Digital generating processing method of pure rolling contact bevel gear

Abstract

The invention relates to the technical field of bevel gears, in particular to a digital generating processing method of a pure rolling contact bevel gear, which comprises the following steps of: discretizing left and right theoretical tooth surfaces according to the same layer number in the tooth profile section curve direction by taking the left and right theoretical tooth surfaces of a tooth socket of the bevel gear as initial tool path boundaries; the discrete points on the same layer are positioned on the same conical surface of the bevel gear; respectively establishing a tool coordinate system and a gear coordinate system, and determining a homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in contact cutting with the theoretical tooth surface; obtaining a cutter center vector and a cutter axis vector which form a cutter location point according to the homogeneous coordinate transformation matrix; cutter location points on the left and right theoretical tooth surfaces serve as boundary conditions of a cutter path, and a machining cutter path track of the tooth groove is generated through intermediate interpolation calculation. Based on a digital generating machining method, the machining precision and efficiency of the pure rolling contact bevel gear are synchronously improved by means of the three-dimensional enveloping principle that a cutting edge of a disc-shaped milling cutter moves along an instantaneous contact trace.

Description

Technical Field

[0001] The present invention relates to the technical field of bevel gears, and in particular to a digital generating method for pure rolling contact bevel gears. Background Art

[0002] In the field of mechanical transmission, bevel gears are core components for power transmission that achieves interlaced axes. Their machining accuracy and efficiency directly impact the performance of the entire system. Domestic research in this field has advanced continuously with the Industrial Revolution. This research not only focuses on improving machining accuracy and efficiency, but also on developing new machining technologies and optimizing existing processes.

[0003] With the continued development of multi-axis CNC technology and its envelope milling theory, the digital generation of gears using universal tooling adapted to flexible manufacturing units has gained widespread application. In the field of complex surface milling, the current mainstream trajectory algorithms can be divided into four categories: isoparametric surface method, plane interception method, rotational surface topology method, and projection mapping method. A comparative analysis of the characteristics of each process method is shown below:

[0004] Isoparametric Surface Method: This process manually segments the tooth surface based on the principle of regular meshing. Its technical advantage lies in the ease of trajectory calculation. However, when processing surfaces with complex topological structures, the uneven distribution of mesh density can easily lead to overlapping cutting paths and the coexistence of blank areas, significantly reducing machining efficiency.

[0005] Plane Interception Method: Based on a plane cutting mechanism, the tool path is determined by pre-setting the intersection line between a plane family and a surface. Compared to parametric methods, this process can effectively handle the problem of stock removal on non-uniform surfaces through the adaptive density of the intersection points of the plane interception. In particular, when the tool cutting points are coplanar, the uniformity of the spacing between the paths improves processing efficiency.

[0006] The surface of revolution topology method uses a geometric intersection algorithm between a periodic surface of revolution and the machined surface to generate the cutting path. This method not only maintains a uniform path distribution but, more importantly, achieves a uniform distribution of surface allowances by adjusting the geometric parameters of the surface of revolution, which is of great value in improving the surface quality of precision gears.

[0007] Projection mapping: This method uses the normal projection of a specified trajectory to determine the cutting contact point, flexibly adapting to complex surface geometry. This algorithm effectively mitigates collision risks by pre-installing an interference detection module, but it is important to note the nonlinear mapping relationship between the cutting trajectory and the tool axis, which can easily lead to position control errors.

[0008] The above trajectory algorithms show that simplifying the processing of involute surfaces to free-form surface processing mode has two technical bottlenecks: the processing strategy based on global discrete approximation directly affects the contour accuracy, and the non-optimal distribution of local allowances further restricts the processing efficiency. Summary of the Invention

[0009] The purpose of the present invention is to provide a digital generating method for pure rolling contact bevel gears, which is based on the digital generating method and relies on the three-dimensional envelope principle of the disc milling cutter cutting edge moving along the instantaneous contact trace to achieve the simultaneous improvement of the pure rolling contact bevel gear processing accuracy and efficiency.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0011] A digital generating method for pure rolling contact bevel gears, comprising:

[0012] The left and right theoretical tooth surfaces of the bevel gear tooth groove are used as the initial tool path boundaries. The left and right theoretical tooth surfaces are discretized in the same number of layers along the tooth profile cross-section curve direction. The discrete points on the same layer are located on the same conical surface of the bevel gear.

[0013] Establish the tool coordinate system and the gear coordinate system respectively, and determine the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in contact with the theoretical tooth surface for cutting;

[0014] According to the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system, a tool center vector and a tool axis vector constituting the tool position point are obtained, wherein the tool center vector is a radial vector from the origin of the tool coordinate system to the origin of the gear coordinate system in the gear coordinate system, and the tool axis vector is a vector expression of the tool axis vector of the tool coordinate system in the gear coordinate system;

[0015] The tool position points on the left and right theoretical tooth surfaces are used as the boundary conditions of the tool path, and the machining tool path trajectory of the tooth groove is generated through intermediate interpolation calculation.

[0016] Furthermore, the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system is

[0017] Where, is the tool coordinate system S g The origin of the tool coordinate system O c To the gear coordinate system S c Origin O g The radial vector is the tool center vector; the column vectors α, β, and γ are the tool coordinate system S c The basis vector x c 、y c and z c In the gear coordinate system S g Homogeneous coordinate expressions in .

[0018] Furthermore, the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in contact with the theoretical tooth surface for cutting is determined, specifically including:

[0019] Get the tangent vector τ of the discrete point where the theoretical tooth surface contacts the tool when the tool contacts the theoretical tooth surface for cutting p , normal vector n p and path vector r p , and the tangent vector τ of the cutting point where the tool contacts the theoretical tooth surface p1 , normal vector τ p1 and path vector r p1 ;

[0020] Solving a system of equations simultaneously Get the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system

[0021] Furthermore, when the tool contacts and cuts the left and right theoretical tooth surfaces, the tool tip fillet vertex p m The points of contact with the bevel gear blank are respectively recorded as point A and point A0. Point A and point A0 are located on the same conical surface. In the gear coordinate system, when the tool contacts and cuts the theoretical tooth surface on the left, point p m The radial vector and normal vector of point A are equal; when the tool contacts and cuts the theoretical tooth surface on the right, point p m The radial vector and normal vector of A0 are equal.

[0022] Furthermore, a disc milling cutter is used as a machining tool, the bottom cutting edge of the disc milling cutter is used to machine the theoretical tooth surface on the left side of the bevel gear tooth groove, and the side cutting edge of the disc milling cutter is used to machine the theoretical tooth surface on the right side of the bevel gear tooth groove.

[0023] Furthermore, it also includes interference detection. During the machining process, the minimum distance d = |N·n between the bottom surface of the tool and the tooth profile of the bevel gear is calculated. p0 |, N is a constant, n p0 is the normal vector of any point on the tooth profile;

[0024] If the minimum spacing d is a positive value, it is determined that there is no interference between the tool and the tooth profile of the bevel gear; if the minimum spacing d is zero or a negative value, it is determined that there is interference between the tool and the tooth profile of the bevel gear, and the safety clearance between the tool and the tooth surface is increased by reducing the tool inclination angle.

[0025] The present invention has the following unexpected beneficial effects:

[0026] 1. This invention uses the theoretical tooth surfaces on the left and right sides of the tooth groove as the initial tool path boundaries and discretizes them into the same number of layers along the tooth profile cross-section curve, ensuring accurate and consistent tooth surface machining. Discrete points on the same layer lie on the same conical surface, providing a basis for precise control of the tool's motion trajectory. This ensures that the machined tooth surface more closely matches the theoretical design, reduces machining errors, and thus improves gear meshing accuracy and transmission performance.

[0027] 2. This method utilizes discretization and interpolation to generate toolpaths, enabling efficient cutting. By rationally planning toolpaths, it reduces idle travel and unnecessary cutting motions, improving machining efficiency. For example, in actual machining experiments, this method was able to efficiently complete the machining of pure rolling contact bevel gears on a five-axis Codé vertical machining center, demonstrating its efficiency advantages in actual production.

[0028] 3. The present invention establishes the tool coordinate system and the gear coordinate system respectively, and determines the homogeneous coordinate transformation matrix. This method enables the processing method to adapt to the processing of pure rolling contact bevel gears of different specifications and parameters. Gears of different sizes and tooth shapes can be processed by simply adjusting the relevant parameters, which improves the versatility of the processing method and reduces the processing cost. Compared with traditional bevel gear processing that relies on special equipment and different tooth shapes need to match specific models, this method uses a five-axis linkage CNC machining center and has obvious advantages in single-piece production scenarios. It does not require mold development, can use a universal fixture, and uses CNC programming software to automatically generate processing programs, which is suitable for the rapid processing of bevel gear samples.

[0029] 4. By determining the tool location points (tool center vector and tool axis vector), this method provides a basis for precise tool positioning and posture control, ensuring that the tool maintains correct contact with the tooth surface during machining and avoiding interference. Simulations and actual machining experiments have verified the feasibility of this machining method. The resulting complete tooth surface is relatively smooth, and the tooth shape and contact mark meet design requirements, demonstrating the accuracy of the tool location point calculation and the effectiveness of the digital generation machining method. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the implementation or prior art description. Obviously, the drawings described below are only some embodiments of the present invention.

[0031] Figure 1 A schematic flow chart of a digital generating method for pure rolling contact bevel gears provided by an embodiment of the present invention is shown.

[0032] Figure 2 An axial cross-sectional view of a tool provided by an embodiment of the present invention is shown.

[0033] Figure 3 A schematic diagram of the structure in which the left and right theoretical tooth surfaces are discretized with the same number of layers along the tooth profile cross-section curve is shown.

[0034] Figure 4 A schematic diagram of the tool development machining motion is shown.

[0035] Figure 5 A schematic diagram of the concave boundary tool position points provided by an embodiment of the present invention is shown.

[0036] Figure 6 A schematic diagram of convex boundary tool position points provided by an embodiment of the present invention is shown.

[0037] Figure 7 A schematic diagram of a single-layer reciprocating cutting tool position diagram provided by an embodiment of the present invention is shown.

[0038] Figure 8 A schematic diagram of a complete tooth groove tool position point provided by an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0039] The following describes the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art will readily appreciate the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the various details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are intended only to illustrate the present invention and are not intended to limit the scope of protection of the present invention.

[0040] In one embodiment, see Figure 1 As shown, the present invention provides a digital generating method for pure rolling contact bevel gears, which includes:

[0041] The left and right theoretical tooth surfaces of the bevel gear tooth groove are used as the initial tool path boundaries. The left and right theoretical tooth surfaces are discretized in the same number of layers along the tooth profile cross-section curve direction. The discrete points on the same layer are located on the same conical surface of the bevel gear.

[0042] Establish the tool coordinate system and the gear coordinate system respectively, and determine the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in contact with the theoretical tooth surface for cutting;

[0043] According to the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system, a tool center vector and a tool axis vector constituting the tool position point are obtained, wherein the tool center vector is a radial vector from the origin of the tool coordinate system to the origin of the gear coordinate system in the gear coordinate system, and the tool axis vector is a vector expression of the tool axis vector of the tool coordinate system in the gear coordinate system;

[0044] The tool position points on the left and right theoretical tooth surfaces are used as the boundary conditions of the tool path, and the machining tool path trajectory of the tooth groove is generated through intermediate interpolation calculation.

[0045] This method uses the theoretical tooth surfaces on the left and right sides of the tooth groove as the initial tool path boundaries and discretizes them into the same number of layers along the tooth profile cross-section curve, ensuring accurate and consistent tooth surface machining. Discrete points on the same layer lie on the same conical surface, providing a basis for precise control of the tool's motion trajectory. This ensures that the machined tooth surfaces are closer to the theoretical design, reduces machining errors, and thus improves gear meshing accuracy and transmission performance.

[0046] This method utilizes discretization and interpolation to generate toolpaths, enabling efficient cutting. By rationally planning the toolpath, it reduces idle travel and unnecessary cutting motions, improving machining efficiency. In actual machining experiments, this method was able to efficiently complete the machining of pure rolling contact bevel gears on a five-axis Codé vertical machining center, demonstrating its efficiency advantages in actual production.

[0047] The present invention establishes a tool coordinate system and a gear coordinate system respectively, and determines a homogeneous coordinate transformation matrix. This method enables the processing method to adapt to the processing of pure rolling contact bevel gears of different specifications and parameters. Gears of different sizes and tooth shapes can be processed by simply adjusting the relevant parameters, which improves the versatility of the processing method and reduces processing costs. Compared with traditional bevel gear processing that relies on special equipment and different tooth shapes need to match specific models, this method uses a five-axis linkage CNC machining center and has obvious advantages in single-piece production scenarios. It does not require mold development, can use a universal fixture, and uses CNC programming software to automatically generate processing programs, which is suitable for the rapid processing of bevel gear samples.

[0048] By determining the tool location points (tool center vector and tool axis vector), this method provides a basis for precise tool positioning and posture control, ensuring that the tool maintains correct contact with the tooth surface during machining and avoiding interference. Simulations and actual machining experiments have verified the feasibility of this machining method. The resulting complete tooth surface is relatively smooth, and the tooth shape and contact mark meet design requirements, demonstrating the accuracy of the tool location point calculation and the effectiveness of the digital generation machining method.

[0049] As a preferred embodiment of the present invention, the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system is:

[0050] Where, is the tool coordinate system S g The origin of the tool coordinate system O c To the gear coordinate system S c Origin O gThe radial vector is the tool center vector; the column vectors α, β, and γ are the tool coordinate system S c The basis vector x c 、y c and z c In the gear coordinate system S g Homogeneous coordinate expressions in .

[0051] As a preferred embodiment of the present invention, determining the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in contact with the theoretical tooth surface for cutting specifically includes:

[0052] Get the tangent vector τ of the discrete point where the theoretical tooth surface contacts the tool when the tool contacts the theoretical tooth surface for cutting p , normal vector n p and path vector r p , and the tangent vector τ of the cutting point where the tool contacts the theoretical tooth surface p1 , normal vector τ p1 and path vector r p1 ;

[0053] Solving a system of equations simultaneously Get the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system

[0054] Specifically, a disc milling cutter is used as a machining tool, the bottom cutting edge of the disc milling cutter is used to machine the theoretical tooth surface on the left side of the bevel gear tooth groove, and the side cutting edge of the disc milling cutter is used to machine the theoretical tooth surface on the right side of the bevel gear tooth groove.

[0055] The main components of the universal disc milling cutter are the shank 1 and the blade 2, which are fixed together by bolts. Compared with welded tools, universal disc milling cutters are less likely to crack during high-speed cutting, and for blanks with different material properties, blades of suitable materials can be selected for rapid replacement, demonstrating its advantages of strong processing flexibility and high production efficiency. The cutting edge of blade 2 is a straight edge, which is divided into a side edge 21 and a bottom edge 22, connected together by a radius at the tip. It has high overall strength and is suitable for high-feed and high-efficiency processing of bevel gears. In addition, the radius of the cutting edge on its head is small, which reduces overcutting when processing narrow areas of the bevel gear tooth root, thereby improving the overall strength of the bevel gear tooth root. The tool profile is the tool cutting edge around its axis z c The rotating surface of rotation, the disc milling cutter shaft section is as follows Figure 2 shown.

[0056] According to the digital generation processing theory, the concave and convex tooth surface of the bevel gear can be used as the initial tool path boundary, and the tooth surface is discretized along the cross-sectional curve direction. The discretized tooth surface is as follows Figure 3When machining the tooth surface, the tool cutting edge processes along discrete paths from the outermost layer of the tooth blank, cutting layer by layer until the entire tooth groove is machined.

[0057] When a disc milling cutter is used to digitally generate a gear blank, it is necessary to analyze the relative motion relationship between the cutter and the gear being machined. Figure 2 and 4 As shown, the tool coordinate system S is established respectively. c ={O c ,x c ,y c ,z c}、Gear coordinate system S g ={O g ,x g ,y g ,z g The tooth generation motion of a disc milling cutter can be considered as the meshing process between the tool profile and the tooth surface. Therefore, when the tool cutting edge is machining along the contact trace, the cutting point of the tool must coincide with the point on the contact trace, and the tool profile and the tooth surface must be tangent at this point. The geometric relationship between the tool and the gear being machined in the generation motion is as follows: Figure 4 As shown. Among them, see Figure 2 As shown, the tool coordinate system S is constructed c ={O c ,x c ,y c ,z c}, the origin of the coordinate system O c The positioning of the coordinate system z must meet the following geometric constraints: the origin is completely aligned with the geometric center point of the bottom surface of the milling cutter, and the coordinate system z c The axis direction is consistent with the tool rotation center line. Coordinate orientation is performed according to the right-hand screw rule, where y c Axis pointing bottom edge cutting vector τ p2 .

[0058] See also Figure 2 and Figure 4 As shown in the figure, when the disc milling cutter machines the convex tooth surface on the left side of the tooth groove along the contact path, the following conditions must be met at the cutting point: the tangent vector of the cross-sectional curve of tooth profile I at the discrete point coincides with the disc milling cutter side edge vector, and the tooth surface normal vector is collinear and opposite to the normal vector of the disc milling cutter bottom edge. For the concave tooth surface on the right side, the tangent vector of the disc milling cutter side edge must coincide with the tangent vector of the cross-sectional curve of tooth profile II, and the normal vector of the concave tooth surface at that point must be collinear and opposite to the normal vector of the side edge.

[0059] Taking the machining of the concave tooth surface of a small wheel as an example, the mathematical expression that satisfies its cutting conditions can be expressed as:

[0060]

[0061] Where, τp is the discrete point where the theoretical tooth surface contacts the tool, i.e. the tangent vector of the tooth profile cross-section curve at the contact point p, n p is the normal vector of the tooth surface at the contact point p,

[0062] The radial vector of any point on the tooth surface can be expressed as:

[0063]

[0064] is the tool coordinate system S c To the gear coordinate system S g The homogeneous coordinate transformation matrix corresponds to the different relative postures of the disc milling cutter during the cutting process, which can ensure that the tool maintains the correct cutting contact relationship with the tooth surface during the cutting process. The specific form is as follows:

[0065]

[0066] In the above formula, is the gear coordinate system S g The origin of the tool coordinate system O c To the origin of the gear coordinate system O g The radial vector is the tool center vector. The column vectors α, β, and γ are the tool coordinate system S c The basis vector x c ,y c and z c In the gear coordinate system S g The homogeneous coordinate expression in is expressed as:

[0067]

[0068] Knife Heart Vector In the gear coordinate system S g It can be expressed as:

[0069]

[0070] By giving the design parameters of the tooth blank, the radial vector of any point on the tooth surface can be obtained, that is, the spatial position of the cutting point in the gear coordinate system is known. In the tool coordinate system, the spatial position of any cutting point in the tool coordinate system can be determined. Therefore, it is only necessary to determine the coordinate transformation matrix from the tool coordinate system to the gear coordinate system. The knife center vector Its components along each coordinate axis (d x ,d y ,d z ) is the tool center coordinate.

[0071] From the mathematical model of the disc milling cutter, we can know that the coordinate transformation matrix The relative posture of the corresponding tool when machining along the instantaneous contact trace. During the machining process, the disc milling cutter moves around the tool spindle z c In order to meet the cutting conditions at all times, the tangent vector τ at the cutting point p1 is rotated at high speed. p1 Should coincide with the tangent vector of the cross-section curve at that point, and the normal vector n p1 It should be collinear and opposite to the normal vector of the tooth surface at that point.

[0072] Obviously, formula (1) and formula (2) are independent of each other. Solving the equations together can obtain the coordinate transformation matrix and the tool center coordinates. In the figure, γ is the tool coordinate system S c The basis vector z c The vector expression in the gear coordinate system is the tool axis vector. The tool center coordinates and the tool axis vector together constitute the tool location point. The same method can be extended to the calculation of the tool location point for large wheel machining to solve the corresponding tool center coordinates and tool axis vector.

[0073] According to the above method, the tool position points on the theoretical tooth surfaces on the left and right sides of the tooth groove, that is, the concave and convex tooth surfaces on the left and right sides of the tooth groove, can be obtained respectively. These tool position points are used as the boundary conditions of the tool path, and the machining tool path trajectory of the complete tooth groove can be generated through intermediate interpolation calculation.

[0074] As a preferred embodiment of the present invention, when the tool contacts and cuts the left and right theoretical tooth surfaces, the tool tip fillet vertex p m The points of contact with the bevel gear blank are respectively recorded as point A and point A0. Point A and point A0 are located on the same conical surface. In the gear coordinate system, when the tool contacts and cuts the theoretical tooth surface on the left, point p m The radial vector and normal vector of point A are equal; when the tool contacts and cuts the theoretical tooth surface on the right, point p m The radial vector and normal vector of A0 are equal.

[0075] Figure 4 It shows that when the cutting position is at point p, p0, the actual cutting depth in the tooth height direction is determined by the tool tip fillet vertex p m To prevent geometric interference between the tool profile and the tooth surface boundary during the intermediate tool path processing, the following constraints must be met: point p m It must coincide with point A and point A0, and in the gear coordinate system S g The radial vector and the normal vector are equal. Under this condition, point A and point A0 are located on the same conical surface, and the mathematical expression can be constructed as follows:

[0076]

[0077] In the above formula, R is the radius of the cone surface, and δ is the cone angle of the cone surface. When the disc milling cutter is in position I, the conditions that need to be met are:

[0078]

[0079] r A0 is the radius vector of point A0, r P3 is the radial vector of point pm, M OgOc (I) is the coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in position I.

[0080] By combining formula (6) and formula (7), we can obtain the cone radius corresponding to point p3 when the tool is in position Ι. It should be noted that when the tool moves along the instantaneous contact path, the cone angle t is different, and the cone radius obtained is different. When the disc milling cutter is in position ΙΙ, in order to make the cutting depth of this layer consistent, point A and point A0 should be located on the cone surface of the same radius. Therefore, the origin of the tool coordinate system at position ΙΙ should be along the vector τ p Move k times, so that:

[0081]

[0082] Substitute the relevant parameters obtained from posture II into formula (6), and calculate the parameter k by combining formula (6) and formula (8), thereby obtaining the tool center coordinates and tool axis vector of posture II at the same cutting depth.

[0083] After determining the tooth gap width according to the tooth blank design parameters, interpolate the equidistant points A and A0 to obtain point A. i , that is, the radial vector of the middle tooth groove cutting point According to formula (9), the relative pose matrix at pose i is solved as above: Get the tool center vector of the middle reciprocating tool path and the tool axis vector γ(i). By varying the parameter u angle, the instantaneous contact trajectory corresponding to the next tooth surface boundary is obtained. The tool cuts along this contact trajectory, layer by layer, from the outermost layer inward, until the entire tooth groove is machined. The parameter u angle refers to the angle parameter corresponding to the tangent direction of the tooth profile cross-section curve.

[0084]

[0085] Based on the above calculation process, the obtained concave and convex tooth surface boundaries and a series of tool position data of the complete tooth groove are imported into the 3D modeling software, and the results are as follows Figures 5 to 8 shown.

[0086] As a preferred embodiment of the present invention, it also includes interference detection. During the machining process, the minimum distance d from the bottom surface of the tool to the tooth profile of the bevel gear is calculated. p0 |, N is a constant, n p0 is the normal vector of any point on the tooth profile;

[0087] If the minimum spacing d is a positive value, it is determined that there is no interference between the tool and the tooth profile of the bevel gear; if the minimum spacing d is zero or a negative value, it is determined that there is interference between the tool and the tooth profile of the bevel gear, and the safety clearance between the tool and the tooth surface is increased by reducing the tool inclination angle α.

[0088] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or modification made by those skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A digital generating method for pure rolling contact bevel gears, characterized in that: include: The left and right theoretical tooth surfaces of the bevel gear tooth groove are used as the initial tool path boundaries. The left and right theoretical tooth surfaces are discretized in the same number of layers along the tooth profile cross-section curve direction. The discrete points on the same layer are located on the same conical surface of the bevel gear. Establish the tool coordinate system and the gear coordinate system respectively, and determine the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool is in contact with the theoretical tooth surface for cutting; According to the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system, a tool center vector and a tool axis vector constituting the tool position point are obtained, wherein the tool center vector is a radial vector from the origin of the tool coordinate system to the origin of the gear coordinate system in the gear coordinate system, and the tool axis vector is a vector expression of the tool axis vector of the tool coordinate system in the gear coordinate system; The tool position points on the left and right theoretical tooth surfaces are used as the boundary conditions of the tool path, and the machining tool path trajectory of the tooth groove is generated through intermediate interpolation calculation.

2. The digital generating method for pure rolling contact bevel gears according to claim 1, characterized in that: The homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system is: Where, is the tool coordinate system S g The origin of the tool coordinate system O c To the gear coordinate system S c Origin O g The radial vector is the tool center vector; the column vectors α, β, and γ are the tool coordinate system S c The basis vector x c 、y c and z c In the gear coordinate system S g Homogeneous coordinate expressions in .

3. The digital generating method for pure rolling contact bevel gears according to claim 1, characterized in that: The homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system when the tool contacts and cuts the theoretical tooth surface specifically includes: Get the tangent vector τ of the discrete point where the theoretical tooth surface contacts the tool when the tool contacts the theoretical tooth surface for cutting p , normal vector n p and path vector r p , and the tangent vector τ of the cutting point where the tool contacts the theoretical tooth surface p1 , normal vector τ p1 and path vector r p1 ; Solving a system of equations simultaneously Get the homogeneous coordinate transformation matrix from the tool coordinate system to the gear coordinate system 4. The digital generating method for pure rolling contact bevel gears according to claim 1, characterized in that: When the tool contacts and cuts the left and right theoretical tooth surfaces, the tool tip fillet vertex p m The points of contact with the bevel gear blank are respectively recorded as point A and point A0. Point A and point A0 are located on the same conical surface. In the gear coordinate system, when the tool contacts and cuts the theoretical tooth surface on the left, point p m The radial vector and normal vector of point A are equal; when the tool contacts and cuts the theoretical tooth surface on the right, point p m The radial vector and normal vector of A0 are equal.

5. The digital generating method for pure rolling contact bevel gears according to claim 1, characterized in that: A disc milling cutter is used as a machining tool, the bottom cutting edge of the disc milling cutter is used to machine the theoretical tooth surface on the left side of the bevel gear tooth groove, and the side cutting edge of the disc milling cutter is used to machine the theoretical tooth surface on the right side of the bevel gear tooth groove.

6. The digital generating method for pure rolling contact bevel gears according to claim 1, characterized in that: It also includes interference detection. During the machining process, the minimum distance d = |N·n between the bottom surface of the tool and the tooth profile of the bevel gear is calculated. p0 |, N is a constant, n p0 is the normal vector of any point on the tooth profile; If the minimum spacing d is a positive value, it is determined that there is no interference between the tool and the tooth profile of the bevel gear; if the minimum spacing d is zero or a negative value, it is determined that there is interference between the tool and the tooth profile of the bevel gear, and the safety clearance between the tool and the tooth surface is increased by reducing the tool inclination angle.

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