CN108508848B - An Evaluation Method of Milling Contour Error Based on Interpolation Data - Google Patents

Abstract

The invention discloses a method for evaluating the contour error of milling machining based on interpolation data, which belongs to the field of processing error evaluation and includes the following steps: Step 1: Triangular surface of the workpiece design surface is sliced to obtain the geometric model of the workpiece; Step 2: Establishing The geometric model of the effective cutting contour of the tool; Step 3: Construct a parallel calculation model of the contour error, calculate the contour error of each group in parallel based on the interpolation data grouping, and return the result. In the present invention, each tool position point on the interpolation data calculates the contour error by comparing the effective cutting contour of the tool with the design model of the processed surface. The error can correspond to the position of the tool point, and the contour error of each tool point can be calculated in parallel, which is more efficient, and takes into account the errors of the G code, the numerical control system and the servo system, and is closer to the actual machining process. exercise position.

Description

An Evaluation Method of Milling Contour Error Based on Interpolation Data

technical field

The invention belongs to the field of processing error evaluation, and more particularly relates to an evaluation method of milling processing contour error based on interpolation data.

Background technique

In traditional production, due to the existence of various processing error factors, it is necessary to use a three-coordinate measuring instrument to measure the test-cut workpieces for accuracy evaluation before batch processing to ensure the processing accuracy of parts. The disadvantage of the three-coordinate measuring instrument evaluation method is that it is necessary to try to cut the workpiece first, and then use the three-coordinate measuring instrument to measure the contour error after the trial cutting. The cost is high, and the measurement method is inefficient and takes a long time.

In addition to using measuring equipment to evaluate the contour error of trial cutting, there is a virtual evaluation method for contour error, which evaluates the contour error through processing simulation software or 3D engine simulation process. For example, there are such functions in CAM software such as UG and Verycut, mainly Machining simulation through G code. During the G code machining simulation process, the simulation error is obtained by comparing the IPW (In Process Workpiece) with the design model through the calculation of intersection between the tool and the workpiece blank. Figure 1 shows the basic process of measuring the machining contour error through a three-coordinate measuring instrument and G-code machining simulation.

G code is a processing instruction to ensure the given contour accuracy of the design surface, and the data density is small. Moreover, in the method based on G code simulation, the intersection calculation of the blank between the front and rear tool points is related. The result of the calculation of the tool and the blank at the previous tool point is the blank calculated by the intersection calculation of the next tool point, which cannot be independent of each other. The simulation needs Carry out in the order of G code, it is difficult to achieve parallel simulation.

However, a three-coordinate measuring instrument cannot perform parallel measurement, and it is also difficult to separate G code parallel simulation in processing simulation.

Contents of the invention

Aiming at the above defects or improvement needs of the prior art, the present invention provides a method for evaluating milling contour errors based on interpolation data. Grouping is performed sequentially, and the effective cutting contour error of each group is calculated in parallel, thereby realizing simulation processing while improving measurement efficiency.

In order to achieve the above object, according to one aspect of the present invention, a method for evaluating milling contour errors based on interpolation data is provided, including the following steps:

Step 1: Thinning the triangular surface of the workpiece design surface to obtain the geometric model of the workpiece;

Step 2: Establish a tool coordinate system (X, Y, Z) on the tool according to the machining track of the tool on the workpiece geometric model, the origin O is at the tool position, the tool movement speed is in the XOZ plane, and the Z axis is along the tool axis direction arrangement;

The cutting edge of the tool includes three parts: the upper conical surface _, the transitional toroidal surface _and the lower conical surface. Effective cutting profile of conical surface Sweep _L,C :

Among them, α is the half-cone angle of the lower conical surface, 0≤α<90°,

β is the half-cone angle of the upper conical surface, 0≤β<90°,

R ₁ is the distance from the center of the arc part of the transition ring to the tool axis,

R ₂ is the radius of the arc portion of the transition ring,

L is the total length of the cutting edge,

h is the distance from the center of the arc of the transition ring to the OXY plane of the tool coordinate system;

Vel.x is the component of the tool speed in the X-axis direction,

Vel.y is the component of the tool speed in the Y-axis direction;

Step 3: According to the effective cutting contour of the tool, group the interpolation data according to the interpolation sequence, and calculate the effective cutting contour error of each group in parallel according to steps 3.1 to 3.3. Steps 3.1 to 3.3 are as follows:

Step 3.1. Estimating the direction of the tool speed at the current tool position;

Step 3.2, at different tool positions, the coordinates of the effective cutting contour of the tool in the tool coordinate system are converted to the workpiece coordinate system to obtain the effective cutting contour of the tool in the workpiece coordinate system;

Step 3.3. According to the effective cutting contour of the tool in the workpiece coordinate system, combined with the theoretical contour of the tool, the effective cutting contour error of each tool position is calculated and the error type is distinguished as undercutting, overcutting or ideal machining.

Further, in step 3.2, the conversion matrix R _toolToWork from the tool coordinate system to the workpiece coordinate system is:

Where (x′, y′, z′) is the unit vector of the tool speed vector in the workpiece coordinate system, and CL is the coordinate of the tool position point in the workpiece coordinate system;

Solve the instantaneous contour in the workpiece coordinate system through the conversion matrix from the tool coordinate system to the workpiece coordinate system:

p = R _toolToWork p' (17)

p is the coordinate of a point on the effective cutting contour in the workpiece coordinate system, p′ is the coordinate of a point on the effective cutting contour in the tool coordinate system, and the tool in the workpiece coordinate system can be obtained by formulas (12)~(14) and formula (17) Effectively cuts contours.

Further, in step 3.3, during point milling, the number n of intersection points between the effective cutting contour of the tool and the design surface is used to distinguish whether the current tool position of the tool is undercut, overcut or ideal processing:

When n=0, it belongs to the undercutting condition of the tool; when undercutting, the contour error is expressed as the shortest distance ε between the effective cutting contour of the tool and the ideal machining contour of the workpiece;

When n=2, it is an overcutting situation; during overcutting, there are at least two intersection points P ₁ and P ₂ between the effective cutting contour of the tool and the theoretical machining contour of the workpiece; the contour error during overcutting is measured as the difference between the two intersection points of the tool contour The part of , that is, the one-way Hausdorff distance between the P ₁ P ₂ segment curve and the theoretical tool cutting profile:

in,

A represents the P ₁ P ₂ segment curve on the tool profile, and discretizes A into a series of points a ₁ , a ₂ , a ₃ ...a _m , expressed as A={a ₁ ,a ₂ ,a ₃ ...a _m } ; B is the theoretical machining contour surface of the workpiece, and the theoretical machining contour surface of the workpiece is recorded as the set B={b ₁ ,b ₂ ,b ₃ ...b _k };

When n=1, it is an ideal processing situation; at this time, the effective cutting contour of the tool is tangent to the theoretical processing contour of the workpiece, and the contour error is 0;

During side milling, the effective cutting contour of the tool is discretized into points P ₁ , P ₂ ,...,P _t , and the corresponding theoretical workpiece contour is discretized into points P ₁ ′P ₂ ′,...,P _t ′,P ₁ ,P ₂ ,...,P _t have one-to-one correspondence with P ₁ ′P ₂ ′,...,P _t ′, the vector The normal vector to the theoretical contour of the workpiece at the point P _t ′ The included angle is if Then point P _t ′ is undercut, if is overcut if is an ideal processing situation.

Further, in step 2, the geometric contours of the upper cone, transition ring and lower cone of the tool in the tool coordinate system are shown in the following formulas:

CS _C ＝CS _U,C ∪CS _T,C ∪CS _L,C (7)

in,

CS _{U, C} are the geometric contours of the conical surface on the tool,

CS _{T, C} is the geometric profile of the tool transition torus,

CS _{L, C} are the geometric contours of the lower conical surface of the tool,

CS _C is the geometric profile of the entire surface of the tool.

Further, in step 2, during the tool movement, the mathematical model of the effective cutting profile of the tool is expressed by the following formula:

in, is the normal vector of each point on the tool surface, is the cutting direction of the tool;

The normal vector of each point on the tool surface Including the following components:

in,

n _{U, C} are the normal vectors of each point on the conical surface of the tool,

n _{T, C} are the normal vectors of the tool at each point on the transition ring,

n _{L, C} (θ) is the normal vector of each point on the lower conical surface of the tool.

Further, in step 3.1, the method of estimating the tool speed direction at the current tool position is as follows:

For the first tool point P ₀ of interpolation, select the first three tool points P ₀ , P ₁ , and P ₂ to fit the arc, and use the tangent vector of P ₀ on the arc as the tool speed direction at P ₀ , where, with vector The included angle is less than 180°;

For the interpolated intermediate tool point P _i , use the previous tool point P _i-1 , the current tool point P _i and the next tool point P _i+1 to fit a circular arc, and the current tool point P The tangent and vector of _i on the arc Directions where the included angle is less than 180° As the tool speed direction on the tool point, i≥1;

For the last tool point of interpolation, the last three tool points are used to fit the arc, and the tangent direction of the last tool point on the arc is As the tool speed direction on the tool point.

Further, step 4 is also included: According to the effective cutting contour error and error type of the tool corresponding to each tool position obtained in step 3.3, adjust the G code so that the effective cutting contour error of the tool does not exceed the preset accuracy range, so as to realize machining Simulation and simulation verify the contour accuracy of the trial-cut workpiece.

Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

1. Since the interpolation data of the numerical control system is a control command that directly controls the movement of each axis of the machine tool, the data density is high. The present invention compares the effective cutting contour of the tool with the design model of the processed surface at each tool position point of the interpolation data. Calculate the contour error, the contour error calculation between each point has no connection, and the contour error calculated by each tool point can correspond to the position of the tool point, and can be calculated in parallel; the simulation based on the interpolation data of the present invention is closer to the actual processing During the process, the movement position of the tool relative to the processing surface takes into account the errors of the G code, the numerical control system and the servo system. Compared with the method of processing and simulating through the G code in the prior art, the error consideration is more comprehensive.

2. The method based on interpolation data of the present invention takes into account the error before machine tool processing, and can be used in combination with the method based on G code simulation and the measurement method of the three-coordinate measuring instrument, so as to determine which link the contour error comes from, and has good compatibility;

3. The contour error evaluation method based on interpolation data is very suitable for parallel calculation because the contour error calculation of each tool position point is not related to each other.

Description of drawings

Fig. 1 is a flow comparison diagram of three kinds of contour error evaluation methods based on interpolation data of the existing three-coordinate measuring instrument, G code processing simulation and the present invention;

Fig. 2 is a schematic diagram of swept volume and effective cutting profile;

Fig. 3 is the definition of a seven-parameter tool, wherein, 3(a) is a schematic diagram of the tool coordinate system, 3(b) is a schematic diagram of the cutting edge structure of the tool, and 3(c) is a schematic diagram of the tool parameters;

Fig. 4 is a schematic diagram of the effective cutting profile of the tool;

Fig. 5 is the contour error model based on interpolation data parallel calculation of the present invention;

Fig. 6 is a schematic diagram of the speed direction of the tool at the middle tool position point (that is, the tool position point between the first tool position point and the last tool position point) of the present invention;

Fig. 7 is a schematic diagram of determining the speed direction of the tool at the first tool position point of the present invention;

Fig. 8 is a schematic diagram of determining the speed direction of the tool at the last tool position point of the present invention;

Fig. 9 is a schematic diagram of contour error calculation in the undercut situation of the present invention;

Fig. 10 is a schematic diagram of contour error calculation in the case of overcut in the present invention;

Figure 11 is a schematic diagram of contour error calculation in an ideal situation;

Fig. 12 is a flow chart of calculating the contour error of a single tool point in the point milling process of the present invention;

Fig. 13 is a schematic diagram of side milling of the present invention;

Fig. 14 is a schematic diagram of side milling error distribution of the present invention;

Fig. 15 is a schematic diagram of point-by-point contour error calculation of interpolation data in the present invention;

Fig. 16 is a schematic diagram of the generation process of interpolation data.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.

Before introducing the present invention formally, introduce a few terms first:

Imputation data:

In the process of CNC machining, the processing code input by the CNC system is the G code obtained by the post-processing of the CAD/CAM system, but the G code cannot directly control the rotation of the servo system motor of each axis of the machine tool, so the CNC system needs to interpolate the G code And speed planning, get the instruction data to control the movement of each motor, through the instruction data, each axis moves to the specified position, the interpolation data used in the present invention is the actual position data fed back by the servo motor of each axis in each interpolation cycle . The generation process of interpolation data is shown in Figure 16.

The concept of the effective cutting contour of the tool:

When a solid is in rigid motion, all points on its outer surface contour form a spatial area called the swept volume. In CNC machining, when the tool processes a blank along the cutting path, the part of the workpiece that is machined is the swept volume of the tool. This machining process can be regarded as a certain contour of the outer surface of the tool cutting the blank along the tool trajectory, and the contour of the outer surface of the tool is defined as the effective cutting contour of the tool, as shown in Figure 2.

The basic definition of Hausdorff distance (HD) is as follows:

A={a ₁ , a ₂ , a ₃ ...a _m }, B={b ₁ , b ₂ , b ₃ ...b _k } represent two sets of finite points respectively. HD is defined as

H(A,B)=max(h(A,B),h(B,A)) (1)

In the formula, h(A,B) is called the one-way Hausdorff distance from the set A to B, defined as

h(B,A) is called the one-way Hausdorff distance from the set B to A, defined as

The concept of parallel computing:

Parallel computing (Parallel Computing) refers to the process of using multiple computing resources to solve computing problems at the same time. It is an effective means to improve the computing speed and processing capacity of computer systems. Its basic idea is to use multiple processors to solve the same problem cooperatively, that is, to decompose the problem to be solved into several parts, and each part is calculated in parallel by an independent processor. Parallel computing requires that the technical content has no relationship with each other, and can be divided into multiple sets of data for simultaneous calculation.

Introduce below the main steps of a kind of evaluation method of the milling processing outline error based on interpolation data of the present invention, please refer to Fig. 1, the steps of the present invention are as follows:

Step 1: Prepare data, including: collecting interpolation data during the machining process of the CNC system; discretizing the workpiece model, making the triangular surface of the workpiece design surface into slices; reading the processing tool parameters from the CNC system. Among them, collecting interpolation data and reading processing tool parameters can also be executed in real time when needed in subsequent steps.

Step 2: Establish a geometric model of the effective cutting profile of the tool

According to the definition of APT tool, a universal tool is determined by seven parameters. In order to facilitate the description of the tool, a tool coordinate system (X, Y, Z) is established on the tool, so that the tool coordinates satisfy that the origin O is at the tool position, the tool movement speed is in the XOZ plane, and Z is along the tool axis. Taking the APT tool as an example, its definition method is shown in Figure 3(a), 3(b) and 3(c).

Among them, the parameters of the tool:

α is the half cone angle at the bottom of the tool, 0≤α＜90°,

β is the semi-cone angle of the cutting edge, 0≤β＜90°,

R ₁ is the distance from the center of the arc part of the tool transition ring to the tool axis,

R ₂ is the radius of the arc portion of the tool transition ring,

L is the total length of the cutting edge of the tool,

h is the distance from the center of the arc part of the tool transition ring to the OXY plane of the tool coordinate system.

A general tool consists of three parts: upper cone, transition ring, and lower cone. Thus, the geometric descriptions of the three parts of the milling cutter in the tool coordinate system are shown in the following formulas.

CS _C ＝CS _U,C ∪CS _T,C ∪CS _L,C (7)

where a∈[0,1], b∈[0,1], θ∈[0,2π], the subscript C indicates the tool coordinate system, the subscript U indicates the upper cone, the subscript T indicates the transition ring, and the subscript L indicates the lower cone, so CS _{U, C} are the upper conical surface of the tool, CS _{T, C} are the transition torus of the tool, CS _{L, C} are the lower conical surface of the tool, CS _C is the entire surface of the tool, and the entire surface of the tool is composed of an upper conical surface, a transitional torus, and a lower conical surface.

During the movement of the tool, the mathematical model of the effective cutting profile of the tool can be obtained by the following formula:

in is the normal vector of each point on the tool surface, is the cutting direction of the tool.

According to the mathematical expression (7) of the tool surface CS _C (s), the normal vector of the tool surface It can be expressed as:

Among them, n _{U, C} is the normal vector of each point on the upper conical surface of the tool, n _{T, C} is the normal vector of each point of the tool on the transition ring, n _{L, C} (θ) is the normal vector of each point on the lower conical surface of the tool vector.

Therefore, the mathematical expressions of the effective cutting contours of the moving tool in each segment obtained from formulas (8) to (11) are:

where a∈[0,1], b∈[0,1], Sweep _{U, C} are the effective cutting contours of the upper conical surface of the tool, Sweep _{T, C} are the effective cutting contours of the tool transition torus, and Sweep _{L, C} are the effective cutting contours of the lower conical surface of the tool. From the value range of a and b, the effective cutting contours of the upper and lower conical surfaces of the tool can be obtained. Vel.x is the component of the tool speed in the X-axis direction, and Vel.y is the component of the tool speed in the Y-axis direction, so when the cutting direction of the tool is known, for each Values can be calculated as a point on Sweep _T,C . The effective cutting contour of the tool is composed of the effective cutting contour (Sweep _U,C ) of the upper conical surface of the tool, the effective cutting contour (Sweep _T,C ) of the transitional toroidal surface and the effective cutting contour (Sweep _L,C ) of the lower conical surface of the tool, Therefore, a complete model of the effective cutting contour of the tool can be established in the tool coordinate system, as shown in Figure 4.

Step 3: Build a parallel computing model for contour errors

Due to the high precision of the interpolation data and the large amount of data, and the present invention uses the effective cutting contour of the tool to calculate the contour error, there is no necessary relationship between the tool positions, so the parallel calculation according to steps 3.1 to 3.4 improves the efficiency. By grouping the interpolation data, use CPU, GPU or computer cluster to calculate the contour error of each group in parallel and return the result. Figure 5 is a model for parallel computing of imputation data. The steps of parallel computing are as follows:

Step 3.1. Estimate the speed direction of the current tool position point

Since the interpolation point contains the discrete tool position points in the tool movement process, and has no tool movement speed direction, the tool speed direction of the current tool position point can be estimated by various methods, for example, the previous tool position point P _i-1 , the current tool position point can be used Tool position point P _i and the next tool position point P _i+1 three points fit a circular arc to calculate the direction of tool movement speed, as shown in Figure 6, the arc is on the tangent line of the current tool position point and the vector Directions where the included angle is less than 180° is the velocity direction of the tool position point. Similarly, use the first three tool points P ₀ , P ₁ , and P ₂ to fit the arc at the first position of the interpolation point, as shown in Figure 7, the velocity vector is the arc at the first tool point P ₀ Kiriya with vector The included angle is less than 180°. The last position uses the last three points to fit the arc, and the velocity direction is the tangent vector of the arc at the last point, as shown in Figure 8.

Step 3.2, tool effective cutting contour coordinate conversion

The effective cutting contour model of the tool established in step 2 is in the tool coordinate system, while the machining surface design model is in the workpiece coordinate system, so the effective cutting contour coordinates are transformed to the workpiece coordinate system at different tool positions.

Because the tool coordinate origin O is at the tool position, the tool movement speed is on the XOZ plane, and Z is along the tool axis, so the conversion matrix R _toolToWork from tool coordinates to workpiece coordinates is:

Where (x′, y′, z′) is the unit vector of the tool velocity vector in the workpiece coordinate system, and CL is the coordinate of the tool position in the workpiece coordinate system.

Solve the instantaneous contour in the workpiece coordinate system through the conversion matrix from the tool coordinate system to the workpiece coordinate system:

p＝R _t o _lT o _W o _rk ·p′ (17)

p is the coordinate of the point on the effective cutting contour in the workpiece coordinate system, and p′ is the coordinate of the point on the effective cutting contour in the tool coordinate system. Through formulas (12)-(14) and formula (17), we can get the Effectively cuts contours.

Step 3.3 Calculation of contour error

In spot milling, there are three situations: undercutting, overcutting, and ideal processing. The number n of intersections between the effective cutting contour of the tool and the design surface is used to distinguish which situation it belongs to:

When n=0, it belongs to the situation of tool undercut. The contour error during undercutting is expressed as the shortest distance ε between the effective cutting contour of the tool and the rational machining contour of the workpiece, as shown in Figure 9.

When n=2, it is the case of overcut. When overcutting, there are at least two intersection points between the effective cutting contour of the tool and the theoretical machining contour of the workpiece. As shown in Figure 10, there are two intersection points P ₁ and P ₂ between the tool contour and the ideal contour. The contour error during overcutting is measured as the one-way Hausdorff distance between the part of the tool contour between two intersection points (that is, the P ₁ P ₂ segment curve) and the theoretical contour. At this time, the error is marked as overcutting, as follows:

Among them, A is the curve P ₁ P ₂ on the tool profile, discretize A into a series of points a ₁ , a ₂ , a ₃ ...a _m , expressed as A={a ₁ ,a ₂ ,a ₃ ...a _m }, similarly, the theoretical contour of the workpiece is recorded as the set B={b ₁ ,b ₂ ,b ₃ . . . b _k }.

When n=1, it is an ideal processing situation. At this time, the effective cutting contour of the tool is tangent to the theoretical machining contour of the workpiece, and the contour error is measured as 0, as shown in Figure 11. Fig. 12 is a flow chart of calculating the contour error of a single tool point in the point milling process.

Theoretically, during side milling, the side edge of the tool is in line contact with the surface of the workpiece, as shown in Figure 13, so the side milling situation is simplified to the distance distribution between the side edge of the effective cutting contour of the tool and the surface of the workpiece whose distance from the surface of the workpiece is less than the radius of the tool, First, the effective cutting contour of the tool is discretized into points, and then the shortest distance between the discrete points and the theoretical contour of the workpiece is calculated. As shown in Figure 14, the distances from each discrete point to the theoretical contour of the workpiece are P ₁ P ₁ ′, P ₂ P ₂ ′, ..., P _t P _t ′, point P _n is on the side edge of the effective cutting contour of the tool, point P _t ′ is on the theoretical surface contour, vector and the normal vector of the theoretical surface contour at point P _n ′ The included angle is if Then the error sign of this point is undercut, if is overcut if is an ideal processing situation.

Through the continuous interpolation data at each tool point to calculate the contour error according to the above steps, the virtual calculation of the contour error of the curved surface can be obtained. The calculation process is shown in Figure 15.

Step 4: Contour Error Evaluation

After calculating the contour error of all interpolation points in parallel, output the contour error corresponding to each tool position point, and display the undercut or overcut situation of each tool position point in the form of a graph for the output contour error, for example, use the chromatogram display The contour error status of each point on the machining surface design model. Through the evaluation of the contour error, adjust the G code at the position where the accuracy is out of tolerance, so that the contour error does not exceed the accuracy range, and achieve the effect of machining simulation and three-coordinate measurement test cutting parts to verify the contour accuracy.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (6)

1. an evaluation method of milling contour error based on interpolation data is characterized by comprising the following steps:

Step 1: triangularization is carried out on the workpiece design curved surface to obtain a geometric model of the workpiece;

step 2: establishing a tool coordinate system (X, Y, Z) on the tool according to the processing track of the tool on the geometric model of the workpiece, wherein an original point O is at the position of a tool position point, the moving speed of the tool is on an XOZ plane, and a Z axis is arranged along the axial direction of the tool;

The cutting edge of cutter includes circular conical surface, transition ring surface and circular conical surface three part down, and the effective cutting profile of cutter includes circular conical surface effective cutting profile sweet U, C, transition ring surface effective cutting profile sweet pT, C and circular conical surface effective cutting profile sweet L, C down:

Wherein alpha is the half cone angle of the lower conical surface, alpha is more than or equal to 0 and less than 90 degrees,

Beta is the half cone angle of the upper conical surface, beta is more than or equal to 0 and less than 90 degrees,

R1 is the distance from the sphere center of the arc part of the transition ring to the cutter shaft,

R2 is the radius of the arc portion of the transition circle,

l is the total length of the cutting edge,

h is the distance from the spherical center of the arc part of the transition ring to the OXY plane of the cutter coordinate system;

a∈[0,1],b∈[0,1],θ∈[0,2π]，

x is the component of the tool velocity in the X-axis direction,

Ve.y is the component of the tool speed in the Y-axis direction;

and step 3: grouping the interpolation data according to the interpolation sequence according to the effective cutting profile of the cutter, and calculating the error of the effective cutting profile of the cutter of each group in parallel according to the steps 3.1-3.3, wherein the steps 3.1-3.3 are as follows:

step 3.1, estimating the speed direction of the cutter at the current cutter location point;

3.2, converting the coordinates of the effective cutting profile of the cutter in the cutter coordinate system to a workpiece coordinate system at different cutter positions to obtain the effective cutting profile of the cutter in the workpiece coordinate system;

3.3, calculating the effective cutting contour error of each tool location point by combining the theoretical contour of the tool according to the effective cutting contour of the tool in the workpiece coordinate system, and distinguishing whether the error type is under-cut, over-cut or ideal processing;

in step 3.3, during point milling, whether the current tool location point of the tool is under-cut, over-cut or ideal is distinguished through the number n of intersection points of the effective cutting profile of the tool and the designed curved surface:

when n is 0, the condition of the cutter under-cutting is adopted; the contour error in the case of under-cutting is expressed as the shortest distance epsilon between the effective cutting contour of the cutter and the ideal processing contour of the workpiece;

an over-cut condition when n is 2; when the cutter is over-cut, at least two intersection points P1 and P2 are arranged between the effective cutting profile of the cutter and the theoretical machining profile of the workpiece; the profile error at overcutting is measured as the one-way Housdov distance between the portion of the tool profile between the two intersection points, i.e., the curve for segment P1P2, and the theoretical tool cutting profile:

Wherein,

a represents a curve of segment P1P2 on the tool profile, and a is discretized into a series of points a1, a2 and a3 … am, which are collectively represented as a ═ a1, a2 and a3 … am; b is a theoretical machining contour curved surface of the workpiece, and the theoretical machining contour curved surface of the workpiece is recorded as a set B ═ B1, B2 and B3 … bk;

When n is 1, the ideal processing condition is obtained; at the moment, the effective cutting profile of the cutter is tangent to the theoretical machining profile of the workpiece, and the profile error is 0;

in the side milling process, the effective cutting profile of the cutter is scattered into points P1, P2, the right angle and Pt, the corresponding theoretical profile of the workpiece is scattered into points P1 'P2', the right angle, Pt ', P1, P2, the right angle and P1' P2 ', the right angle and Pt' are in one-to-one correspondence, and the included angle between the vector and the normal vector of the theoretical profile of the workpiece on the point Pt 'is an undercut point if the included angle is the point Pt', and is an over-cut point if the included angle is the ideal processing condition.

2. the method for evaluating the milling machining contour error based on the interpolation data as claimed in claim 1, wherein in step 3.2, the transformation matrix RtoolToWo from the tool coordinate system to the workpiece coordinate system is:

Wherein (x ', y ', z ') is a unit vector of a tool velocity vector under the workpiece coordinate system, and CL is a tool position point coordinate under the workpiece coordinate system;

And (3) solving the instantaneous profile under the workpiece coordinate system through a conversion matrix from the tool coordinate system to the workpiece coordinate system:

p＝R·p′ (17)

and p is the coordinate of a point on the effective cutting contour under the workpiece coordinate system, p' is the coordinate of a point on the effective cutting contour under the tool coordinate system, and the effective cutting contour of the tool under the workpiece coordinate system is obtained through the equations (12) to (14) and (17).

3. the method for evaluating the milling machining contour error based on the interpolation data as claimed in claim 1 or 2, wherein in the step 2, the geometric contours of the upper cone, the transition ring and the lower cone of the tool in the tool coordinate system are respectively as follows:

CS＝CS∪CS∪CS (7)

wherein,

CSU, C is the geometrical outline of the conical surface on the cutter,

CST, C is the geometrical outline of the transition ring surface of the cutter,

CSL and C are the geometrical outline of the lower conical surface of the cutter,

CSC is the geometric profile of the entire surface of the tool.

4. the method for evaluating the error of the milling machining profile based on the interpolation data as claimed in claim 3, wherein in the step 2, during the movement of the tool, the mathematical model of the effective cutting profile of the tool is represented by the following formula:

wherein, the normal vector of each point on the surface of the cutter is the cutting direction of the cutter;

The normal vector of each point on the surface of the tool comprises the following components:

Wherein,

nU and C are normal vectors of each point on the conical surface of the cutter,

nT and C are normal vectors of each point of the cutter on the transition ring,

nL and C (theta) are normal vectors of each point of the conical surface under the cutter.

5. The method for evaluating the milling machining contour error based on the interpolation data as claimed in claim 1 or 2, wherein in step 3.1, the method for estimating the tool speed direction of the current tool location is as follows:

for the interpolated first cutter position P0, selecting the fitting circular arc of the first three cutter positions P0, P1 and P2, and taking the tangent vector of P0 on the circular arc as the cutter speed direction at P0, wherein the included angle between the tangent vector and the cutter speed direction is less than 180 degrees;

for the interpolated middle cutter point Pi, fitting an arc by using three points of a previous cutter point Pi-1, a current cutter point Pi and a next cutter point Pi +1, and taking the direction in which the included angle between the tangent of the current cutter point Pi on the arc and a vector is less than 180 degrees as the speed direction of a cutter on the cutter point, wherein i is more than or equal to 1;

And for the last interpolated tool location point, fitting an arc by using the last three tool location points, and taking the tangential direction of the last tool location point on the arc as the tool speed direction on the tool location point.

6. the method for evaluating the milling machining contour error based on the interpolation data as claimed in claim 1 or 2, further comprising the step 4: and 3.3, adjusting the G code according to the effective cutting contour error and the error type of the cutter corresponding to each cutter location point obtained in the step 3.3, so that the effective cutting contour error of the cutter does not exceed the preset precision range, and thus, the contour precision of the trial-cut workpiece is realized through machining simulation and simulation verification.