position, and the bow height error verification is more accurate. The bow height error of each discrete straight line segment obtained in the tool position planning is uniform and consistent and closer to the bow height tolerance, the number of tool positions is reduced, the overall processing quality and processing efficiency are improved, and the optimal tool position planning for non-developable ruled surfaces based on equal bow height errors is realized, which has good application prospects.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart showing optimal tool position planning for a non-developable ruled surface based on an equal bow height error method according to an embodiment of the present invention.

FIG. 2 is a schematic diagram of a non-developable ruled surface part according to an embodiment of the present invention.

FIG. 3 is a schematic diagram showing the upper and lower alignment lines of a ruled surface according to an embodiment of the present invention.

FIG. 4 is a schematic diagram showing the solution of the upper and lower directrix contact points at the tool position according to an embodiment of the present invention.

FIG. 5 is a schematic diagram of a method of equal bow height error step length according to an embodiment of the present invention.

FIG. 6 is a schematic diagram showing tool position selection under an optimal processing step length according to an embodiment of the present invention.

FIG. 7 is a diagram showing a comparison between the optimal tool position planning method according to an embodiment of the present invention and discrete tool contact points automatically generated by software.

FIG. 8 is a diagram showing the distribution of bow height errors under the optimal tool position planning method according to an embodiment of the present invention.

Figure numerals: 1—non-developable ruled surface; 2—upper alignment line; 3—lower alignment line; 4—tool.

Detailed ways

The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Figure 1 is a flowchart of the optimal tool position planning for non-developable ruled surfaces based on the equal bow height error method. The method first determines the parametric equation of the ruled surface to be processed, and derives the curvature of the upper and lower directrixes on the ruled surface at the tool position. Secondly, the initial processing step lengths corresponding to the upper and lower directrixes are calculated according to the curvature and the bow height tolerance, and the bow height error is checked. The processing step length is further iteratively adjusted to maximize it within the bow height tolerance. Finally, the tool positions of the upper and lower directrixes under their respective processing steps are compared to obtain the tool position under the optimal processing step length within the bow height tolerance. The entire tool path trajectory is traversed to complete the optimal tool position planning for non-developable ruled surfaces based on the equal bow height error method. The present invention uses the upper and lower directrixes of the non-developable ruled surface as constraints, and adopts a method of accurately searching for the maximum processing step length within a range and selecting the best to determine the next tool position. The bow height error verification is more accurate, and the obtained tool position planning has uniform bow height errors in each discrete straight line segment and is closer to the bow height tolerance. The number of tool positions is reduced, and the overall processing quality and processing efficiency are improved. The optimal tool position planning for non-developable ruled surfaces based on equal bow height errors is realized, and it has good application prospects. The specific implementation steps are as follows:

Step 1, according to the respective control points (16, the control points are known and set by themselves) of the upper and lower directrixes of the non-developable ruled surface as shown in FIG. 2 , the corresponding cubic B-spline curve parametric equation is obtained, and the parametric expression of the non-developable ruled surface represented by the upper and lower directrixes is determined;

1) 13 segments of cubic B-spline curves are determined by 16 control points of the upper and lower directrixes, where each cubic B-spline curve is determined by four consecutive control points, as shown in Figure 3. Any cubic B-spline curve can be expressed as:

P _j (t) = [x _j (t) y _j (t)] = UM _j Q _j

Where t is the curve parameter, j represents the number of segments of the spline curve j=1~13, U represents the parameter matrix, _Mj represents the coefficient matrix and is related to the weights defined by the curve control points, _Qj represents the control point matrix, _xj (t) is the component of the curve on the x-axis, and _yj (t) is the component of the curve on the y-axis; they are respectively expressed as follows:

U＝[1 tt ² t ³ ]，

Among them, q _j,x , q _j+1,x , q _j+2,x , q _j+3,x represent four consecutive control points on the x-axis, and q _j,y , q _j+1,y , q _j+2,y , q _j+3,y represent four control points on the y-axis. The 16 control points are given by the international standard ISO 10791-7:2020 "Test conditions for machining centers - Part 7: Test of finished test pieces", and the M _j matrix is also given by this international standard.

2) Solve the 13 cubic B-spline curves corresponding to the upper and lower directrixes as follows, and compose the upper and lower directrixes C ₁ (u) and C ₂ (u) respectively according to their respective cubic B-spline curves:

Among them, z=0 is the horizontal plane where the lower directrix is located, and z=20 is the horizontal plane where the upper directrix is located.

3) Determine the parameter expression of the non-developable ruled surface represented by upper and lower directrixes:

P(u,v)＝(1-v)C ₁ (u)+vC ₂ (u)(0≤v≤1)

Among them, C ₁ (u) and C ₂ (u) are the upper and lower directrixes of the ruled surface, that is, the two directrixes determined in step 1, u and v are surface parameters, u controls the corresponding positions of the upper and lower directrixes, and v controls the position of the points on the straight generatrix.

Step 2, calculating the curvature of the upper and lower directrixes at the tool position;

1) The parametric equations of the upper and lower directrixes are:

Among them, _a1x , _b1x , _c1x , _d1x , _{a1y , b1y, c1y, d1y, a2x, b2x, c2x, d2x, a2y , b2y , c2y , d2y are polynomial coefficients of} the parametric equation and are known quantities;

By taking the derivative of each parameter equation separately, we can get:

x′ ₁ (u) = 3a _1x u ² + 2b _1x u + c _1x , x ₁ ″ (u) = 6a _1x u + 2b _1x

y′ ₁ (u) = 3a _1y u ² + 2b _1y u + c _1y , y ₁ ″ (u) = 6a _1y u + 2b _1y

x′ ₂ (u) = 3a _2x u ² + 2b _2x u + c _2x , x ₂ ″ (u) = 6a _2x u + 2b _2x

y′ ₂ (u) = 3a _2y u ² + 2b _2y u + c _2y , y ₂ ″ (u) = 6a _2y u + 2b _2y

The curvatures of the upper and lower directrixes at different positions are

2) The contact point between the tool and the upper and lower directrixes at the current position is solved by using the tool position coordinates and the tool axis vector. As shown in Figure 4, the tool position coordinates are T ₀ = (x ₀ , y ₀ , z ₀ ) and the tool axis vector is The tool radius is R, solve the following equations:

That is, the coordinates of the contact point between the tool and the lower guideline at the current position are C ₂ =(x _2i ,y _2i ) _z=0 =(x,y), and the corresponding coordinates of the contact point between the tool and the upper guideline are C ₁ =(x _1i ,y _1i ) _z=20 , where x _1i , y _1i are respectively expressed as:

Substitute the contact point coordinates C ₁ and C ₂ into the parametric equations of the upper and lower directrixes to obtain the corresponding parameters of the current contact point coordinates C ₁ and C ₂ on the upper and lower directrixes as u _1i and u _2i , respectively. Substituting them into the corresponding curvature expressions, we can obtain the curvatures ρ ₁ (u _1i ) and ρ ₂ (u _2i ) of the upper and lower directrixes at the current tool position.

Step 3, calculating the corresponding initial processing step lengths according to the curvature of the upper and lower directrixes at the tool position and the bow height tolerance;

The initial processing step length is based on the curvature of the directrix at the current tool position (i.e., the solid arc in Figure 5), and is solved by assuming that the curvature near the tool position remains unchanged (i.e., the dotted arc in Figure 5) (that is, the chord length ΔL _i calculated based on the constant curvature near the tool position is used as the initial processing step length at the curvature at the current tool position), as shown in Figure 5. According to the geometric relationship, it can be obtained:

Among them, ΔL ₁ and ΔL ₂ are the initial processing steps of the upper and lower directrixes at the tool position, ρ ₁ and ρ ₂ are the curvatures of the upper and lower directrixes at the tool position, and e is the bow height tolerance, which is 0.01 mm.

Step 4, calculating the actual maximum bow height error of the upper and lower alignments under the initial processing step length;

1) The upper and lower directrix contact points at the tool position are C ₁ (u _1i ) and C ₂ (u _2i ), respectively, and the following equations are solved:

That is, the corresponding points of the upper and lower directrixes under their respective initial processing steps are obtained.

2) Calculate the actual maximum bow height error ε of the upper and lower alignments under the initial processing step length as shown in Figure 5. The specific steps are as follows:

(1) The initial parameter range of the upper criterion is Let _ua = _u1i ,

(2) Let u _I =u _a +(1-λ)(u _b -u _a ), u _II =u _a +λ(u _b -u _a ), λ is the interval compression coefficient, which is 0.6; calculate the bow height errors at points C ₁ (u _I ) and C ₁ (u _II ) respectively:

Wherein, ε _I , ε _II are the bow height errors at points C ₁ (u _I ) and C ₁ (u _II ) on the upper directrix, respectively; V _I , V _II , and V _L are vectors V _I =C ₁ (u _1i )C ₁ (u _I ) and V _II =C ₁ (u _1i )C ₁ (u _II ), respectively.

(3) If ε _I ＞ε _II , let u _b ＝u _II ; otherwise, let u _a ＝u _I ;

(4) Determine whether |ε _I -ε _II |＜Δε, where Δε is the iteration accuracy. If so, output the actual maximum bow height error ε ₁ =(ε _I +ε _II )/2 of the upper alignment under the initial processing step and the maximum bow height error point parameter u ₁ =(u _I +u _II )/2; otherwise, go to step (2);

(5) Using the same method as (1) to (4) above, calculate the actual maximum bow height error ε ₂ and the corresponding parameter u ₂ of the lower alignment line at the initial processing step length;

(6) Define function ε = f(u _a , u _b ) as the maximum bow height error function, then

Step 5: Check the bow height errors of the upper and lower alignment lines, and iteratively adjust the respective processing step lengths to maximize them within the bow height tolerance;

The initial parameter range of the upper line is Determine whether the actual maximum bow height error ε ₁ of the upper alignment under the initial processing step satisfies:

e-Δe≤ε ₁ ≤e

Among them, e is the bow height tolerance, which is 0.01mm, and Δe is the error accuracy, which is 0.0005mm;

If so, output the corresponding point parameters If not, there are two situations:

(1) If ε ₁ ＞e

a) Let _ua = _u1i ,

b) Find the midpoint of the parameter interval [u _a ,u _b ] Calculate f(u _1i ,u _m );

c) If f(u _1i ,u _m )＞e, let u _b =u _m ; otherwise, let u _a =u _m ;

d) Determine whether f(u _1i , _um ) satisfies e-Δe≤f(u _1i , _um )≤e. If so, output parameter u _1i+1 = _um ; if not, go to step b);

(2) If ε ₁ ＜e-Δe

a) Order Where η is the upper limit interval coefficient, which is 3;

b) Find the midpoint of the parameter interval [u _a ,u _b ] Calculate f(u _1i ,u _m );

c) If f(u _1i ,u _m )＞e, let u _b =u _m ; otherwise, let u _a =u _m ;

d) Determine whether f(u _1i , _um ) satisfies e-Δe≤f(u _1i , _um )≤e. If so, output parameter u _1i+1 = _um ; if not, go to step b);

That is, the corresponding point parameter u _1i+1 of the upper alignment line under the maximum processing step length within the bow height tolerance is obtained, and the corresponding point parameter u _2i+1 of the lower alignment line under the maximum processing step length within the bow height tolerance is solved by the same method as above;

Step 6, compare the tool positions of the upper and lower alignments under their respective maximum processing steps, and the position closer to the previous tool position is the tool position under the optimal processing step based on the equal bow height error;

As shown in Figure 6, the previous tool position is u _i , and the corresponding contact point parameters of the upper and lower alignments are u _1i , u _2i , respectively. The tool position of the upper alignment under the maximum machining step length is The corresponding upper and lower reference line contact point parameters are u _1i+1 and u′ _2i+1 respectively, where u′ _2i+1 is the lower reference line contact point parameter corresponding to the tool position based on the upper reference line contact point parameter u _1i+1 ; the tool position of the lower reference line under the maximum processing step length The corresponding upper and lower reference line contact point parameters are u′ _1i+1 and u _2i+1 respectively, where u′ _1i+1 is the lower reference line contact point parameter and u _2i+1 is the upper reference line contact point parameter corresponding to the tool position; determine whether the following conditions are met:

u′ _2i+1 ＜u _2i+1

If so, the tool position under the optimal machining step is If not, then

Step 7, traverse the entire tool path trajectory to obtain the tool position under all optimal processing steps, that is, the optimal tool position planning for non-developable ruled surfaces based on the equal bow height error method is completed.

A comparison between the optimal tool position planning method of the present invention and the discrete cutting points automatically generated by the software is shown in FIG7 . The number of tool position points of the tool position planning method of the present invention is 121, and the number of tool position points automatically generated by the software is 153, which is reduced by 20%; the bow height error distribution based on the optimal tool position planning method is shown in FIG8 . The bow height errors in all discrete straight line segments are within the set range (0.0095, 0.01), which verifies the high efficiency and effectiveness of the present invention.

The present invention also provides an electronic device, which is a device that can automatically perform numerical calculations and/or information processing according to pre-set or stored instructions. For example, it can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a server, etc. The electronic device at least includes, but is not limited to, a memory and a processor that are connected to each other in communication. Wherein: the memory includes at least one type of computer-readable storage medium, and the readable storage medium includes flash memory, hard disk, multimedia card, card-type memory (for example, SD or DX memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory can be an internal storage unit of the electronic device, such as a hard disk or memory of the electronic device. In other embodiments, the memory can also be an external storage device of the electronic device, such as a plug-in hard disk equipped on the electronic device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. Of course, the memory may also include both the internal storage unit of the electronic device and its external storage device. In this embodiment, the memory is usually used to store the operating system and various application software installed in the electronic device, such as the non-developable ruled surface optimal tool position planning program code, etc. In addition, the memory may also be used to temporarily store various data that have been output or are to be output.

In some embodiments, the processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chips. The processor is generally used to control the overall operation of the electronic device, such as executing control and processing related to data interaction or communication with the electronic device. In this embodiment, the processor is used to run the program code stored in the memory or process data, such as running the non-developable ruled surface optimal tool position planning program.

The memory including the readable storage medium may include an operating system, an optimal tool location planning program for non-developable ruled surfaces, etc. When the processor executes the optimal tool location planning program for non-developable ruled surfaces in the memory, the steps described above are implemented, which will not be described in detail here. In this embodiment, the optimal tool location planning program for non-developable ruled surfaces stored in the memory may be divided into one or more program modules, and the one or more program modules are stored in the memory and can be executed by one or more processors to complete the present application, for example, a non-developable ruled surface parameter expression acquisition module, which is used to obtain the corresponding cubic B-spline curve parameter equations according to the respective control points of the upper and lower directrixes of the non-developable ruled surface, so as to determine the parameter expression of the non-developable ruled surface represented by the upper and lower directrixes, such as a curvature calculation module, which is used to calculate the curvature of the upper and lower directrixes at the current tool position, respectively, which will not be described in detail here.

Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations shall fall within the protection scope of the claims of the present invention.

Claims (10)

1. A method for optimal tool position planning for a non-developable ruled surface, characterized by comprising: Step S1, obtaining corresponding cubic B-spline curve parameter equations according to respective control points of upper and lower directrixes of the non-developable ruled surface, thereby determining a parameter expression of the non-developable ruled surface represented by upper and lower directrixes; Step S2, respectively calculating the curvature of the upper and lower directrixes at the current tool position; Step S3, calculating the corresponding initial processing step lengths according to the curvatures of the upper and lower directrixes at the current tool position and the bow height tolerance, wherein the curvature at the current tool position is used as the curvature between the next tool position obtained according to the initial processing step length and the current tool position; Step S4, calculating the actual maximum bow height error of the upper and lower alignments under the initial processing step length; Step S5, respectively checking the actual maximum bow height errors of the upper and lower alignments, and iteratively adjusting the initial processing step lengths of each to maximize the actual maximum bow height error within the bow height tolerance, thereby obtaining the maximum processing step lengths of the upper and lower alignments; Step S6, comparing the tool positions of the upper and lower alignments at their respective maximum processing step lengths, and the position closer to the current tool position is the tool position at the current optimal processing step length based on the equal bow height error; Step S7, traverse the entire tool path trajectory to obtain the tool positions under all optimal processing steps, so as to obtain the optimal tool position planning position for the non-developable ruled surface based on the equal bow height error method. 2. The method for optimal tool position planning for non-developable ruled surfaces according to claim 1, characterized in that in step S1, the corresponding cubic B-spline curve parameter equations are obtained according to the respective control points of the upper and lower directrixes of the non-developable ruled surface, thereby determining the parameter expression of the non-developable ruled surface represented by the upper and lower directrixes, including: 1) Multiple cubic B-spline curves are determined by multiple control points of the upper and lower directrixes, where each cubic B-spline curve is determined by multiple continuous control points. Any cubic B-spline curve is expressed as: P _j (t) = [x _j (t) y _j (t)] = UM _j Q _j Wherein, P _j (t) is the cubic B-spline curve equation, t is the curve parameter, j represents the number of segments of the spline curve, U represents the parameter matrix, M _j represents the coefficient matrix and is related to the weights defined by the curve control points, Q _j represents the control point matrix, x _j (t) is the component of the spline curve on the x-axis, and y _j (t) is the component of the spline curve on the y-axis; 2) solving the multiple segments of cubic B-spline curves corresponding to the upper and lower directrixes, and respectively forming the upper directrix C ₁ (u) and the lower directrix C ₂ (u) according to the respective cubic B-spline curves; 3) Establish the parametric expression of non-developable ruled surfaces using upper and lower directrixes P(u,v)＝(1-v)C ₁ (u)+vC ₂ (u) (0≤v≤1) Among them, u and v are surface parameters, u controls the corresponding positions of the upper and lower directrixes, and v controls the position of the points on the straight generatrix. 3. The method for optimal tool position planning for a non-developable ruled surface according to claim 2, characterized in that in step S2, respectively calculating the curvatures of the upper and lower directrixes at the current tool position comprises: Step S21, construct the parametric equations of the upper and lower directrixes as follows: C ₁ (u): C ₂ (u): Among them, _a1x , _b1x , _c1x , _d1x , _{a1y , b1y, c1y, d1y, a2x, b2x, c2x, d2x, a2y , b2y , c2y , d2y are polynomial coefficients of} the parametric equation and are known quantities; Step S22, the curvature formulas of the upper and lower directrixes are respectively Step S23, respectively substitute the parameters u corresponding to the contact point positions of the upper and lower guidelines at the current tool position to obtain the upper curvature ρ ₁ (u _1i ) at the current tool position and the lower curvature ρ ₂ (u _2i ) at the current tool position, where u _1i represents the surface parameters of the upper guideline at the current tool position, and u _2i represents the surface parameters of the lower guideline at the current tool position. 4. The optimal tool position planning method for non-developable ruled surfaces according to claim 3 is characterized in that, in step S3, the corresponding initial processing step length is calculated according to the curvature and bow height tolerance of the upper and lower directrixes at the current tool position, including: Among them, ΔL ₁ is the initial machining step length of the upper reference line at the current tool position; ΔL ₂ is the initial machining step length of the lower guideline at the current tool position; ρ ₁ is the curvature of the upper directrix at the current tool position; ρ ₂ is the curvature of the lower guideline at the current tool position; e is the allowable error of bow height. 5. The method for optimal tool position planning for non-developable ruled surfaces according to claim 4, characterized in that, in step S4, the actual maximum bow height error of the upper and lower alignments under the initial processing step length is calculated, comprising: Step S41, the upper guideline initial parameter interval is Let _ua = _u1i , Step S42, let u _I =u _a +(1-λ)(u _b -u _a ), u _II =u _a +λ(u _b -u _a ), λ is the interval compression coefficient, and calculate the bow height error at point C ₁ (u _I ): And the bow height error at point C ₁ (u _II ): Wherein, V _I , V _II , and V _L are vectors, V _I =C ₁ (u _1i )C ₁ (u _I ), V _II =C ₁ (u _1i )C ₁ (u _II ), Step S43, if ε _I > ε _II , then set u _b = u _II ; otherwise, set u _a = u _I ; Step S44, judging whether |ε _I -ε _II |＜Δε holds, where Δε is the iteration accuracy. If so, outputting the actual maximum bow height error ε ₁ =(ε _I +ε _II )/2 of the upper alignment line under the initial processing step, and the corresponding maximum bow height error point parameter u ₁ =(u _I +u _II )/2; otherwise, returning to step S42; Step S45, using the method of steps S41 to S44 to obtain the actual maximum bow height error ε ₂ of the lower alignment line under the initial processing step length and the corresponding parameter u ₂ ; Step S46, define function ε=f(u _a ,u _b ) as the maximum bow height error function, then 6. The optimal tool position planning method for non-developable ruled surfaces according to claim 5 is characterized in that, in step S5, the actual maximum bow height errors of the upper and lower alignments are respectively checked, and the respective initial processing step lengths are iteratively adjusted so that the actual maximum bow height error is maximized within the bow height tolerance, comprising: Step S51, the upper guideline initial parameter interval is Determine whether the actual maximum bow height error ε ₁ of the upper alignment under the initial processing step satisfies: e-Δe≤ε ₁ ≤e Among them, e is the bow height tolerance, Δe is the error accuracy; Among them, the upper and lower guideline contact points at the current tool position are C ₁ (u _1i ) and C ₂ (u _2i ), and the corresponding points of the upper and lower guidelines at their respective initial processing steps are ΔL ₁ and ΔL ₂ are the initial processing steps of the upper and lower alignments, respectively. If so, output the surface parameters of the corresponding points If not, proceed as follows: (1) If ε ₁ ＞e, then execute a1) Let _ua = u _1i , b1) Find the midpoint of the parameter interval [u _a ,u _b ] Calculate f(u _1i ,u _m ); c1) If f(u _1i ,u _m )＞e, let u _b =u _m ; otherwise, let u _a =u _m ; d1) Determine whether f(u _1i , _um ) satisfies e-Δe≤f(u _1i , _um )≤e. If so, output parameter u _1i+1 = _um ; if not, go to step b1); (2) If ε ₁ ＜e-Δe, then execute a2) Order Where η is the upper interval coefficient; b2) Find the midpoint of the parameter interval [u _a ,u _b ] Calculate f(u _1i ,u _m ); c2) If f(u _1i ,u _m )＞e, let u _b =u _m ; otherwise, let u _a =u _m ; d2) Determine whether f(u _1i , _um ) satisfies e-Δe≤f(u _1i , _um )≤e. If so, output parameter u _1i+1 = _um ; if not, go to step b2); That is, the corresponding point parameter u _1i+1 of the upper alignment line under the maximum processing step length within the bow height tolerance is obtained; The same method as step S51 is used to obtain the corresponding point parameter u _2i+1 of the lower alignment line at the maximum processing step length within the bow height tolerance. 7. The method for optimal tool position planning for non-developable ruled surfaces according to claim 6, characterized in that in step S6, the tool positions of the upper and lower directrixes under their respective maximum processing steps are compared, and the position closer to the current tool position is the tool position under the optimal processing step based on the equal bow height error, comprising: The current tool position is u _i, and the corresponding contact point parameter of the upper reference line is u _1i . The current tool position is u _i , and the corresponding contact point parameter of the lower reference line is u _2i . The tool position of the upper reference line at the maximum processing step length is The corresponding upper guideline contact point parameter is u _1i+1 , and the tool position of the upper guideline at the maximum processing step length is The corresponding lower guideline cutting contact point parameter is u′ _2i+1 , where u′ _2i+1 is the lower guideline cutting contact point parameter corresponding to the tool position based on the upper guideline cutting contact point parameter u _1i+1 ; Tool position of lower guideline at maximum machining step length The corresponding upper guideline contact point parameter is u′ _1i+1 , and the tool position of the lower guideline at the maximum machining step length is The corresponding lower guideline cutting contact point parameter is u _2i+1 , where u′ _1i+1 is the upper guideline cutting contact point parameter corresponding to the tool position based on the lower guideline cutting contact point parameter u _2i+1 ; Determine whether it meets the following requirements: u′ _2i+1 ＜u _2i+1 If so, the tool position under the optimal machining step is If not, then 8. The method for optimal tool position planning for non-developable ruled surfaces according to claim 2, characterized in that, in step S1, 13 segments of cubic B-spline curves are determined by 16 control points of the upper directrix, and 13 segments of cubic B-spline curves are determined by 16 control points of the lower directrix, wherein each cubic B-spline curve is determined by four continuous control points, wherein the 16 control points and the M _j matrix are given by the international standard "Inspection Conditions for Machining Centers", U＝[1t t ² t ³ ]， Among them, q _j,x , q _j+1,x , q _j+2,x , and q _j+3,x represent four consecutive control points on the x-axis, and q _j,y , q _j+1,y , q _j+2,y , and q _j+3,y represent four consecutive control points on the y-axis. 9. The optimal tool position planning method for non-developable ruled surfaces according to claim 5, characterized in that, in step S41, the upper directrix initial parameter interval is Let _ua = _u1i , Previously, it also included: The upper and lower guideline contact points at the current tool position are C ₁ (u _1i ) and C ₂ (u _2i ), respectively, and the following equations are solved: Get the corresponding point of the upper alignment at its initial processing step and the corresponding point of the lower guideline at its initial processing step 10. An electronic device, characterized in that it comprises a processor and a memory, wherein an optimal tool position planning program for non-developable ruled surfaces is stored in the memory, and when the optimal tool position planning program for non-developable ruled surfaces is executed by the processor, the optimal tool position planning method for non-developable ruled surfaces described in any one of claims 1 to 9 is completed.