Complex curve indexable blade grinding method based on NURBS curve fitting

Abstract

The invention relates to the technical field of grinding machining, in particular to a complex curve indexable blade grinding method based on NURBS curve fitting, and the method comprises the following steps: S1, collecting and processing data, extracting coordinates, denoising and homogenizing the data; s2, performing NURBS curve fitting, and solving an equation to fit a curve; s3, back calculation of the adaptive interpolation curve is carried out, and curvature smoothness is verified; s4, curve machining acceleration and deceleration control, segmented acceleration and deceleration and dynamic parameter adjustment are carried out; and S5, the numerical control grinding machine executes machining, coordinate conversion is conducted, and real-time error monitoring is passed. Complex curve machining is achieved based on URBS curve fitting, a seven-section S-shaped curve acceleration and deceleration control algorithm is adopted, it is guaranteed that the machining speed reaches the planned maximum speed and cannot reach the planned maximum acceleration, acceleration sudden change is eliminated, mechanical shock and vibration are effectively reduced, and the machining precision is improved. And the requirements of different working conditions can be met by adjusting parameters such as the maximum speed, the maximum acceleration and the jerk.

Description

Technical Field

[0001] The invention relates to the technical field of grinding processing, and in particular to a grinding method for a complex curve indexable insert based on NURBS curve fitting. Background Art

[0002] Non-uniform rational B-spline (NURBS) is a very useful tool for geometric modeling. It is increasingly valued by the engineering community for its excellent properties. It can represent regular surfaces and free-form surfaces in a unified mathematical form. It has the ability to manipulate control vertices and weights, providing full flexibility for the design of various shapes. It has powerful geometric supporting technology and can be used in various aspects such as design, analysis and processing. It is a good generalization of the non-rational B-spline form and the rational and non-rational Bezier forms.

[0003] For blades such as involutes, traditional peripheral grinding methods often use multiple arc segments for approximation. The fitting processing accuracy is poor and the measurement process is extremely complicated. It is no longer suitable for grinding such complex curves. In fact, blades are often connected by multiple curves. This error will also cause joints to form at the connection points of the curves. This is also a long-standing difficult problem in peripheral grinding. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of joint marks formed at the connection points of multiple curves in the prior art and to propose a complex curve indexable insert grinding method based on NURBS curve fitting.

[0005] In order to achieve the above object, the present invention adopts the following technical solution: a complex curve indexable insert grinding method based on NURBS curve fitting, comprising the following steps:

[0006] Step S1, data acquisition and processing, extracting coordinates, denoising and homogenizing data;

[0007] Step S2, NURBS curve fitting, solving the equation to fit the curve;

[0008] Step S3, back calculation of the adaptive interpolation curve to verify the curvature smoothness;

[0009] Step S4, curve processing acceleration and deceleration control, segmented acceleration and deceleration, dynamic adjustment of parameters;

[0010] Step S5, the CNC grinding machine performs machining, coordinate conversion, and real-time error monitoring.

[0011] Furthermore, in step S1, the following sub-steps are also included:

[0012] S1-1, geometric modeling and feature analysis, based on the space geometric feature parameters of the blade edge shape, back angle, tangent direction, and corner parameters, a mathematical model of the tool position point is established to extract the geometric information of the curvature and deviation value of the tool position point, and identify the continuous straight line segments and curved surface areas that need to be optimized;

[0013] S1-2, collect discrete tool position points, give a set of discrete shape value points in the NURBS curve and surface, construct the curve and surface through these shape value points, and the shape value points are also called curve and surface interpolation;

[0014] S1-2, discrete value point preprocessing, identifying and correcting the defective points in the value points, mainly noise points or measurement error points, performing data cleaning on these abnormal points in the value points, and then using wavelet smoothing method to remove data noise.

[0015] Further, in step S2, the rational fraction expression of the NURBS curve equation is:

[0016]

[0017] Where:

[0018]

[0019] Agreement:

[0020] p(u) is the coordinate of the point on the curve corresponding to parameter u;

[0021] d i is the control vertex, i.e., the key point that affects the shape of the curve, i=0, 1, ..., n, representing the sequence number, and moving the control vertex can significantly change the shape of the curve;

[0022] ω i is the weight factor, respectively related to the control vertex d i Correspondingly, and ω i >0, sequential connection d i A control polygon is formed and the weight factor can be adjusted to fine-tune the local shape of the curve;

[0023] N i,k (u) is the k-th canonical B-spline basis function of degree i, which is the k-th canonical B-spline basis function calculated by the node vector U, where k is the spline order, k=3, i.e., a cubic curve;

[0024] The node vector U represents a non-uniform ordered real number sequence U = {u 0 ,u 1 ,…,u m}, m = n + k + 1, the node distribution determines the local support of the basis function and affects the smoothness and flexibility of the curve;

[0025] u is a curve parameter, and its value range is determined by the node vector U, usually u∈[u k-1 ,u k+1 ];

[0026] molecular Represents the control vertex d i A weighted linear combination of i N i,k (u), denominator is the normalization factor, which ensures that the curve has affine invariance and is not affected by translation, rotation, and scaling.

[0027] Furthermore, in step S3, the following sub-steps are also included:

[0028] S3-1, calculate the node vector, given a set of type value points P of a K-order NURBS curve i (i=0,1,…,n), the first and last points of the curve are required to coincide with the type value point and P i Sequentially with the nodes u in the domain of the construction curve i+k (i=0,1,…,n) one by one, parameterize the type value points to determine the type value point P i The parameter value u i+k (i=0,1,…,n), with n+1 type value points P i The k-th degree NURBS curve will consist of n+3 control vertices d i (i=0,1,…,n,n+1,n+2) and its weight factors and node vector U=[u 0 ,u 1 ,…,u n+k+3 ]definition;

[0029] The improved modified chord length parameterization method plays a role in correcting curve segments with large absolute curvature and shorter chord length than the actual arc length, and the generated interpolation curve has good smoothness. The modified chord length parameterization algorithm is as follows:

[0030] u 0 =u 1 =u 2 =u 3 =0

[0031] This formula indicates that the parameters of the first four nodes all start from zero, which is used to fix the parameterization starting point to ensure the stability of the initial segment of the curve;

[0032] u n+3 =u n+4 =u n+5 =u n+6 =1

[0033] This formula indicates that the final parameter value is fixed to 1, where i = 1, 2, ..., n-1, n represents the total number of data, and the parameter recursive formula is as follows:

[0034]

[0035] p i represents the coordinates of the i-th data point, numerator |p i -p i-1 | represents the Euclidean distance between adjacent points, that is, the chord length, the denominator represents the weighted sum of all chord lengths, used to normalize the parameter increment, k i is the weight coefficient used to adjust the contribution of the chord length and is calculated as follows:

[0036]

[0037] where Δp i is the difference vector, Δp i =p i+1 -p i ,|Δp i | represents the modulus of the differential vector, that is, the distance between adjacent points, θ i is the local angle factor:

[0038]

[0039] ∠p i-1 p i p i+1 For p i-1 、p i and p i+1 The angle formed by the three points, and p i is a vertex, so π-∠p i-1 p i p i+1 is the complementary angle of the included angle, which indicates the local curvature of the curve. This formula limits θ i Maximum Avoid excessive influence of sharp angles on weights, θ i The smaller the k, the more severe the local bending. i The weight of increases, and the parameter intervals become denser;

[0040] In addition, boundary conditions are required:

[0041] |Δp -1 |=|Δp n |=0

[0042] Δp -1 and Δp n is a virtual difference vector used to process the boundary conditions of the end node in calculating k1 and k n These terms are automatically zeroed to ensure the universality of the formula.

[0043] S3-2, calculate boundary conditions. The linear equations for solving the spline curve parameters are composed of n+1 vector equations with n+3 unknown control vertices. The equations are as follows:

[0044]

[0045] Where p(u 3+i ) indicates that the parameter is u 3+i When the point on the cubic B-spline curve, d j are control points, there are n+3 of them, j=0,1,...,n+2; N j,3 (u 3+i ) represents the jth cubic B-spline basis function (the subscript 3 indicates the degree is 3), defined on a certain node vector; u 3+i is the parameter value, located at the node with index 3+i in the node vector, p i is a given type value point, with n = 1 in total, i = 0, 1, ..., n, and the curve is required to be 3+i Pass through these points exactly;

[0046] S3-3, inverse calculation of control vertices, for c 2 Continuous, that is, a second-order continuous NURBS cubic closed curve, the first and last data points overlap, n-1 equations are used to calculate n+1 control vertices, and the matrix expression for the inverse calculation of the control vertices of the NURBS cubic closed curve is:

[0047]

[0048] Where di is the control vertex, Δ i =u i+1 -u i , i=0,1,…,n-2);

[0049] For NURBS cubic open curves, two additional equations that satisfy the boundary conditions need to be added. The repetition of the two end points of the NURBS cubic open curve is 4. The first and last control vertices of the NURBS cubic curve are the type value points of its first and last ends, that is: d 0 =p 0 , d n+2 =p n , the boundary condition is the tangent vector condition, and the expression of the inverse calculation of the control vertex of the NURBS cubic open curve is given in the form of a matrix:

[0050]

[0051] Where: di is the control vertex, Δi =u i+1 -u i (i=0,1,…,n), then:

[0052]

[0053]

[0054] By solving the above linear equations, we can obtain all unknown control vertices, select weight factors, and finally determine the expression of the NURBS curve.

[0055] Furthermore, in step S4, the acceleration and deceleration control algorithm in the motion control adopts a flexible S-curve acceleration and deceleration algorithm, which has a seven-segment S-curve acceleration and deceleration algorithm and a five-segment S-curve acceleration and deceleration algorithm. A seven-segment S-curve acceleration and deceleration control algorithm is adopted. The seven-segment S-shaped speed curve generally includes acceleration, uniform acceleration, deceleration, uniform speed, acceleration and deceleration, uniform deceleration, and deceleration, a total of 7 segments. The acceleration and deceleration control process needs to set parameters first, then perform time segmentation, determine whether the acceleration can reach the maximum, calculate the uniform speed segment time, and determine the displacement, speed, acceleration, and jerk according to the above steps, so as to achieve the best grinding processing effect and processing efficiency.

[0056] Further, in step S4, the tool path is verified by using a virtual simulation platform, the tool path is verified by using a virtual environment of a numerical control system, the interference risk between the grinding wheel and the fixture is detected, error compensation is performed, the machining accuracy is ensured, the optimized NURBS trajectory is converted into a code adapted to the numerical control system, and the grinding machine is driven to complete high-precision machining;

[0057] Fixture optimization: improve fixture structure based on finite element analysis, reduce deformation and vibration caused by clamping force, and improve positioning accuracy.

[0058] The beneficial effects brought about by the technical solution provided by the present invention include at least:

[0059] The present invention adopts a seven-segment S-curve acceleration and deceleration control algorithm to ensure that the processing speed reaches the planned maximum speed and cannot reach the planned maximum acceleration. Analysis and adjustment are performed according to different situations. The seven-segment S-curve eliminates acceleration mutations and effectively reduces mechanical shock and vibration. The maximum speed, maximum acceleration, jerk and other parameters can be adjusted to adapt to different motion requirements. The seven-segment curve optimized by polynomial fitting can retain the original smooth characteristics and eliminate the acceleration inflection point. The symmetrical design simplifies the derivation of the displacement formula, is convenient for practical application, and supports dynamic speed regulation. The speed can be segmented and planned on the path with large curvature changes to ensure processing accuracy.

[0060] The present invention uses NURBS curve fitting to achieve accurate description of complex curves using control points, node vectors and weight factors, avoiding the contour error and surface unevenness problems caused by traditional methods of dividing the curve into a large number of small line segments. NURBS directly describes the curve with mathematical equations. By adjusting the control points, weights or node vectors, the curve can be locally modified without affecting the overall shape. This feature is particularly suitable for the optimal design of complex blade contours.

[0061] The present invention adopts an improved modified chord length parameterization method, which plays a role in correcting curve segments with large absolute curvature and shorter chord lengths than actual arc lengths, and the generated interpolation curve has better smoothness. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0063] Figure 1 A method step diagram provided for an embodiment of the present invention;

[0064] Figure 2 This is an S-shaped acceleration and deceleration control curve provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following is a detailed description of the specific implementation method, structure, features and effects of a complex curve indexable insert grinding method based on NURBS curve fitting proposed by the present invention in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form.

[0066] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0067] The following examples are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0068] A specific solution of a complex curve indexable insert grinding method based on NURBS curve fitting provided by the present invention is described in detail below in conjunction with the accompanying drawings.

[0069] Example

[0070] See also Figure 1 , which shows a method flow chart of a complex curve indexable insert grinding method based on NURBS curve fitting provided by an embodiment of the present invention, the method comprising the following steps:

[0071] Step S1, data acquisition and processing, extracting coordinates, denoising and homogenizing data;

[0072] Wherein step S1 also includes the following sub-steps:

[0073] S1-1, geometric modeling and feature analysis, the blade edge shape, blade geometric parameters, blade back angle, transition arc radius, edge shape and other parameters directly affect the mathematical model construction of the grinding trajectory; grinding wheel parameters, grinding wheel shape, size, posture, etc., are used to calculate the contact trajectory between the grinding wheel and the blade, and extract the geometric information of the curvature and deviation value size of the tool position point;

[0074] Identify the continuous straight line segments and curved surface areas that need to be optimized, and establish a mathematical model of the tool position point.

[0075] S1-2, collect discrete tool position points. In the NURBS curve and surface application, a set of discrete shape value points is given, and the curve and surface are constructed through these shape value points, that is, collect curve and surface interpolation;

[0076] S1-2, discrete value point preprocessing, identify and correct defective points in the tool position points, mainly noise points or measurement error points, perform data cleaning on these abnormal points, and then use wavelet smoothing to remove data noise. Use convolutional neural network to perform semantic segmentation on the tool position point cloud, automatically identify the curvature mutation area and divide it into fitting sub-segments. The training data can come from historical processing cases, and the generalization ability is improved through transfer learning.

[0077] Step S2, NURBS curve fitting, solving equations to fit the curve;

[0078] In step S3, the rational fraction expression of the NURBS curve equation is:

[0079]

[0080] Where:

[0081]

[0082] Agreement:

[0083] p(u) is the coordinate of the point on the curve corresponding to parameter u;

[0084] d iis the control vertex, i.e., the key point that affects the shape of the curve, i=0, 1, ..., n. Moving the control vertex can significantly change the shape of the curve.

[0085] ω i is the weight factor, respectively related to the control vertex d i Correspondingly, and ω i >0, sequential connection d i A control polygon is formed, and k consecutive weight factors cannot be zero at the same time. Adjusting the weight factors can fine-tune the local shape of the curve;

[0086] N i,k (u) is the i-th k-order canonical B-spline basis function, which is represented by the node vector U = [u0,u1,…,u n+k+1 ] Calculate and determine the k-order canonical B-spline basis function, i represents the serial number, k is the spline order, k = 3, that is, a cubic curve;

[0087] The node vector U represents a non-uniform ordered real number sequence U = {u 0 ,u 1 ,…,u m}, m = n + k + 1, the node distribution determines the local support of the basis function and affects the smoothness and flexibility of the curve;

[0088] u is a curve parameter, and its value range is determined by the node vector U, usually u∈[u k-1 ,u k+1 ];

[0089] molecular Represents the control vertex d i A weighted linear combination of i N i,k (u), denominator is the normalization factor, which ensures that the curve has affine invariance and is not affected by translation, rotation, and scaling.

[0090] For NURBS curves with disjoint data points at the beginning and end, i.e. open curves, the repetition degree of the nodes at both ends is usually taken as r = k + 1, i.e. u 0 =u 1 =…=u k ,u n+1 =u n+2 =…=u n+k+1 In many practical applications, the end node values ​​are often 0 and 1, so the domain of the NURBS curve can be expressed as It can be obtained that when n = k, the k-order NURBS curve degenerates into a k-order rational Bezier curve, and its node vector has the same geometric properties as the endpoints of the rational Bezier curve of the same order. If the first and last weight factors are not zero, that is, ω 0 >0,ωn >0, the first and last points of the curve coincide with the first and last vertices of the control polygon respectively, and the curve is tangent to the first and last edges of the control polygon at this point.

[0091] Step S3, back-calculating the adaptive interpolation curve to verify the curvature is smooth;

[0092] In step S3, given a set of shape value points, a NURBS curve passing through these shape value points is generated, which is called the inverse calculation of the curve, and generally includes the following steps:

[0093] S3-1, calculate the node vector; given a set of shape value points P of a K-order NURBS curve i (i=0,1,…,n), the first and last points of the curve are required to coincide with the type value point and P i Sequentially with the nodes u in the domain of the construction curve i+k (i=0,1,…,n) one by one, parameterize the type value points to determine the type value point P i The parameter value u i+k (i=0,1,…,n), with n+1 type value points P i The k-th degree NURBS curve will consist of n+3 control vertices d i (i=0,1,…,n,n+1,n+2) and its weight factors and node vector U=[u 0 ,u 1 ,…,u n+k+3 ]definition;

[0094] The final subscript of the node vector is n+k+3 because the number of nodes is r=k+1 more than the number of control vertices, and the number of control vertices is 2 more than the number of value points, so the final subscript of the node vector is =n+2+k+1=n+k+3 value points, the subscript starts from 0 and ends at n), and the repetition of the first and last nodes is r=k+1. The first k+1 nodes have a value of 0, and the last k+1 nodes have a value of 1.

[0095] The length of each node interval is expressed as: Δ i =u i+1 -u i Taking the cubic curve (k=3) as an example, the commonly used parameterization methods include uniform parameterization, cumulative chord length parameterization, centripetal parameterization and modified chord length parameterization. Because the curvature of the spline curve of the actual blade may be large, and it may also be connected with other curves with large curvature to form an arc, the actual processing of the workpiece usually produces a joint mark, which is also a difficulty that has always existed in grinding. Therefore, the improved modified chord length parameterization method is finally adopted, which can correct the curve segment with large absolute curvature and shorter chord length than the actual arc length, and the generated interpolation curve has good smoothness. The modified chord length parameterization algorithm is as follows:

[0096] u 0 =u 1 =u 2 =u 3 =0

[0097] The initial parameter value indicates that the parameters of the first four nodes all start from zero, which is used to fix the parameterization starting point to ensure the stability of the initial segment of the curve;

[0098] u n+3 =u n+4 =u n+5 =u n+6 =1

[0099] The final parameter value is fixed to 1, where i = 1, 2, ..., n-1, n represents the total number of data, and the parameter recursive formula is as follows:

[0100]

[0101] p i represents the coordinates of the i-th data point, numerator |p i -p i-1 | represents the Euclidean distance between adjacent points, that is, the chord length, the denominator represents the weighted sum of all chord lengths, used to normalize the parameter increment, k i is the weight coefficient used to adjust the contribution of the chord length and is calculated as follows:

[0102]

[0103] where Δp i is the difference vector, Δp i =p i+1 -p i ,|Δp i | represents the modulus of the differential vector, that is, the distance between adjacent points, θ i is the local angle factor:

[0104]

[0105] ∠p i-1 p i p i+1 For p i-1 、p i and p i+1 The angle formed by the three points, and p i is a vertex, so π-∠p i-1 p i p i+1 is the complementary angle of the included angle, which can express the local curvature of the curve. Limit θ iMaximum Avoid excessive influence of sharp angles on weights, θ i The smaller the k, the more severe the local bending. i The weight of increases, and the parameter intervals become denser;

[0106] There are also boundary conditions:

[0107] |Δp -1 |=|Δp n |=0

[0108] Δp -1 and Δp n is a virtual difference vector used to process the boundary conditions of the end node in calculating k 1 and k n These terms are automatically zeroed to ensure the universality of the formula.

[0109] S3-2, calculate boundary conditions. The linear equations for solving the spline curve parameters are composed of n+1 vector equations with n+3 unknown control vertices. The equations are as follows:

[0110]

[0111] Where p(u 3+i ) indicates that the parameter is u 3+i When the point on the cubic B-spline curve, d j are control points, there are n+3 of them, j=0,1,...,n+2; N j,3 (u 3+i ) represents the jth cubic B-spline basis function (the subscript 3 indicates the degree is 3), defined on a certain node vector; u 3+i is the parameter value, located at the node with index 3+i in the node vector, p i is a given type value point, with n = 1 in total, i = 0, 1, ..., n, and the curve is required to be 3+i Pass through these points exactly;

[0112] S3-3, inverse calculation of control vertices, for c 2 Continuous, that is, a second-order continuous NURBS cubic closed curve, the first and last data points overlap, n-1 equations are used to calculate n+1 control vertices, and the matrix expression for the inverse calculation of the control vertices of the NURBS cubic closed curve is:

[0113]

[0114] Where di is the control vertex, Δ i =u i+1 -u i , i=0,1,…,n-2;

[0115] For NURBS cubic open curves, two additional equations that satisfy the boundary conditions need to be added. The repetition of the two end points of the NURBS cubic open curve is 4. The first and last control vertices of the NURBS cubic curve are the type value points of its first and last ends, that is: d 0 =p 0 , d n+2 =p n , the boundary condition is the tangent vector condition, and the expression of the inverse calculation of the control vertex of the NURBS cubic open curve is given in the form of a matrix:

[0116]

[0117] Where: di is the control vertex, Δ i =u i+1 -u i (i=0,1,…,n), then:

[0118]

[0119] By solving the above linear equations, we can obtain all unknown control vertices, select weight factors, and finally determine the expression of the NURBS curve. This curve processing algorithm is applicable to both two-dimensional plane curves and three-dimensional space curves, and has good robustness.

[0120] Step S4, curve processing acceleration and deceleration control, segmented acceleration and deceleration, dynamic adjustment of parameters;

[0121] Among them, the commonly used acceleration and deceleration control algorithms in motion control in step S4 include linear curve and S-curve acceleration and deceleration control algorithms. The acceleration of linear acceleration and deceleration is not zero at the start, acceleration and deceleration transition, and stop. There is a sudden change in speed, which produces a rigid impact and cannot be applied to high-speed CNC systems. The S-shaped curve is smoother and avoids the impact of the linear curve at the speed inflection point. However, under the same expected speed and acceleration conditions, it takes a little longer to move the same distance. Commonly used flexible S-curve acceleration and deceleration algorithms include the seven-segment S-curve acceleration and deceleration algorithm and the five-segment S-type acceleration and deceleration algorithm. Compared with the seven-segment S-type acceleration and deceleration algorithm, the five-segment S-type acceleration and deceleration algorithm omits the uniform acceleration and deceleration stages, and eliminates the restriction that the initial velocity and the final velocity are equal.

[0122] Reference Figure 2 The present invention adopts a seven-segment S-curve acceleration and deceleration control algorithm. The seven-segment S-curve speed curve generally includes acceleration, uniform acceleration, deceleration, uniform speed, acceleration and deceleration, uniform deceleration, and deceleration, a total of 7 segments, corresponding to T in 2 respectively. 1 ~T 7 , T corresponds to the time 0, T j1 , T a -T j1 , Ta , T a +T v TT d +T j2 TT j2 and T, the acceleration and deceleration control process of the present invention is analyzed.

[0123] First set the relevant parameters:

[0124] p 0 and v 0 are the position and velocity of the starting point, respectively, 1 and v 1 are the position and velocity of the end point, v max 、a max and j max are the planned maximum speed, maximum acceleration and maximum jerk, v lim and a lim are the actual achievable speed and acceleration respectively.

[0125] Time segment

[0126] The acceleration segment t∈[0,T j1 ), with the maximum jerk making the acceleration a max ;

[0127] Uniform acceleration segment t∈[T j1 , T a -T j1 ), with maximum acceleration a max To accelerate;

[0128] Deceleration segment t∈[T a -T j1 , T a ), with maximum jerk -j max Make the acceleration become 0;

[0129] Uniform speed segment t∈[T a , T a +T v ), at a constant speed v max Uniform processing speed;

[0130] Acceleration and deceleration section t∈[T a +T v , TT d +T j2 ), with maximum jerk -j max Change the acceleration from 0 to -a max ;

[0131] Uniform deceleration segment t∈[TT d +T j2 , TTj2 ), with maximum acceleration -a max To decelerate;

[0132] Deceleration and deceleration segment t∈[TT j2 , T):, with maximum jerk-j max Make the acceleration 0.

[0133] Determine whether the acceleration can reach the maximum

[0134] For the acceleration section, if the planned maximum acceleration cannot be achieved, then:

[0135]

[0136] a lim =v max -v 0 .

[0137] At this time, the acceleration period is:

[0138]

[0139] T a =2T j1 ;

[0140] If the planned maximum acceleration is reached, then:

[0141]

[0142] a lim =a max .

[0143] For the deceleration section, if the planned maximum acceleration -a is not reached max ,but:

[0144]

[0145] a lin =v max -v 1 .

[0146] At this time, the deceleration time is:

[0147]

[0148] T a =2T j2 ;

[0149] a lim =a max .

[0150] If the planned maximum acceleration -a is reached max,but:

[0151]

[0152] Calculate the time T of the uniform speed segment v

[0153]

[0154] If T v >0, it means that there is a uniform speed period and the planned maximum speed and maximum acceleration can be reached, that is, v lim =v max ,a lim =a max ;

[0155] If T v =0, it means that there is no uniform speed segment, and the planned maximum speed and maximum acceleration have just been reached. At this time, there are:

[0156]

[0157] v lim =a max ×T a -T j ;

[0158] T=T a +T d ;

[0159] If T v <0, it means that the planned maximum speed cannot be achieved, but whether the planned maximum acceleration can be achieved depends on T a With 2T j1 , T d With 2T j2 The size of . At this time:

[0160]

[0161] Now let’s discuss T a With 2T j1 , T d With 2T j2 Size:

[0162] If T v <0, and T a ≥2T j1 , T d ≥2T j2 , indicating that the planned maximum speed cannot be reached at this time, but the planned maximum acceleration can be reached. At this time, there are:

[0163] v lim =v 0 +amax ×(T a -T j );

[0164] T=T a +T j .

[0165] If T v <0, and T a <2T j1 , T d <2T j2 , indicating that the planned maximum speed and maximum acceleration cannot be achieved at this time. The method at this time is to gradually reduce the set maximum acceleration and reduce the step size when necessary until T is satisfied. a ≥2T j1 , T d ≥2T j2 until.

[0166] Finally, according to the above steps, the displacement, velocity, acceleration and jerk are determined to achieve the best grinding effect and processing efficiency.

[0167] Step S5, the CNC grinding machine performs machining, coordinate conversion, and real-time error monitoring;

[0168] In step S5, the tool path is verified by using a virtual simulation platform, the tool path is verified by using a virtual environment of a numerical control system, the risk of interference between the grinding wheel and the fixture is detected, error compensation is performed, machining accuracy is ensured, the optimized NURBS trajectory is converted into a code adapted to the numerical control system, and the grinding machine is driven to complete high-precision machining;

[0169] Fixture optimization: improve fixture structure based on finite element analysis, reduce deformation and vibration caused by clamping force, and improve positioning accuracy.

[0170] In this way, a complex curve indexable insert grinding method based on NURBS curve fitting can be realized.

[0171] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for grinding complex curve indexable inserts based on NURBS curve fitting, characterized in that: The method includes: Step S1, data acquisition and processing, extracting coordinates, denoising and homogenizing data; Step S2, NURBS curve fitting, solving the equation to fit the curve; Step S3, back calculation of the adaptive interpolation curve to verify the curvature smoothness; Step S4, curve processing acceleration and deceleration control, segmented acceleration and deceleration, dynamic adjustment of parameters; Step S5, the CNC grinding machine performs machining, coordinate conversion, and real-time error monitoring.

2. The complex curve indexable insert grinding method based on NURBS curve fitting according to claim 1, characterized in that: Wherein step S1 also includes the following sub-steps: S1-1, geometric modeling and feature analysis, based on the space geometric feature parameters of the blade edge shape, back angle, tangent direction, and corner parameters, a mathematical model of the tool position point is established to extract the geometric information of the curvature and deviation value of the tool position point, and identify the continuous straight line segments and curved surface areas that need to be optimized; S1-2, collect discrete tool position points, give a set of discrete shape value points in the NURBS curve and surface, construct the curve and surface through these shape value points, and the shape value points are also called curve and surface interpolation; S1-2, discrete value point preprocessing, identifying and correcting the defective points in the value points, mainly noise points or measurement error points, performing data cleaning on these abnormal points in the value points, and then using wavelet smoothing method to remove data noise.

3. The method for grinding complex curve indexable inserts based on NURBS curve fitting according to claim 1, characterized in that: In step S2, the rational fraction expression of the NURBS curve equation is: Where: Agreement: p(u) is the coordinate of the point on the curve corresponding to parameter u; d i is the control vertex, i.e., the key point that affects the shape of the curve, i=0, 1, ..., n, representing the sequence number, and moving the control vertex can significantly change the shape of the curve; ω i is the weight factor, respectively related to the control vertex d i Correspondingly, and ω i >0, sequential connection d i A control polygon is formed and the weight factor can be adjusted to fine-tune the local shape of the curve; N i,k (u) is the k-th canonical B-spline basis function of degree i, which is the k-th canonical B-spline basis function calculated by the node vector U, where k is the spline order, k=3, i.e., a cubic curve; The node vector U represents a non-uniform ordered real number sequence U = {u0,u1,…,u m }, m = n + k + 1, the node distribution determines the local support of the basis function and affects the smoothness and flexibility of the curve; u is a curve parameter, and its value range is determined by the node vector U, usually u∈[u k-1 ,u k+1 ]; molecular Represents the control vertex d i A weighted linear combination of i N i,k (u), denominator is the normalization factor, which ensures that the curve has affine invariance and is not affected by translation, rotation, and scaling.

4. The method for grinding complex curve indexable inserts based on NURBS curve fitting according to claim 1, characterized in that: Wherein step S3 also includes the following sub-steps: S3-1, calculate the node vector, given a set of type value points P of a K-order NURBS curve i (i=0,1,…,n), the first and last points of the curve are required to coincide with the type value point and P i Sequentially with the nodes u in the domain of the construction curve i+k (i=0,1,…,n) one by one, parameterize the type value points to determine the type value point P i The parameter value u i+k (i=0,1,…,n), with n+1 type value points P i The k-th degree NURBS curve will consist of n+3 control vertices d i (i=0,1,…,n,n+1,n+2) and its weight factors and node vector U=[u0,u1,…,u n+k+3 ]definition; The improved modified chord length parameterization method plays a role in correcting curve segments with large absolute curvature and shorter chord length than the actual arc length, and the generated interpolation curve has good smoothness. The modified chord length parameterization algorithm is as follows: u0=u1=u2=u3=0 This formula indicates that the parameters of the first four nodes all start from zero, which is used to fix the parameterization starting point to ensure the stability of the initial segment of the curve; in n+3 =in n+4 =in n+5 =in n+6 =1 This formula indicates that the final parameter value is fixed to 1, where i = 1, 2, ..., n-1, n represents the total number of data, and the parameter recursive formula is as follows: p i represents the coordinates of the i-th data point, numerator |p i -p i-1 | represents the Euclidean distance between adjacent points, that is, the chord length, the denominator represents the weighted sum of all chord lengths, used to normalize the parameter increment, k i is the weight coefficient used to adjust the contribution of the chord length and is calculated as follows: Where Δp i is the difference vector, Δp i =p i+1 -p i , |Δp i | represents the modulus of the differential vector, that is, the distance between adjacent points, θ i is the local angle factor: ∠p i-1 p i p i+1 For p i-1 、p i and p i+1 The angle formed by the three points, and p i is a vertex, so π-∠p i-1 p i p i+1 is the complementary angle of the included angle, which indicates the local curvature of the curve. This formula limits θ i Maximum Avoid excessive influence of sharp angles on weights, θ i The smaller the k, the more severe the local bending. i The weight of increases, and the parameter intervals become denser; In addition, boundary conditions are required: |Δp -1 |=|Δp n |=0 Δp -1 and Δp n is a virtual difference vector used to process the boundary conditions of the end node in calculating k1 and k n These terms are automatically zeroed to ensure the universality of the formula. S3-2, calculate boundary conditions. The linear equations for solving the spline curve parameters are composed of n+1 vector equations with n+3 unknown control vertices. The equations are as follows: Where p(u 3+i ) indicates that the parameter is u 3+i When the point on the cubic B-spline curve, d j are control points, there are n+3 of them, j=0,1,...,n+2; N j,3 (u 3+i ) represents the jth cubic B-spline basis function, defined on a certain node vector; u 3+i is the parameter value, located at the node with index 3+i in the node vector, p i is a given type value point, with n = 1 in total, i = 0, 1, ..., n, and the curve is required to be 3+i Pass through these points exactly; S3-3, inverse calculation of control vertices, for c 2 Continuous, that is, a second-order continuous NURBS cubic closed curve, the first and last data points overlap, n-1 equations are used to calculate n+1 control vertices, and the matrix expression for the inverse calculation of the control vertices of the NURBS cubic closed curve is: Where di is the control vertex, Δ i =u i+1 -u i , i=0,1,…,n-2); For NURBS cubic open curves, two additional equations that satisfy the boundary conditions need to be added. The repetition of the two end points of the NURBS cubic open curve is 4. The first and last control vertices of the NURBS cubic curve are the type value points of its first and last ends, that is: d0 = p0, d n+2 =p n , the boundary condition is the tangent vector condition, and the expression of the inverse calculation of the control vertex of the NURBS cubic open curve is given in the form of a matrix: Where: di is the control vertex, Δ i =u i+1 -u i (i=0,1,…,n), then: By solving the above linear equations, we can obtain all unknown control vertices, select weight factors, and finally determine the expression of the NURBS curve.

5. The method for grinding complex curve indexable inserts based on NURBS curve fitting according to claim 1, characterized in that: Among them, in step S4, the acceleration and deceleration control algorithm in the motion control adopts a flexible S-curve acceleration and deceleration algorithm, there are seven-segment S-curve acceleration and deceleration algorithms and five-segment S-curve acceleration and deceleration algorithms, and a seven-segment S-curve acceleration and deceleration control algorithm is adopted. The seven-segment S-shaped speed curve generally includes acceleration, uniform acceleration, deceleration, uniform speed, acceleration and deceleration, uniform deceleration, and deceleration, a total of 7 segments. The acceleration and deceleration control process needs to set parameters first, and then perform time segmentation, determine whether the acceleration can reach the maximum, calculate the uniform speed segment time, and determine the displacement, speed, acceleration, and jerk according to the above steps, so as to achieve the best grinding effect and processing efficiency.

6. The method for grinding complex curve indexable inserts based on NURBS curve fitting according to claim 1, characterized in that: Use the virtual simulation platform to verify the tool path, use the virtual environment of the CNC system to verify the tool path, detect the interference risk between the grinding wheel and the fixture, perform error compensation, ensure processing accuracy, convert the optimized NURBS trajectory into code suitable for the CNC system, and drive the grinder to complete high-precision processing; Fixture optimization: improve fixture structure based on finite element analysis, reduce deformation and vibration caused by clamping force, and improve positioning accuracy.

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