A flexible dressing method for complex profile grinding wheels

Abstract

The application discloses a flexible dressing method for a complex profile grinding wheel, comprising the following steps: S1, acquiring a profile drawing of the grinding wheel, and obtaining a continuous fine dressing curve by using an isometric line method according to the profile drawing of the grinding wheel; S2, extracting entity section data information of the continuous fine dressing curve, and obtaining fine dressing track information; S3, presetting a theoretical single cutting depth, discretizing the continuous fine dressing curve, obtaining fine dressing discrete points, and creating fine dressing discrete tracks according to the fine dressing discrete points; S4, constructing a profiling allowance distribution model; including establishing a rough dressing boundary and a tool withdrawal position boundary based on the fine dressing discrete points according to a preset profiling allowance, and creating a rough dressing track according to the rough dressing boundary and the tool withdrawal position boundary; and S5, dressing the grinding wheel according to the rough and fine dressing discrete tracks in sequence. The application improves the flexible degree, the dressing precision and the universality of the dressing of the grinding wheel by automatically discretizing the continuous fine dressing curve and designing a dressing path under the condition of the profiling allowance.

Description

Technical Field

[0001] This invention belongs to the field of grinding wheel manufacturing and grinding processing applications, and mainly relates to a flexible dressing method for grinding wheels with complex surface shapes. Background Technology

[0002] As modern manufacturing evolves towards higher precision, higher efficiency, and greater complexity, ordinary-shaped grinding wheels, limited by their standard geometry, struggle to meet the machining demands of complex contours, fine structures, and surfaces with special functions. Complex-shaped grinding wheels (such as irregular contours, curved surfaces, tooth profiles, and helical grooves) have emerged to address this need. For example, precision parts with complex shapes, such as engine crankshaft flanges, aircraft blade tenons, bearing grooves, gears, and worm gears, typically require grinding with complex-shaped grinding wheels. The common machining method for these high-precision workpieces involves first dressing the grinding wheel to a specific shape, followed by profile grinding. However, because high-precision workpieces are often customized products with significant shape variations, the current method of using a profile roller for copying and dressing presents a significant technological challenge due to its high cost, poor versatility, and lack of adjustable dressing accuracy.

[0003] Therefore, it is necessary to solve the problems of difficult surface dressing of complex-shaped grinding wheels and the inability to control precision. There is an urgent need to develop a method with strong versatility and high flexibility to achieve precise dressing of grinding wheels of different shapes. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art, improve the versatility and flexibility of grinding wheel dressing, and provide a flexible dressing method for grinding wheels with complex shapes.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A flexible dressing method for grinding wheels with complex surface shapes includes the following steps:

[0007] S1: Obtain the sand profile diagram, and use the equidistant line method to obtain the continuous fine trimming curve based on the sand profile diagram. The continuous fine trimming curve includes straight line segments and / or circular arc segments.

[0008] S2: Extract the entity segment data information of the continuous fine-tuning curve to obtain fine-tuning trajectory information. The fine-tuning trajectory information includes curve type, number of curve segments and curve position. The curve type includes straight line segments and circular arc segments. The curve position of the straight line segment includes the starting point coordinates and ending point coordinates of each straight line segment. The curve position of the circular arc segment includes the center coordinates, radius value, starting angle and ending angle of each circular arc segment.

[0009] S3: Preset theoretical single cut depth, discretize the continuous fine trimming curve according to the theoretical single cut depth and fine trimming trajectory information to obtain fine trimming discrete points, and create a fine trimming discrete trajectory according to the fine trimming discrete points. The fine trimming discrete points include linear segment discrete points and / or circular arc segment discrete points. The linear segment discrete points are obtained by performing layered discretization on the linear segment according to the theoretical single cut depth of each linear segment. The circular arc segment discrete points are obtained by performing equal-angle discretization on the circular arc segment according to the theoretical single cut depth of each circular arc segment.

[0010] S4: Construct a contouring allowance distribution model; including: establishing a coarse trimming boundary and a tool retraction position boundary based on the fine trimming discrete points according to the preset contouring allowance, obtaining a contouring allowance distribution model composed of the coarse trimming boundary and the tool retraction position boundary, and creating a coarse trimming trajectory based on the coarse trimming boundary and the tool retraction position boundary.

[0011] S5: First, perform rough dressing on the grinding wheel according to the rough dressing trajectory, and then perform fine dressing on the grinding wheel according to the fine dressing discrete trajectory.

[0012] Preferably, the equidistant line method in step S1 is as follows: drawing equidistant lines outward from the normal direction of the sand profile curve in the sand profile diagram to obtain the continuous finishing curve of the grinding wheel, wherein the equidistant distance of the equidistant lines outward from the normal direction is the radius r of the tool tip arc. d ;

[0013] In step S2, the dxflib library function is used to extract the entity segment data information of the continuous fine-tuning curve.

[0014] Preferably, step S2 further includes the following steps: obtaining the number of curve segments of the straight line segment as n1, and storing the data information of the curve position of the straight line segment in matrix form in the first matrix L. l ,but:

[0015]

[0016] Where [x1,y1] is the starting point coordinate of the first line segment, and [x1′,y1′] is the ending point coordinate of the first line segment; Let be the coordinates of the starting point of the n1-th straight line segment. Let be the coordinates of the endpoint of the n1-th line segment, and [] be an empty matrix;

[0017] Obtain the number of curve segments n2 of the circular arc segment, and store the curve position data of the circular arc segment in matrix form in the second matrix L. c ,but:

[0018]

[0019] Where [xc1,yc1] are the coordinates of the center of the first arc segment, [r1] is the radius of the first arc segment; α1 and α1′ are the starting angle and ending angle of the first arc segment, respectively. Let the coordinates be the center coordinates of the n2th arc segment. Let be the radius of the n2th circular arc segment; These are the starting angle and ending angle of the n2th arc segment, respectively.

[0020] Preferably, step S3 specifically comprises:

[0021] S3.1: Set the theoretical single cutting depth of a straight line segment to sp, and set the theoretical single cutting depth of a circular arc segment to sp′;

[0022] S3.2: Based on the theoretical single cutting depth of the straight line segment, and the coordinates of the starting point and the ending point of each straight line segment, obtain the number of discrete points of each straight line segment. Based on the theoretical single cutting depth of the arc segment, and the coordinates of the center, radius, starting angle and ending angle of each arc segment, obtain the number of discrete points of each arc segment.

[0023] S3.3: Discretize the line segment by layer according to the number of discrete points of the line segment, and obtain the coordinates of the discrete points of the line segment; discretize the arc segment by equal angle according to the number of discrete points of the arc segment, and obtain the coordinates of the discrete points of the arc segment.

[0024] S3.4: Merge the coordinates of the discrete points of the straight line segment and the discrete points of the circular arc segment, and use a sorting function to sort the Y-axis coordinates of the merged discrete points in descending order to obtain the set of discrete points, i.e., the refined discrete point P. m (xp m ,yp m m = 1, 2, 3, ..., N, where N is the total number of discrete points of the line segment and the circular arc segment;

[0025] S3.5: Create a fine-tuning discrete trajectory based on the fine-tuning discrete points. The fine-tuning discrete trajectory is the movement of the tool tip center from top to bottom according to the fine-tuning discrete point coordinates P1 to P. N The trajectory.

[0026] Preferably, step S3.2, which involves obtaining the number of discrete points for each line segment based on the theoretical single cutting depth of the line segment and the coordinates of the starting and ending points of each line segment, specifically includes:

[0027] The number of discrete points Nl of the line segment is obtained based on the curve position of the line segment. i .

[0028] If |y i ′-y i If |≤sp, then the starting point (x) of the i-th line segment.i ,y i ) and termination point (x) i ′,y i ′) as discrete points, number of discrete points:

[0029] Nl i =2;

[0030] Where i is the index of the line segment number n1, y i and y i Let ' and ' be the ordinates of the starting and ending points of the i-th line segment, respectively; if |y' i ′-y i If |> sp, then the number of discrete points:

[0031]

[0032] Here, ceil is the floor function.

[0033] Preferably, step S3.2 further includes: correcting the theoretical single cutting depth sp of the straight line segment to obtain the actual single cutting depth ap. i Its expression is:

[0034]

[0035] Preferably, the step S3.3, which involves discretizing the line segment into layers based on the number of discrete points to obtain the coordinates of the discrete points, specifically involves:

[0036] Using the interval division function in the Y-axis interval [y i ′,y i Nl is generated at equal intervals within the range. i 1 number of values, to obtain the array My i Its expression is:

[0037] My i =linspace(y i ′,y i ,Nl i );

[0038] The linspace function is an interval division function;

[0039] Using an interpolation function at the starting point (x) of the line segment i ,y i ) and endpoint (x) i ′,y i (′) between arrays My i Nl in i Perform linear interpolation on the values ​​to obtain the linearly interpolated Nl iAn array Mx of corresponding x-coordinate values i Its expression is:

[0040] Mx i =interp1([y i ,y i ′],[x i ,x i ′],My i ,′linear′);

[0041] Where interp1 is the interpolation function and 'linear' is the linear interpolation method;

[0042] Using [Mx i My i [] represents the coordinates of discrete points on a line segment.

[0043] Preferably, the step S3.2, which involves obtaining the number of discrete points for each arc segment based on the theoretical single cutting depth of the arc segment, and the center coordinates, radius, starting angle, and ending angle of each arc segment, specifically includes:

[0044] The coordinates of the starting and ending points of each arc segment are calculated based on the coordinate expression of the arc segment. The coordinate expression of the arc segment is as follows:

[0045]

[0046]

[0047] Among them, [xc j ,yc j Let r be the coordinates of the center of the j-th arc segment. j Let α be the radius of the j-th arc segment; j α j '' represents the starting angle and ending angle of the j-th arc segment, respectively, where j is the index of the arc segment number n2. j ,ya j Let (xa) be the coordinates of the starting point of the j-th arc segment. j ′,ya j (′) represents the coordinates of the endpoint of the j-th circular arc segment;

[0048] And the termination angle α j Angle correction is performed to obtain the correction termination angle α. j ", specifically:

[0049] When α j ′<α j At that time, α j "=α j +360°;

[0050] When α j ′>α j At that time, α j "=α j ′;

[0051] The number of discrete points, Nc, is obtained based on the curve position of the arc segment. j ,

[0052] If |ya j ′-ya j If |≤sp′, then the starting point of the j-th arc segment (xa) j ,ya j ) and endpoint (xa) j ′,ya j ′) as discrete points, number of discrete points:

[0053] Nc j =2;

[0054] If |ya j ′-ya j If |> sp′, then the number of discrete points is:

[0055]

[0056] Here, ceil is the floor function.

[0057] Preferably, in step S3.3, the circular arc segment is discretized at equal angles based on the number of discrete points to obtain the coordinates of the discrete points of the circular arc segment, specifically as follows:

[0058] Using the interval division function in the angle interval [α] of the arc segment j ,α j Nc is generated at equal intervals within the range of "". j Given several angle values, we obtain the array Nα. j Its expression is:

[0059] Nα j =linspace(α) j ,α j ",Nc j );

[0060] Based on the coordinate expression of the arc segment, the array Nα j Nc j Calculate Nc using each angle value. j By using a set of coordinate points, we can obtain the discrete coordinates of the arc segment.

[0061] Preferably, step S4 specifically comprises:

[0062] S4.1: Based on the preset contouring allowance and the fine trimming discrete points, establish the coarse trimming boundary and the tool retraction position boundary to obtain the contouring allowance distribution model, including the following steps:

[0063] The conforming allowance includes allowance value t1 and rough trimming amount t2, then fine trimming amount t3 = t1 - t2;

[0064] Establish the tool retraction position boundary on an equidistant line at a distance of one allowance value t1 from the fine-tuning discrete point in the X-axis direction.

[0065] Establish a coarse trimming boundary on an equidistant line from the retraction position boundary in the X-axis direction, at a coarse trimming amount t2.

[0066] The coordinates of point P on the rough trimmed boundary m ′(xp m ′,yp m The coordinates of point P on the boundary of the tool retraction position and the point of the tool retraction position. m "(xp m ″,yp m The expression for "") is:

[0067]

[0068] S4.2: Establish a rough trimming trajectory based on the rough trimming boundary and the tool retraction position boundary. The rough trimming trajectory includes an initial rough trimming path and cyclically executed rough trimming path units.

[0069] The initial rough dressing path includes an initial rough cutting path and an initial tool retraction path. The initial rough cutting path is the path from P1″ to P1′ for the tool tip center, and the initial tool retraction path is the path from P1′ to P1″ for the tool tip center.

[0070] The rough dressing path unit includes a sequentially arranged infeed path, a unit rough cutting path, and a unit retraction path. The infeed path starts from the tool tip center and proceeds from P... q "Move towards P" q+1 The path of the unit cutting path is the path from the tip center to P. q+1 "Move towards P" q+1 The path of the unit retraction path is the center of the tool tip from P. q+1 'Move towards P q+1 The path of ', where q takes the values ​​1, 2, ..., N-1.

[0071] The beneficial effects of this invention are as follows:

[0072] This invention extracts the fine dressing trajectory information that forms the sand profile based on a two-dimensional electronic graphic file of the sand profile curve and the shape parameters of the dressing tool. By rationally discretizing the continuous fine dressing curve, discrete point information data with controllable fitting accuracy is formed. Based on the discrete point data, the coarse dressing trajectory and fine dressing discrete trajectory of the grinding wheel are automatically generated, thereby dressing the grinding wheel.

[0073] This invention can improve the discretization accuracy by increasing the number of discrete points by reducing the theoretical single cutting depth, thereby achieving adjustment and control of trimming accuracy.

[0074] Compared with traditional methods, it has a high degree of flexibility and is suitable for precision dressing of grinding wheels with various complex shapes. Attached Figure Description

[0075] The present invention will now be described in further detail with reference to the accompanying drawings:

[0076] Figure 1 This is a method block diagram of the present invention;

[0077] Figure 2 This is a schematic diagram of the connection between the continuous fine-tuning curve of the straight segment and the continuous fine-tuning curve of the straight segment in this invention.

[0078] Figure 3 This is a schematic diagram of the connection between the straight segment continuous fine trimming curve and the circular arc segment continuous fine trimming curve of the present invention;

[0079] Figure 4 This is a schematic diagram of the distribution of fine-tuning discrete points on the fine-tuning discrete trajectory of the present invention;

[0080] Figure 5 This is a schematic diagram of the fine-tuning discrete trajectory of the present invention;

[0081] Figure 6 This is a schematic diagram of the contouring margin distribution model of the present invention;

[0082] Figure 7 This is a schematic diagram of the coarse trimming trajectory of the present invention;

[0083] Figure 8 This is a schematic diagram of the sand profile used in the implementation of this invention;

[0084] Figure 9 This is a schematic diagram of the continuous fine-tuning curve during the implementation of this invention;

[0085] Figure 10 This is a schematic diagram of the distribution of fine-tuned discrete points during the implementation of this invention;

[0086] Figure 11 This is a simulation diagram of the fine-tuned discrete trajectory during the implementation of this invention;

[0087] Figure 12 This is a simulation diagram of the coarse trimming trajectory during the implementation of this invention. Detailed Implementation

[0088] like Figure 1 As shown, the present invention provides a flexible dressing method for grinding wheels with complex surface shapes, comprising the following steps:

[0089] S1: Obtain the sand profile diagram. Based on the sand profile diagram, use the equidistant line method to obtain the continuous fine-tuning curve. The continuous fine-tuning curve includes straight line segments and / or circular arc segments. In this embodiment, the continuous fine-tuning curve is output as a two-dimensional electronic DXF drawing file.

[0090] Specifically, the equidistant line method involves drawing equidistant lines outwards from the normal direction of the sand profile curve in the sand profile diagram to obtain the continuous finishing curve of the grinding wheel. The equidistant distance between the equidistant lines outwards is the radius r of the tool tip arc B11. d In this embodiment, CAD software was used for drawing. Since irregularly shaped grinding wheels are mostly used for combined grinding of outer diameters, conical surfaces, end faces, and shaft shoulders, their grinding profile A is often a combination of straight-segment grinding profile A1 and circular arc-segment grinding profile A2. Therefore, when drawing the continuous finishing curve B, two cases are considered: the connection between two straight-segment continuous finishing curves B1 and B2, respectively. Figure 2 and Figure 3 As shown.

[0091] S2: Extract the entity segment data information of the continuous fine-tuning curve to obtain the fine-tuning trajectory information. In this embodiment, the dxflib library function in the MATLAB programming software is used to extract the entity segment data information of the continuous fine-tuning curve. The fine-tuning trajectory information includes the curve type, the number of curve segments, and the curve position. The curve type includes straight line segments and circular arc segments. The curve position of a straight line segment includes the coordinates of the starting point and the ending point of each straight line segment. The curve position of a circular arc segment includes the coordinates of the center of each circular arc segment, the radius value, the starting angle, and the ending angle.

[0092] S3: Preset theoretical single cut depth, discretize the continuous fine trimming curve based on the theoretical single cut depth and fine trimming trajectory information to obtain fine trimming discrete points, create fine trimming discrete trajectories based on the fine trimming discrete points, the fine trimming discrete points include linear segment discrete points and / or circular arc segment discrete points, each linear segment discrete point is obtained after the linear segment is discretized in layers based on the theoretical single cut depth of each linear segment, each circular arc segment discrete point is obtained after the circular arc segment is discretized at equal angles based on the theoretical single cut depth of each circular arc segment.

[0093] S4: Construct a contouring allowance distribution model; including: establishing a coarse trimming boundary and a tool retraction position boundary based on the fine trimming discrete points according to the preset contouring allowance, obtaining a contouring allowance distribution model composed of the coarse trimming boundary and the tool retraction position boundary, and creating a coarse trimming trajectory based on the coarse trimming boundary and the tool retraction position boundary.

[0094] S5: First, perform rough dressing on the grinding wheel according to the rough dressing trajectory, and then perform fine dressing on the grinding wheel according to the fine dressing discrete trajectory.

[0095] In this embodiment, step S2 further includes the following steps: obtaining the number of curve segments of the straight line segment as n1, and storing the data information of the curve position of the straight line segment in the first matrix L in matrix form. l ,but

[0096]

[0097] Where [x1,y1] are the coordinates of the starting point of the first line segment, and [x1′,y1′] are the coordinates of the ending point of the first line segment; Let be the coordinates of the starting point of the n1-th straight line segment. Let L be the coordinates of the endpoint of the n1-th line segment, and [] be an empty matrix. When n1 = 0, there are no line segments, and L is the endpoint of the n1-th line segment. l It is an empty matrix.

[0098] In this embodiment, the number of curve segments n2 of the arc segment is obtained, and the data information of the curve position of the arc segment is stored in the second matrix L in matrix form. c ,but:

[0099]

[0100] Where [xc1,yc1] are the coordinates of the center of the first arc segment, [r1] is the radius of the first arc segment; α1 and α1′ are the starting angle and ending angle of the first arc segment, respectively. Let the coordinates be the center coordinates of the n2th arc segment. Let be the radius of the n2th circular arc segment; These are the starting and ending angles of the n2th arc segment, respectively. When n2 = 0, there is no arc segment, and L... c It is an empty matrix.

[0101] In this embodiment, as Figure 4 As shown in the figure, b is the intersection point of the straight line segment and the circular arc segment. To discretize the continuous fine-tuning curve and obtain the fine-tuning discrete trajectory, step S3 specifically involves:

[0102] S3.1: Set the theoretical single cutting depth of the straight segment to sp, and set the theoretical single cutting depth of the arc segment to sp′; to ensure the service life of the dressing tool roller, the theoretical single cutting depth of the straight segment and the theoretical single cutting depth of the arc segment are usually selected to be between 0.002mm and 0.5mm.

[0103] S3.2: Based on the theoretical single cutting depth of the line segment and the coordinates of the starting and ending points of each line segment, obtain the number of discrete points of each line segment; in this embodiment, the specific details are as follows.

[0104] The number of discrete points Nl of the line segment is obtained based on the curve position of the line segment. i ,

[0105] If |y i ′-y i If |≤sp, then the starting point (x) of the i-th line segment. i ,y i ) and termination point (x) i ′,y i ′) as discrete points, number of discrete points:

[0106] Nl i =2;

[0107] Where i is the index of the line segment number n1, y i and y i ' and ' are the ordinates of the starting and ending points of the i-th line segment, respectively.

[0108] If |y i ′-y i If |> sp, then the number of discrete points:

[0109]

[0110] Here, ceil is the floor function.

[0111] The theoretical single-cut depth sp of the straight line segment is corrected to obtain the actual single-cut depth ap of the straight line segment. i Its expression is:

[0112]

[0113] In this embodiment, the actual single-cut depth ap i This is used to compare and view the theoretical single cutting depth (sp) of a straight segment, making it easier for operators to obtain execution information.

[0114] The number of discrete points for each arc segment is obtained based on the theoretical single cutting depth of the arc segment, as well as the center coordinates, radius, starting angle, and ending angle of each arc segment. In this embodiment, the specific details are as follows.

[0115] Calculate the coordinates of the starting and ending points of each arc segment using the coordinate expression of the arc segment. The coordinate expression of the arc segment is:

[0116]

[0117]

[0118] Among them, [xc j ,yc j Let r be the coordinates of the center of the j-th arc segment. j Let α be the radius of the j-th arc segment; j α j '' represents the starting angle and ending angle of the j-th arc segment, respectively, where j is the index of the arc segment number n2. j ,ya j Let (xa) be the coordinates of the starting point of the j-th arc segment. j ′,ya j ′) represents the coordinates of the endpoint of the j-th circular arc segment.

[0119] And the termination angle α j Angle correction is performed to obtain the correction termination angle α. j ", specifically:

[0120] When α j ′<α j At that time, α j "=α j +360°;

[0121] When α j ′>α j At that time, α j "=α j ′.

[0122] In this embodiment, the actual angle range of the arc segment is obtained by correcting the termination angle.

[0123] The number of discrete points, Nc, is obtained based on the curve position of the arc segment. j ,

[0124] If |ya j ′-ya j If |≤sp′, then the starting point of the j-th arc segment (xa) j ,ya j ) and endpoint (xa) j ′,ya j ′) as discrete points, number of discrete points:

[0125] Nc j =2;

[0126] If |ya j ′-ya j If |> sp′, then the number of discrete points is:

[0127]

[0128] Here, ceil is the floor function.

[0129] S3.3: Discretize the line segment into layers based on the number of discrete points, and obtain the coordinates of the discrete points of the line segment; in this embodiment, specifically:

[0130] Using the interval division function in the Y-axis interval [y i ′,y i Nl is generated at equal intervals within the range. i 1 number of values, to obtain the array My i Its expression is:

[0131] My i =linspace(y i ′,y i ,Nl i );

[0132] The linspace function is an interval division function.

[0133] Using an interpolation function at the starting point (x) of the line segment i ,y i ) and endpoint (x) i ′,y i (′) between arrays My i Nl in i Perform linear interpolation on the values ​​to obtain the linearly interpolated Nl i An array Mx of corresponding x-coordinate values i Its expression is:

[0134] Mx i =interp1([y i ,y i ′],[x i ,x i ′],My i ,′linear′);

[0135] Where interp1 is the interpolation function and 'linear' is the linear interpolation method;

[0136] Using [Mx i My i [] represents the coordinates of discrete points on a line segment.

[0137] The circular arc segment is discretized at equal angles based on the number of discrete points, and the coordinates of the discrete points of the circular arc segment are obtained. In this embodiment, the specific steps are as follows.

[0138] Using the interval division function in the angle interval [α] of the arc segment j ,α j Nc is generated at equal intervals within the range of "". j Given several angle values, we obtain the array Nα. j Its expression is:

[0139] Nα j =linspace(α) j ,α j ",Nc j );

[0140] Based on the coordinate expression of the arc segment, the array Nα j Nc j Calculate Nc using each angle value. j By using a set of coordinate points, we can obtain the discrete coordinates of the arc segment.

[0141] S3.4: Merge the coordinates of the discrete points of the straight line segment and the discrete points of the circular arc segment, and use a sorting function to sort the Y-axis coordinates of the merged discrete points in descending order to obtain the set of discrete points, i.e., the refined discrete point P. m (xp m ,yp m ); m = 1, 2, 3, ..., N, where N is the total number of discrete points of the line segment and the discrete points of the circular arc segment.

[0142] S3.5: Create a fine-tuning discrete trajectory based on the fine-tuning discrete points. The fine-tuning discrete trajectory is the movement of the tool tip center from top to bottom according to the coordinates of the fine-tuning discrete point P1 to P. N The trajectory, such as Figure 5 As shown.

[0143] like Figure 6 As shown, with the upper end face G1 of the grinding wheel layer as the X-axis and the lower end face G2 of the grinding wheel layer located below the X-axis, step S4 is as follows:

[0144] S4.1: Based on the preset contouring allowance and the fine trimming discrete points, establish the coarse trimming boundary D and the tool retraction position boundary E to obtain the contouring allowance distribution model, including the following steps:

[0145] The contouring allowance includes the allowance value t1 and the rough finishing allowance t2, then the fine finishing allowance t3 = t1 - t2; the allowance value t1 usually ranges from 0.5 to 5 mm, and the rough finishing allowance t2 usually ranges from 0.3 to 4.8 mm.

[0146] Establish a tool retraction position boundary E on an equidistant line in the X-axis direction from the fine dressing discrete point by a margin value t1. Establish a coarse dressing boundary D on an equidistant line in the X-axis direction from the tool retraction position boundary by a coarse dressing amount t2. Then, the coordinates of point P of the coarse dressing boundary D are... m ′(xp m ′,yp m The coordinates of point P on the boundary E of the tool retraction position and the tool retraction position are given. m "(xp m ″,yp m The expression for "") is:

[0147]

[0148] S4.2: Establish the rough dressing trajectory based on the rough dressing boundary D and the tool retraction position boundary E. The rough dressing trajectory includes the initial rough dressing path and the cyclically executed rough dressing path units. For example... Figure 7 As shown, the initial rough dressing path includes the initial rough cutting path and the initial tool retraction path. The initial rough cutting path is the path from P1″ to P1′ for the tool tip center, and the initial tool retraction path is the path from P1′ to P1″ for the tool tip center. Specifically... Figure 7 Path ① and path ② in the text.

[0149] The rough dressing path unit includes a sequentially set infeed path, unit rough cutting path, and unit retraction path. The infeed path starts from the tool tip center and moves from P... q "Move towards P" q+1 The path of the unit cutting path is the tool tip center from P. q+1 "Move towards P" q+1 The path of ′, the unit retraction path is the tool tip center from P q+1 'Move towards P q+1 The path is given by , where q takes values ​​of 1, 2, ..., N-1. Specifically... Figure 7 Paths ③, ④, ⑤, ... in the path.

[0150] In this embodiment, the retraction boundary E is located outside the grinding wheel layer blank boundary F.

[0151] In specific implementation of the method of the present invention, it is assumed that the profile of a certain specification of sand is as follows: Figure 8 As shown, the sand profile consists of two straight line segments and three circular arc segments. The continuous refinement curve extracted using MATLAB software is shown below. Figure 9 As shown. There are a total of 5 solid segments, 2 of which are straight lines and 3 of which are circular arcs, i.e., n = 5, n1 = 2, n2 = 3.

[0152] The curve positions of the straight line segments are stored in matrix L in matrix form. l middle:

[0153]

[0154] Matrix L l The first row [11.373,-8.464] and [11.373,-11] are the starting and ending coordinates of the first straight line segment; the second row [10.684,-1.333] and [9.566,1] are the starting and ending coordinates of the second straight line segment.

[0155] The position of the arc segment is stored in matrix L in matrix form. c middle:

[0156]

[0157] Matrix L c In the first row, [12.373, -8.464] represents the center coordinates of the first arc segment, and [1] represents the radius of the first arc segment; [270, 330.001] represents the starting angle and ending angle of the first arc segment, respectively. In the second row, [12.487, -0.469] represents the center coordinates of the second arc segment, and [2] represents the radius of the second arc segment; [205.012, 244.406] represents the starting angle and ending angle of the second arc segment, respectively. In the third row, [10.373, -5] represents the center coordinates of the third arc segment, and [3] represents the radius of the third arc segment; [25.012, 150] represents the starting angle and ending angle of the third arc segment, respectively.

[0158] In this embodiment, when discretizing the straight line segment, sp = 0.5 mm is taken. For the discretization of the first straight line segment, since |y1'-y1| = |-11-(-8.464)| = 2.536 > sp = 0.5, the two endpoints of this straight line segment are greater than the theoretical single cutting depth of the straight line segment in the Y-axis direction. Therefore, the number of discretization points of the first straight line segment is:

[0159]

[0160] The actual depth of cut in a single operation is:

[0161] The `linspace` function in MATLAB can be used to divide an interval into equal parts. The syntax is as follows: `My1 = linspace(-11, -8.464, 7) = (-11, -10.577, -10.155, -9.732, -9.309, -8.887, -8.464)`. This generates Nl1 = 7 equally spaced values ​​within the Y-axis interval [-11, -8.464], and represents these 7 values ​​as `My1`, which is a 1-row, 7-column array. The interpolation function `interp1` in MATLAB can be used to perform linear interpolation between the two endpoints of a line segment. The syntax is as follows: `Mx1 = interp1([-8.464, -11], [11.373, 11.373], My1, 'linear') = (11.373, 11.373, 11.373, 11.373, 11.373, 11.373, 11.373)`. This means that linear interpolation is performed on the line connecting the points [11.373, -8.464] and [11.373, -11], using the seven values ​​in array `My1` as the Y-value variables. Interpolation yields 7 corresponding X values. 'linear' indicates linear interpolation. Mx1 is the set of 7 corresponding X values ​​obtained after linear interpolation, which is an array of 1 row and 7 columns. Therefore, [Mx1, My1] can be used to represent the coordinates of the 7 discrete points of the line segment. The coordinates of the discrete points are as follows: [11.373, -11], [11.373, -10.577], [11.373, -10.155], [11.373, -9.732], [11.373, -9.309], [11.373, -8.887], [11.373, -8.464].

[0162] Similarly, the discretization of the second straight line segment can be completed using the method described above.

[0163] For the discretization of the arc segment, sp′ = 0.5 mm is also taken. Before discretizing the first arc segment, the coordinates of the two endpoints of the arc segment need to be calculated, and α1 = 270 < α'1 = 330.001 must be satisfied. The calculation method is as follows:

[0164] Coordinates of the starting point of the first arc segment:

[0165] Coordinates of the endpoint of the first arc segment:

[0166] Therefore, the starting point coordinates of the first arc segment are [11.373, -8.464], and the ending point coordinates are [11.873, -7.598]. Since |-8.464-(-7.598)|=0.866>sp′=0.5, the two endpoints of this arc segment are greater than the theoretical single cutting depth of the arc segment in the Y-axis direction. Therefore, the number of discrete points of the first arc segment is:

[0167]

[0168] Divide the arc segment into (Nc1-1) = (3-1) = 2 equal parts according to the angle. That is, the linspace function in MATLAB software can be used to achieve the function of dividing the interval equally. The specific syntax is as follows: linspace(270°, 330.001°, 3) = (270°, 300.0005°, 330.001°). That is, Nc1 = 3 angle values ​​are generated equally within the angle interval [270°, 300.001°]. Then the angle of the arc segment is: Δα = 300.0005° - 270° = 330.001° - 300.0005° = 30.0005°. Substituting these three angle values ​​into the coordinate expression of the arc segment yields three discrete coordinate points: [11.373, -8.464], [11.507, -7.964], and [11.873, -7.598].

[0169] Similarly, the discretization of the second and third circular arc segments is completed sequentially using the method described above.

[0170] Finally, the coordinates of the discrete points on the straight line segment and the discrete points on the circular arc are merged. The Y-coordinate values ​​of the discrete points are then sorted in descending order using the `sort` function in MATLAB software, resulting in a set of 31 discrete points with Y-coordinate values ​​from largest to smallest. The resulting discrete points are shown in Table 1, which represents the refined discrete points. The distribution of the refined discrete points is as follows: Figure 10 As shown, the simulation diagram of the refined discrete trajectory is as follows: Figure 11 As shown, Figure 11 In the diagram, C represents the finely trimmed discrete trajectory, and A represents the sand profile.

[0171] Table 1. Coordinates of the fine-tuned discrete points

[0172]

[0173]

[0174] In this embodiment, when establishing the contour allowance distribution model, considering factors such as irregular deformation during the sintering process of the grinding wheel block, the allowance value is set to t1 = 3mm, the rough dressing amount is set to t2 = 2.8mm, and the fine dressing amount is set to t3 = t1 - t2 = 0.2mm. The coordinate points of the rough dressing boundary are shown in Table 2, and the coordinate points of the retraction position boundary are shown in Table 3.

[0175] Table 2 Coordinates of the rough trimmed boundary

[0176] 1 [9.766，1] 12 [12.794，-2.982] 23 [11.707，-7.964] 2 [9.990，0.533] 13 [13.148，-3.459] 24 [11.573，-8.464] 3 [10.213，0.067] 14 [13.401，-3.997] 25 [11.573，-8.464] 4 [10.437，-0.400] 15 [13.543，-4.573] 26 [11.573，-8.887] 5 [10.660，-0.866] 16 [13.569，-5.167] 27 [11.573，-9.309] 6 [10.884，-1.333] 17 [13.477，-5.754] 28 [11.573，-9.732] 7 [10.884，-1.333] 18 [13.272，-6.311] 29 [11.573，-10.155] 8 [11.280，-1.890] 19 [12.961，-6.817] 30 [11.573，-10.577] 9 [11.842，-2.281] 20 [12.556，-7.252] 31 [11.573，-11] 10 [11.842，-2.281] 21 [12.073，-7.598] 11 [12.353，-2.585] 22 [12.073，-7.598]

[0177] Table 3 Coordinates of the retraction position boundary

[0178] 1 [12.566，1] 12 [15.594，-2.982] 23 [14.507，-7.964] 2 [12.790，0.533] 13 [15.948，-3.459] 24 [14.373，-8.464] 3 [13.013，0.067] 14 [16.201，-3.997] 25 [14.373，-8.464] 4 [13.237，-0.400] 15 [16.343，-4.573] 26 [14.373，-8.887] 5 [13.460，-0.866] 16 [16.369，-5.167] 27 [14.373，-9.309] 6 [13.684，-1.333] 17 [16.277，-5.754] 28 [14.373，-9.732] 7 [13.684，-1.333] 18 [16.072，-6.311] 29 [14.373，-10.155] 8 [14.080，-1.890] 19 [15.761，-6.817] 30 [14.373，-10.577] 9 [14.642，-2.281] 20 [15.356，-7.252] 31 [14.373，-11] 10 [14.642，-2.281] 21 [14.873，-7.598] 11 [15.153，-2.585] 22 [14.873，-7.598]

[0179] Therefore, the simulation diagram of the coarse trimming trajectory is as follows: Figure 12 As shown, Figure 12 In the diagram, H represents the coarse trimming trajectory.

[0180] In this embodiment, the rough dressing feed rate v1 ranges from 10 to 50 mm / min, the rough dressing cutting rate v2 ranges from 10 to 20 mm / min, and the fine dressing cutting rate v3 ranges from 2 to 10 mm / min.

[0181] In this embodiment, during the rough dressing process, the feed rate is set to v1 = 20 mm / min, and the rough dressing cutting speed is set to v2 = 10 mm / min. First, the initial rough dressing path is executed. After the initial rough dressing path is completed, the rough dressing path unit is executed repeatedly until the tool tip center retracts to coordinate point P on the retraction position boundary. N After the rough dressing is completed, the fine dressing process begins. Specifically, during fine dressing, the cutting speed is set to v3 = 5 mm / min, and the tool tip center moves sequentially from top to bottom according to the discrete point coordinates P1 to P... N Then, finish the final touches.

[0182] This invention achieves automated grinding wheel dressing by discretizing the grinding wheel dressing trajectory and designing contour allowance paths. At the same time, by setting fine dressing discrete trajectories and coarse dressing trajectories, it improves the flexibility and accuracy of grinding wheel dressing, enhances versatility, and realizes flexible dressing processing for irregularly shaped grinding wheels.

[0183] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A flexible dressing method for grinding wheels with complex surface shapes, characterized in that, Includes the following steps: S1: Obtain the sand profile diagram, and use the equidistant line method to obtain the continuous fine trimming curve based on the sand profile diagram. The continuous fine trimming curve includes straight line segments and / or circular arc segments. S2: Extract the entity segment data information of the continuous fine-tuning curve to obtain fine-tuning trajectory information. The fine-tuning trajectory information includes curve type, number of curve segments and curve position. The curve type includes straight line segments and circular arc segments. The curve position of the straight line segment includes the starting point coordinates and ending point coordinates of each straight line segment. The curve position of the circular arc segment includes the center coordinates, radius value, starting angle and ending angle of each circular arc segment. S3: A theoretical single-cut depth is preset. Based on the theoretical single-cut depth and the fine-tuning trajectory information, the continuous fine-tuning curve is discretized to obtain fine-tuning discrete points. A fine-tuning discrete trajectory is created based on these discrete points. The fine-tuning discrete points include discrete points for straight line segments and / or discrete points for circular arc segments. The discrete points for each straight line segment are obtained by performing layered discretization on the straight line segment based on the theoretical single-cut depth. The discrete points for each circular arc segment are obtained by performing equal-angle discretization on the circular arc segment based on the theoretical single-cut depth. Specifically, step S3 involves: S3.1: Set the theoretical single-step depth of cut for the straight line segment as... The theoretical single-cut depth of the circular arc segment is set as... ; S3.2: Based on the theoretical single cutting depth of the straight line segment, and the coordinates of the starting point and the ending point of each straight line segment, obtain the number of discrete points of each straight line segment. Based on the theoretical single cutting depth of the arc segment, and the coordinates of the center, radius, starting angle and ending angle of each arc segment, obtain the number of discrete points of each arc segment. S3.3: Discretize the line segment by layer according to the number of discrete points of the line segment, and obtain the coordinates of the discrete points of the line segment; discretize the arc segment by equal angle according to the number of discrete points of the arc segment, and obtain the coordinates of the discrete points of the arc segment. S3.4: Merge the coordinates of the discrete points of the straight line segment and the discrete points of the circular arc segment, and use a sorting function to sort the Y-axis coordinates of the merged discrete points in descending order to obtain the set of discrete points, i.e., the refined discrete points. ; , where N is the total number of discrete points of the line segment and the circular arc segment; S3.5: Create a fine-tuning discrete trajectory based on the fine-tuning discrete points. The fine-tuning discrete trajectory is the path from the center of the tool tip to the coordinates of the fine-tuning discrete points. Move from top to bottom sequentially to The trajectory; S4: Construct a contouring allowance distribution model; including: establishing a coarse trimming boundary and a tool retraction position boundary based on the fine trimming discrete points according to the preset contouring allowance, obtaining a contouring allowance distribution model composed of the coarse trimming boundary and the tool retraction position boundary, and creating a coarse trimming trajectory based on the coarse trimming boundary and the tool retraction position boundary. S5: First, perform rough dressing on the grinding wheel according to the rough dressing trajectory, and then perform fine dressing on the grinding wheel according to the fine dressing discrete trajectory.

2. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, The equidistant line method in step S1 is as follows: draw the outward equidistant lines of the normal direction of the sand profile curve in the sand profile diagram to obtain the continuous finishing curve of the grinding wheel. The equidistant distance of the outward equidistant lines is equal to the radius of the tool tip arc. ; In step S2, the dxflib library function is used to extract the entity segment data information of the continuous fine-tuning curve.

3. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, Step S2 further includes the following step: obtaining the number of curve segments of the straight line segment. The data information of the curve position of the straight line segment is stored in the first matrix in matrix form. ,but: ； in, The coordinates of the starting point of the first straight line segment are: The coordinates of the endpoint of the first straight line segment; For the first The coordinates of the starting point of the straight line segment. For the first The coordinates of the endpoint of the line segment, [] is an empty matrix; Obtain the number of curve segments of the arc segment. The data on the position of the arc segment is stored in matrix form in the second matrix. ,but: ； in, Here are the coordinates of the center of the first arc segment. This is the radius of the first circular arc segment; These are the starting angle and ending angle of the first arc segment, respectively. For the first The coordinates of the center of the arc segment, [ ] is the first The radius of the circular arc segment; The first The starting angle and ending angle of the circular arc segment.

4. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, The step S3.2, which involves obtaining the number of discrete points for each line segment based on the theoretical single cutting depth of the line segment and the coordinates of the starting and ending points of each line segment, specifically involves: The number of discrete points of a line segment is obtained based on its position on the curve. , like Then the first The starting point of a straight line segment and termination point As discrete points, the number of discrete points: ； in, Number of line segments index, and The first The ordinates of the starting and ending points of a straight line segment; like Then the number of discrete points: ； Here, ceil is the floor function.

5. The flexible dressing method for complex-shaped grinding wheels according to claim 4, characterized in that, Step S3.2 further includes: calculating the theoretical single-cut depth of the straight line segment. After correction, the actual single-cut depth is obtained as follows: Its expression is: 。 6. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, The step S3.3, which involves discretizing the line segment into layers based on the number of discrete points to obtain the coordinates of the discrete points, specifically involves: Using the interval division function in the Y-axis interval of the line segment Generate at equal intervals within the range 1 number of values, to obtain an array Its expression is: ； The linspace function is an interval division function; Using an interpolation function at the starting point of a line segment and the end point Interspersed with arrays In Perform linear interpolation on the values ​​to obtain the linearly interpolated result. An array of corresponding x-coordinate values Its expression is: ； Where interp1 is the interpolation function, and 'linear' is the linear interpolation method; use Represents the coordinates of discrete points on a line segment.

7. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, The step S3.2, which involves obtaining the number of discrete points for each arc segment based on the theoretical single cutting depth of the arc segment, as well as the center coordinates, radius, starting angle, and ending angle of each arc segment, specifically involves: The coordinates of the starting and ending points of each arc segment are calculated based on the coordinate expression of the arc segment. The coordinate expression of the arc segment is as follows: ； ； in, For the first The coordinates of the center of the arc segment. For the first The radius of the circular arc segment; The first The starting angle and ending angle of the circular arc segment. Number of arc segments index, For the first The coordinates of the starting point of the circular arc segment. For the first The coordinates of the endpoint of the circular arc segment; And the termination angle Perform angle correction to obtain the correction termination angle. Specifically: when hour, ; when hour, ; The number of discrete points is obtained based on the curve position of the arc segment. , like Then the first The starting point of the arc segment and the end point As discrete points, the number of discrete points: ； like Then the number of discrete points: ； Here, ceil is the floor function.

8. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, In step S3.3, the arc segment is discretized at equal angles based on the number of discrete points to obtain the coordinates of the discrete points. Specifically: Using the interval division function in the angle interval of the circular arc segment Generate at equal intervals within the range Each angle value yields an array. Its expression is: ； Based on the coordinate expression of the arc segment, the array of Calculate each angle value to obtain By using a set of coordinate points, we can obtain the discrete coordinates of the arc segment.

9. The flexible dressing method for complex-shaped grinding wheels according to claim 1, characterized in that, Step S4 specifically involves: S4.1: Based on the preset contouring allowance and the fine trimming discrete points, establish the coarse trimming boundary and the tool retraction position boundary to obtain the contouring allowance distribution model, including the following steps: The conforming allowance includes an allowance value. and rough trimming amount Then refine the quantity ; Distance of one margin value from the X-axis direction of the fine-tuned discrete point Establish the tool retraction position boundary on the equidistant line. A coarse dressing amount is placed at the X-axis distance from the boundary of the tool retraction position. Establish rough trimming boundaries on equidistant lines. The coordinates of the rough trimmed boundary Coordinates of the boundary of the tool retraction position The expression is: ； S4.2: Establish a rough trimming trajectory based on the rough trimming boundary and the tool retraction position boundary. The rough trimming trajectory includes an initial rough trimming path and cyclically executed rough trimming path units. The initial rough dressing path includes an initial rough cutting path and an initial tool retraction path. The initial rough cutting path is formed by the tool tip center starting from... Move towards The initial retraction path is the path from the center of the tool tip. Move towards The path; The coarse dressing path unit includes a sequentially arranged infeed path, a unit rough cutting path, and a unit retraction path. The infeed path starts from the center of the tool tip... Move towards The cutting path of the unit is from the center of the tool tip... Move towards The path of the unit's retraction path is from the center of the tool tip... Move towards The path, where q takes the values ​​1, 2, ..., N-1.

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