Method for generating five-axis finish machining variable-step-length spiral tool path of annular cutter for blade curved surface

Abstract

The invention discloses a blade curved surface ring cutter five-axis finish machining variable step length spiral cutter path generation method, which comprises the following steps of: firstly, importing a curved surface model to be machined, and setting parameter information such as a machining cutter, an approximation error maximum allowable value, a minimum iteration frequency and line spacing; secondly, respectively planning cutter contact point trajectory lines of a blade head-tail row cutter path and a spiral cutter path of a molded surface between the head row and the tail row, calculating an initial step length for the cutter contact point trajectory lines according to a maximum linear error, obtaining discrete cutter contact points, and calculating cutter location points and cutter axis vectors of the cutter contact points; replacing a cutter motion envelope surface and a cutter contact trajectory between adjacent cutter location points with a discrete cutter cutting surface and a cutter contact point set, and proposing a calculation method for an approximation error of two adjacent cutter location points; and comparing the approximation error with the maximum allowable value, and adjusting the step length to enable the approximation error between the adjacent cutter location points to be within a set range so as to obtain the variable-step-length spiral cutter path.

Description

Technical Field

[0001] The invention belongs to the technical field of computer-aided manufacturing (CAM), and in particular relates to a method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter. Background Art

[0002] As a key component of aircraft engines and gas turbines, blades are generally composed of free-form surfaces, and their processing accuracy directly affects the performance of the entire machine. Different from the commonly used isoparametric method to generate the line cutting tool path, the variable step length spiral tool path can better adapt to the change of surface curvature. By controlling the step length between adjacent tool contacts to make the approximation error less than or equal to the maximum allowable value, the step length can be maximized as much as possible, the number of tool contacts / tool ​​positions can be minimized, and the number of redundant tool paths can be effectively reduced. Compared with the line cutting tool path, the spiral tool path can complete the processing of the entire surface in one advance and retreat, reducing the number of advances and retreats and processing time.

[0003] The variable step length spiral tool path has obvious advantages in adapting to the change of surface curvature. The main process of calculating the five-axis variable step length spiral tool path is to first calculate the initial tool path, then adjust the step length according to the approach error between adjacent tool position points, and then obtain the variable step length spiral tool contact point that meets the approach error requirements, and then calculate the tool position point and tool axis vector. The approach error calculation of the five-axis machining of the circular cutter is difficult, which makes the calculation of the variable step length spiral tool contact point more difficult, and each tool contact point needs to be calculated one by one based on the previous tool contact point.

[0004] The invention patent with Chinese patent application number 202410275161.5 discloses a nonlinear error compensation method based on the optimization of the tool contact trajectory of five-axis machining, which is used to solve the problem that the actual tool contact trajectory deviates from the ideal trajectory during five-axis linear interpolation and produces a large nonlinear error. First, a mathematical model of machine tool motion transformation is established, and the positions of the actual tool center point and the actual tool contact point in the five-axis linear interpolation process are solved based on the data sampling interpolation principle. Based on the least squares method, the tool contact plane is compensated and fitted to obtain the actual tool contact trajectory, and the tool contact plane coordinate system is established, and the conversion of the two-dimensional and three-dimensional actual interpolation tool contacts is realized. Quadratic polynomial fitting is performed on the tool contact plane coordinate system, and a nonlinear error model is established. The nonlinear error of the actual tool contact is calculated and the trajectory nonlinear error compensation is implemented in the machining program segment with large errors. The nonlinear error at the tool contact point is reduced by changing the position of the tool center point, thereby achieving the purpose of improving the position control accuracy of the five-axis CNC system.

[0005] The invention patent with Chinese patent application number 201810282266.8 discloses a five-axis ball head milling geometric error compensation method, which belongs to the field of machine tool error compensation. It includes: considering the structural parameters of the five-axis CNC machine tool, establishing the forward kinematics equation and post-processing program of the five-axis CNC machine tool; according to the workpiece processing code, combined with the forward kinematics equation, obtaining the ideal tool posture file of the workpiece; establishing the conversion relationship between the tool posture of the ball head milling cutter and the tool contact representing the workpiece texture; according to the exponential product theory, establishing a comprehensive geometric error analytical model for five-axis ball head milling; establishing tool contact protection measures in five-axis ball head milling geometric error compensation; applying the swarm intelligence optimization algorithm to obtain the compensated rotation axis angle; calculating the translation axis motion of the compensated rotation axis angle; reading the ideal tool posture file of the workpiece, and calculating the compensation processing code. This invention ensures the texture quality of the workpiece while compensating for the geometric error, and can further improve the processing accuracy and surface quality of the five-axis machine tool.

[0006] The invention patent with Chinese patent application number CN202110004876.3 discloses a method for calculating equal-error tool paths for five-axis CNC flat-bottom tool machining parametric surfaces. First, the errors are classified and calculated: linear error and nonlinear error. By analyzing the cutting process of the flat-bottom tool in five-axis machining, the linear error and nonlinear error points between the tool envelope surface and the tool contact curve are iteratively calculated. Thus, the interval in which the approximation error of the flat-bottom tool in five-axis CNC machining is established, that is, between the linear error point and the nonlinear error point. The maximum value in the interval can be obtained by discrete iterative calculation, which is the approximation error value between adjacent tool location points. The flat-bottom tool machining step length is planned by specifying the maximum approximation error value, so as to achieve the minimum tool contact and the minimum number of calculations for free-form surface machining, thereby obtaining the equal-error tool path generation of the free-form surface and achieving higher machining efficiency.

[0007] The purpose of the above-mentioned invention patents and papers is to reduce the error size in five-axis machining, thereby further improving machining accuracy and efficiency. The invention patent with Chinese patent application number 202410275161.5 establishes a nonlinear error model by fitting a quadratic polynomial on the tool contact plane coordinate system, calculates the actual tool contact nonlinear error and implements compensation in the program segment with large errors, thereby reducing the nonlinear error at the tool contact point by changing the position of the tool center point, thereby achieving the purpose of improving five-axis accuracy. The invention patent with Chinese patent application number 201810282266.8 establishes a five-axis forward kinematics equation and implements corrections, establishes a comprehensive geometric error analytical model for five-axis ball head milling, compensates for the rotation axis angle and the translation axis motion, and corrects the machining code, thereby achieving the purpose of compensating for five-axis geometric errors and improving machining accuracy. The invention patent with Chinese patent application number 202110004876.3 analyzes the processing process of the flat-bottomed tool and establishes an approximation error calculation model for the five-axis cutting of the flat-bottomed tool, thereby achieving the purpose of limiting the processing step length of the flat-bottomed tool using the specified maximum approximation error value to obtain a more efficient free-form surface processing tool path. The actual approximation error in five-axis machining is jointly determined by the nonlinear error and the linear error, but it is not a simple superposition. It is necessary to obtain the real tool motion envelope surface and local surface information for calculation. The first two invention patents are error optimization processing for existing tool paths, so they cannot be used for approximation error calculation and variable step tool path generation. The third invention patent can only generate equal error tool paths for flat-bottomed tools, and does not involve the generation of variable step tool paths for five-axis machining of circular cutters for blade models. Summary of the invention

[0008] The purpose of the embodiments of the present invention is to provide a method for generating a variable-step spiral tool path for five-axis finishing of a blade surface with a circular cutter, so as to improve error accuracy and reduce the number of tool position points.

[0009] Specifically, the technical solution of the present invention is as follows:

[0010] The method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter includes the following steps:

[0011] Step 1: Import the blade surface model and set the processing parameters;

[0012] Step 2 calculates the initial tool position point and tool axis vector of the spiral tool track contact point trajectory;

[0013] Step 3: Calculate the approximation error value between two adjacent tool position points;

[0014] Step 4 generates a variable-step spiral tool path for the blade surface.

[0015] Furthermore, the processing parameters in step 1 include: setting the tool radius R, the fillet radius r, the tool length LT and the total number of tool paths n, the rake angle α, and the maximum allowable value of the approach error e max , maximum number of iterations Approximation error accuracy Δe.

[0016] Furthermore, the step 2 of calculating the initial tool position point and tool axis vector of the spiral tool track contact point trajectory line includes:

[0017] Step 2.1 For the first and last tool paths and the front and rear edge tool paths of the profile, plan the cutting tool paths, calculate the initial step length according to the maximum linear error, and obtain the corresponding tool contact point set;

[0018] Step 2.2: For the spiral tool path on the molding surface, the initial step length of the spiral tool path is calculated according to the maximum linear error by calculating the intersection line between the section plane and the suction and compression surfaces, and the corresponding tool contact point set is obtained;

[0019] Step 2.3 integrates the above tool paths to obtain a complete tool contact point set, and calculates the tool position point and tool axis vector of the tool contact point;

[0020] Furthermore, the step 3 of calculating the approximation error value between two adjacent tool position points includes:

[0021] Step 3.1 calculate the point set of the discrete tool cutting surface and tool contact trajectory of the tool envelope surface;

[0022] Step 3.2: for any tool posture on the tool envelope surface between adjacent tool positions, calculate the approach error of the cutting edge at a cutting angle and obtain the corresponding tool contact point;

[0023] Step 3.3 iterates the cutting angle of the cutting edge, and takes the minimum value of the approximation error of the cutting angle as the approximation error of the tool posture;

[0024] Step 3.4 obtains the corresponding tool posture by iterating the tool vertex position on the tool vertex line, calculates the approximation error for each tool posture, and takes its maximum value as the approximation error between adjacent tool positions;

[0025] Furthermore, the step 4 of generating a variable step length spiral tool path includes:

[0026] Step 4.1 compares the approximation error between adjacent tool positions with the maximum allowable value, and iteratively adjusts the step size;

[0027] Step 4.2 obtains an approximation error that is greater than the minimum number of iterations and within the maximum allowable error range;

[0028] Step 4.3 calculates the variable step length spiral tool path.

[0029] Furthermore, in step 2.1, for the first and last tool paths and the front and rear edge tool paths of the profile, the cutting tool paths are planned, and the initial step length is calculated according to the maximum linear error, and the corresponding tool contact point set is obtained, including:

[0030] Get the tool contact trajectory, let u and v be the line spacing and feed direction of the blade parameter surface S to be processed respectively. The first and last tool contact trajectory are parameter intervals u = u s , v∈[v 0 ,v 4 ] and u=u e , v∈[v 0 ,v 4 ] parameter line, the knife contact trajectory on the leading edge is u = u im ,v∈[v 1 ,v 2 ] parameter line, the knife contact trajectory on the trailing edge is u = u i ,v∈[v 3 ,v 4 ] parameter line; the i-th knife contact trajectory line CC can be calculated by formula (1) i The leading and trailing edge tool path u i and u im , where n is the total number of toolpaths, u min and u max are the minimum and maximum values ​​of the u parameter respectively;

[0031]

[0032] Taking the suction surface tool path of the first line of tool path as an example, the tool contact point trajectory line CC 1.1 The parameter interval is [v 0 ,v 1 ]. Let CC 1,1 The jth knife contact point and its curvature radius are Contact with the next knife The local knife contact trajectory between is short and the curvature does not change much. It is assumed to be of equal curvature and the parameter v is linearly related to the curve length. Calculated by formula (2) arrive The parameter increment Δv CC , where L i for The length of the knife contact trajectory between the two points, so as to obtain the next CC point All knife contact points can be obtained by analogy.

[0033]

[0034] Furthermore, in step 2.2, for the spiral tool path on the profile surface, the initial step length of the spiral tool path is calculated according to the maximum linear error by calculating the intersection of the section plane with the suction and compression surfaces, and the corresponding tool contact point set is obtained, including:

[0035] The i-th knife contact point trajectory CC i The v parameter ranges of the suction surface, leading edge, compression surface, and trailing edge are [v 0 ,v 1 ]、[v 1 ,v 2 ]、[v 2 ,v 3 ]、[v 3 ,v 4 ], since the spiral tool path is a closed curve, v 0 and v 4 The corresponding points coincide; the first line of spiral tool path For example, the starting point of the spiral knife contact trajectory line is and end point The parameters are (u 0 ,v 0 )、(u 1m ,v 1 ), obtain the blade surface S(u,v) in the parameter interval [u 0 ,u 1m ]、[v 0 ,v 1 ] local surface S L Calculated by formula (3) The midpoint P mid , calculate P mid To S L The minimum distance point P f .by and P f Construct the cutting plane F, F and S L The intersection line is the spiral tool track contact point trajectory line on the suction surface. Similarly, the knife contact trajectory lines of the suction surface, leading edge, compression surface, and trailing edge are calculated respectively, and are respectively brought into equation (2) to calculate the corresponding knife contact point set.

[0036]

[0037] like Figure 2 As shown, let the line segment and arc The maximum linear error between l , For point The radius of curvature, Then the knife contact trajectory line CC iThe actual knife contact on V j+1 It can be obtained by formula (4).

[0038]

[0039] Furthermore, the step 2.3 integrates the above tool paths to obtain a complete tool contact point set, and the tool contact point calculation of the tool position point and the tool axis vector includes:

[0040] The calculated tool contact point sets of the first and last rows and the surface between the first and last rows are integrated to obtain the complete blade spiral tool contact trajectory. The initial tool position and tool axis vector of any tool contact point in the blade tool contact trajectory can be calculated by formula (5), where the rake angle α is the angle between the tool axis vector T and the surface normal vector, and β is the rotation angle around the surface normal vector.

[0041]

[0042] Furthermore, the point set of the discrete tool cutting surface and tool contact point trajectory line of the tool envelope surface calculated in step 3.1 includes:

[0043] Knife contact and The local knife contact trajectory CC between i,j It can be expressed by formula (6), and CC can be calculated by using formula (7) in an equal parameter manner: i,j n discrete points on In order to improve the calculation efficiency, the present invention uses discrete knife contact point set Replace the local knife contact track line CC i,j Carry out subsequent calculations.

[0044] CC i,j =CC i (v),v∈[v j ,v j+1 ] (6)

[0045]

[0046] Furthermore, the step 3.2, for any tool posture on the tool envelope surface between adjacent tool positions, calculates the approach error of the cutting edge at a cutting angle and obtains the corresponding tool contact point, including:

[0047] Step 3.2.1 Calculate tool vertex O m Tool pose information at

[0048] Tool vertex O m Coordinate information, tool position point Coordinate information, tool axis vector T m , location coefficient km It can be calculated by formula (8), where k m is the tool vertex O m Connect the line O at the tool vertex i,j O i,j+1 Position coefficient on tool vertex O i,j and tool vertex O i,j+1 It can be obtained by formula (9).

[0049]

[0050] Step 3.2.2 Calculate the m Minimum distance d at a single cutting angle min (θ)

[0051] like Figure 5 As shown in the figure, the cutting edge surface of the circular cutter is an arc surface with a radius from Rr to R, and the center of different circles on the arc surface is O m (θ) and the corresponding radius R(θ) can be calculated by formula (10), where θ is the cutting angle of the arc surface, θ∈[0°,90°]. In order to simplify the calculation process of the minimum distance from the arc surface to the point set, the present invention discretizes the arc cutting surface into multiple cutting circles according to the cutting angle, and iteratively calculates the minimum distance d from the cutting circle to the point set. min (θ).

[0052]

[0053] like Figure 6 and 7 As shown, the point set Any point in For example, take point O m (θ) and Three points construct plane F k , plane F k With cutting circle O m The two intersection points of (θ) are and Let the distance between the two intersection points be The closer point is but yes To cutting circle O m The shortest distance of (θ) Line segment is the cutting circle O m The radius R(θ) of (θ) is As the common side, construct two triangles and The shortest distance It can be calculated by formula (11). Similarly, the point set is calculated All discrete points in the cutting circle O m The minimum distance of (θ) and put it into the distance set In the distance set The minimum value in the discrete knife contact point set To cutting circle O m The minimum distance d of (θ) min (θ).

[0054]

[0055] Step 3.2.3 Determine d min (θ) Whether it meets the accuracy requirements

[0056] The above steps 3.2.1 to 3.2.2 can calculate the discrete point set To cutting circle O m The minimum distance d of (θ) min (θ). Let the point set Points in Corresponding to d min (θ), Two adjacent points and To circle O m The distances of (θ) are and The minimum distance difference is calculated by formula (12): If the minimum distance difference If it is greater than the set approximation error precision Δe, it means that the current minimum distance d min (θ) does not meet the accuracy requirements, go to step 3.2.4; if Description min (θ) meets the accuracy requirement, go to step 3.2.5.

[0057]

[0058] Step 3.2.4 Calculate d to meet the accuracy requirements min (θ)

[0059] Current minimum distance d min (θ) does not meet the accuracy requirements, and it is necessary to add a new knife contact point to reduce the approximation error value. Calculate the point through formula (13) and The parameter value corresponding to the parameter midpoint and The two parameter values and Substitute them into formula (14) respectively to calculate the two parameter values ​​in CC i,j The corresponding parameter midpoint and Go to step 3.2.2 and use the method in step 3.2.2 to calculate the point and To circle O m The minimum distance of (θ) and Recalculate the minimum distance d min (θ) and the minimum difference like d min (θ) meets the imprecision requirement, go to step 3.2.4; if d min (θ) meets the accuracy requirement, go to step 3.3.

[0060]

[0061] Furthermore, the step 3.3 iterates the cutting angle of the cutting edge, and takes the minimum value of the approximation error of the cutting angle as the approximation error of the tool posture, including:

[0062] Steps 3.1 and 3.2 can calculate O m The upper circle O of the tool cutting edge m (θ) to point set The minimum distance d min (θ), d min (θ) is the minimum distance value corresponding to the current cutting angle θ. However, the cutting edge of the circular cutter is a circular surface, and the interval of θ is [0°, 90°]. Therefore, the d of these angle values ​​needs to be calculated by iterating the discrete angle values ​​within [0°, 90°]. min (θ), with their minimum value d min As O m Approach error of tool posture at .

[0063] Step 3.3.1 Calculate the critical iteration value d within the range of cutting angle θ min (θ)

[0064] The present invention iteratively calculates d in the interval [0°, 90°] min (θ), with the minimum value d min As O m The initial search interval of θ is [0°, 90°], and the leading angle α, the median of the angles in the intervals [0°, α] and [α, 90°], α / 2, and (α+90°) / 2 are selected as the three key iteration values. Go to step 3 and calculate the corresponding minimum distance d min (α), d min (α / 2) and d min ((α+90°) / 2). The minimum distance difference is calculated by formula (15): If the current number of iterations n is satisfied at the same time it Greater than or equal to the minimum number of iterations set and If the approximation error precision Δe is less than or equal to the set value, it means that the result of this calculation meets the accuracy requirement. The minimum value of the three minimum distances is the required d min , the calculation ends. or It is necessary to continue iterative calculation and go to step 3.3.2 to calculate the next search interval of θ.

[0065]

[0066] Step 3.3.2 Calculate the next search interval of θ

[0067] Among the three minimum distances mentioned above, if d min (α) is the smallest, and α / 2 and (α+90°) / 2 adjacent to α constitute the second search interval [α / 2, (α+90°) / 2]. min (α / 2) is the smallest, and the second search interval is [0°,α]. min ((α+90°) / 2) is the smallest, and the second search interval is [α,90°]. That is, taking the iteration value corresponding to the minimum distance as the center, we obtain the next search interval that is smaller than the current interval, and the number of iterations n it Increase by 1 and go to step 3.3.1 for the next calculation. The entire calculation process is as follows Figure 8 shown.

[0068] Furthermore, the step 3.4 obtains the corresponding tool posture by iterating the tool vertex position on the tool vertex line, calculates the approximation error for each tool posture, and takes the maximum value as the approximation error between adjacent tool position points, including:

[0069] Step 3.3 proposes a method to calculate the approximation error of a single tool position during machining, and gives the tool position at O i,j O i,j+1 Any tool vertex O on m The approximation error at e(O m ) calculation process. The circular knife is calculated from the knife position Cut to the next tool position The formed tool envelope surface and the local tool contact trajectory CC i,j The maximum error is the approach error e of this section of the tool path. i,j Therefore, in O i,j O i,j+1 There is a point on the cutting surface where the tool approach error is the largest. Searching for the minimum value d in the cutting angle θ interval [0°, 90°] minSimilarly, the present invention connects the tool vertex line O i,j O i,j+1 The maximum value of the approximation error is calculated by the previous iteration and used as the tool position point The approach error e between tool paths i,j , the detailed calculation process is as follows:

[0070] Step 3.4.1 Set the key iteration value within the tool vertex interval

[0071] Taking 8 equal parts as an example, let the position coefficient k of the tool vertex be m = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875, each value represents a tool position. The initial search interval for the tool vertex is [O i,j ,O i,j+1 ], taking all equally divided points in the interval as key iteration values.

[0072] Step 3.4.2 Calculate the approximation error of the key iteration value

[0073] Using formula (8), we can calculate the different position coefficients k in step 3.4.1: m Corresponding tool posture information, including different position coefficients k m Corresponding knife point Tool axis vector T m and tool vertex O m Information, calculate the position coefficient k m = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875 corresponding to the approximation error, denoted as the approximation error set {e(k m )}.

[0074] Let the key iteration value k m = 0.5 approximation error e(0.5) is {e(k m )}, and use formula (16) to calculate the minimum difference Δe min If the current number of iterations n it Greater than or equal to the minimum number of iterations set And Δe min Less than or equal to the set approximation error precision Δe, indicating that the result of this calculation meets the accuracy requirements, {e(k m The maximum value among )} is the required approximation error e i,j , the calculation ends. or Δe min >Δe, it is necessary to continue the iterative calculation and go to step 3.4.3 to calculate the next search interval.

[0075] Δe min=min(e(0.5)-e(0.375),e(0.5)-e(0.625))(16)

[0076] Step 3.4.3 Calculate the next search interval

[0077] {e(k m )} is the midpoint of the key iteration value, and half of the current search interval is created as a smaller next search interval. If e(0.5) is the largest, the next search interval is [0.25,0.75], and go to step 3.4.1 to recalculate.

[0078] Furthermore, the step 4 includes comparing the approximation error between adjacent tool positions with the maximum allowable value, iteratively adjusting the step length, obtaining an approximation error greater than the minimum number of iterations and within the maximum allowable error range, and obtaining a variable step length spiral tool path.

[0079] Step 4.1 Compare the approximation error between adjacent tool positions with the maximum allowable value and iteratively adjust the step size

[0080] If e j,j+1 =e max , then go to step 4.1 to continue calculating the next segment and The approach error between the tool paths; if e j,j+1 <e max and Then go to step 4.2 to continue calculating the next segment and The approach error between the tool paths; if e j,j+1 <e max and Go to step 4.2. If j,j+1 >e max ,generate midpoint Calculate Add the tool position point and tool axis vector to the tool contact point set, go to step 4.1, and recalculate The approximation error between .

[0081] Step 4.2 Obtain an approximation error greater than the minimum number of iterations and within the maximum allowable error range

[0082] Skip Point Remove from knife contact point set Tool position and tool axis vector information, go to step calculation The approximation error between j,j+2 , the current number of iterations n it Add 1 and re-check the approximation error.

[0083] Step 4.3 Obtain variable step length spiral tool path

[0084] Calculate adjacent knife contacts Similarly, the subsequent variable-step spiral knife contact points and knife contact point trajectory lines can be calculated in sequence using steps 1, 2, 3, and 4, and the knife position point and knife axis vector of the variable-step spiral knife contact trajectory lines can be calculated.

[0085] The present invention also provides a terminal, comprising:

[0086] at least one processor; and,

[0087] a memory communicatively connected to the at least one processor; wherein,

[0088] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method for generating variable-step spiral tool paths for five-axis finishing of blade surfaces by circular cutters as described in any one of claims 1 to 13.

[0089] An embodiment of the present invention also provides a computer-readable storage medium storing a computer program, characterized in that when the computer program is executed by a processor, it implements the method for generating a variable-step spiral tool path for five-axis finishing of a blade surface with a circular cutter according to any one of claims 1 to 13.

[0090] The present invention provides a method for generating a variable-step spiral tool path for five-axis machining of a blade curved surface circular cutter. According to the proposed method, the tool contact point trajectory lines of the blade's first and last line tool paths and the spiral tool path of the intermediate profile are respectively planned, and the initial step length is calculated according to the maximum linear error of the tool contact point trajectory line, and the discrete tool contact points are obtained and the tool position points and tool axis vectors of the tool contact points are calculated; the tool motion envelope surface and the tool contact trajectory line between adjacent tool position points are replaced by discrete tool cutting surfaces and tool contact point sets, and a method for calculating the approximation error between two adjacent tool position points is proposed; the approximation error is compared with the maximum allowable value, and the step length is adjusted so that the approximation error between adjacent tool position points is within a set range, thereby obtaining a variable-step spiral tool path. Compared with the tool path calculated by the equal parameter method, the variable-step spiral tool path for five-axis finishing machining of the blade curved surface circular cutter calculated by the calculation method proposed by the present invention has a longer calculated step length and a smaller number of tool position points while meeting the approximation error requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] One or more embodiments are exemplarily described by the pictures in the corresponding drawings. These exemplifications do not constitute limitations on the embodiments. Elements with the same reference numerals in the drawings represent similar elements unless otherwise stated. The drawings in the drawings do not constitute a scale limitation.

[0092] Figure 1 It is a flow chart of a method for generating a variable-step-length spiral tool path for five-axis finishing machining of a blade surface with a circular cutter according to one embodiment of the present invention;

[0093] Figure 2 is a schematic diagram of chord error according to one embodiment of the present invention;

[0094] Figure 3 is a schematic diagram of a tool position point and a tool axis vector according to one embodiment of the present invention;

[0095] Figure 4 is a schematic diagram of errors between adjacent tool position points according to one embodiment of the present invention;

[0096] Figure 5 is a schematic diagram of the outline of a circular ring knife on a plane according to one embodiment of the present invention;

[0097] Figure 6 is a schematic diagram of the geometric relationship between the tool contact points and the tool cutting surface circle when the tool contact point set is concave according to one embodiment of the present invention;

[0098] Figure 7 is a schematic diagram of the geometric relationship between the tool contact points and the tool cutting surface circle when the tool contact point set is convex according to one embodiment of the present invention;

[0099] Figure 8 According to one embodiment of the present invention, the tool position O is obtained. m Schematic diagram of the approximation error process;

[0100] Fig. 9 is a schematic diagram of a blade curved surface according to one embodiment of the present invention;

[0101] Fig.10 A method for generating a blade curved surface using a variable step length spiral tool path according to one embodiment of the present invention;

[0102] Fig.11 A method for generating blade curved surfaces using isoparametric tool paths according to one embodiment of the present invention;

[0103] Fig.12 is a schematic diagram of an approximation error of a variable-step-length spiral tool path according to one embodiment of the present invention;

[0104] Fig.13 FIG. 4 is a schematic diagram of the approximation error of the isoparametric tool path according to one embodiment of the present invention. DETAILED DESCRIPTION

[0105] To make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. However, it will be appreciated by those skilled in the art that in the embodiments of the present invention, many technical details are proposed in order to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed in the present application can be implemented. The division of the following embodiments is for the convenience of description, and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined and referenced with each other without contradiction.

[0106] The present invention proposes a variable step length spiral tool path generation method for five-axis machining of blade curved surface circular cutter, see Figure 1 , including the following specific steps:

[0107] Step 1 Import the surface model and set the tool radius R, fillet radius r, and tool length L T and the total number of tool paths n, the rake angle α, and the maximum allowable value of the approach error e max , maximum number of iterations Approximation error accuracy Δe.

[0108] Step 2 calculates the initial tool position point and tool axis vector of the spiral tool track contact point trajectory;

[0109] Step 2.1 For the first and last tool paths and the front and rear edge tool paths, plan the cutting tool paths, and calculate the initial step length according to the maximum linear error to obtain the corresponding tool contact point set. Let u and v be the line spacing and feed direction of the blade parameter surface S to be processed respectively. The first and last tool contact point trajectory lines are parameter intervals u = u s , v∈[v 0 ,v 4 ] and u=u e , v∈[v 0 ,v 4 ] parameter line, the knife contact trajectory on the leading edge is u = u im ,v∈[v 1 ,v 2 ] parameter line, the knife contact trajectory on the trailing edge is u = u i ,v∈[v 3 ,v 4 ] parameter line; the i-th knife contact trajectory line CC can be calculated by formula (1) i The leading and trailing edge tool path u i and u im , where n is the total number of toolpaths, u min and u max are the minimum and maximum values ​​of the u parameter respectively;

[0110]

[0111] Taking the suction surface tool path of the first line of tool path as an example, the tool contact point trajectory line CC 1.1 The parameter interval is [v 0 ,v 1 ]. Let CC 1,1 The jth knife contact point and its curvature radius are Contact with the next knife The local knife contact trajectory between is short and the curvature does not change much. It is assumed to be of equal curvature and the parameter v is linearly related to the curve length. Calculated by formula (2) arrive The parameter increment Δv CC , where L i for The length of the knife contact trajectory between the two points, so as to obtain the next CC point All knife contact points can be obtained by analogy.

[0112]

[0113] Step 2.2 For the spiral tool path on the profile, calculate the intersection of the cutting plane and the suction and compression surfaces, calculate the initial step length of the spiral tool path according to the maximum linear error, and obtain the corresponding tool contact point set. The i-th line tool contact trajectory line CC i The v parameter ranges of the suction surface, leading edge, compression surface, and trailing edge are [v 0 ,v 1 ]、[v 1 ,v 2 ]、[v 2 ,v 3 ]、[v 3 ,v 4 ], since the spiral tool path is a closed curve, v 0 and v 4 The corresponding points coincide; the first line of spiral tool path For example, the starting point of the spiral knife contact trajectory line is and end point The parameters are (u 0 ,v 0 )、(u 1m ,v 1 ), obtain the blade surface S(u,v) in the parameter interval [u 0 ,u 1m ]、[v 0 ,v 1 ] local surface S L Calculated by formula (3) The midpoint P mid , calculate Pmid To S L The minimum distance point P f .by and P f Construct the cutting plane F, F and S L The intersection line is the spiral tool track contact point trajectory line on the suction surface. Similarly, the knife contact trajectory lines of the suction surface, leading edge, compression surface, and trailing edge are calculated respectively, and are respectively brought into equation (2) to calculate the corresponding knife contact point set.

[0114]

[0115] like Figure 2 As shown, let the line segment and arc The maximum linear error between l , For point The radius of curvature, Then the knife contact trajectory line CC i The actual knife contact on V j+1 It can be obtained by formula (4).

[0116]

[0117] Step 2.3 calculates the initial tool position point and tool axis vector of the tool contact point. Figure 3 As shown, with knife contact For example, create

[0118] by is the local coordinate system with the origin, let Y L =t j , Z L =n j , X L =t j ×n j , the tool position point and tool axis vector are determined by the rake angle α, point The initial tool position point and tool axis vector of the spiral tool path can be calculated by formula (5); similarly, the initial tool position point and tool axis vector of all spiral tool path tool contact points can be calculated.

[0119]

[0120] Iterative steps 2.1 to 2.3 can determine the initial tool position points and tool axis vectors of all tool contact points in the spiral tool path.

[0121] Step 3 calculates the approximation error between two adjacent tool positions, taking the jth and j+1th tool positions on the i-th tool path as and Take this as an example to describe the calculation process.

[0122] Step 3.1 Calculate the discrete tool cutting surface of the tool envelope surface and the point set of the tool contact trajectory line

[0123] Knife contact and The local knife contact trajectory CC between i,j It can be expressed by formula (6), and CC can be calculated by using formula (7) in an equal parameter manner: i,j n discrete points on In order to improve the calculation efficiency, the present invention uses discrete knife contact point set Replace the local knife contact track line CC i,j Carry out subsequent calculations.

[0124] CC i,j =CC i (v),v∈[v j ,v j+1 ](6)

[0125]

[0126] Step 3.2 Calculate any tool pose O m Approximation error value of a single cutting angle

[0127] like Figure 4 As shown, tool vertex O i,j Clamped by the tool holder and moved to the tool vertex O i,j+1 , driving the circular knife from the knife contact point Processing to The circular cutter has a complex shape, and the tool envelope formed by the movement is difficult to accurately express, resulting in the two adjacent points and The calculation of the tool path approximation error is difficult. i,j O i,j+1 Tool vertex O on m For example, calculate the tool vertex O m The tool posture information at the location is used to calculate the local tool contact trajectory CC i,j Point set Minimum distance d to the cutting edge surface of the circular cutter min , which is O m The approach error value e(O m ), the detailed calculation process is as follows:

[0128] Step 3.2.1 Calculate tool vertex O m Tool pose information at

[0129] Tool vertex O m Coordinate information, tool position point Coordinate information, tool axis vector T m , location coefficient k m It can be calculated by formula (8), where k m is the tool vertex O m Connect the line O at the tool vertex i,j O i,j+1 Position coefficient on tool vertex O i,j and tool vertex O i,j+1 It can be obtained by formula (9).

[0130]

[0131] Step 3.2.2 Calculate the m Minimum distance d at a single cutting angle min (θ)

[0132] like Figure 5 As shown in the figure, the cutting edge surface of the circular cutter is an arc surface with a radius from Rr to R, and the center of different circles on the arc surface is O m (θ) and the corresponding radius R(θ) can be calculated by formula (10), where θ is the cutting angle of the arc surface, θ∈[0°,90°]. In order to simplify the calculation process of the minimum distance from the arc surface to the point set, the present invention discretizes the arc cutting surface into multiple cutting circles according to the cutting angle, and iteratively calculates the minimum distance d from the cutting circle to the point set. min (θ).

[0133]

[0134] like Figure 6 and 7 As shown, the point set Any point in For example, take point O m (θ) and Three points construct plane F k , plane F k With cutting circle O m The two intersection points of (θ) are and Let the distance between the two intersection points be The closer point is but yes To cutting circle O m The shortest distance of (θ) Line segment is the cutting circle O m The radius R(θ) of (θ) is As the common side, construct two triangles and The shortest distance It can be calculated by formula (11). Similarly, the point set is calculated All discrete points in the cutting circle O m The minimum distance of (θ) and put it into the distance set In the distance set The minimum value in the discrete knife contact point set To cutting circle O m The minimum distance d of (θ) min (θ).

[0135]

[0136] Step 3.2.3 Determine d min (θ) Whether it meets the accuracy requirements

[0137] The above steps 3.2.1 to 3.2.2 can calculate the discrete point set To cutting circle O m The minimum distance d of (θ) min (θ). Let the point set Points in Corresponding to d min (θ), Two adjacent points and To circle O m The distances of (θ) are and The minimum distance difference is calculated by formula (12): If the minimum distance difference If it is greater than the set approximation error precision Δe, it means that the current minimum distance d min (θ) does not meet the accuracy requirements, go to step 3.2.4; if Description min (θ) meets the accuracy requirement, go to step 3.2.5.

[0138]

[0139] Step 3.2.4 Calculate d to meet the accuracy requirements min (θ)

[0140] Current minimum distance d min (θ) does not meet the accuracy requirements, and it is necessary to add a new knife contact point to reduce the approximation error value. Calculate the point through formula (13) and The parameter value corresponding to the parameter midpoint and The two parameter values and Substitute them into formula (14) respectively to calculate the two parameter values ​​in CC i,j The corresponding parameter midpoint and Go to step 3.2.2 and use the method in step 3.2.2 to calculate the point and To circle O m The minimum distance of (θ) and Recalculate the minimum distance d min (θ) and the minimum difference like d min (θ) meets the imprecision requirement, go to step 3.2.4; if d min (θ) meets the accuracy requirement, go to step 3.3.

[0141]

[0142] Step 3.3 Iterate the cutting angle of the cutting edge and calculate the tool posture O m The approximation error of

[0143] Steps 3.1 and 3.2 can calculate O m The upper circle O of the tool cutting edge m (θ) to point set The minimum distance d min (θ), d min (θ) is the minimum distance value corresponding to the current cutting angle θ. However, the cutting edge of the circular cutter is a circular surface, and the interval of θ is [0°, 90°]. Therefore, the d of these angle values ​​needs to be calculated by iterating the discrete angle values ​​within [0°, 90°]. min (θ), with their minimum value d min As O m Approach error of tool posture at .

[0144] Step 3.3.1 Calculate the critical iteration value d within the range of cutting angle θ min (θ)

[0145] The present invention iteratively calculates d in the interval [0°, 90°] min (θ), with the minimum value d min As O m The initial search interval of θ is [0°, 90°], and the leading angle α, the median of the angles in the intervals [0°, α] and [α, 90°], α / 2, and (α+90°) / 2 are selected as the three key iteration values. Go to step 3 and calculate the corresponding minimum distance d min (α), d min (α / 2) and dmin ((α+90°) / 2). The minimum distance difference is calculated by formula (15): If the current number of iterations n is satisfied at the same time it Greater than or equal to the minimum number of iterations set and If the approximation error precision Δe is less than or equal to the set value, it means that the result of this calculation meets the accuracy requirement. The minimum value of the three minimum distances is the required d min , the calculation ends. or It is necessary to continue iterative calculation and go to step 3.3.2 to calculate the next search interval of θ.

[0146]

[0147] Step 3.3.2 Calculate the next search interval of θ

[0148] Among the three minimum distances mentioned above, if d min (α) is the smallest, and α / 2 and (α+90°) / 2 adjacent to α constitute the second search interval [α / 2, (α+90°) / 2]. min (α / 2) is the smallest, and the second search interval is [0°,α]. min ((α+90°) / 2) is the smallest, and the second search interval is [α,90°]. That is, taking the iteration value corresponding to the minimum distance as the center, we obtain the next search interval that is smaller than the current interval, and the number of iterations n it Increase by 1 and go to step 3.3.1 for the next calculation. Figure 8 shown.

[0149] Step 3.4 Iterate the tool vertex pose and calculate the approximation error between adjacent tool positions

[0150] Step 3.3 proposes a method to calculate the approximation error of a single tool position during machining, and gives the tool position at O i,j O i,j+1 Any tool vertex O on m The approximation error at e(O m ) calculation process. The circular knife is calculated from the knife position Cut to the next tool position The formed tool envelope surface and the local tool contact trajectory CC i,j The maximum error is the approach error e of this section of the tool path. i,j Therefore, in O i,j O i,j+1 There is a point on the cutting surface where the tool approach error is the largest. Searching for the minimum value d in the cutting angle θ interval [0°, 90°] minSimilarly, the present invention connects the tool vertex line O i,j O i,j+1 The maximum value of the approximation error is calculated by the previous iteration and used as the tool position point The approach error e between tool paths i,j , the detailed calculation process is as follows:

[0151] Step 3.4.1 Set the key iteration value within the tool vertex interval

[0152] Taking 8 equal parts as an example, let the position coefficient k of the tool vertex be m = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875, each value represents a tool position. The initial search interval for the tool vertex is [O i,j ,O i,j+1 ], taking all equally divided points in the interval as key iteration values.

[0153] Step 3.4.2 Calculate the approximation error of the key iteration value

[0154] Using formula (8), we can calculate the different position coefficients k in step 3.4.1: m Corresponding tool posture information, including different position coefficients k m Corresponding knife point Tool axis vector T m and tool vertex O m Information, calculate the position coefficient k m = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875 corresponding to the approximation error, denoted as the approximation error set {e(k m )}.

[0155] Let the key iteration value k m = 0.5 approximation error e(0.5) is {e(k m )}, and use formula (16) to calculate the minimum difference Δe min If the current number of iterations n it Greater than or equal to the minimum number of iterations set And Δe min Less than or equal to the set approximation error precision Δe, indicating that the result of this calculation meets the accuracy requirements, {e(k m The maximum value among )} is the required approximation error e i,j , the calculation ends. or Δe min >Δe, it is necessary to continue the iterative calculation and go to step 3.4.3 to calculate the next search interval.

[0156] Δe min=min(e(0.5)-e(0.375),e(0.5)-e(0.625))(16)

[0157] Step 3.4.3 Calculate the next search interval

[0158] {e(k m )} is the midpoint of the key iteration value, and half of the current search interval is created as a smaller next search interval. If e(0.5) is the largest, the next search interval is [0.25,0.75], and go to step 3.4.1 to recalculate.

[0159] Step 4: Calculate the variable step length tool contact point and tool path

[0160] The approximation error e obtained in step 3 above is i,j That is, the circular knife is at the adjacent knife position If the calculated approximation error e i,j Less than the maximum value allowed max , and the current iteration number n it Greater than the minimum number of iterations Think i,j To meet the error requirements, This is the desired variable step long knife position. Otherwise, adjust Parameters, so that e i,j Meet the approximation error requirements. The specific process is as follows:

[0161] Step 4.1 Compare the approximation error between adjacent tool positions with the maximum allowable value and iteratively adjust the step size

[0162] If e j,j+1 =e max , then go to step 1 to continue calculating the next segment and The approach error between the tool paths; if e j,j+1 <e max and Go to step 1 to continue calculating the next segment and The approach error between the tool paths; if e j,j+1 <e max and Go to step 3.2. If j,j+1 >e max ,generate midpoint Calculate The tool position point and tool axis vector are added to the tool contact point set, go to step 1, and recalculate The approximation error between .

[0163] Step 4.2 Obtain an approximation error greater than the minimum number of iterations and within the maximum allowable error range

[0164] Skip Point Remove from knife contact point set Tool position and tool axis vector information, go to step 1 to calculate The approximation error between j,j+2 , the current number of iterations n it Add 1 and re-check the approximation error.

[0165] Step 4.3 Obtain variable step length spiral tool path

[0166] Calculate adjacent knife contacts Similarly, the subsequent variable-step spiral knife contact points and knife contact point trajectory lines can be calculated in sequence using steps 1, 2, 3, and 4, and the knife position point and knife axis vector of the variable-step spiral knife contact trajectory lines can be calculated.

[0167] An embodiment of the present invention further provides a terminal, including:

[0168] at least one processor; and,

[0169] a memory communicatively connected to the at least one processor; wherein,

[0170] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the equal-error tool path generation method for five-axis machining of parametric surface flat-bottom tool proposed by the present invention.

[0171] Among them, the memory and the processor are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripherals, voltage regulators, and power management circuits, which are well known in the art and are therefore not further described herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on a wireless medium via an antenna, and further, the antenna also receives data and transmits the data to the processor.

[0172] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0173] The embodiment of the present invention further provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the method for generating equal-error tool paths for five-axis machining of a parametric surface flat-bottom tool proposed by the present invention is implemented. The computer program is stored. When the computer program is executed by a processor, the above method embodiment is implemented.

[0174] That is, those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including several instructions to enable a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0175] A typical implementation example of the present invention is as follows:

[0176] The examples chosen are typical blade surfaces, such as Fig. 9 As shown, the tool selected is a circular cutter with a radius of 3 mm and a fillet radius of 1.5 mm. The total number of tool paths is 106, and the maximum allowable approach error is e max 0.01mm, the forward tilt angle is 15°, and the minimum number of iterations is 5, and the calculation accuracy Δe is 0.0002mm.

[0177] Fig.10 The variable step length spiral tool path is generated by the method proposed by the present invention. As a comparison, the blade machining tool path is generated by the isoparametric method, and the maximum number of tool paths per row in the present invention is selected for isoparametric method generation. Fig.11 The blade tool path generated by the equal parameter method. Since the total number of tool paths is large, the linear difference selects 9 tool paths to compare their approximation error distribution. The selected 9 tool paths are the 1st, 14th, 27th, 40th, 53rd, 66th, 79th, 92nd, and 106th lines respectively; Table 1 shows the approximation error distribution of the 9 tool paths in the variable step length tool path in the method of the present invention, and Table 2 shows the approximation error distribution of the 9 tool paths in the equal parameter method tool path. Compared with the equal parameter method, the error distribution of the variable step length tool path is more uniform and controllable, can better adapt to the change of blade curvature, and requires fewer tool contacts.

[0178] Fig.12 The approximation errors of the 9 tool paths in the variable step length tool path are all within the range of (0, 0.01mm]. Fig.13It is the approximation error of 9 tool paths in the equal parameter tool path. Some approximation errors are too small, and some approximation errors seriously exceed the accuracy requirements.

[0179] Compared with the tool path with equal parameters, the variable step length tool path proposed in the present invention has a more uniform and controllable error distribution, can better adapt to the change of blade curvature, and requires fewer tool contact points.

[0180] Table 1 Error distribution of 9 tool paths in variable step length tool path

[0181]

[0182] Table 2 Error distribution of 9 tool paths in equal parameter tool paths

[0183]

[0184] In summary, the present invention provides a method for generating a variable-step spiral tool path for five-axis finishing of blade curved surface circular cutter. According to the proposed method, the tool contact point trajectory lines of the blade first and last row tool paths and the spiral tool path of the profile between the first and last rows are respectively planned, and the initial step length is calculated according to the maximum linear error of the tool contact point trajectory line, and the discrete tool contact points are obtained and the tool position points and tool axis vectors of the tool contact points are calculated; the tool motion envelope surface and the tool contact trajectory line between adjacent tool position points are replaced by discrete tool cutting surfaces and tool contact point sets, and a calculation method for the approximation error of two adjacent tool position points is proposed; the approximation error is compared with the maximum allowable value, and the current number of iterations is compared with the minimum number of iterations. The approximation error is compared with the maximum allowable value, and the step length is adjusted so that the approximation error between adjacent tool position points is within the set range, thereby obtaining a variable-step spiral tool path. Compared with the blade tool path generated by the equal parameter method, the variable-step spiral tool path for five-axis finishing of blade curved surface circular cutter calculated by the calculation method proposed by the present invention meets the requirements of the approximation error while having a longer step length and a smaller number of tool position points.

[0185] Those skilled in the art will appreciate that the above-mentioned embodiments are specific examples for implementing the present invention, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present invention.

Claims

1. A method for generating a variable-step spiral tool path for five-axis finishing of a blade surface by a circular cutter, characterized in that: The following steps are involved: Step 1: Import the blade surface model and set the processing parameters; Step 2 calculates the initial tool position point and tool axis vector of the spiral tool track contact point trajectory; Step 3: Calculate the approximation error value between two adjacent tool position points; Step 4 generates a variable-step spiral tool path for the blade surface.

2. A method for generating a variable-step spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 1, characterized in that: The step 2 of calculating the initial tool position point and tool axis vector of the spiral tool track contact point trajectory includes: Step 2.1 For the first and last tool paths and the front and rear edge tool paths of the profile, plan the cutting tool paths, calculate the initial step length according to the maximum linear error, and obtain the corresponding tool contact point set; Step 2.2: For the spiral tool path on the molding surface, the initial step length of the spiral tool path is calculated according to the maximum linear error by calculating the intersection line between the section plane and the suction and compression surfaces, and the corresponding tool contact point set is obtained; Step 2.3 integrates the above tool paths to obtain a complete set of tool contact points, and calculates the tool position point and tool axis vector for the tool contact points.

3. A method for generating a variable-step spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 1, characterized in that: The step 3 of calculating the approximation error value between two adjacent tool position points includes: Step 3.1 calculate the point set of the discrete tool cutting surface and tool contact trajectory of the tool envelope surface; Step 3.2: for any tool posture on the tool envelope surface between adjacent tool positions, calculate the approach error of the cutting edge at a cutting angle and obtain the corresponding tool contact point; Step 3.4 iterates the cutting angle of the cutting edge, and takes the minimum value of the approximation error of the cutting angle as the approximation error of the tool posture; Step 3.5 obtains the corresponding tool posture by iterating the tool vertex position on the tool vertex line, calculates the approximation error for each tool posture, and takes its maximum value as the approximation error between adjacent tool position points.

4. A method for generating a variable-step spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 1, characterized in that: The step 4 of generating a variable step length spiral tool path for the blade surface comprises: Step 4.1 compares the approximation error between adjacent tool positions with the maximum allowable value, and iteratively adjusts the step size; Step 4.2 obtains an approximation error that is greater than the minimum number of iterations and within the maximum allowable error range; Step 4.3 obtains the variable step length spiral tool path.

5. A method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 2, characterized in that: For the first and last tool paths and the front and rear edge tool paths of step 2.1, the cutting tool paths are planned, and the initial step length is calculated according to the maximum linear error to obtain the corresponding tool contact point set, including: Get the tool contact trajectory, let u and v be the line spacing and feed direction of the blade parameter surface S to be processed, and the first and last tool contact trajectory are parameter intervals u=u s , v∈[v0,v4] and u=u e , the parameter line of v∈[v0,v4], and the knife contact trajectory on the leading edge is u=u im , v∈[v1,v2], the knife contact trajectory on the trailing edge is u=u i , v∈[v3,v4] parameter line; the i-th knife contact trajectory CC can be calculated by formula (1): i The leading and trailing edge tool path u i and u im , where n is the total number of toolpath rows, u min and u max are the minimum and maximum values ​​of the u parameter respectively; Taking the suction surface tool path of the first line of tool path as an example, the tool contact point trajectory line CC 1.1 The parameter interval is [v0,v1], let CC 1,1 The jth knife contact point and its curvature radius are Contact with the next knife The local tool contact trajectory between is short and has little curvature change. Assuming that the curvature is constant and the parameter v is linearly related to the curve length, it can be calculated by formula (2): arrive The parameter increment Δv CC , where L i for The length of the knife contact trajectory between the two points, so as to obtain the next CC point All knife contact points can be obtained by analogy.

6. A method for generating a variable-step spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 2, characterized in that: In step 2.2, for the spiral tool path on the profile, the initial step length of the spiral tool path is calculated according to the maximum linear error by calculating the intersection of the section plane and the suction and compression surfaces, and the corresponding tool contact point set is obtained, including: The i-th knife contact point trajectory CC i The v parameter ranges of the suction surface, leading edge, compression surface, and trailing edge are [v0, v1], [v1, v2], [v2, v3], and [v3, v4], respectively. Since the spiral tool path is a closed curve, the points corresponding to v0 and v4 coincide. For example, the starting point of the spiral knife contact trajectory line is and end point The parameters are (u0,v0), (u 1m ,v1), obtain the blade surface S(u,v) in the parameter interval [u0,u 1m ], local surface S in [v0,v1] L ; Calculated by formula (3) The midpoint P mid , calculate P mid To S L The minimum distance point P f ;by and P f Construct the cutting plane F, F and S L The intersection line is the spiral tool track contact point trajectory line on the suction surface. Similarly, the knife contact trajectory lines of the suction surface, leading edge, compression surface, and trailing edge are calculated respectively, and the corresponding knife contact point sets are calculated by substituting them into equation (2); let the line segment and arc The maximum linear error between l , For point The radius of curvature, Then the knife contact trajectory line CC i The actual knife contact on V j+1 It can be obtained by formula (4).

7. A method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 2, characterized in that: According to step 2.3, the above tool paths are integrated to obtain a complete tool contact point set. The tool contact point calculation tool position point and tool axis vector include: The calculated tool contact point sets of the first and last rows and the surface between the first and last rows are integrated to obtain the complete blade spiral tool contact trajectory. The initial tool position point and tool axis vector of any tool contact point in the blade tool contact trajectory can be calculated by formula (5), where the rake angle α is the angle between the tool axis vector T and the surface normal vector, and β is the rotation angle around the surface normal vector.

8. A method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 3, characterized in that: The point set of the discrete tool cutting surface and tool contact trajectory line for calculating the tool envelope surface in step 3.1 includes: CC i,j =CC i (v),v∈[v j ,in j+1 ] (6) Knife contact and The local knife contact trajectory CC between i,j It can be expressed by formula (6), and CC can be calculated by using formula (7) in an equal parameter manner: i,j n discrete points on In order to improve the calculation efficiency, the present invention uses discrete knife contact point set Replace the local knife contact track line CC i,j Carry out subsequent calculations.

9. A method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 3, characterized in that: The step 3.2, for any tool posture on the tool envelope surface between adjacent tool positions, calculates the approach error of the cutting edge at a cutting angle and obtains the corresponding tool contact point, including: Step 3.2.1 Calculate tool vertex O m Tool pose information at Tool vertex O m Coordinate information, tool position point Coordinate information, tool axis vector T m , location coefficient k m It can be calculated by formula (8), where k m is the tool vertex O m Connect the tool vertices to O i,j O i,j+1 Position coefficient on the tool vertex O i,j and tool vertex O i,j+1 It can be obtained by formula (9); Step 3.2.2 Calculate the m Minimum distance d at a single cutting angle min (θ) The cutting edge surface of the circular cutter is an arc surface with a radius from Rr to R. The center of the different circles on the arc surface is O. m (θ) and the corresponding radius R(θ) can be calculated by formula (10), where θ is the cutting angle of the arc surface, θ∈[0°,90°]; In order to simplify the calculation process of the minimum distance from the arc surface to the point set, the present invention discretizes the arc cutting surface into multiple cutting circles according to the cutting angle, and iteratively calculates the minimum distance d from the cutting circle to the point set. min (θ); Point Set Any point in For example, take point O m (θ) and Three points construct plane F k , plane F k With cutting circle O m The two intersection points of (θ) are and Let the distance between the two intersection points be The closer point is but yes To cutting circle O m The shortest distance of (θ) Line segment is the cutting circle O m The radius R(θ) of (θ) is As the common side, construct two triangles and The shortest distance It can be calculated by formula (11); similarly, the point set is calculated All discrete points in the cutting circle O m The minimum distance of (θ) and put it into the distance set In the distance set The minimum value in the discrete knife contact point set To cutting circle O m The minimum distance d of (θ) min (θ); Step 3.2.3 Determine d min (θ) Whether it meets the accuracy requirements The above steps 3.2.1 to 3.2.2 can calculate the discrete point set To cutting circle O m The minimum distance d of (θ) min (θ), set the point set Points in Corresponding to d min (θ), Two adjacent points and To circle O m The distances of (θ) are and The minimum distance difference is calculated by formula (12): If the minimum distance difference If it is greater than the set approximation error precision Δe, it means that the current minimum distance d min (θ) does not meet the accuracy requirements, go to step 3.2.4; if Description min (θ) meets the accuracy requirement, go to step 3.2.5; Step 3.2.4 Calculate d to meet the accuracy requirements min (θ) Current minimum distance d min (θ) does not meet the accuracy requirements, and it is necessary to add a new tool contact point to reduce the approximation error value. The point is calculated by formula (13) and The parameter value corresponding to the parameter midpoint and The two parameter values and Substitute them into formula (14) respectively to calculate the two parameter values ​​in CC i,j The corresponding parameter midpoint and Go to step 3.2.2 and use the method in step 3.2.2 to calculate the point and To circle O m The minimum distance of (θ) and Recalculate the minimum distance d min (θ) and the minimum difference like d min (θ) meets the accuracy requirement, go to step 3.2.

4. If d min (θ) meets the accuracy requirement, go to step 3.

3.

10. A method for generating a variable-step-length spiral tool path for five-axis finishing of a blade surface by a circular cutter according to claim 3, characterized in that: The step 3.3 iterates the cutting angle of the cutting edge, and takes the minimum value of the approximation error of the cutting angle as the approximation error of the tool posture, including: Step 3.3.1 Calculate the critical iteration value d within the range of cutting angle θ min (θ) The present invention iteratively calculates d in the interval [0°, 90°] min (θ), with the minimum value d min As O m The initial search interval of θ is [0°, 90°]. The leading angle α, the median of the angles α / 2 and (α+90°) / 2 in the intervals [0°, α] and [α, 90°] are selected as the three key iteration values. Go to step 3.2 and calculate the corresponding minimum distance d min (α), d min (α / 2) and d min ((α+90°) / 2), the minimum distance difference is calculated by formula (15) If the current number of iterations n is satisfied at the same time it Greater than or equal to the minimum number of iterations set and If the value is less than or equal to the set approximation error precision Δe, it means that the result of this calculation meets the accuracy requirements. The minimum value of the three minimum distances is the required d min , the calculation ends, if or It is necessary to continue iterative calculation and go to step 3.3.2 to calculate the next search interval of θ; Step 3.3.2 Calculate the next search interval of θ Among the three minimum distances mentioned above, if d min (α) is the smallest, and α / 2 and (α+90°) / 2 adjacent to α constitute the second search interval [α / 2, (α+90°) / 2]. If d min (α / 2) is the smallest, and the second search interval is [0°,α]. If d min ((α+90°) / 2) is the smallest, and the second search interval is [α,90°], that is, the next search interval smaller than the current interval is obtained with the iteration value corresponding to the minimum distance as the center, and the number of iterations n it Increase by 1 and go to step 3.3.1 for the next calculation.

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