Parametric design method for space curve of gradual forming and tenon-slot cutter with same profile

Abstract

The present application relates to the gradual formation and the same profile combination tenon and slot cutter blade shape space curve parameterization design method, including the following steps: step one, shooting tenon and slot image; Step two, tenon and slot shape curve is discrete; Step three, calculate control point and fit approximation curve; Step four, the same profile cutter tooth space curve design: step five, gradual formation type cutter tooth space curve design; Step six, tenon and slot broach cutter tooth space curve output. The present application reduces the difficulty of tenon and slot broaching cutter space curve parameterization design; The parameterization of the cutter blade space curve realizes the unity of parameter selection, improves the stability of the broach design, and proposes the transition boundary and method of the gradual formation and the same profile combination, solves the problem of difficult to determine the gradual formation and the same profile transition method, reduces the design difficulty; At the same time, the parameterization design solves the long cycle and low efficiency problem of the traditional design method, improves the design efficiency of the broach, and reduces the cost of broach design and manufacturing.

Description

TECHNICAL FIELD

[0001] The application relates to a method for parametric design of a space curve of a gradually formed and homologous combined tenon and slot cutter blade, and belongs to the technical field of parametric design of cutters. BACKGROUND

[0002] An engine turbine tenon and slot shape is complex, and the corresponding broaching cutter design is also relatively difficult, especially the tooth structure of the broach is special, the precision of the broach is high, and the design difficulty of the tenon and slot broach is increased. The geometric structure of the broach is usually complex, a plurality of parameters are involved in the design, the calculation amount is large, and the calculation process is complicated, which increases the design difficulty of the broach, and different parameter values also affect the stability of the broach. The tooth rise of the homologous layered broach is small, the broaching quality is high, and the broach is long. The homologous gradually formed broach is easy to manufacture when forming a surface by broaching, the broaching quality is poor; the tooth rise of the block type broach is large, the block type broach is suitable for broaching large-size and large-amount surfaces, and can also be used for broaching a blank surface, the length of the broach is short, the efficiency is high, but the broaching quality is not easy to improve. The broach of the combined gradually formed and homologous broaching mode has the advantages of the homologous layered and block type broaching, and at present, a combined round broach is usually used for broaching a large-amount round hole. However, the traditional design method of the combined broach is long in period, low in efficiency, and easy to make mistakes, it is difficult to determine the gradually formed and homologous transition method, once there is a design error, great economic loss will be caused, and the manufacturing cost of the broach is increased. Therefore, the space curve model and the correlation model of the cutter cutting blade are constructed, and the progressive design of the tenon and slot broach teeth is realized through the research on the space curve function.

[0003] At present, there are some related technologies and methods for the parameterization design method of such mortise and tenon cutter. For example, the invention patent with the application number CN202010616830.2 discloses a precision broach tooth parameter implementation method, which proposes a multi-constraint response surface method for determining the flexible parameter set of the precision broach structure element design, which is also applicable to the mortise and tenon precision broach tooth parameter design of similar conditions. For example, the invention patent with the application number CN202111259751.1 discloses a residual height prediction method for curve cutting under variable parameter conditions, which obtains a curve equation according to the processed curve, establishes a variable parameter elliptical vibration equation, obtains an elliptical trajectory equation of ultrasonic elliptical vibration processing, and determines the intersection coordinates of the curve and the elliptical trajectory by combining the elliptical trajectory equation with the curve equation obtained in step one. The intersection coordinates of the elliptical vibration trajectory equations of the nth cutter contact point and the adjacent cutter contact point are calculated, and finally the residual height between the adjacent elliptical vibration trajectories is calculated. For example, the invention patent with the application number CN201510797462.5 discloses a same-profile single-side broaching gear broach, which includes a front section and a rear section. The front section is a gradual forming structure rough broach tooth section, and the rear section is a same-profile forming structure precision broach tooth section. The rear section tooth is a single-side tooth lifting broaching.

[0004] However, the above design methods cannot realize the space curve parameterization of each tooth of the mortise and tenon broach combined with gradual and same-profile, so as to realize the complete design of the turbine fir-tree mortise and tenon. SUMMARY

[0005] The purpose of the present application is to overcome the shortcomings of the existing methods and provide a gradual and same-profile combined mortise and tenon cutter blade space curve parameterization design method. The method is a design method for driving the cutter blade geometry parameter by inputting the mortise and tenon space curve parameter, a design method for inversely solving the same-profile blade feature point coordinates through the mortise and tenon space curve discretization model, a design method for determining the transition of the same-profile blade to the gradual blade through the coincidence degree of the same-profile feature point coordinates and the trapezoidal curve feature point coordinates, a parameterization design method for solving the gradual feature point coordinates through the equal division of the trapezoidal curve feature point coordinates, and a parameterization design method for fitting the blade curve through the feature point coordinates.

[0006] To achieve the above purpose, the technical scheme of the present application is as follows:

[0007] The gradual and same-profile combined mortise and tenon cutter blade space curve parameterization design method comprises the following steps:

[0008] Step one, shooting the mortise image: shoot the mortise under the condition of backlight, process the image to black and white, and symmetrically translate the mortise image Y axis to the X-Y coordinate system, and sample and mark the black and white pixel boundary at the same time;

[0009] Step two, the discrete of the tenon and groove shape curve: extract the discrete points on the tenon and groove shape curve, according to the longitudinal tree tenon and groove shape, take the coordinate points D on the discrete curve and determine the B-spline curve, the fir tree type line fitting into a spline curve needs a set of discrete data points on the curve, shape control points and interpolation points;

[0010] Step three, calculate the control points and fit the approximation curve: put the values in step two into the formula to calculate the control points, compare them with the actual profile in CAD, set the deviation threshold, if the actual and calculated values deviate more than the deviation threshold, reduce the sampling interval by 75% and re-sample, calculate and verify until the deviation threshold condition is met to approximate the actual curve; Based on the parameterization of the program, the tenon and groove shape is discretely processed, combined with the API interface provided by the CAD system platform to write appropriate programs to realize parameterized design. Using VB language, following the point, line, surface, body and other feature modeling methods, according to the modeling sequence of the corresponding platform, combined with the open application program interface API provided by the CAD software, the corresponding algorithm program is developed and written, the point, line, surface, body and other internal design features of the model are generated, and finally the parameterization and discretization of the broach curve are realized.

[0011] Step four, the same profile cutter tooth space curve design: based on the spline curve that finally meets the deviation threshold, recursively operate on the control points and fit the space curve in CAD according to the position of the control point P;

[0012] Taking the control point of the right spline curve as an example, the topmost control point (P0) has coordinates (P0x, P0y), P0x remains unchanged, P0y(n+1) = P0y(n)-0.01, i.e. P0(n+1) = [P0x(n), P0y(n)-0.01]; The rest of the odd control points (Po) move closer to the center line, and the coordinate recursive relationship is Po(n+1) = [Pox(n)-0.04, Poy(n)], and the even control points (Pe) move away from the center line, and the coordinate recursive relationship is Pe(n+1) = [Pex(n)+0.02, Pey(n)]. Fit a straight line on the curve, when the curve is approximately a straight line within a reasonable range, i.e. when the farthest point of the curve is within 0.02 mm of the straight line, set it as the boundary line between the same profile broach space curve and the gradual broach space curve.

[0013] In addition, when the Y-direction coordinate of the next group P0 is less than the Y-direction coordinate of P1, the Y-axis coordinate of P0 is no longer reduced, that is, P0y(n+1) < P1y(n), and the progressive operation of P0y(n) is no longer performed. At the same time, when the X-direction coordinate of any odd control point (P0) is about to be less than the X-direction coordinate of P0 or any even control point (Pe), that is, Pox(n+1) < P0x(n) or Pox(n+1) < Pex(n+1), the progressive operation ends, and it is also determined that the boundary of the space curve of the same profile type broach and the space curve of the gradual forming type broach is formed.

[0014] Step five, gradual forming type cutter tooth space curve design: after the calculation of the control points of the space curve of the same profile type cutter tooth and the fitting of the curve are completed, the gradual forming type machining adopts a tooth increment of 0.04 mm, and the boundary of the space curve of the same profile type broach and the space curve of the gradual forming type broach is used as a constraint, and the space curve of the gradual forming type broach is calculated from the bottom of the mortise and tenon space curve to the top of the mortise and tenon space curve with a tooth increment of 0.04 mm per tooth.

[0015] The space curve shape is an isosceles trapezoid, and the necessary coordinate points of the constraint shape are: the upper base Y-axis coordinate (YU), the lower base Y-axis coordinate (YD), the upper base corresponding boundary X-axis coordinate (XU), and the lower base corresponding boundary X-axis coordinate (XD). It is assumed that the discrete data points on the boundary space curve are (D), the upper base corresponding boundary X-axis coordinate (XU) and the lower base corresponding boundary X-axis coordinate (XD) are obtained from the discrete data points (D). The relationship between the upper base corresponding boundary X-axis coordinate (XU) and the lower base corresponding boundary X-axis coordinate (XD) is XD(n+1) = XU(n), which can be simplified as an array X(n); the relationship between the upper base Y-axis coordinate (YU) and the lower base Y-axis coordinate (YD) is YU(n) = YD(n+1) = YD(n) + 0.04, which can be simplified as an array Y(n), Y(0) = 0. The trapezoidal coordinates can be represented as (YU, YD, XU, XD), and the first trapezoidal three-point coordinate progressive formula of the isosceles trapezoid is [0.04, 0, X(1), X(0)], and then it is progressive to [Y(n+1), Y(n), X(n+1), X(n)].

[0016] Until Y(n+2) is greater than the Y-axis coordinate of the topmost discrete point of the boundary, that is, the upper base of the next trapezoid exceeds the boundary, the progressive operation is stopped, and the calculation of the gradual forming type broach space curve is completed.

[0017] Step six, output of the mortise and tenon broach tooth space curve: the space curve control points of each cutter tooth obtained are output on the graph using a secondary development language, and the final space curve of each cutter tooth of the broach is obtained.

[0018] The sampling interval of the discrete points in step two is 0.001 mm.

[0019] The step two includes the following steps:

[0020] The coordinates of the control points P are calculated from the data points (D0, D1,..., Dn) on the B-spline curve according to N base functions;

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] Wherein the matrix D is a discrete data point along the cutting edge curve, the curve discrete data point D and the base function N are known, the control point parameter P of the spline curve can be solved; and the cutting edge curve S(u) of the B-spline curve is obtained according to D=P×N.

[0027] The step four specifically comprises:

[0028] Fitting a straight line on the curve, when the curve is approximately a straight line within a reasonable range, that is, when the farthest point of the curve is not more than 0.02 mm away from the straight line, it is set as the boundary of the space curve of the same profile type broach and the space curve of the gradual forming broach.

[0029] The invention patent with the patent number CN202010616830.2 discloses a precision broach tooth parameter implementation method, which can multi-constraint respond to the surface different from the broach blade shape space curve, and does not design and process the broach blade shape space curve and the broach cutter based on the parameters; the invention patent with the patent number CN202111259751.1 discloses a residual height prediction method for cutting along the curve under variable parameter conditions, which is a prediction of the influence of adjacent two teeth of the existing broach, and does not involve the field of broach design; the invention patent with the patent number CN201510797462.5 discloses a same profile single-sided broach for gear broaching, which is a machining process of wheel broach, different from the mortise and tenon broach with complex shape, and does not describe the space curve and transition method of the same profile gradual forming combined broach in a parameterized and unified manner.

[0030] The gradual forming and same profile combined tenon and groove cutter blade shape space curve parameterized design method reduces the difficulty of tenon and groove broaching cutter design, realizes the unity of parameter selection, improves the stability of broaching cutter design, avoids the problems of small tooth rise, long broaching cutter and low efficiency of the same profile broaching cutter, improves the final broaching quality compared with the gradual forming broaching cutter, solves the problem of difficult determination of the gradual forming and same profile transition method, reduces the design difficulty, solves the problems of long cycle and low efficiency of the traditional design method, improves the design efficiency of the broaching cutter and reduces the cost of broaching cutter design and manufacturing. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0032] Figure 1 The method flow chart of the gradual forming and same profile combined tenon and groove cutter blade shape space curve parameterized design method of the present application;

[0033] Figure 2 The fir tree type tooth profile data point and B spline curve control point of the gradual forming and same profile combined tenon and groove cutter blade shape space curve parameterized design method of the present application;

[0034] Figure 3 The spline curve control point change process and recursive design end effect diagram of the cutter same profile part space curve of the gradual forming and same profile combined tenon and groove cutter blade shape space curve parameterized design method of the present application;

[0035] Figure 4 The final space curve effect diagram of the broaching cutter gradual forming part space curve recursive calculation design of the gradual forming and same profile combined tenon and groove cutter blade shape space curve parameterized design method of the present application. DETAILED DESCRIPTION

[0036] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0037] Figure 1 As a method flow chart, the application provides a gradual formation and same-profile combined tenon and slot cutter blade shape space curve parameterized design method,

[0038] The gradual formation and same-profile combined tenon and slot cutter blade shape space curve parameterized design method comprises the following steps:

[0039] Step one, shoot the tenon and slot image: shoot the tenon and slot under the condition of backlight, process the image to be black and white, move the tenon and slot image Y axis symmetrically to the X-Y coordinate system, and sample and mark the black and white pixel boundary at the same time;

[0040] Step two, tenon and slot shape curve discretization: extract the discrete points on the tenon and slot shape curve, according to the vertical tree type tenon and slot shape, take the coordinate point D on the discretized curve and determine the B-spline curve, and the fir tree type line fitting needs a group of discrete data points on the curve, shape control points and interpolation points;

[0041] Step three, calculate the control point and then fit the approximation curve: put the numerical value in step two into the formula to calculate the control point, compare it with the actual contour in CAD, set the deviation threshold, if the actual and calculated value deviation is greater than the deviation threshold, reduce the sampling interval by 75% and then resample, calculate and verify, until the deviation threshold condition is met to approximate the actual curve; based on the program parameterization, discretize the tenon and slot shape, write a suitable program combining the API interface provided by the CAD system platform, realize the parameterized design. Use VB language, follow the point, line, surface and body feature modeling method, according to the corresponding platform modeling sequence, combine the open application program interface API provided by the CAD software, develop and write the corresponding algorithm program, generate the point, line, surface and body design features inside the platform, and finally realize the parameterization and discretization of the broach curve.

[0042] Step four, same-profile cutter tooth space curve design: based on the spline curve that finally meets the deviation threshold, recursively operate on the control points, and fit the space curve according to the position of the control point P in CAD;

[0043] Taking the right side spline curve control point as an example, the coordinate of the topmost control point (P0) is (P0x, P0y), P0x is constant, P0y (n+1) = P0y (n) - 0.01, that is, P0 (n+1) = [P0x (n), P0y (n) - 0.01]; the rest of the odd control points (Po) are close to the center line, and the coordinate recursive relationship is Po (n+1) = [Pox (n) - 0.04, Poy (n)], the even control points (Pe) move away from the center line, and the coordinate recursive relationship is Pe (n+1) = [Pex (n) + 0.02, Pey (n)]. Fitting a straight line on the curve, when the curve is approximately a straight line within a reasonable range, that is, when the farthest point of the curve is less than 0.02 mm from the straight line, it is set as the boundary line of the space curve of the same profile broach and the space curve of the gradual forming broach.

[0044] In addition, when the Y direction coordinate of the next group P0 is less than the Y direction coordinate of P1, the Y axis coordinate of P0 is no longer reduced, that is, P0y (n+1) < P1y (n), P0y (n) no longer performs progressive operation. At the same time, when the X direction coordinate of any odd control point (Po) is about to be less than the X direction coordinate of P0 or any even control point (Pe), that is, Pox (n+1) < P0x (n) or Pox (n+1) < Pex (n+1) progressive operation ends, the same is recognized as the boundary line of the space curve of the same profile broach and the space curve of the gradual forming broach, please refer to Figure 3 .

[0045] Step five, gradual forming tool tooth space curve design: after completing the calculation of the space curve control points of the same profile tool tooth and curve fitting, the gradual forming machining adopts a tooth increment of 0.04 mm, and the boundary line of the space curve of the same profile broach and the space curve of the gradual forming broach is used as a constraint, starting from the bottom of the mortise and tenon space curve, and increasing by 0.04 mm per tooth;

[0046] The spatial curve shape is an isosceles trapezoid, and necessary coordinate points of the shape constraint are: upper base Y-axis coordinate (YU), lower base Y-axis coordinate (YD), upper base corresponding boundary X-axis coordinate (XU), and lower base corresponding boundary X-axis coordinate (XD). Discrete data points on the boundary spatial curve are set as (D), and the upper base corresponding boundary X-axis coordinate (XU) and the lower base corresponding boundary X-axis coordinate (XD) are obtained from the discrete data points (D). The relationship between the upper base corresponding boundary X-axis coordinate (XU) and the lower base corresponding boundary X-axis coordinate (XD) is XD(n+1)=XU(n), which can be simplified as an array X(n); the relationship between the upper base Y-axis coordinate (YU) and the lower base Y-axis coordinate (YD) is YU(n)=YD(n+1)=YD(n)+0.04, which can be simplified as an array Y(n), Y(0)=0. The trapezoidal coordinates can be expressed as (YU, YD, XU, XD), and the first trapezoidal isosceles trapezoidal three-point coordinate progressive formula is [0.04, 0, X(1), X(0)], and then the progression is [Y(n+1), Y(n), X(n+1), X(n)].

[0047] Until Y(n+2) is greater than the Y-axis coordinate of the topmost discrete point of the boundary, that is, the upper base of the next trapezoid exceeds the boundary, the progression is stopped, and the calculation of the gradual generating type broach spatial curve is completed, referring to Figure 4 .

[0048] Step six, tenon and slot broach tooth spatial curve output: the obtained spatial curve control points of each tooth are used to output the results on the graph by using a secondary development language, and the final spatial curve of each tooth of the broach is obtained.

[0049] The sampling interval of the discrete points in the step two is based on 0.001 mm.

[0050] The step two includes the following steps:

[0051] The coordinates of the control points P are obtained from the data points (D0, D1,..., Dn) on the B-spline curve and according to N base functions;

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Wherein the matrix D is discrete data points along the cutting edge curve, the curve discrete data points D and the base function N are known, then the control point parameters P of the spline curve can be solved; then the cutting edge curve S(u) of the B-spline curve is obtained according to D=P*N, referring to Figure 2 .

[0058] The step four specifically includes:

[0059] Fitting a straight line on the curve, when the curve is approximately a straight line within a reasonable range, that is, when the farthest point of the curve is not more than 0.02mm away from the straight line, it is set as the boundary line of the space curve of the same profile type broach and the space curve of the gradual type broach.

[0060] The RLXSS data set is an adversarial data set used by the RLXSS attack method disclosed in 2019.

[0061] The embodiments of the application are described in detail above with reference to the drawings, but the application is not limited to the described embodiments. For those skilled in the art, various changes, modifications, replacements and variations of the embodiments can be made without departing from the principles and spirits of the application, and still fall within the protection scope of the application.

Claims

1. A method for parametric design of the profile space curve of a progressive and congruent combination type mortise and tenon tool, characterized in that: It comprises the following steps: Step one, take the tenon groove image: in the case of backlight, after placing the reference scale, take the tenon groove, process the image to black and white, and move the tenon groove image Y axis to the X-Y coordinate system symmetrically according to the reference scale, and sample and mark the junction of black and white pixels, with the sampling interval of discrete points being 0.001 mm; Step two, discretization of tenon groove shape curve: extract the discrete points on the tenon groove shape curve, and determine the B-spline curve according to the vertical tree tenon groove shape, and fit the fir tree type line into the spline curve, which needs a set of discrete data points on the curve, shape control points and interpolation points; Step three, calculation of control points and fitting of approximate curve: after substituting the numerical value in step two into the formula, the control points are obtained, which are compared with the actual profile in CAD, and the deviation threshold is set, if the deviation between the actual value and the calculated value is greater than the deviation threshold, the sampling interval of discrete points is reduced by 75%, and the sampling, calculation and verification are performed again until the deviation threshold condition is met to approximate the actual curve; Step four, design of the same profile type cutter tooth space curve: based on the spline curve that finally meets the deviation threshold, the control points are recursively calculated, and the odd control points Po are moved to the center line by 0.04 mm, and the even control points Pe are moved away from the center line by 0.02 mm, and the space curve is fitted in CAD according to the position of the control point P; Step five, design of the gradual formation type cutter tooth space curve: after the calculation of the control points of the space curve of the same profile type cutter and the fitting of the curve are completed, the gradual formation type machining adopts a tooth increment of 0.04 mm, and the boundary between the space curve of the same profile type cutter and the space curve of the gradual formation type cutter is used as a constraint, and the space curve of each tooth is obtained from the bottom of the tenon groove space curve, and the tooth increment is 0.04 mm per tooth; Step six, output of the tenon groove broach tooth space curve: the space curve control points of each tooth are obtained, the results are output on the graph using the secondary development language, the projection method is used for the same profile verification, and the final space curve of each tooth of the broach is obtained.

2. The method according to claim 1, wherein the method is characterized in that: The step two comprises the following steps: The coordinates of the control points P are obtained from the data points (D0, D1,..., Dn) on the B-spline curve and according to N basis functions; Wherein, the matrix D is the discrete data points along the cutting edge curve, the curve discrete data points D and the basis function N are known, and then the control point parameters P of the spline curve can be solved, and then the cutting edge curve S(u) of the B-spline curve is obtained according to D=P*N.

3. The generative and congruent combination of slot cutter blade space curve parameterization design method according to claim 1, characterized in that: The step four specifically comprises: Fitting a straight line on the curve, when the curve is approximately a straight line within a reasonable range, that is, when the farthest point of the curve is not more than 0.02 mm away from the straight line, the straight line is set as the boundary between the space curve of the same profile type cutter and the space curve of the gradual formation type cutter.

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