Spiral bevel gear universal tool five-axis machining tool path planning method based on conjugate characteristic line

Abstract

The invention discloses a spiral bevel gear general tool five-axis machining tool path planning method based on conjugate characteristic lines, which comprises the steps of designing a conjugate characteristic line calculation and solution method of a spiral bevel gear tooth surface, and designing a tool path planning method taking the maximum residual height of adjacent tool paths as an optimization target. And designing a strategy for optimizing the tool path by controlling the maximum residual height according to the distribution condition of conjugate characteristic lines and geometric structure characteristics. According to position information of tooth surface points of the spiral bevel gear, the tooth surface points are divided and dispersed, and a tooth surface machining conjugate characteristic line is obtained through calculation according to information such as coordinate systems of a cutter and the gear. And the processing tool path planning based on the conjugate characteristic line is optimized by taking the residual height as a target, so that a more efficient and higher-precision general tool five-axis processing tool path planning method is established. The method is high in innovativeness, and the tooth surface of the spiral bevel gear can be machined more efficiently according to the requirement for the meshing performance of the gear.

Description

Technical Field

[0001] This invention relates to the field of spiral bevel gear machining technology, and proposes a five-axis machining toolpath planning method for spiral bevel gears based on conjugate feature lines. Background Technology

[0002] Spiral bevel gears are a general term for bevel gears with curved pitch lines, encompassing commonly referred to as arc bevel gears, arc hypoid gears, cycloidal bevel gears, and cycloidal hypoid gears. Spiral bevel gears can transmit motion and power between intersecting or staggered shafts. They are characterized by smooth transmission, high load-bearing capacity, and good meshing performance, and are therefore widely used as key transmission components in large-scale heavy-duty equipment in national pillar industries such as aero-engines, helicopter reducers, large ships, vehicle rear axle transmission systems, and mining, metallurgy, building materials, and energy.

[0003] The common machining method for spiral bevel gears is to use dedicated machine tools and cutting tools. This dedicated machining method is suitable for mass production and has the advantage of low average cost per unit. However, the disadvantages of dedicated machining include numerous supporting equipment, complex cutting tools, high initial investment in machine tools and daily consumption costs of dedicated cutting tools, and long preparation cycles for these tools. With the rapid iteration requirements in product development and the trend towards integrated components in large and complex equipment, dedicated machining based on cutting tools has become increasingly inadequate and fails to meet market demands for machining technology. In contrast, using machining centers and general-purpose cutting tools to machine gears offers high flexibility, eliminates the need for lengthy preparation cycles for dedicated cutting tools, significantly shortens the gear development cycle, and allows for the machining of large and complex gears. However, existing main machining methods struggle with NURBS surface fitting for theoretical tooth surface modeling of complex tooth surfaces such as spiral bevel gears. Current CAM systems treat complex tooth surfaces as ordinary complex surfaces for toolpath planning, losing information such as surface curvature, leading to suboptimal machining accuracy. Furthermore, for machining complex modified tooth surfaces like spiral bevel gears with varying performance requirements, high-precision machining should consider the modified geometry of the tooth surface. Toolpath planning based on the geometric information of the conjugate feature lines of the tooth surface takes into account the inherent geometric characteristics of the complex tooth surface, better improving machining accuracy and efficiency.

[0004] Publication No. CN 108568567 A discloses "A Machining Method for Spiral Bevel Gears Based on a General-Purpose Four-Axis CNC Machine Tool and a Ball End Mill." This patent utilizes a general-purpose ball end mill to machine spiral bevel gears, achieving a layered cutting path from tooth tip to tooth root and back to tooth tip through tooth surface calculation, modeling, and toolpath creation. Publication No. CN 117548744 A discloses "A Machining Method for Line Contact Gradient Spiral Bevel Gear Pairs." This patent designs a method based on the principle of conjugate tooth surfaces, using a forming method for the large gear and a generating method for the small gear with the cutter head cutting surface as the production surface. By establishing meshing and cutting models, it achieves an efficient method for machining line contact gradient spiral bevel gear pairs. Publication No. CN 120115763 A discloses "A Machining Method for Spiral Bevel Gears Based on Error Compensation." This patent designs a method where, after machining a predetermined number of spiral bevel gears, the spacing error is measured online. If the error exceeds the tolerance, the deformation is detected to calculate the tool displacement compensation value, and the machine tool is adjusted to improve accuracy. None of the above patents consider the inherent geometric features of the conjugate feature lines on the tooth surface, making it difficult to improve their machining accuracy and efficiency. For a given machining accuracy requirement, the machining method proposed in this invention can significantly improve machining efficiency compared to existing methods. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing spiral bevel gear machining methods, such as high cost of dedicated cutting tools and machine tools, low machining efficiency, and difficulty in controlling tooth surface accuracy. This invention provides a new, efficient, and high-precision machining method for spiral bevel gear tooth surface finishing.

[0006] To achieve the above objectives, the technical solution adopted in this invention is as follows: Based on the positional information of the tooth surface points of the spiral bevel gear, the tooth surface points are divided and discretized. After calculation based on information such as the coordinate system of the tool and the gear, the conjugate feature lines for tooth surface machining are obtained. The machining toolpath planning based on the conjugate feature lines is optimized with the residual height as the target, thereby realizing a more efficient and higher-precision general-purpose five-axis machining toolpath planning method.

[0007] This invention proposes a five-axis toolpath planning method for general-purpose spiral bevel gear machining based on conjugate feature lines, comprising the following steps: Step A: Toolpath planning based on machining conjugate feature lines; Step B: Calculation of residual height on tooth surface; Step C: Optimize the toolpath with the goal of controlling the residual height; Step D: Calculation of tool position points for general-purpose tool machining.

[0008] Through the above steps, the finishing of the tooth surface of a spiral bevel gear based on conjugate feature lines can be achieved. This method is highly innovative and can more efficiently machine the tooth surface of a spiral bevel gear according to the requirements of gear meshing performance. This invention is mainly illustrated through several embodiments.

[0009] The "tool path planning based on machining conjugate feature lines" mentioned in step A is performed as follows: First, take the point where the tool is exactly tangent to the gear workpiece as the starting point. In the workpiece coordinate system, let the radial vector of the tooth surface be r. w =r w ( Z , R Based on the meshing equation and by establishing a mathematical model for gear machining with a universal cutting tool, the position information of the tooth surface point at any given time can be solved, including its r( s, θ , f The tooth surface and transition fillet portion are discretized using Newton's iterative method until a complete set of working tooth surface points is obtained. The tooth surface points obtained iteratively are based on... Z , R Inverse coordinate calculation of the tooth surface ( s, θ , f The coordinates of the coordinates are obtained through calculation. f Line, here f The line is the machining conjugate feature line of the tooth surface, that is, the path of the tool when cutting the spiral bevel gear.

[0010] The calculation of "residual tooth surface height" in step B is as follows: The residual height is the maximum normal deviation between the machined residual tooth surface and the theoretical tooth surface after machining along the planned toolpath, i.e., the height of the protrusion formed by the material residue not completely removed by the cutting edge between adjacent tool paths. This is based on known machining conjugate characteristics. f The initial machining direction and tool pose can be determined by the line. However, the tool path distance needs to be determined through optimization calculations, and its key constraint is the machining residual height (i.e., surface roughness). Based on the residual height accuracy requirements specified in the national standard, an optimization model is established. Under the premise of satisfying this constraint, the optimal tool path distance is solved, thereby planning the tool machining path based on the conjugate feature lines.

[0011] Step C, "optimizing the toolpath with the goal of controlling the residual height," is implemented as follows: Based on the residual height calculation formula, the toolpath planning objective is primarily residual height control, while also considering machining efficiency optimization. This is achieved by using a refined toolpath planning method to ensure that conjugate feature lines complete tooth surface machining with the fewest possible passes, avoiding redundant cutting paths. First, it is necessary to clarify the changes in residual height on the tooth surface as a function of various values. i and f How the value discretization changes is clarified, and the residual height on the tooth surface is determined as a function of the value. i and f To investigate the pattern of how the discrete values ​​change, an encrypted optimization method is proposed. This algorithm is suitable when the initial toolpath spacing is approximately equal to the toolpath spacing that meets the residual height requirement. However, if some toolpaths do not meet the residual height requirement, then encrypted toolpath modifications are necessary.

[0012] The "tool position point calculation for general tool machining" in step D is performed as follows: After deriving the constant feed and unequal feed step size planning algorithms, to facilitate subsequent simulation analysis, the planned coordinate points of the spiral bevel gear tooth surface need to be converted into tool position points during machining. In this design, the tool tip is selected as the tool center point. After conversion, the data is imported into CAM software for toolpath analysis. First, the positional relationship between the tooth surface coordinate points and the tool tip center is established. Then, based on the tooth surface point information, the positional information between the tool position point and the tool axis is established.

[0013] This invention has the following innovative features: 1. This invention is not directed at a specific machining method for a particular spiral bevel gear, but rather at a highly efficient, universal five-axis machining toolpath planning method for finishing gear tooth surfaces with conjugate characteristics and instantaneous contact lines, based on gear structure and meshing relationships. Compared to known machining methods, this invention provides a novel toolpath planning approach during the machining process, which can significantly improve machining efficiency.

[0014] 2. This invention has low requirements for cutting tools. Based on the gear to be machined, this design uses general-purpose cutting tools and a five-axis machining center for machining. It proposes a machining toolpath planning method for general-purpose cutting tools in machining centers, which is different from the traditional gear-specific cutting tool machining method.

[0015] 3. This invention proposes a refined toolpath optimization method for optimizing residual height. This method plans the toolpath, reduces the number of tool passes, and improves machining efficiency, providing a reference for residual height optimization methods in other curved surface machining processes.

[0016] 4. This invention is also applicable to the machining of complex modified tooth surfaces. For the finishing of modified tooth surfaces such as tooth surface normal deviation, toolpath planning based on conjugate feature lines is achieved by adjusting the tool position point using tooth surface information.

[0017] In summary, this five-axis machining toolpath planning method for spiral bevel gears based on conjugate feature lines, utilizing general-purpose cutting tools, can improve gear machining efficiency and provides a new solution for the machining and manufacturing of high-performance gears. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the tooth surface division for calculating tooth surface points according to the present invention.

[0019] Figure 2This is a schematic diagram of the instantaneous contact line during machining on the concave and convex surfaces of the large gear, as described in this invention.

[0020] Figure 3 This is a schematic diagram of the instantaneous contact line during machining on the concave and convex surfaces of the pinion, as described in this invention.

[0021] Figure 4 This is a schematic diagram of the processing of conjugate feature lines according to the present invention.

[0022] Figure 5 This is a schematic diagram of the tool used in this invention cutting a gear.

[0023] Figure 6 This is a schematic diagram illustrating the calculation of the residual height of the present invention.

[0024] Figure 7 This is a schematic diagram of the instantaneous contact line and residual height of the large gear tooth surface in the equal feed distance planning of this invention.

[0025] Figure 8 This is a schematic diagram of the instantaneous contact line and residual height during machining of the small gear tooth surface with equal tool travel distance according to the present invention.

[0026] Figure 9 The large concave surface of the present invention A schematic diagram showing the relationship between the value and the residual height.

[0027] Figure 10 The large wheel convex surface of this invention A schematic diagram showing the relationship between the value and the residual height.

[0028] Figure 11 The concave surface of the small wheel of this invention A schematic diagram showing the relationship between the value and the residual height.

[0029] Figure 12 The small wheel convex surface of the present invention A schematic diagram showing the relationship between the value and the residual height.

[0030] Figure 13 This is a schematic diagram of the encryption method optimization process of the present invention.

[0031] Figure 14 This is a schematic diagram showing the effects before and after planning the large gear tooth surface densification optimization method of the present invention.

[0032] Figure 15 This is a schematic diagram showing the effect before and after planning the optimization method for refining the small gear tooth surface according to the present invention.

[0033] Figure 16 This is a schematic diagram illustrating the calculation of the ball end mill cutting tool position in this invention.

[0034] Figure 17 This is a schematic diagram illustrating the calculation of the flat-bottomed end mill position point according to the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be further described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0036] like Figure 1 to Figure 17 As shown, this embodiment of the invention provides a five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines, comprising the following steps: The "tool path planning based on machining conjugate feature lines" mentioned in step A is performed as follows: First, take the point where the tool is exactly tangent to the gear workpiece as the starting point. In the workpiece coordinate system, let the radial vector of the tooth surface be r. w =r w ( s, θ , f )=( x w , y w , z w According to the meshing equation, we can obtain: (1) in, Z These are the axial projection coordinates of the tooth surface points. R radial projection coordinates of tooth surface points x w , y w , z w Let these be the coordinates of the tooth surface points in the workpiece coordinate system. Here is the equation for the conjugate meshing of the cutting tool and the tooth surface, where s This is the parameter for the blade arc length. i These are the parameters for the tool's rotational motion. f These are the tool generating motion parameters.

[0037] By establishing a mathematical model for gear machining with a universal cutting tool, the position information of points on the tooth surface at any given time can be solved, including their r w ( s, θ , f ) and the Dharma Arrow.

[0038] The tooth surface is discretized using Newton's iterative method: First, the working tooth surface is divided into grids along the tooth width and tooth height directions. The midpoint of the grid is used as the initial value for iteration in the projection plane. The tooth surface is then obtained through coordinate transformation. Z , R Coordinates. For example... Figure 1As shown, the tooth surface is discretized into m×n points, where m is the discrete value in the tooth height direction and n is the discrete value in the tooth width direction. The working tooth surface is discretized into m1×n points. The initial values ​​are continuously updated through bidirectional iteration, and the validity of the projection area of ​​the points is verified to finally obtain the complete set of points on the working tooth surface. The transition fillet portion is discretized into m2×n points, which, after being merged with the working tooth surface, form the complete (m... 1+ The tooth surface points obtained through iteration are based on m2)×n tooth surfaces. Z , R Inverse coordinate calculation of the tooth surface ( s ,θ , f Coordinate points in the form of () are obtained by combining the conjugate meshing equation of the tool and the tooth surface with coordinate transformation. f The line is here. f The line is the machining conjugate feature line of the tooth surface, that is, the path of the tool when cutting the spiral bevel gear. f Different values ​​represent different conjugate characteristic lines; for a given conjugate characteristic line... i Different values ​​represent different points on the conjugate characteristic line. s Different values ​​represent different positions of the contact point between the tool and the tooth surface on the tool.

[0039] like Figure 2 and Figure 3 The figures show the machining conjugate features of the large and small gears of a spiral bevel gear. f Line. Among them, the conjugate characteristic line of the combined equation (1) and i and f The diagram illustrating the generation relationship is as follows: Figure 4 As shown, where f i and f i+1 This represents two adjacent conjugate characteristic lines. i The position of the tool is on a conjugate feature line.

[0040] The calculation of the residual height of the tooth surface in step B is performed as follows: based on known machining conjugate features. f The initial machining direction and tool pose (including tool position coordinates and tool axis direction) can be determined by the lines. However, the tool path distance needs to be determined by calculation, and its key constraint is the machining residual height (i.e., surface roughness). Based on the residual height accuracy requirements specified in national standards, the machining residual height of the tooth surface is calculated. Under the premise of satisfying this constraint, the optimal tool path distance is solved, thereby planning the tool machining path based on conjugate feature lines. First, it is necessary to further determine each pair of machining conjugate feature lines based on the previously obtained tooth surface geometry information. f The formula for calculating the residual height between lines is as follows: (1) When the tool is cutting the gear, the conjugate feature is machined. fi Tool position vectors and machining conjugate features at various points online f i+1 The tool position vectors at each point on the line intersect, and the distance from the intersection point to the tooth surface is the residual height. (2) Based on the above intersection conditions, the processing conjugate characteristics can be determined. f i+1 The tooth surface information of each point on the line is obtained, and the position vector of each intersection point is calculated. The position vector of the intersection point can be determined by equation (2). (2) In the formula, p0 is f i The position vector of the point on the upper tooth surface; l 0 is f i The position vector parameter of the upper tool; τ0 is f i The position vector direction of the upper tool; p1 is f i+1 The position vector of the point on the upper tooth surface; l 1 is f i+1 The position vector parameter of the upper tool; τ1 is f i+1 The position vector direction of the upper tool.

[0041] (3) After the intersection point position vector is determined, the intersection point can be projected onto the tooth surface to obtain the projection point on the tooth surface. Let the projection point be O and the intersection point be C, and the residual height value can be obtained. .

[0042] The cutting tool cuts the gear along the toolpath, such as Figure 5 As shown, the residual height is as follows Figure 6 As shown. Where T1 and T2 are the tool axis directions, n1 and n2 are the normal directions of the tool axis, and h is the residual height after machining. Df It is the feed step size for tool machining.

[0043] Step C, "optimizing the toolpath with the goal of controlling the residual height," is implemented as follows: Based on the machining conjugate feature lines on the tooth surface of the spiral bevel gear, each pair of machining conjugate features... f The spacing between the lines is considered as the tool feed distance. Depending on the parameters of different gears and cutting tools, the value of the constant tool feed distance needs to be set by adjusting the generating angle of the conjugate tooth surfaces. As a specific example of the implementation of the method of this invention, when the tool feed distance of the large gear is set to 0.028 rad and the tool feed distance of the small gear is set to 0.006 rad, all residual heights on the tooth surface can be guaranteed to be below 1 μm, meeting the surface roughness requirements for tooth surface machining. Figure 7 and Figure 8 The machining conjugate features on the tooth surface after equal feed path planning are shown respectively. f Line graph and residual height graph on tooth surface (where sh is the residual height value in μm).

[0044] like Figure 9 to Figure 12 The figure shows the distribution of residual height values ​​on the tooth surfaces of the large and small gears. The horizontal axis represents different values. i The vertical axis represents the residual height value. On the concave and convex surfaces of the large gear and the convex surface of the small gear, each of the two machining conjugate features... f The residual height between lines will change as i The value decreases as it increases, following a decreasing function. For the concave surface of the pinion, each pair of machining conjugate features... f The residual height between lines will change as i The value increases with increasing, forming an increasing function. This clarifies that the residual height on the tooth surface increases with... i Value and f Based on the discrete variation patterns and distribution of the values, a method for refining toolpath planning is proposed. This algorithm is suitable when the initial toolpath spacing already meets the residual height requirement. However, due to the uneven distribution of feature lines, some sections may not meet the residual height requirement. Therefore, additional conjugate feature lines need to be inserted in areas with sparse conjugate feature line distribution to refine and optimize the toolpath. Figure 13 This is a flowchart of the method. Figure 14 Figures 1 and 5 show the results of path optimization for the concave and convex surfaces of the large wheel using an adaptive encryption optimization method. The upper part of the figures shows the conjugate features of the concave and convex tooth surfaces of the large wheel before optimization. f The lower part of the line graph shows the conjugate features of the optimized large wheel's concave and convex tooth surfaces. f Line chart.

[0045] The "tool position point calculation for general tool machining" in step D is performed as follows: After the toolpath planning is completed, to facilitate subsequent simulation analysis, the planned coordinate points of the spiral bevel gear tooth surface need to be converted into tool position points during machining. In this design, the tool tip point is selected as the tool center point. After conversion, the data is imported into CAM software for toolpath analysis. This invention relates to two types of end mills: ball end mills and flat end mills. First, for ball end mills, the positional relationship between the tooth surface coordinate points and the tool tip center during machining is established, such as... Figure 16 The diagram shows the calculation of the tool pose and tool position point in ball end milling. The tooth surface coordinate point is set as point O, and the position vector of this point is... The position vector of the blade tip center is obtained after transformation. .

[0046] (3) In the formula, r The radius of a general-purpose cutting tool; s It should be 1 / 2 to 1 / 5 of the selected blade tip arc length; r For the direction of the tool radius, select the normal vector n when the tool is tangent to the tooth surface; s T represents the direction of the tool generatrix.

[0047] Secondly, regarding the tool position calculation for flat end mills, the side-edge milling method for flat end mills is adopted, according to... Figure 17 The solution formula for the cutting tool position of the side edge of a flat end mill is as follows: (4) In the formula, n P Let i be the normal vector of the point of contact between the tooth surface and the cutting tool. m The vector along the tool axis. l It is the distance r between the cutting contact point and the tool end face. P and r CL They are points P and C respectively. L In spatial positioning, the distance between point A and the adjacent tooth surface should be ensured during machining. d Take a safe value.

[0048] It should be noted that the terms "comprising," "invention," or any other variations used herein are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0049] Although the invention has been described with reference to numerous embodiments, it should be understood that the invention is not limited to its specific forms. Various changes, modifications, substitutions, and alterations can be made to these embodiments by those skilled in the art without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A five-axis toolpath planning method for general-purpose spiral bevel gear machining based on conjugate feature lines, characterized in that: The steps include the following: Step A: Toolpath planning based on machining conjugate feature lines; Taking the moment when the cutting tool is tangent to the gear workpiece as the starting point, in the workpiece coordinate system, let the radial vector of the tooth surface be r. w =r w ( Z , R Based on the meshing equation and a mathematical model for gear machining using a general-purpose tool, the position information of the tooth surface points at any given time is solved. The Newton-Raphson iteration method is used to discretize the tooth surface and transition fillet portions until a complete set of working tooth surface points is finally obtained. The tooth surface points obtained through iteration are based on... Z , R Inverse coordinate calculation of the tooth surface ( s, θ , φ The coordinates of the coordinates are obtained through calculation. φ The line is the path taken by the cutting tool when cutting the spiral bevel gear. Step B: Calculation of residual height on tooth surface; The residual height is the maximum normal deviation between the machined residual tooth surface and the theoretical tooth surface after machining along the planned toolpath, that is, the height of the protrusion formed by the material residue not completely removed by the cutting edge between adjacent tool paths; Based on processing conjugation characteristics φ The initial machining direction and tool pose are determined by the line; the tool path distance needs to be determined through optimization calculation, with the key constraint being the machining residual height; an optimization model is established to solve for the optimal tool path distance under the premise of satisfying the constraints, and to plan the tool machining path based on the conjugate feature line; Step C: Optimize the toolpath with the goal of controlling the residual height; Based on the residual height calculation formula, the method of planning the encrypted toolpath enables the conjugate feature lines to complete the tooth surface machining with the fewest tool passes, thus avoiding redundant cutting paths. Step D: Calculation of tool position points for general-purpose tooling; The planned coordinate points of the spiral bevel gear tooth surface are converted into tool position points during machining, and the tool tip is selected as the tool center point. After the conversion, the points are imported into CAM software for toolpath analysis. The positional relationship between the tooth surface coordinate points and the tool tip center is established during machining, and then the positional information between the tool position point and the tool axis is established based on the tooth surface point information.

2. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 1, characterized in that: In step A, let the radial vector of the tooth surface be r. w =r w ( s, θ , φ )=( x w , y w , z w According to the meshing equation, we get: (1) in, Z These are the axial projection coordinates of the tooth surface points. R radial projection coordinates of tooth surface points x w , y w , z w Let these be the coordinates of the tooth surface points in the workpiece coordinate system. Here is the equation for the conjugate meshing of the cutting tool and the tooth surface, where, s This is the parameter for the blade arc length. θ These are the parameters for the tool's rotational motion. φ These are the tool generating motion parameters.

3. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 1 or 2, characterized in that: The tooth surface is discretized using Newton's iterative method: the working tooth surface is divided into grids along the tooth width and tooth height directions, and the midpoint of the grid is used as the initial value for iteration in the projection plane. The tooth surface is then obtained through coordinate transformation. Z , R Coordinates; the tooth surface is discretized into m×n points, where m is the discrete value in the tooth height direction and n is the discrete value in the tooth width direction; the working tooth surface is discretized into m1×n points, and the initial values ​​are continuously updated through bidirectional iteration, and the validity of the projection area of ​​the points is verified, so as to finally obtain the complete working tooth surface point set.

4. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 3, characterized in that: The transition fillet portion is discretized into m²×n points, which, after merging with the working tooth surface, form a complete (m²×n) point. 1+ The tooth surface points obtained through iteration are based on m2)×n tooth surfaces. Z , R Inverse coordinate calculation of the tooth surface ( s,θ , φ Coordinate points in the form of () are obtained by combining the conjugate meshing equation of the tool and the tooth surface with coordinate transformation. φ Wire, φ Different values ​​represent different conjugate characteristic lines; for a given conjugate characteristic line... θ Different values ​​represent different points on the conjugate characteristic line. s Different values ​​represent different positions of the contact point between the tool and the tooth surface on the tool.

5. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 1, characterized in that: In step B, each pair of processing conjugate features is determined. φ The formula for calculating the residual height between lines is as follows: (1) When the tool is cutting the gear, the conjugate feature is machined. φ i Tool position vectors and machining conjugate features at various points online φ i+1 The tool position vectors at each point on the line intersect, and the distance from the intersection point to the tooth surface is the residual height. (2) Based on processing conjugate features φ i+1 The tooth surface information of each point on the line is used to calculate the position vector of each intersection point, where the position vector of the intersection point is determined by equation (2); (2) In the formula, p0 is φ i The position vector of the point on the upper tooth surface; l 0 is φ i The position vector parameter of the upper tool; τ0 is φ i The position vector direction of the upper tool; p1 is φ i+1 The position vector of the point on the upper tooth surface; l 1 is φ i+1 The position vector parameter of the upper tool; τ1 is φ i+1 The position vector direction of the upper tool; (3) After the intersection point position vector is determined, the intersection point is projected onto the tooth surface to obtain the projection point on the tooth surface. Let the projection point be O and the intersection point be C, and the residual height value is obtained. .

6. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 1, characterized in that: In step C, based on the machining conjugate feature lines on the tooth surface of the spiral bevel gear, each pair of machining conjugate feature lines is... φ The interval between lines is considered as the feed distance; depending on the different parameters of the gears and tools, the feed distance value needs to be set by adjusting the generating angle of the conjugate tooth surface.

7. A five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines, as described in claim 1 or 6, characterized in that: On the concave and convex surfaces of the large gear and the convex surface of the small gear, every two machining conjugate features φ The residual height between lines will change as θ The value decreases as it increases, following a decreasing function. For the concave surface of the pinion, each pair of machining conjugate features... φ The residual height between lines will change as θ It increases with the increase of its value, and is an increasing function.

8. A five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines, as described in claim 1 or 6, characterized in that: The encrypted toolpath planning method is applicable when the initial toolpath setting already meets the residual height requirement. Due to the uneven distribution of feature lines, some parts do not meet the residual height requirement. Therefore, it is necessary to insert additional conjugate feature lines in areas where the conjugate feature lines are sparsely distributed to optimize the encrypted part of the toolpath.

9. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 1, characterized in that: Step D further includes a ball end mill. For the ball end mill, the positional relationship between the tooth surface coordinate point and the tip center is first established during machining. The tooth surface coordinate point is set as point O, and the position vector of this point is... The position vector of the blade tip center is obtained after transformation. ; (3) In the formula, r The radius of a general-purpose cutting tool; s It should be 1 / 2 to 1 / 5 of the selected blade tip arc length; r For the direction of the tool radius, select the normal vector n when the tool is tangent to the tooth surface; s T represents the direction of the tool generatrix.

10. The five-axis machining toolpath planning method for helical bevel gears based on conjugate feature lines according to claim 1, characterized in that: Step D further includes a flat-end mill. For the tool position calculation of the flat-end mill, a side-edge milling method is used. The formula for solving the side-edge milling tool position of the flat-end mill is: (4) In the formula, n P Let i be the normal vector of the point of contact between the tooth surface and the cutting tool. m The vector along the tool axis. l It is the distance r between the cutting contact point and the tool end face. P and r CL They are points P and C respectively. L In spatial positioning, the distance between point A and the adjacent tooth surface should be ensured during machining. d Take a safe value.

Images