A Design Method for the Edge Curve of a Precision Milling Insert

Abstract

The present invention provides a design method for the edge curve of a fine milling blade. First, the theoretical profile of the workpiece to be machined is obtained, and the involute part of a single tooth profile is evenly divided in a rectangular coordinate system as the original coordinate points for curve fitting. Secondly, the improved moving least squares method (MLS) is used to fit the tooth profile coordinate points to obtain a curve shape that conforms to the involute of the tooth profile, and then it is reflected on the edge curve of the fine milling cutter head. Finally, a comparison is made between it and the edge curve of the tool designed by the traditional method: the approximate circular arc design based on the least squares method during milling, and the tooth profile allowance conditions after machining with the two different tools are obtained to verify the effectiveness of the proposed method. By constructing a new function, the present invention reduces the errors existing in the curve fitting process and applies it to the design of the edge curve of the fine milling blade, making the edge shape of the blade closer to the actual profile of the workpiece, optimizing the blade, and improving the accuracy of gear milling.

Description

Technical Field

[0001] The present invention relates to the field of mechanical design and manufacturing, particularly to the technical field of manufacturing milling inserts, and specifically relates to a design method for the edge curve of a finish milling insert. Background Art

[0002] The indexable form milling cutter head is a form cutter for machining gears. Through the rotational movement of the main shaft and the feed movement in the tooth direction, it efficiently removes the blank material, thereby completing the milling of the gear tooth groove part. The forming method uses a cutter that conforms to the tooth profile shape of the gear being milled. The edge curve of the milling cutter directly affects the forming accuracy of the gear. If the design of the cutter edge curve does not meet the requirements of the tooth profile shape accuracy, machining errors will be formed during the actual milling process, which may lead to a reduction in the milling accuracy, unable to meet the machining tolerance requirements of the gear, reducing the efficiency of the gear during machine transmission, and slowing down the industrial process on the production line. Therefore, there is an urgent need for a milling insert design method with higher accuracy to improve the milling accuracy, make the manufacturing process of the milling cutter head more efficient and more flexible. Summary of the Invention

[0003] To solve the problem of the accuracy of machining gears with a finish milling cutter head, based on the gear meshing principle and the forming milling machining mechanism, the present invention provides a design method for the edge curve of a finish milling insert. Starting from the design and manufacturing of the cutter itself, it is proposed to use the improved moving least squares method (MLS) to design the cutter edge curve, aiming to improve the milling accuracy, thereby ensuring the accuracy requirements of the milling process, and facilitating the formulation of the milling process plan.

[0004] To achieve the above object, the technical solution of the present invention is as follows:

[0005] A design method for the edge curve of a finish milling insert, characterized by comprising the following steps:

[0006] Step S1: Obtain the parameter information of the tooth profile coordinate points of the workpiece;

[0007] Respectively: the single-row vector X = [x1, x2,..., x n , the single-column vector Y = [y1, y2,..., y n , i = 1, 2,..., n. Where x and y are the horizontal and vertical coordinates of the selected tooth profile respectively, and i is the number of tooth profile coordinate points.

[0008] Step S2: Perform curve fitting on the tooth profile of the involute cylindrical spur gear;

[0009] Use the improved moving least squares method (MLS) to perform the fitting of the tooth profile curve.

[0010] Step S3: Obtain the edge curve of the finish milling insert based on Step S1 and Step S2;

[0011] Step S4: Determine the form in which the finish milling insert overlaps on the cutter head substrate to obtain the milling tooth cutter head model;

[0012] Step S5: Establish a simulation model of the milling process. Use the three-dimensional model of the milling tooth cutter head established in Step S4, save it in the STL format, and then establish a milling tooth machining model through the machining simulation software to obtain the allowance distribution level of the milling tooth profile.

[0013] In the said Step S2, the improved moving least squares method MLS is used to fit the tooth profile curve of the workpiece.

[0014] The main body of the finish milling insert in the said Step S3 is made of coated cemented carbide material and undergoes full annealing treatment.

[0015] The size of the top edge milling surface of the finish milling insert in the said Step S3 is the same as the fillet size at the root of the gear, specifically 0.3 to 0.38 times the module M of the gear.

[0016] On the milling tooth cutter head obtained in the said Step S4, 24 groups of inserts are arranged in a staggered and equally spaced manner, and each group of inserts is loaded on the cutter head substrate through hexagon socket head cap screws.

[0017] The said Step S2 includes the following steps:

[0018] Step S2.1: Obtain the set of discrete data points of the tooth profile given in Step S1, and express the fitting curve function according to the moving least squares method;

[0019] Step S2.2: Discretize the solution region with N nodes, and define a weight function at each node;

[0020] Step S2.3: Calculate that the neighborhood of the selected point contains N nodes, and obtain the weighted sum of squared errors of the fitting curve function at these nodes;

[0021] Step S2.4: Obtain the function expression of the curve fitted based on the moving least squares method;

[0022] Step S2.5: Set the form of the improved moving least squares method curve function, and add an error compensation value, which compensates for the overall offset degree of the fitting curve.

[0023] The said Step S2.5 includes the following steps:

[0024] Step S2.5.1: First, obtain the general moving least squares method fitting curve according to the discrete data points;

[0025] Step S2.5.2: Select discrete data points evenly distributed on the theoretical tooth profile, and calculate the sum of squared deviations δ of these points s =(u h (s) - y s ) 2 and the function l s (x); where u h (s) is the ordinate value obtained by the point s according to the general moving least squares formula, y s is the ordinate value of the tooth profile of the point s, and the function

[0026] Step S2.5.3: Organize and substitute into the improved moving least squares curve function form to obtain the result of the improved moving least squares fitting curve

[0027] For the tooth profile coordinate points selected in Step S1, during the fitting process of the tooth profile curve, generally, the number of tooth profile coordinate points selected is required to be 6 - 20. To ensure the fitting accuracy requirement, 9 equally spaced tooth profile coordinate points are selected

[0028] The curve fitting method in Step S2 specifically includes the following steps

[0029] Step S2.1: Obtain the set of tooth profile discrete data points (x i , y i ), i = 1, 2,..., n, given in Step S1, and express the fitting curve function in the form of the moving least squares method as follows

[0030]

[0031] In the formula: a T (x) = [a1(x), a2(x),..., a m (x)], where a i (x) is the undetermined coefficient containing x, is the basis function, the parameter x is the abscissa value of the selected tooth profile coordinate point, and m is the number of basis functions

[0032] Step S2.2: Discretize the solution region Ω with N nodes, and define a weight function w i (ζ) = w(x - x i ) at each node x i (1, 2,..., N)

[0033] Step S2.3: Calculate that the neighborhood Ω x of the point x contains N nodes, and obtain the error weighted sum of squares of the fitting curve function at these nodes as follows

[0034]

[0035] The above formula is represented in matrix form as: J = (PA - u) T ·W(x)·(PA - u), where: u T =(u1, u2,..., u n );

[0036] W(x)=diag(ω(x - x1), ω(x - x2),..., ω(x - x n ));

[0037] Step S2.4: Obtain the function expression fitted by the moving least squares method:

[0038]

[0039] where φ(x) is the shape function, specifically φ(x)=[φ1(x), φ2(x),...φ N (x)] = P T (x)·A -1 (x)·B(x).

[0040] Step S2.5: Set the form of the improved moving least squares curve function as:

[0041]

[0042] where s is the number of compensation points (x s , y s ) of the fitted curve, s ≤ N; δ s =(u h (x s ) - y s ). Take δ 2 as the compensation value after fitting the curve using the moving least squares method, which compensates for the overall offset degree of the fitted curve. Its specific calculation process is: In step S2.5.1, first obtain the general moving least squares fitted curve according to the discrete data points; in step S2.5.2, select the discrete data points (x s ) evenly distributed on the theoretical tooth profile, calculate the sum of the squared deviations δ s =(u s ) of these points, and the function l s =(u h (s) - y s ) 2 and the function l s(x); In step S2.5.3, organize and substitute into the formula f(x) to obtain the fitting curve result of the improved moving least squares method.

[0043] The basis function in step S2.1 Linear basis x and y are the parameters of the coordinate points of the tooth profile to be removed respectively.

[0044] The weight function w in step S2.2 i (ζ), weight function

[0045] Where h is the support domain radius set for the weight function neighborhood.

[0046] In step S3, use numerical analysis software to perform curve fitting of tooth profile parameters, and then feedback to the edge curve of the finish milling insert.

[0047] In step S4, the staggered teeth of the finish milling inserts are evenly overlapped on both sides of the cutter head matrix, and 24 groups of inserts are arranged at equal intervals. The finish milling inserts on the left and right sides are loaded on the cutter head matrix through hexagon socket head cap screws to jointly overlap into a complete tooth profile shape.

[0048] In step S5, based on the gear milling principle, use mathematical software to write the path program of the gear milling tool and the digital model of the workpiece tooth profile, output the point position data of gear milling, save it in TXT format, and import it into the design part of the machining simulation software to obtain the distribution level of the milling allowance.

[0049] Compared with the prior art, the beneficial effects of the present invention:

[0050] Compared with the traditional method for designing the edge curve of the tool, the improved moving least squares method (MLS) is used to optimize the design of the edge curve of the tool, which improves the fitting accuracy of the edge curve of the tool and reduces the shape deviation of the tooth profile after gear milling. At the same time, taking the fitting accuracy of the edge curve of the tool as the optimization goal of milling, it is verified through simulation that the proposed new method can meet the requirements of gear milling accuracy, which is convenient for formulating the milling process plan. Brief description of the drawings

[0051] Figure 1 It represents the analysis flow chart of the design method of the edge curve of the finish milling insert of the present invention;

[0052] Figure 2 It represents the fitting result of the edge curve of the tool of the present invention;

[0053] Figure 3 It represents the finish milling cutter head model of the present invention;

[0054] Figure 4 is Figure 3 a half-sectional view of;

[0055] Figure 5 is Figure 3 the initial milling machining drawing of;

[0056] Figure 6 is the comparison result drawing of the tooth groove milling model.

[0057] In the figure: 1 is the finish milling cutter head, 2 is the workpiece, 3 is the left blade, 4 is the right blade, and 5 is the socket head cap screw. Specific implementation manners

[0058] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0059] A design method for the edge curve of a finish milling blade, characterized in that the method includes:

[0060] First, obtain the parameter information of the tooth profile coordinate points of the workpiece

[0061] As shown in Table 1, the selected workpiece is an internal cylindrical gear, and its basic parameters are: Z = 248, M = 16, X n = 0, α = 20°, Cn * = 0.25, ha * = 1. In a rectangular coordinate system, construct the tooth profile coordinate diagram of the selected gear, evenly divide one tooth profile on the left side of the Y-axis of the ordinate, and select 9 coordinate points of the tooth profile equal division points.

[0062] Table 1 Coordinate information of the equal division tooth profile points of the present invention (unit: mm)

[0063]

[0064] Second, perform curve fitting on the tooth profile of the involute cylindrical gear

[0065] Such as Figure 1 , perform the fitting of the tooth profile curve according to the curve fitting flow chart shown in Figure 1 . After obtaining the involute tooth profile information of the gear, use the numerical analysis software Matlab to perform curve fitting, and the selected method is the improved moving least squares method MLS.

[0066] The process is as follows: The given discrete data points of the tooth profile in step S1 are (x i , y i ), i = 1, 2,..., N, and the fitting curve function is expressed in the form of the moving least squares method as follows:

[0067]

[0068] where: a T (x) = [a1(x), a2(x),..., a m (x)], where a i (x) is a coefficient to be determined containing x; is a basis function, and m is the number of basis functions. In two-dimensional space, the basis functions are divided into: linear basis quadratic basis

[0069] Step S2 discretizes the solution region Ω with N nodes, and defines a weight function w i (ζ) = w(x - x i ) at each node x i ), and w i (ζ) is greater than zero only in the finite region Ω i around the node x x and is zero outside this region. Therefore, the neighborhood Ω x of the calculation point x contains N nodes, and the error weighted sum of squares of the fitting curve function at these nodes is:

[0070]

[0071] Expressed in matrix form as: J = (PA - u) T ·W(x)·(PA - u), where: u T = (u1, u2,..., u n );

[0072] W(x) = diag(ω(x - x1), ω(x - x2),..., ω(x - x n ));

[0073] Step S3 To obtain a(x), taking the extreme value of J gives:

[0074]

[0075] That is: A(x)·a(x) = B(x)·u, where A(x) and B(x) are respectively: A(x) = P T ·W(x)·P; B(x) = P T ·W(x).

[0076] Furthermore, it can be obtained:

[0077] a(x) = A -1 (x)·B(x)·u(x)

[0078] Step S4 is based on the function obtained by fitting with the moving least squares method The expression is:

[0079]

[0080] In the formula, φ(x) is the shape function, specifically φ(x) = [φ1(x), φ2(x),... φ N (x)] = P T (x) · A -1 (x) · B(x).

[0081] After step S5 uses the moving least squares method to obtain the fitting curve function of discrete points The improved form of the fitting curve of the moving least squares method is:

[0082]

[0083] In the formula, s is the number of compensation points (x s , y s ) of the fitting curve, s ≤ N; δ s = (u h (x s ) - y s ) 2 .

[0084] Take δ s as the compensation value after fitting the curve with the moving least squares method, which compensates for the overall deviation degree of the fitting curve. The specific calculation process is as follows: In step S2.5.1, first obtain the general moving least squares fitting curve according to the discrete data points; in step S2.5.1, select the discrete data points (x s , y s ) evenly distributed on the theoretical tooth profile, calculate the sum of squared deviations δ s = (u h (s) - y s ) 2 and the function l s (x); in step S2.5.1, organize and substitute into the formula f(x) to obtain the result of the improved moving least squares fitting curve.

[0085] Third, the edge curve fitting of the finish milling insert

[0086] Such as Figure 2, the involute part of the theoretical tooth profile is fitted using the numerical analysis software Matlab, and the curve of the cutting tool edge shape is designed using the improved method. The blue dashed line is the theoretical tooth profile of the gear, and the red solid line is the cutting tool edge shape designed by the improved MLS. There is no discontinuous part in the middle of the cutting tool edge shape curve designed by the new method, and the fitted edge shape curve is smooth and linearly distributed.

[0087] Fourth, obtain the model of the finish milling cutter head

[0088] Such as Figure 3 And Figure 4 , specifically including the finish milling cutter head 1, the left blade 3, the right blade 4 and the hexagon socket head screw 5. The creation of the matrix models of the finish milling cutter blade and the finish milling cutter head 1 is completed using 3D modeling software. In the present invention, there are 24 groups of finish milling cutter blades in the created finish milling cutter head 1. There are 12 left blades 3 evenly distributed on the left side and 12 right blades 4 evenly distributed on the right side. The blades on the left and right sides jointly lap out the complete tooth profile shape. The blades are connected to the cutter head matrix through the hexagon socket head screws 5. The blade arrangement is simple but compact, and the overall structure of the finish milling cutter head is reasonable.

[0089] Preferably, the main body of the finish milling cutter blade is made of coated cemented carbide material and is subjected to full annealing treatment to make the ductility of the finish milling cutter blade structure the best.

[0090] Preferably, the size of the top edge milling surface of the finish milling cutter blade is the same as the size of the fillet at the root of the gear, specifically 0.3 to 0.38 times the module M of the gear.

[0091] Fifth, establish a simulation model of the milling process

[0092] Such as Figure 5 , specifically including the workpiece 2. The finish milling cutter head performs milling processing through the set cutting tool spindle rotation program. Two cutter head models under two cutting tool edge shapes are established respectively. One is the traditional method: the milling cutter head model obtained by designing the cutting tool edge shape based on the approximate arc of the least squares method, and the other is the milling cutter head model obtained by designing the cutting tool edge shape using the improved MLS. And save the two as STL format and import them into the simulation processing software Vericut, and set the same machining program according to the actual milling process, so as to compare the tooth profile allowance levels of the two cutter heads for milling gears.

[0093] After completing the design of the cutting tool edge shape curve of the finish milling cutter blade and the simulation of the milling process of the finish milling cutter head, select some tooth grooves in the machined area to compare the milling allowances, such as Figure 6As shown, the milling profile allowances of the two cutter heads for machining gears in Step 5 are obtained. For the milling profile allowances of some tooth profiles in the machined area, the overall level of the milling profile allowances of the cutter obtained by using the improved moving least squares method (MLS) fitting has been reduced, and the effect of milling the partial profile allowances is overall relatively good.

[0094] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification are only preferred examples of the present invention and are not used to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A design method for the edge curve of a precision milling blade, characterized in that It includes the following steps: Step S1: Obtain the tooth profile coordinate point information of the workpiece; Step S2: Perform curve fitting on the tooth profile of the involute cylindrical spur gear; Step S3: Based on Step S1 and Step S2, obtain the edge curve of the finish milling cutter blade; Step S4: Determine the form in which the finish milling cutter blade is lapped on the cutter head base to obtain the milling cutter head model; Step S5: Establish a simulation program for milling machining; The said Step S2 includes the following steps: Step S2.1: Obtain the set of discrete data points of the tooth profile given in Step S1, and express the fitting curve function according to the moving least squares method; Step S2.2: Discretize the solution region with N nodes and define a weight function at each node; Step S2.3: Calculate that the neighborhood of the selected point contains N nodes, and obtain the weighted sum of squared errors of the fitting curve function at these nodes; Step S2.4: Obtain the function expression of the curve fitted based on the moving least squares method; Step S2.5: Set the form of the improved moving least squares curve function, and increase the error compensation value, which compensates for the overall offset degree of the fitting curve; The said Step S2.5 includes the following steps: Step S2.5.1: First, obtain the general moving least squares fitting curve obtained according to the discrete data points; Step S2.5.2: Select discrete data points evenly distributed on the theoretical tooth profile and calculate the sum of squared deviations of these points and function ; where u h (s) is the ordinate value obtained by point s according to the general moving least squares formula, y s is the ordinate value of the tooth profile of point s , function , (j = 1, 2, …, N; s = 1, 2, …, T); Step S2.5.3: Organize and substitute it into the form of the improved moving least squares curve function to obtain the result of the improved moving least squares fitting curve.

2. The design method of the edge curve of a precision milling blade according to claim 1, characterized in that: In the said Step S2, the improved moving least squares method MLS is used to fit the tooth profile curve of the workpiece.

3. A design method for the edge curve of a precision milling blade according to claim 1, characterized in that: The main body of the finish milling cutter blade in the said Step S3 is made of coated cemented carbide material and is subjected to full annealing treatment.

4. The design method of the fine milling blade edge curve according to claim 1, characterized in that: The size of the top edge milling surface of the finish milling cutter blade in the said Step S3 is the same as the size of the fillet at the root of the gear, specifically 0.3 to 0.38 times the module M of the gear.

5. The design method of the fine milling blade edge curve according to claim 1, characterized in that: On the milling cutter head obtained in the said Step S4, 24 groups of blades are arranged in a staggered and equally spaced manner, and each group of blades is loaded on the cutter head base through internal hexagonal screws.

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