Instruction Point Interpolation Method Applicable to the Sawing Process of Cylindrical Ruled Surfaces

Abstract

The present invention relates to an instruction point interpolation method applicable to the sawing process of a cylindrical ruled surface, comprising the following steps: determining the maximum sawing depth of a cylindrical workpiece based on the contour error of the cylindrical workpiece; obtaining the tilt angle of a circular saw blade according to the maximum sawing depth; determining the number of full-cut layers according to the maximum sawing depth; performing instruction point interpolation according to the interpolation period of the circular saw blade to obtain the position of the cutting contact point between the circular saw blade and the workpiece in each interpolation period; for each layer of full-cut of the workpiece, obtaining the attitude of the circular saw blade according to the tilt angle of the circular saw blade and the parameters in each interpolation period. The present invention meets the requirements of machining accuracy. By determining parameters such as the cutting depth and the saw blade tilt angle according to the maximum contour error, it can ensure that the requirements of the machining accuracy of the product are met. The machining efficiency is high. Compared with the traditional turning and milling machining, using a circular saw blade for machining increases the contact between the tool and the workpiece, and the machining efficiency is higher.

Description

Technical Field

[0001] The present invention relates to an instruction point interpolation algorithm for sawing cylindrical straight-grooved surface parts, belonging to the field of numerical control sawing processing. Background Art

[0002] Sawing processing uses a disk-shaped tool for cutting. Compared with traditional turning and milling processing, its contact surface with the workpiece is larger, and it has the characteristics of fast cutting speed and high processing efficiency. It is an effective means to realize cylindrical surface cutting. Due to the differences in the tool structures between the circular saw blade and traditional turning and milling cutters, the instruction point interpolation algorithms applicable to the motion control of turning tools and milling cutters cannot be directly applied to circular saw blade cutting, which limits the further exertion of its application potential. Studying the instruction point interpolation method applicable to the sawing of cylindrical straight-grooved surfaces is of great significance for improving processing efficiency and giving full play to the potential of five-axis sawing machine tools. Summary of the Invention

[0003] Aiming at the situation that the existing numerical control interpolation methods cannot meet the requirements of sawing cylindrical straight-grooved surfaces, the technical problem to be solved by the present invention is to provide an instruction point interpolation method applicable to the sawing of cylindrical straight-grooved surfaces.

[0004] The technical solution adopted by the present invention to achieve the above object is: an instruction point interpolation method applicable to the sawing of cylindrical straight-grooved surfaces, which performs instruction point interpolation on a cylindrical workpiece to realize the sawing of the cylindrical workpiece, including the following steps:

[0005] Determine the maximum sawing depth of the cylindrical workpiece based on the contour error of the cylindrical workpiece;

[0006] Obtain the tilt angle of the circular saw blade according to the maximum sawing depth;

[0007] Determine the number of full-cut layers according to the maximum sawing depth;

[0008] For each layer of full-cut of the workpiece, perform instruction point interpolation according to the interpolation period of the circular saw blade to obtain the position of the contact point between the circular saw blade and the workpiece in each interpolation period; obtain the attitude of the circular saw blade according to the tilt angle of the circular saw blade and the parameters in each interpolation period.

[0009] Saw the workpiece according to the position of the contact point between the circular saw blade and the workpiece and the attitude of the circular saw blade.

[0010] The determination of the sawing depth of the cylindrical workpiece based on the contour error of the cylindrical workpiece is obtained through the following formula:

[0011]

[0012] d max is the maximum sawing depth, and δ maxis the set maximum contour error, and R is the radius of the bottom circular surface of the cylindrical workpiece.

[0013] The tilt angle of the circular saw blade is obtained by the following formula:

[0014]

[0015] α is the tilt angle of the saw blade surface, r is the radius of the saw blade surface, d max is the maximum sawing depth, δ max is the set maximum contour error, and R is the radius of the bottom circular surface of the cylindrical workpiece.

[0016] The number of full-cut layers h is the height of the cylindrical workpiece, d max is the maximum sawing depth.

[0017] The position of the contact point between the circular saw blade and the workpiece is as follows:

[0018]

[0019] x ik+1 , y ik+1 , z ik+1 represents the coordinate values in the x, y, and z directions of the saw blade contact point on the cylindrical ruled surface at the (k + 1)-th interpolation cycle when sawing the i-th layer, and Δθ ik+1 represents the θ corresponding to the k-th interpolation cycle to the (k + 1)-th interpolation cycle when sawing the i-th layer ik and θ ik+1 angle change value.

[0020] The attitude of the circular saw blade is obtained by the following formula:

[0021] Let V ik (V ikx , V iky , V ikz ) be the tool axis vector corresponding to the saw blade contact point P on the cylindrical ruled surface at the k-th interpolation cycle when sawing the i-th layer ik corresponding to, and V ik is a unit vector starting from P ik and parallel to P ik O 3 satisfies:

[0022]

[0023] Then the tool axis vector V ik+1 corresponding to the saw blade contact point P on the cylindrical ruled surface at the (k + 1)-th interpolation cycle ik+1 can be expressed as:

[0024]

[0025] Among them, P k O 3 represents the sawing starting point P k and the line segment with the center O of the circular saw blade, α is the inclination angle of the saw blade surface, and θ 3 is the polar angle of the saw blade cutting contact point in the k-th interpolation cycle when sawing the i-th layer. ik For the instruction point interpolation device applicable to the sawing processing of a cylindrical ruled surface, it includes:

[0026] A saw blade attitude module, which is used to determine the maximum sawing depth of the cylindrical workpiece based on the contour error of the cylindrical workpiece; obtain the inclination angle of the circular saw blade according to the maximum sawing depth;

[0027] A workpiece integral cutting module, which is used to determine the number of integral cutting layers according to the maximum sawing depth;

[0028] An instruction point interpolation module, which is used for each layer of integral cutting of the workpiece, performs instruction point interpolation according to the interpolation cycle of the circular saw blade, and obtains the position of the cutting contact point between the circular saw blade and the workpiece in each interpolation cycle; obtains the attitude of the circular saw blade according to the inclination angle of the circular saw blade and the parameters of each interpolation cycle.

[0029] The instruction point interpolation device applicable to the sawing processing of a cylindrical ruled surface includes a memory and a processor; the memory is used to store a computer program; the processor is used to, when executing the computer program, implement the instruction point interpolation method applicable to the sawing processing of a cylindrical ruled surface as described in claim 1.

[0030] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the instruction point interpolation method applicable to the sawing processing of a cylindrical ruled surface as described in claim 1.

[0031] The present invention has the following beneficial effects and advantages:

[0032] (1) Meet the processing accuracy requirements. By determining parameters such as the cutting depth and the saw blade inclination angle according to the maximum contour error, it can ensure that the processing accuracy requirements of the product are met.

[0033] (2) High processing efficiency. Compared with traditional turning and milling processing, using a circular saw blade for processing increases the contact between the tool and the workpiece, and the processing efficiency is higher.

[0034] BRIEF DESCRIPTION OF THE DRAWINGS BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the program flow chart of the method of the present invention;

[0036] Figure 2 is the schematic diagram of the geometric relationship of circular saw blade processing of the method of the present invention;

[0037] Figure 3 Schematic diagram of contour error of the method of the present invention;

[0038] Figure 4 Schematic diagram of cylindrical ruled surface of the method of the present invention;

[0039] Figure 5 Simulation diagram of sawing processing of the method of the present invention. Specific embodiments

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0041] As Figure 1 shown, the method of the present invention includes the following steps:

[0042] 1) Determination of sawing depth based on contour error control;

[0043] 2) Determination of saw blade tilt angle;

[0044] 3) Determination of the number of integral cutting layers;

[0045] 4) Instruction point interpolation;

[0046] 5) Determination of saw blade attitude.

[0047] In the method of the present invention, the specific process of step 1) determination of sawing depth based on contour error control is as follows:

[0048] As Figure 2 shown, O 3 is the center of the circle of the saw blade surface. In sawing processing, the saw blade intersects the lower bottom surface circle of the cylinder at point B and the upper bottom surface circle of the cylinder at point P. AB is the diameter on the saw blade surface. To make the radii of the upper and lower surface circles equal, the cutting tool needs to be tilted at an angle α during sawing processing. At any moment t during the formation of the envelope surface, a normal line n 3 perpendicular to the saw blade surface is drawn through the center O 1 of the saw blade. Then, for any point O 1 on the normal line n 1 , since O 1 O 3 ⊥ plane ABP, it can be obtained that △PO 3 O 1 ≌△BO 3 O 1 , and thus PO 1 = BO 1 . By the same token, it can be proved that AO 1 = BO 1 , that is, for A, B, and P on the saw blade, it satisfies O 3 A = O 3 P = O 3 B. Therefore, there is a certain point O on the normal line n1 such that at any moment during the sawing process of the cylindrical ruled surface, all points on the circumference of the saw blade are always located on the spherical surface with point O 1 as the center of the sphere.

[0049] Taking the center O of the spherical surface where the circular saw blade is located 1 as the origin, taking the line connecting the center of the sphere and the center of the upper surface as the y-axis, and the direction perpendicular to the circular saw blade as the x-axis, a right-handed Cartesian coordinate system XO Figure 3 Y as shown in the figure is established, and during the processing of the circular saw blade, the following coordinate relationship is satisfied: 1 In the formula, d is the depth of the cylindrical ruled surface, and R is the radius of the upper and lower bottom circles.

[0050]

[0051] As can be seen from the above formula, when y is zero, x takes the maximum value x

[0052] , and when y takes the boundary values of ±d / 2, x takes the minimum value x max , so the contour error δ can be expressed as: min

[0053]

[0054] x max and x min respectively represent the maximum and minimum values of the x-axis coordinates.

[0055] It can be found from the above formula that the contour error δ is only related to the depth d of the cylindrical ruled surface and the radius R of the upper and lower bottom circles. Further, the partial derivatives of the contour error δ with respect to the two variables are solved:

[0056]

[0057]

[0058] That is, the contour error δ is positively correlated with the depth d of the cylindrical ruled surface and negatively correlated with the radius R of the upper and lower bottom circles. From the above analysis, when the radius R of the upper and lower bottom circles of the cylindrical ruled surface to be processed is fixed, the maximum sawing depth d max that meets the machining accuracy requirements can be determined according to the set maximum contour error δ max :

[0059]

[0060] In the method of the present invention, the specific process for determining the tilt angle of the saw blade in step 2) is as follows:

[0061] After the saw blade surface is tilted by an angle α, during the formation of the envelope surface, the radii of the circles formed by the intersection points of the saw blade surface and the upper and lower surfaces of the cylinder are the same. At this time, draw AR⊥BO through point A 2, then ∠BAR is the inclination angle α. O 1 is in the same plane as A, B, and O 2 .

[0062] According to the geometric relationships in the plane ABO 1 O 2 , it can be deduced that the inclination angle α of the saw blade surface satisfies:

[0063] α = 90° - ∠ABO 2

[0064] = 90° - (∠ABO 1 + ∠O 1 BO 2 )

[0065] = 90° - (90° - ∠O 3 O 1 B) - ∠O 1 BO 2

[0066] = ∠O 3 O 1 B - ∠O 1 BO 2

[0067] That is, when using a saw blade with a radius r to perform sawing processing on a cylindrical ruled surface with a bottom circle radius of R to a depth of d max , in order to ensure that the upper and lower surface radii of the sawn cylindrical ruled surface are equal, the inclination angle α of the saw blade surface needs to be:

[0068]

[0069] The specific process for determining the number of integral cutting layers in step 3) of the method of the present invention is as follows:

[0070] In sawing processing, after knowing the maximum sawing depth d max , the number of integral cutting layers n can be determined as:

[0071]

[0072] where h is the height of the cylindrical ruled surface to be processed, and d max is the maximum sawing depth. After dividing the two and performing a floor operation. After completing n layers of sawing, recalculate the height h and the maximum sawing depth d max of the remaining cylindrical ruled surface to be processed:

[0073] d max = h - nd max

[0074] h = d max

[0075] In the method of the present invention, the specific process of the instruction point interpolation in step 4) is as follows:

[0076] After the saw blade machining angular velocity and the interpolation period are determined, the Taylor series expansion can be used to approximately estimate the parameters corresponding to the interpolation point in the next interpolation period. Substituting the parameter value into the expression of the surface to be machined, the position of the tool contact point in the next interpolation period can be obtained.

[0077] θ ik is the polar angle of the tool contact point in the k-th interpolation period when sawing the i-th layer, and can be expressed as a function θ k with the k-th interpolation period T i as the independent variable: k )

[0078] θ ik = θ i (T k )

[0079] Then, the position vector of the tool contact point on the cylindrical ruled surface in the k-th interpolation period when sawing the i-th layer can be expressed as:

[0080] P ik = [x ik , y ik , z ik = [Rcosθ ik , Rsinθ ik , (i - 1)d max θ ik ∈[0, 2π]

[0081] x ik , y ik , z ik represent the coordinate values of the tool contact point on the cylindrical ruled surface in the x, y, and z directions in the k-th interpolation period when sawing the i-th layer. From the above formula, given the angle value of θ ik , the corresponding tool contact point coordinates can be determined on the cylindrical ruled surface to be machined. Therefore, in the tool contact point interpolation part, how to determine the angle value of θ k corresponding to each interpolation period T ik becomes the key problem to be solved below.

[0082] Let ω be the saw blade machining angular velocity, then the change in the corresponding angle value from the k-th interpolation period to the k + 1-th interpolation period is expressed as:

[0083]

[0084] The position vector of the tool contact point on the cylindrical ruled surface in the k + 1-th interpolation period can be expressed as:

[0085] P ik+1= [x ik+1 , y ik+1 , z ik+1 = [Rcosθ ik+1 , Rsinθ ik+1 , (i - 1)d max θ k+1 ∈ [0, 2π]

[0086] x ik+1 , y ik+1 , z ik+1 represent the coordinate values of the tool cutting contact point on the cylindrical ruled surface at the (k + 1)-th interpolation cycle during the sawing of the i-th layer in the x, y, and z directions. After expansion and arrangement, we can obtain:

[0087]

[0088] Expand the sine and cosine functions in terms of the Taylor series:

[0089]

[0090] Let ε 1 and ε 2 be the truncation errors after taking the second-order approximation of the sine and cosine trigonometric functions respectively. Then it can be simplified to

[0091]

[0092] Obtain

[0093]

[0094] Then, if the second-order approximation is used to estimate the sine and cosine functions, the radial error at each moving point can be approximately expressed as:

[0095]

[0096] In the method of the present invention, the specific process of determining the saw blade attitude in step 5) is as follows:

[0097] Let V ik (V ikx , V iky , V ikz ) be the tool axis vector corresponding to the tool cutting contact point P ik on the cylindrical ruled surface at the k-th interpolation cycle during the sawing of the i-th layer. V ik is a unit vector with P ik as the starting point and parallel to P ik O 3 . It satisfies:

[0098]

[0099] Then, the tool contact point P on the ruled surface of the cylinder in the (k + 1)-th interpolation cycle ik+1 The corresponding tool axis vector V ik+1 Can be expressed as:

[0100]

[0101] For Figure 4 The ruled surface of the cylinder shown was experimentally verified, and its parametric curve equation is:

[0102] θ ∈ [0, 2π], z ∈ [0, 8]

[0103] Its simulation machining diagram is as shown in Figure 5 The figure. The experimental results show that this algorithm can control the movement direction and tilt angle of the saw blade so that it is always tangent to the surface to be machined, meeting the machining requirements of the ruled surface of the cylinder of stone products.

Claims

1. Instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces, Characterized in that, Performing instruction point interpolation on a cylindrical workpiece to achieve sawing of the cylindrical workpiece, including the following steps: Determining the maximum sawing depth of the cylindrical workpiece based on the contour error of the cylindrical workpiece; Obtaining the inclination angle of the circular saw blade according to the maximum sawing depth; Determining the number of full-cut layers according to the maximum sawing depth; For each layer of full-cut of the workpiece, performing instruction point interpolation according to the interpolation period of the circular saw blade to obtain the position of the contact point between the circular saw blade and the workpiece for each interpolation period; obtaining the attitude of the circular saw blade according to the inclination angle of the circular saw blade and the parameters of each interpolation period; The position of the contact point between the circular saw blade and the workpiece is as follows: x ik+1 , y ik+1 , z ik+1 represent the coordinate values in the x, y, and z directions of the saw blade cutting contact point on the cylindrical ruled surface at the (k + 1)-th interpolation cycle when sawing the i-th layer, and Δθ ik+1 represents the θ corresponding to the k-th interpolation cycle to the (k + 1)-th interpolation cycle when sawing the i-th layer ik and θ ik+1 angle change value; The attitude of the circular saw blade is obtained by the following formula: Let V ik (V ikx ,V iky ,V ikz ) be the cutter axis vector corresponding to the saw blade cutting contact point P ik on the cylindrical ruled surface during the k-th interpolation cycle for the i-th layer cutting, and V ik is the unit vector starting from P ik and parallel to P ik O 3 , satisfying: Then, the saw blade cutting contact point P on the cylindrical ruled surface at the (k + 1)-th interpolation cycle ik+1 The corresponding cutter axis vector V ik+1 Can be expressed as: Among them, P k O 3 represents the sawing starting point P k and the center O of the circular saw blade 3 of the line segment, α is the inclination angle of the saw blade surface, θ ik is the polar angle of the saw blade cutting contact point at the k-th interpolation cycle when sawing the i-th layer.

2. The instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces according to claim 1, Characterized in that, Sawing the workpiece according to the position of the contact point between the circular saw blade and the workpiece and the attitude of the circular saw blade.

3. The instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces according to claim 1, Characterized in that, Determining the sawing depth of the cylindrical workpiece based on the contour error of the cylindrical workpiece, obtained by the following formula: d max is the maximum sawing depth, and δ max is the set maximum contour error, and R is the radius of the bottom circle of the cylindrical workpiece.

4. The instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces according to claim 1, Characterized in that, The inclination angle of the circular saw blade is obtained by the following formula: α is the inclination angle of the saw blade surface, r is the radius of the saw blade surface, d max is the maximum sawing depth, δ max is the maximum contour error, and R is the radius of the bottom circle of the cylindrical workpiece.

5. The instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces according to claim 1, Characterized in that, The number of integral cutting layers where h is the height of the cylindrical workpiece and d max is the maximum sawing depth.

6. Instruction point interpolation device applicable to the sawing process of cylindrical ruled surfaces, Characterized in that, Including: Saw blade attitude module, used to determine the maximum sawing depth of the cylindrical workpiece based on the contour error of the cylindrical workpiece; obtaining the inclination angle of the circular saw blade according to the maximum sawing depth; Workpiece full-cut module, used to determine the number of full-cut layers according to the maximum sawing depth; Instruction point interpolation module, used for each layer of full-cut of the workpiece, performing instruction point interpolation according to the interpolation period of the circular saw blade to obtain the position of the contact point between the circular saw blade and the workpiece for each interpolation period; obtaining the attitude of the circular saw blade according to the inclination angle of the circular saw blade and the parameters of each interpolation period.

7. Instruction point interpolation device applicable to the sawing process of cylindrical ruled surfaces, Characterized in that, Including a memory and a processor; the memory is used to store a computer program; the processor is used to, when executing the computer program, implement the instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces according to claim 1.

8. A computer-readable storage medium, Characterized in that, A computer program is stored on the storage medium, and when the computer program is executed by a processor, the instruction point interpolation method applicable to the sawing process of cylindrical ruled surfaces according to claim 1 is implemented.

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