Digital design method and system for hypoid gear

Abstract

The application discloses a hypoid gear digital design method and system, and is applied to the technical field of gear design and manufacturing. The method comprises the following steps: according to initial design parameters, solving the gear blank parameters of a hypoid gear pair, the forming method machining parameters of a large gear and the cutter tilt method machining parameters of a small gear; based on gear machining principles and space meshing principles, establishing the large gear tooth surface equation and the small gear tooth surface equation, determining the theoretical boundary of the rotary projection tooth surface, and dividing discrete grid nodes; constructing an objective function for iterative solving, obtaining tooth surface discrete point cloud data; constructing a cubic spline curve, reconstructing the tooth surface spline surface; establishing a gear blank solid model, cutting the gear blank by using the reconstructed tooth surface through Boolean operation, and generating a hypoid gear three-dimensional entity model. The application overcomes the disadvantages of the traditional design method, such as design and modeling simulation fragmentation, low efficiency of artificial optimization iteration, and greatly improves the design efficiency through full-automatic modeling process and fast design optimization response.

Description

Technical Field

[0001] This invention relates to the field of gear design and manufacturing technology, and more specifically to a digital design method and system for quasi-hyperboloid gears. Background Technology

[0002] Hypoid gears, as core components of spatial interlaced shaft drives, are widely used in fields requiring high spatial structural compactness and transmission smoothness, such as automotive drive axles and aerospace main reducers, due to their high overlap ratio, strong load-bearing capacity, smooth transmission, low noise, and long service life. However, the complex geometry of quasi-hypoid gears means that most mainstream multibody dynamics simulation software lacks parametric modeling capabilities for such gears, failing to support automatic generation of 3D models by users directly inputting or modifying design parameters. This leads to a disconnect between the design and verification stages: designers typically need to first use external tools to calculate the blank and machining parameters of the quasi-hypoid gear, use third-party mathematical calculation software to solve for discrete tooth surface data, manually build a 3D model, and finally import it into simulation software for subsequent parameter verification.

[0003] For example, invention patent CN108241764A discloses a specific process for modeling quasi-hypoid gears. The process involves calculating tooth surface point cloud data in MATLAB software and then importing it into Pro / E software to complete the 3D modeling of the gear. This method is the main method for modeling quasi-hypoid gears; however, if it is necessary to optimize gear parameters or machining parameters, the entire code calculation and model building process must be repeated.

[0004] This non-integrated process makes design optimization extremely difficult. Every time design parameters need adjustment, designers must recalculate the gear blank and machining parameters, resolve the tooth surface data, rebuild the model, and re-import the data. This cumbersome data processing not only increases the workload of designers but also significantly reduces the efficiency of the design and development iteration of hypoid gears. Therefore, providing a digital design method and system for hypoid gears is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a digital design method and system for quasi-hyperboloid gears, which solves the problems of disconnect between the design and simulation verification stages, cumbersome parameter design and model building processes, and low design optimization efficiency in existing methods.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A digital design method for quasi-hyperboloid gears includes the following steps:

[0008] S1. Based on the initial design parameters, solve for the blank parameters of the hypoid gear pair; based on the blank parameters, solve for the machining parameters of the large gear forming method and the small gear cutting tool inclination method respectively.

[0009] S2. Based on the gear machining principle and spatial meshing principle, establish the gear tooth surface equation and the pinion tooth surface equation according to the machining parameters; determine the theoretical boundary of the rotating projection tooth surface according to the gear blank parameters, and divide the discrete mesh nodes within the theoretical boundary of the rotating projection tooth surface.

[0010] S3. Construct a nonlinear least squares objective function based on the tooth surface equation and discrete grid nodes, and call the nonlinear optimization function to iteratively solve the nonlinear least squares objective function to obtain discrete point cloud data of the tooth surface;

[0011] S4. Construct cubic spline curves using discrete point cloud data of the tooth surface to reconstruct the tooth surface spline surface; establish a solid model of the tooth blank based on the tooth blank parameters, and use Boolean operations to trim the tooth blank using the reconstructed tooth surface to generate a quasi-hyperboloid gear 3D solid model.

[0012] S5. Based on the quasi-hyperboloid gear 3D solid model, create a rotary pair, apply load torque, and define solid contact pairs to complete the construction of the multibody dynamics simulation model.

[0013] Optionally, the specific steps for solving the blank parameters of the quasi-hypoid gear pair in S1 are as follows: Based on the initial design parameters, an iterative model is established according to the geometric relationship between the pitch cone parameters, and the offset angle within the small gear shaft section is corrected. and increase the coefficient After determining the pitch cone geometry parameters, and when the convergence condition of the iterative model is met, the distance parameter among the pitch cone geometry parameters is determined, and the outer cone distance of the large wheel is determined based on the pitch cone geometry parameters. Working tooth height at the midpoint of the large wheel and top gap Select the high gear tooth height coefficient With tooth tip height coefficient The full tooth height at the midpoint of the large wheel was calculated. Highest point of the gear teeth at the midpoint and the height of the tooth root at the midpoint of the large wheel Calculate the tooth tip angle based on the tooth height shrinkage method. With tooth root angle This allows for the determination of the complete gear blank parameters for the large wheel;

[0014] Calculate the process pitch cone offset angle based on the pitch cone geometry parameters and the large gear blank parameters. and the offset angle of the large wheel corresponding to the root cone of the small wheel. Thus, the cone angle of the small wheel surface is determined. Small wheel root cone angle pinion tooth tip angle and pinion tooth root angle Based on the pinion gear blank parameters, calculate the distance from the pinion pitch point to the intersection point. Distance from the small wheel crown to the intersection point The distance from the small wheel crown to the intersection point This allows us to obtain the complete gear blank parameters for the pinion.

[0015] Optionally, in S1, the specific steps for solving the machining parameters of the large wheel forming method and the small wheel cutter tilting method are as follows: Calculate the process pitch cone parameters based on the gear cutting principle; calculate the pitch cone distance of the large wheel production wheel based on the process pitch cone parameters and the large wheel blank parameters. relative to the tilt angle of the cutter head This allows for the determination of the machining parameters for the large wheel forming method;

[0016] Determine the normal curvature of the pinion along the tooth height direction based on the process cone parameters. Contact line direction angle of the process cone and cutter head radius Then, the parameters of the pinion gear cutting cone are calculated;

[0017] An iterative model is established based on the pitch cone parameters of the small gear cutting teeth. During the initial value calculation, the helix angle is set. Equal to the helix angle of the small gear cutting pitch cone The pitch cone distance is obtained. and pitch cone angle Initial values ​​are used to iteratively calculate the parameters of the pitch cone of the production wheel:

[0018] ;

[0019] In the formula, The third-order correction value represents the contact region; the convergence criterion for iterative calculation is:

[0020] ;

[0021] In the formula, Indicates the mounting angle of the small wheel blank; The target value is expressed by the following formula:

[0022] ;

[0023] In the formula, This indicates the correction value for the pitch cone angle of the gear train. This represents the correction value for the wheel blank mounting angle. Once the convergence condition is met, the machining parameters for the small wheel tool tilting method are determined based on the machining principle of the tool tilting method and the process cone parameters.

[0024] Optionally, the equation for the large gear tooth surface in S2 is established by: transforming the large gear tool machining surface using a coordinate transformation matrix. and the transition fillet surface of the large wheel tool From the tool coordinate system Transform to workpiece coordinate system The transformation formula is:

[0025] ;

[0026] In the formula, Represents the tool head coordinate system To machine tool coordinate system The transformation matrix, Representing the machine tool coordinate system To the workpiece coordinate system The transformation matrix, Indicates the cutting angle of the cutter head; This represents the distance from the tool tip plane to the cutting point. This indicates the angle between the cutting point and the tool tip plane. , The workpiece coordinate system The machining surface of the large wheel tool and the transition fillet surface of the large wheel tool.

[0027] Optionally, in S2, establishing the pinion tooth surface equation specifically involves using a coordinate transformation matrix to transform the tool equation... From the tool coordinate system Transform to machine tool coordinate system The transformation formula is:

[0028] ;

[0029] In the formula, , , , Represents the transition coordinate matrix. Indicates the angle of the tool tilting table. The transformed tool equation;

[0030] In the machine tool coordinate system Establish the spatial meshing equation:

[0031] ;

[0032] In the formula, This represents the normal vector of the tool working surface within the machine tool coordinate system. Represents the relative velocity within the machine tool coordinate system; the tool equations satisfying the meshing conditions are transferred from the machine tool coordinate system. Transform to workpiece coordinate system The equation for the pinion tooth surface is obtained, and the conversion formula is:

[0033] ;

[0034] In the formula, , , Represents the transition coordinate transformation matrix. The equation for the pinion tooth surface is given.

[0035] Optionally, in S2, the theoretical boundary of the rotating projection tooth surface is determined based on the tooth blank parameters, and the discrete mesh nodes are divided within the theoretical boundary of the rotating projection tooth surface as follows:

[0036] Projecting the large and small gear tooth surfaces of the quasi-hyperboloid gear onto... Within the coordinate system, the correspondence is as follows:

[0037] ;

[0038] In the formula, This represents the x-coordinate of any point within the rotated projected tooth surface. This represents the ordinate of any point within the rotated projected tooth surface. This involves representing the coordinates of points within the 3D tooth surface; calculating the coordinates of boundary points on the rotated projection tooth surface using geometric relationships; and then, based on the tooth root line boundary, enlarging the boundary along both the tooth length and tooth height directions. Discrete mesh points are then generated based on the enlarged boundary. For large wheels, dense discrete mesh nodes are generated directly between the tooth tip line and tooth root line on the rotated projection tooth surface using linear interpolation. For small wheels, a transition fillet line is introduced between the tooth root line and tooth tip line as an intermediate boundary line. Based on this intermediate boundary line, dense discrete mesh nodes are generated using linear interpolation in the regions from the tooth tip line to the transition fillet line and from the transition fillet line to the tooth root line.

[0039] Optionally, S3 specifically involves: for each discrete grid node, constructing a nonlinear least-squares objective function based on the corresponding tooth surface equation. The objective function for the large wheel is:

[0040] ;

[0041] The objective function for the small wheel is:

[0042] ;

[0043] For the objective function of the large wheel, a nonlinear optimization function is called for numerical optimization of each grid point to accurately map the two-dimensional grid nodes to the tooth surface coordinate points in three-dimensional space;

[0044] For the objective function of the pinion, based on the gear meshing principle, a spatial meshing equation is introduced as a constraint condition to construct a nonlinear solution model containing the constraint condition. A multi-level mesh search strategy is introduced to ensure high-precision solutions in complex tooth surface regions through multi-level refinement search. The calculated parameter solution is substituted into the tooth surface equation to calculate the three-dimensional discrete point cloud data of the tooth surface corresponding to the rotated projected tooth surface mesh nodes.

[0045] Optional, the multi-level grid search strategy is as follows:

[0046] First-level solution: Iterative solution based on initial neighborhood values, traversing the rotated projected discrete mesh nodes. For the first computation node, the initial value of the independent variable is:

[0047] ;

[0048] In the formula, Indicates the full tooth height at the midpoint of the pinion. Indicates the pinion tooth profile angle. Indicates radial tool position. Indicates the angular tool position. Indicates the cone distance at the midpoint of the small wheel. Indicates vertical wheel position. This represents the tool rotation angle; if the initial value of the independent variable cannot meet the solution requirements, multiple sets of parameter pairs with uniform values ​​within the parameter boundary range are added as backup initial values; for subsequent nodes of the rotated projected discrete mesh, they are grouped by column, and the nodes within the group use the converged solution of the previous adjacent node as the initial value for the current node's iteration; for the starting nodes of different groups, the converged solution of the starting nodes of the adjacent groups is used as the initial value for iteration; the nonlinear optimization solver is called to find the optimal solution that minimizes the objective function value within the preset parameter boundary constraint range;

[0049] Second-level solution: If the first-level solution returns a successful status and the error value is less than the preset tolerance, the result is output directly; if the first-level solution fails, i.e. it does not converge, gets trapped in a local minimum, or the error is too large, the grid recovery mechanism is triggered, the parameter value range is divided into a coarse discrete grid, each grid intersection is used as an initial guess value, each is substituted into the objective function, the allowable error is set for quick trial calculation, the point with the smallest residual in the trial calculation result is selected as the new initial value, and the nonlinear optimization solver is called again for fine solution;

[0050] Based on the convergent solution, a secondary refinement calculation is performed on the discrete mesh nodes. During the calculation process, it is determined whether the current point is located in the region from the transition fillet line to the tooth root line. If the point is located in the transition fillet region, the transition fillet surface equation is called to replace the working tooth surface equation for coordinate recalculation to ensure the geometric continuity of the transition fillet region. Finally, all the calculation node results are substituted into the tooth surface equation to obtain the complete three-dimensional discrete point cloud data of the pinion tooth surface of the quasi-hyperboloid gear.

[0051] A quasi-hypoid gear digital design system, applying the aforementioned quasi-hypoid gear digital design method, includes:

[0052] The parameter calculation module is used to receive initial design parameters and calculate the blank parameters and corresponding machining parameters of the hyperboloid gear pair.

[0053] The discrete mesh node generation module, connected to the parameter calculation module, is used to determine the discrete mesh nodes of the rotated projected tooth surface;

[0054] The digital tooth surface generation module, connected to the discrete mesh node partitioning module, is used to generate discrete point cloud data of the tooth surfaces of large and small wheels;

[0055] The automatic modeling module, connected to the digital tooth surface generation module, is used to generate a 3D solid model of a quasi-hyperboloid gear and complete the construction of a multibody dynamics simulation model.

[0056] As can be seen from the above technical solution, compared with the prior art, the present invention provides a digital design method and system for quasi-hyperboloid gears, which has the following beneficial effects:

[0057] 1. High system integration: This invention changes the traditional quasi-hyperboloid gear design process, which is fragmented and requires manual iteration. By building an integrated platform that integrates gear blank parameter calculation, machining parameter calculation, 3D model creation and simulation preprocessing, users can achieve a seamless process from theoretical design to simulation verification, which significantly improves the speed of design and modeling, shortens the product development cycle, and greatly improves design and R&D efficiency.

[0058] 2. High degree of automation in modeling: This invention employs parametric and automated modeling techniques, enabling rapid construction of a 3D model simply by inputting basic parameters. Based on the input parameters, the system automatically completes complex numerical calculations and tooth surface point cloud derivation, directly creating a 3D solid model. This fully automated process not only significantly improves design and modeling efficiency but also effectively avoids human errors that are prone to occur in manual modeling.

[0059] 3. Intuitive and Visual Design Results: Addressing the cumbersome calculations and complex spatial structures inherent in quasi-hyperboloid gear theoretical formulas, this invention encapsulates the complex mathematical calculations and the solution process for discrete point cloud data of the tooth surface into an automated backend process, directly outputting the calculation results and establishing a 3D solid model. After users adjust the parameters, the data can be quickly transformed into an intuitive 3D model, facilitating clear observation of the design effect and significantly reducing the difficulty of designing and optimizing quasi-hyperboloid gears.

[0060] 4. Rapid Optimization: This invention provides a flexible interface for interacting with machining parameters, allowing users to quickly adjust parameters according to actual process requirements. The system can respond and update the model rapidly, enabling users to efficiently evaluate the impact of different machining parameters on tooth meshing performance. This rapid iterative approach allows users to more accurately control design variables, thereby improving the final quality and performance of the product. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0062] Figure 1 This is a flowchart of the quasi-hyperboloid gear digital design method of the present invention;

[0063] Figure 2 This is a flowchart illustrating the calculation of parameters for the quasi-hyperboloid gear of the present invention.

[0064] Figure 3 This is a flowchart illustrating the calculation of machining parameters for the quasi-hyperboloid gear of the present invention.

[0065] Figure 4 This is a schematic diagram of the coordinate system transformation for the equation of the large gear tooth surface of the quasi-hyperboloid gear of the present invention;

[0066] Figure 5 This is a schematic diagram of the coordinate system transformation for the pinion tooth surface equation of the quasi-hyperboloid gear of the present invention;

[0067] Figure 6 This is a schematic diagram of the rotational projection of the quasi-hyperboloid gear tooth surface according to the present invention;

[0068] Figure 7 This is a flowchart of cloud computing for the large tooth surface of the quasi-hyperboloid gear of the present invention;

[0069] Figure 8 This is a flowchart of cloud computing for the pinion tooth surface of the quasi-hyperboloid gear of the present invention;

[0070] Figure 9 This is a flowchart illustrating the modeling process of the quasi-hyperboloid gear large wheel of the present invention;

[0071] Figure 10 This is a flowchart illustrating the modeling process of the quasi-hyperboloid gear pinion of the present invention;

[0072] Figure 11 This is a schematic diagram of the multibody dynamics simulation model of the quasi-hyperboloid gear of the present invention. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] This invention discloses a digital design method for quasi-hyperboloid gears, such as... Figure 1 As shown, it includes the following steps:

[0075] S1. Based on the initial design parameters, solve for the blank parameters of the hypoid gear pair; based on the blank parameters, solve for the machining parameters of the large gear forming method and the small gear cutting tool inclination method respectively.

[0076] S2. Based on the gear machining principle and spatial meshing principle, establish the gear tooth surface equation and the pinion tooth surface equation according to the machining parameters; determine the theoretical boundary of the rotating projection tooth surface according to the gear blank parameters, and divide the discrete mesh nodes within the theoretical boundary of the rotating projection tooth surface.

[0077] S3. Construct a nonlinear least squares objective function based on the tooth surface equation and discrete grid nodes, and call the nonlinear optimization function to iteratively solve the nonlinear least squares objective function to obtain discrete point cloud data of the tooth surface;

[0078] S4. Construct cubic spline curves using discrete point cloud data of the tooth surface to reconstruct the tooth surface spline surface; establish a solid model of the tooth blank based on the tooth blank parameters, and use Boolean operations to trim the tooth blank using the reconstructed tooth surface to generate a quasi-hyperboloid gear 3D solid model.

[0079] S5. Based on the quasi-hyperboloid gear 3D solid model, create a rotary pair, apply load torque, and define solid contact pairs to complete the construction of the multibody dynamics simulation model.

[0080] Furthermore, the specific steps for solving the blank parameters of the quasi-hypoid gear pair in S1 are as follows: Figure 2 As shown, based on the initial design parameters, an iterative model is established according to the geometric relationship between the pitch cone parameters, and the offset angle within the small wheel axle section is corrected. and increase the coefficient After determining the pitch cone geometry parameters, and when the convergence condition of the iterative model is met, the distance parameter among the pitch cone geometry parameters is determined, and the outer cone distance of the large wheel is determined based on the pitch cone geometry parameters. Working tooth height at the midpoint of the large wheel and top gap Select the high gear tooth height coefficient With tooth tip height coefficient The full tooth height at the midpoint of the large wheel was calculated. Highest point of the gear teeth at the midpoint and the height of the tooth root at the midpoint of the large wheel Calculate the tooth tip angle based on the tooth height shrinkage method. With tooth root angle This allows for the determination of the complete gear blank parameters for the large wheel;

[0081] In this embodiment, the initial design parameters specifically include: gear helix direction, pinion offset direction, and offset distance. Number of pinion teeth Number of teeth on the large gear outer diameter of the large wheel Large gear tooth surface width Tooth height reduction method and working conditions; if the pinion helix angle If the value is unknown, calculate it using the empirical formula as follows:

[0082] ;

[0083] Pitch cone geometry parameters include pinion pitch cone angle. Large wheel pitch cone angle Small wheel pitch cone Large wheel pitch cone Small wheel pitch circle radius Large wheel pitch circle radius large wheel helix angle Offset angle Ultimate pressure angle and limiting radius of curvature The distance parameter includes the distance from the node along the axis of the large wheel to the intersection. The distance from the apex of the large wheel cone to the intersection point Distance from the vertex of the small wheel cone to the intersection point ;

[0084] The complete gear blank parameters for the large wheel include the face cone angle. Root cone angle external tooth tip height , outer end tooth root height Full tooth height Distance from the vertex of the root cone to the intersection point Distance from the vertex of the cone to the intersection point and the outer diameter of the large wheel .

[0085] Calculate the process pitch cone offset angle based on the pitch cone geometry parameters and the large gear blank parameters. and the offset angle of the large wheel corresponding to the root cone of the small wheel. Thus, the cone angle of the small wheel surface is determined. Small wheel root cone angle pinion tooth tip angle and pinion tooth root angle Based on the pinion gear blank parameters, calculate the distance from the pinion pitch point to the intersection point. Distance from the small wheel crown to the intersection point The distance from the small wheel crown to the intersection point This allows us to obtain the complete gear blank parameters for the pinion.

[0086] In this embodiment, specifically, the parameters of the complete gear blank include the midpoint addendum. Midpoint tooth root height external tooth tip height , outer end tooth root height Full tooth height Distance from the vertex of the cone to the intersection point Distance from the vertex of the root cone to the intersection point Tooth surface width outer diameter Pitch circle diameter and outer cone distance .

[0087] Furthermore, the specific steps for solving the machining parameters of the large wheel forming method and the small wheel tool tilting method in S1 are as follows: Figure 3 As shown, the process pitch cone parameters are calculated based on the gear cutting principle; based on the process pitch cone parameters and the large gear blank parameters, the pitch cone distance of the large gear production form is calculated. relative to the tilt angle of the cutter head This allows for the determination of the machining parameters for the large wheel forming method;

[0088] In this embodiment, specifically, the process cone parameters include the process cone small wheel node radius. The pitch of the small wheel of the process cone Process cone large wheel cone distance Process section cone offset angle Small wheel surface cone helix angle Large wheel root cone helix angle and process section cone pressure angle ;

[0089] The machining parameters for the large wheel forming method include: cutter head tip distance. Horizontal tool position Vertical tool position Axial wheel position Radial tool position Angular tool position and wheel blank installation angle ;

[0090] Determine the normal curvature of the pinion along the tooth height direction based on the process cone parameters. Contact line direction angle of the process cone and cutter head radius Then, the parameters of the pinion gear cutting cone are calculated;

[0091] In this embodiment, specifically, the pinion cutting cone parameters include the pinion root cone angle correction value. , cone angle Pitch cone distance Pressure angle helix angle Forming radius The contact line direction angle when the small gear cutting cone meshes with the forming gear And the normal curvature of the calculation point along the height of the bevel tooth of the incisor pitch. ;

[0092] An iterative model is established based on the pitch cone parameters of the small gear cutting teeth. During the initial value calculation, the helix angle is set. Equal to the helix angle of the small gear cutting pitch cone The pitch cone distance is obtained. and pitch cone angle Initial values ​​are used to iteratively calculate the parameters of the pitch cone of the production wheel:

[0093] ;

[0094] In the formula, The third-order correction value represents the contact region; the convergence criterion for iterative calculation is:

[0095] ;

[0096] In the formula, Indicates the mounting angle of the small wheel blank; The target value is expressed by the following formula:

[0097] ;

[0098] In the formula, The correction value representing the pitch cone angle of the production wheel is, in this embodiment, taken as... ; The value represents the correction value for the wheel blank mounting angle. In this embodiment, -4° is taken for the convex surface and -2° is taken for the concave surface. After the convergence condition is met, the machining parameters of the small wheel tool tilting method are determined based on the tool tilting method machining principle and the process cone parameters.

[0099] In this embodiment, specifically, the machining parameters for the small wheel include the vertical wheel position. Horizontal wheel position Radial tool position Angular tool position ,bed knife inclination angle knife corner Wheel blank installation angle And rolling .

[0100] Furthermore, such as Figure 4 As shown, the equation for the large gear tooth surface in S2 is specifically established by: transforming the large gear tool machining surface using a coordinate transformation matrix. and the transition fillet surface of the large wheel tool From the tool coordinate system Transform to workpiece coordinate system The transformation formula is:

[0101] ;

[0102] In the formula, Represents the tool head coordinate system To machine tool coordinate system The transformation matrix, Representing the machine tool coordinate system To the workpiece coordinate system The transformation matrix, Indicates the cutting angle of the cutter head; This represents the distance from the tool tip plane to the cutting point. This indicates the angle between the cutting point and the tool tip plane. , The workpiece coordinate system The machining surface of the large wheel tool and the transition fillet surface of the large wheel tool.

[0103] In this embodiment, the specific equation for the machining surface of the large wheel tool is as follows:

[0104] ;

[0105] In the formula: Indicates the radius of the machining tool. For concave surfaces, use a positive sign; for convex surfaces, use a negative sign. This indicates the tooth profile angle of the cutting tool, with a positive value for concave surfaces and a negative value for convex surfaces. Indicates the cutting angle of the cutter head; This indicates the distance from the tool tip plane to the cutting point.

[0106] The equation for the transition fillet surface of the large wheel cutting tool is as follows:

[0107] ;

[0108] In the formula: , For concave surfaces, use a positive sign; for convex surfaces, use a negative sign. Indicates the fillet radius of the cutting tool tip; This represents the angle between the cutting point and the tool tip plane. The transformation matrix is ​​specifically:

[0109] ;

[0110] .

[0111] Furthermore, such as Figure 5 As shown, the specific steps for establishing the pinion tooth surface equation in S2 are: using the coordinate transformation matrix, the tool equation is transformed... From the tool coordinate system Transform to machine tool coordinate system The transformation formula is:

[0112] ;

[0113] In the formula, , , , Represents the transition coordinate matrix. Indicates the angle of the tool tilting table. The transformed tool equation;

[0114] In the machine tool coordinate system Establish the spatial meshing equation:

[0115] ;

[0116] In the formula, This represents the normal vector of the tool working surface within the machine tool coordinate system. Represents the relative velocity within the machine tool coordinate system; the tool equations satisfying the meshing conditions are transferred from the machine tool coordinate system. Transform to workpiece coordinate system The equation for the pinion tooth surface is obtained, and the conversion formula is:

[0117] ;

[0118] In the formula, , , Represents the transition coordinate transformation matrix. The equation for the pinion tooth surface is given.

[0119] In this embodiment, specifically, the small wheel tool processes the surface. as follows:

[0120] ;

[0121] In the formula: Indicates the radius of the small wheel tool; This indicates the tooth profile angle of the cutting tool; it is positive for concave surfaces and negative for convex surfaces. Indicates the cutting angle of the cutter head; This indicates the distance from the tool tip plane to the cutting point.

[0122] Normal vector of the machining surface of the small wheel tool as follows:

[0123] ;

[0124] Small wheel tool transition rounded corner surface as follows:

[0125] ;

[0126] In the formula: , For concave surfaces, use a positive sign; for convex surfaces, use a negative sign. Indicates the fillet radius of the cutting tool tip; This indicates the angle between the cutting point and the tool tip plane.

[0127] The specific formula for the transition coordinate matrix is ​​as follows:

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] in, This indicates the rotation angle of the tool chuck.

[0133] The spatial meshing equation is as follows:

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] ;

[0139] ;

[0140] in, , , The same applies to other calculations.

[0141] To solve the pinion tooth surface equation, the tool equation is rewritten as about and The specific formula is as follows:

[0142] ;

[0143] ; ;

[0144] After transforming the rewritten tool equations to the machine coordinate system, substituting them into the spatial meshing equations, we obtain the solution. Then, substitute it back into the original tool equation. Thus, the tool equations that satisfy the meshing conditions are obtained. .

[0145] The tool equations that satisfy the meshing conditions are then derived from the machine tool coordinate system. Transform to workpiece coordinate system The final equation for the pinion tooth surface is obtained as follows:

[0146]

[0147] The transition coordinate transformation matrix is ​​as follows:

[0148] ;

[0149] ;

[0150] .

[0151] Furthermore, in S2, the theoretical boundary of the rotating projection tooth surface is determined based on the tooth blank parameters, and the discrete mesh nodes are divided within the theoretical boundary of the rotating projection tooth surface as follows:

[0152] like Figure 6 As shown, the large and small gear tooth surfaces of the quasi-hyperboloid gear are projected onto... Within the coordinate system, the correspondence is as follows:

[0153] ;

[0154] In the formula, This represents the x-coordinate of any point within the rotated projected tooth surface. This represents the ordinate of any point within the rotated projected tooth surface. Represent the coordinates of the corresponding points within the 3D tooth surface; calculate the coordinates of the boundary points of the rotated projected tooth surface using geometric relationships; based on the rotated projected tooth surface boundary and the tooth root line boundary, magnify the boundary along both the tooth length and tooth height directions, respectively, due to the parameters in the tooth height direction. The range is easy to determine, but the direction of influence on tooth length (especially the pinion tooth surface) is affected. The range of parameters (influence) is difficult to define precisely. Therefore, the magnification factor in the tooth length direction is set to be smaller than that in the tooth height direction to facilitate subsequent Boolean operations. Discrete grid points are divided based on the magnification boundary. For large wheels, since their parameters are relatively simple, dense discrete grid nodes are generated directly between the tooth tip line and tooth root line on the rotated projection tooth surface using linear interpolation. For small wheels, considering that sparse grid points at the transition fillet will lead to non-convergence of the numerical solution, a transition fillet line is introduced between the tooth root line and the tooth tip line as an intermediate dividing line. Based on the intermediate dividing line, dense discrete grid nodes are generated by linear interpolation in the region from the tooth tip line to the transition fillet line and in the region from the transition fillet line to the tooth root line, respectively.

[0155] In this embodiment, the specific formula for calculating the coordinates of the boundary points of the rotated projection tooth surface is as follows:

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] In the formula, Indicates the distance between the outer cones; Indicates tooth width; This represents the distance from the vertex of the cone to the intersection point;

[0161] The formula for calculating the transition fillet is as follows:

[0162] ;

[0163] In the formula, Indicates the distance between the transition fillet line and the tooth root line; Indicates the radius of the transition fillet; This indicates the tooth profile angle of the pinion.

[0164] Furthermore, S3 specifically involves: for each discrete grid node, constructing a nonlinear least-squares objective function based on the corresponding tooth surface equation. The objective function for the large wheel is:

[0165] ;

[0166] like Figure 7 As shown, in this embodiment, given that the large wheel is machined using a forming method and its tooth surface geometry is relatively regular, the rotated projection tooth surface is constructed as a dense discrete mesh node with 20 rows and 20 columns through linear interpolation; the calculation function of the large wheel tooth surface equation is based on the distance from the tool tip plane. and the corner of the cutter head is the independent variable.

[0167] Specifically, the objective function of the large-scale calculation adopts an iterative solution strategy based on the initial value of the neighborhood, traversing the nodes of the rotated projection discrete grid. For the first calculation node, the initial value of its independent variable is determined by the following formula:

[0168] ;

[0169] In the formula, Indicates the full tooth height at the midpoint of the large gear. Indicates the tooth profile angle of the large gear. Indicates radial tool position. Indicates the angular tool position. Indicates the cone distance at the midpoint of the large wheel;

[0170] The subsequent nodes of the rotated projected discrete mesh are grouped and calculated by column. Within each group, the convergent solution of the previous adjacent node is selected as the initial value for the current node's iteration. For the starting node of each group, the convergent solution of the starting node of the previous group is selected as the initial value for the iteration.

[0171] The objective function is solved using a nonlinear optimization solver. During the solution process, boundary constraints on the parameters are set to find the optimal solution that minimizes the objective function value. The preset parameter boundary ranges are as follows:

[0172] ;

[0173] In the formula, For the full tooth height of the large wheel, The magnification factor in the tooth height direction of the large wheel's rotating projection tooth surface is determined. Once the solution is successful and the error meets the convergence criterion, the solution result is recorded. Considering the relatively simple nature of the large wheel's tooth surface equation, the parameters obtained from the solution are extracted. The boundary values ​​are substituted into the equation of the large gear tooth surface, thereby generating uniformly distributed three-dimensional discrete tooth surface point cloud data of the quasi-hyperboloid gear large gear within the parameter boundary range.

[0174] like Figure 8 As shown, the calculation function for the pinion tooth surface equation is based on the cutter head rotation angle. and the corner of the rocking platform Let be the independent variable, and let be the objective function of the small wheel:

[0175] ;

[0176] In this embodiment, for the complex geometry of the pinion tooth surface, a regional mesh division is adopted. According to the discrete mesh node division method of the rotating projection tooth surface described in step S2, 10 rows and 20 columns of discrete tooth surface point clouds are divided in the region from the tooth tip line to the transition fillet line and in the region from the transition fillet line to the tooth root line, respectively, so as to determine the target discrete mesh node of the pinion rotating projection tooth surface;

[0177] For the objective function of the large wheel, a nonlinear optimization function is called for numerical optimization of each grid point to accurately map the two-dimensional grid nodes to the tooth surface coordinate points in three-dimensional space;

[0178] For the objective function of the pinion, based on the gear meshing principle, since the pinion machining involves tool tilting machining and complex spatial meshing motion, a spatial meshing equation is introduced as a constraint condition when calculating the objective function value. A nonlinear solution model containing the constraint condition is constructed, and a multi-level mesh search strategy is introduced. Through multi-level refinement search, a high-precision solution is obtained in the complex tooth surface region. The calculated parameter solution is substituted into the tooth surface equation to calculate the three-dimensional discrete point cloud data of the tooth surface corresponding to the rotated projected tooth surface mesh nodes.

[0179] In this embodiment, the meshing constraint is specifically as follows:

[0180] ;

[0181] During the calculation process, the above meshing constraint equation solution function is first called to determine the tooth surface parameters corresponding to the current independent variable. Then, the three-dimensional spatial coordinates corresponding to the current independent variable are calculated, and finally the distance error between the variable and the target mesh node is returned.

[0182] Furthermore, the multi-level grid search strategy is as follows:

[0183] First-level solution: Iterative solution based on initial neighborhood values, traversing the rotated projected discrete mesh nodes. For the first computation node, the initial value of the independent variable is:

[0184] ;

[0185] In the formula, Indicates the full tooth height at the midpoint of the pinion. Indicates the pinion tooth profile angle. Indicates radial tool position. Indicates the angular tool position. Indicates the cone distance at the midpoint of the small wheel. Indicates vertical wheel position. This represents the tool rotation angle; if the initial value of the independent variable cannot meet the solution requirements, multiple sets of parameter pairs with uniform values ​​within the parameter boundary range are added as backup initial values; for subsequent nodes of the rotated projected discrete mesh, they are grouped by column, and the nodes within the group use the converged solution of the previous adjacent node as the initial value for the current node's iteration; for the starting nodes of different groups, the converged solution of the starting nodes of the adjacent groups is used as the initial value for iteration; the nonlinear optimization solver is called to find the optimal solution that minimizes the objective function value within the preset parameter boundary constraint range;

[0186] Second-level solution: If the first-level solution returns a successful status and the error value is less than the preset tolerance, the result is output directly; if the first-level solution fails, i.e. it does not converge, gets trapped in a local minimum, or the error is too large, the grid recovery mechanism is triggered, the parameter value range is divided into a coarse discrete grid, each grid intersection is used as an initial guess value, each is substituted into the objective function, the allowable error is set for quick trial calculation, the point with the smallest residual in the trial calculation result is selected as the new initial value, and the nonlinear optimization solver is called again for fine solution;

[0187] Based on the convergent solution, a secondary refinement calculation is performed on the discrete mesh nodes. During the calculation process, it is determined whether the current point is located in the region from the transition fillet line to the tooth root line. If the point is located in the transition fillet region, the transition fillet surface equation is called to replace the working tooth surface equation for coordinate recalculation to ensure the geometric continuity of the transition fillet region. Finally, all the calculation node results are substituted into the tooth surface equation to obtain the complete three-dimensional discrete point cloud data of the pinion tooth surface of the quasi-hyperboloid gear.

[0188] In this embodiment, specifically, S4 is as follows: Figure 9 and Figure 10 As shown, based on the RecurDyn / ProcessNet secondary development platform, the discrete point cloud data of the tooth surfaces of the large and small gears of the quasi-hyperboloid gear are imported into the RecurDyn multibody simulation software. According to the row and column distribution relationship of the point cloud data, the three-dimensional discrete points of the corresponding columns are imported sequentially through the cubic spline interpolation algorithm to generate a smooth cubic spline curve along the tooth height direction with a specified number of columns. Connecting the first and last data points of each discrete point group, two smooth cubic spline curves are generated along the tooth length direction, namely the tooth tip line and the tooth root line.

[0189] Subsequently, using the cubic spline curves generated above along the tooth height and tooth length directions, a surface lofting operation is performed to reconstruct the spline surface, which is the reconstructed tooth surface. Surface stitching and filling operations are then performed on the reconstructed tooth surface to generate a single-tooth solid model. Based on the tooth blank parameters from the previous steps, a rotation array operation is performed on the single-tooth solid model around the axis to generate a complete tooth surface model of a quasi-hypoid gear containing all teeth.

[0190] Based on the gear blank parameters, draw the two-dimensional closed cross-sectional profile of the gear blank. By rotating the closed profile 360° around the gear axis through the rotation feature operation, a quasi-hyperboloid gear blank solid model is generated.

[0191] Boolean operations are performed between the complete tooth surface model and the quasi-hyperboloid gear blank model. The tooth surface model is then used to trim the gear blank model to remove excess material. Subsequently, the tooth tip of the large gear is chamfered to obtain the complete three-dimensional solid models of the large and small quasi-hyperboloid gears.

[0192] Based on the spatial geometry of the quasi-hyperboloid gear, virtual assembly is performed: First, the large gear is rotated 90° around the intersection of the axes to the designated assembly position; second, based on the offset direction and offset distance of the small gear, the small gear solid model is translated a corresponding distance along the offset direction so that it meets the designed spatial geometric meshing relationship with the large gear, thus completing the assembly of the quasi-hyperboloid gear three-dimensional solid model.

[0193] S5 specifically refers to: (e.g., ...) Figure 11 As shown, based on the assembled 3D solid model, revolute pairs are established at the axial positions of the large and small gears, respectively, and kinematic constraints are applied to the 3D solid model. Loads and drives are applied to the 3D solid model according to actual process conditions: a load torque is applied to the large gear revolute pair to simulate the resistance torque in actual working conditions, and a drive speed is applied to the small gear revolute pair to simulate the input speed. The tooth surfaces of the large and small gears are defined as contact surfaces, establishing contact pairs between the solids. Contact mechanical parameters are configured, including dynamic parameters such as contact stiffness coefficient, friction coefficient, and damping coefficient, to simulate the actual tooth surface meshing contact behavior. Thus, the construction of the quasi-hypoid gear multibody dynamics simulation model is completed.

[0194] and Figure 1 Corresponding to the method described above, this embodiment of the invention also discloses a quasi-hypoid gear digital design system, which, when applied to the aforementioned quasi-hypoid gear digital design method, includes:

[0195] The parameter calculation module is used to receive initial design parameters and calculate the blank parameters and corresponding machining parameters of the hyperboloid gear pair.

[0196] The discrete mesh node generation module, connected to the parameter calculation module, is used to determine the discrete mesh nodes of the rotated projected tooth surface;

[0197] The digital tooth surface generation module, connected to the discrete mesh node partitioning module, is used to generate discrete point cloud data of the tooth surfaces of large and small wheels;

[0198] The automatic modeling module, connected to the digital tooth surface generation module, is used to generate a 3D solid model of a quasi-hyperboloid gear and complete the construction of a multibody dynamics simulation model.

[0199] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0200] Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for designing a digital hypoid gear, characterized in that, The method comprises the following steps: S1, according to the initial design parameters, the tooth blank parameters of the hypoid gear pair are solved; according to the tooth blank parameters, the forming machining parameters of the large gear and the cutter tilt machining parameters of the small gear are solved respectively; S2, based on the gear machining principle and the space meshing principle, the large gear tooth surface equation and the small gear tooth surface equation are established according to the machining parameters; the theoretical boundary of the rotary projection tooth surface is determined according to the tooth blank parameters, and the discrete grid nodes are divided in the theoretical boundary of the rotary projection tooth surface; S3, the nonlinear least squares objective function is constructed according to the tooth surface equation and the discrete grid nodes, the nonlinear optimization function is called to iteratively solve the nonlinear least squares objective function, and the tooth surface discrete point cloud data is obtained; S4, the cubic spline curve is constructed by using the discrete point cloud data of the tooth surface, the tooth surface spline surface is reconstructed; the tooth blank entity model is established according to the tooth blank parameters, the tooth blank is trimmed by using the reconstructed tooth surface through Boolean operation, and the three-dimensional entity model of the hypoid gear is generated; S5, based on the three-dimensional entity model of the hypoid gear, the rotary pair is created, the load torque is applied, and the entity contact pair is defined, and the construction of the multi-body dynamics simulation model is completed.

2. The method for digital design of a hypoid gear according to claim 1, characterized in that, The specific steps for solving the blank parameters of the quasi-double curved gear pair in S1 are as follows: based on initial design parameters, an iterative model is established according to the geometric relationship between the pitch cone parameters, the offset angle in the small wheel shaft section is corrected and the coefficient is increased to determine the pitch cone geometric parameters; when the convergence condition of the iterative model is met, the distance parameter in the pitch cone geometric parameters is determined, the outer pitch distance of the large wheel is determined based on the pitch cone geometric parameters , the midpoint working tooth height of the large wheel and the tip clearance ; the tooth height coefficient of the large wheel and the addendum coefficient are selected, and the midpoint full tooth height of the large wheel , the midpoint addendum of the large wheel and the midpoint dedendum of the large wheel are calculated. According to the tooth height shrinkage mode, the addendum angle is calculated and the dedendum angle , and then the complete tooth blank parameters of the large gear are determined. Based on the parameters of the pitch cone and the big gear tooth blank, the process pitch cone offset angle is calculated and the big gear offset angle corresponding to the small gear root cone , so as to determine the small gear face cone angle , the small gear root cone angle , the small gear addendum angle and the small gear dedendum angle ; according to the parameters of the small gear tooth blank, the distance from the small gear node to the intersection point is calculated , the distance from the small gear crown to the intersection point and the distance from the small gear face crown to the intersection point , and then the complete small gear tooth blank parameters are obtained.

3. The method for digital design of a hypoid gear according to claim 1, wherein, The solving of the large wheel forming method machining parameter and the small wheel cutter tilt method machining parameter in S1 is specifically: calculating the process pitch cone parameter based on the cutting tooth machining principle; calculating the large wheel forming wheel pitch cone distance based on the process pitch cone parameter and the large wheel tooth blank parameter and the cutter disc tilt angle , and further determining the large wheel forming method machining parameter; According to the process pitch cone parameters, the normal curvature of the pinion along the tooth height direction is determined , the contact line direction angle of the process pitch cone , and the cutter head radius , and then the pinion gear cutting pitch cone parameters are calculated An iterative model is established based on the pitch cone parameters of the small gear cutting teeth. During the initial value calculation, the helix angle is set. Equal to the helix angle of the small gear cutting pitch cone The pitch cone distance is obtained. and pitch cone angle Initial values ​​are used to iteratively calculate the parameters of the pitch cone of the production wheel: ； wherein represents the third-order correction of the contact area; the convergence criterion for the iterative calculation is ； In the formula, represents the small wheel blank installation angle; represents the target value, and the calculation formula is: ； In the formula, represents the correction value of the shape wheel segment cone angle, represents the wheel blank installation angle correction value, when the convergence condition is met, the small wheel tool tilt method processing parameters are determined based on the tool tilt method processing principle and the process segment parameters.

4. The method for digital design of a hypoid gear according to claim 1, wherein, The establishment of the large gear tooth surface equation in S2 is specifically: through a coordinate transformation matrix, the large gear cutter machining surface and the large gear cutter transition fillet surface are transformed from the cutter coordinate system to the workpiece coordinate system , and the transformation formula is: ； In the formula, Represents the tool head coordinate system To machine tool coordinate system The transformation matrix, Representing the machine tool coordinate system To the workpiece coordinate system The transformation matrix, Indicates the cutting angle of the cutter head; This represents the distance from the tool tip plane to the cutting point. This indicates the angle between the cutting point and the tool tip plane. , The workpiece coordinate system The machining surface of the large wheel tool and the transition fillet surface of the large wheel tool.

5. The method for digital design of a hypoid gear according to claim 1, wherein, The small gear tooth surface equation is established in S2, specifically: using a coordinate transformation matrix, the cutter equation is transformed from the cutter coordinate system to the machine tool coordinate system by the transformation formula ​​ ； wherein , , , denotes the transition coordinate matrix, denotes the tool turret rotation angle, is the transformed tool equation; In the machine coordinate system The spatial engagement equations are established in the machine coordinate system: ； wherein represents the normal vector of the tool face in the machine coordinate system, represents the relative velocity in the machine coordinate system; the tool equation satisfying the engagement condition is converted from the machine coordinate system to the workpiece coordinate system to obtain the pinion tooth surface equation, and the conversion formula is: ； wherein , , denotes the transition coordinate transformation matrix, is the small gear tooth surface equation.

6. The method for digital design of a hypoid gear according to claim 1, wherein, In S2, the theoretical boundary of the rotary projection tooth surface is determined according to the tooth blank parameters, and the discrete grid nodes are divided in the theoretical boundary of the rotary projection tooth surface. The tooth surface of the large gear of the hypoid gear is projected to the tooth surface of the small gear In the coordinate system, the corresponding relationship is: ； In the formula, represents the horizontal coordinate of any point in the projected tooth surface, represents the vertical coordinate of any point in the projected tooth surface, represents the corresponding point coordinate in the three-dimensional tooth surface; the boundary point coordinate of the projected tooth surface is calculated by using geometric relationship; based on the boundary of the projected tooth surface, the boundary is enlarged in the tooth length direction and the tooth height direction respectively based on the boundary of the dedendum line; for a large gear, dense discrete grid nodes are generated by linear interpolation directly between the addendum line and the dedendum line of the projected tooth surface; for a small gear, a transition fillet line is introduced as an intermediate boundary line between the dedendum line and the addendum line, and dense discrete grid nodes are generated by linear interpolation in the region from the addendum line to the transition fillet line and in the region from the transition fillet line to the dedendum line respectively based on the intermediate boundary line.

7. The method for digital design of a hypoid gear according to claim 1, wherein, S3 is specifically: for each discrete grid node, the nonlinear least squares objective function is constructed in combination with the corresponding tooth surface equation, the large gear objective function is: ； The small gear objective function is: ； For the large gear objective function, the nonlinear optimization function is called for numerical optimization for each grid point, and the two-dimensional grid node is accurately mapped to the tooth surface coordinate point in three-dimensional space; For the small gear objective function, according to the gear meshing principle, the space meshing equation is introduced as a constraint condition to construct a nonlinear solving model containing the constraint condition, a multi-level grid search strategy is introduced, and high-precision solutions are obtained in complex tooth surface areas through multi-level refinement search; The calculated parameter solution is substituted into the tooth surface equation to calculate the three-dimensional tooth surface discrete point cloud data corresponding to the rotary projection tooth surface grid nodes.

8. The method for digital design of a hypoid gear according to claim 7, characterized in that, The multi-level grid search strategy is specifically: First level solution: iterative solution based on neighborhood initial value, traverse the rotary projection discrete grid nodes, for the first calculation node, the independent variable initial value is: ； wherein, represents the full tooth height at the midpoint of the pinion, represents the pinion tooth profile angle, represents the radial tool position, represents the angular tool position, represents the pinion midpoint pitch, represents the perpendicular wheel position, represents the tool rotation angle; if the initial values of the arguments cannot meet the requirements for solving, a plurality of groups of parameters are taken within the uniform value range of the parameter boundary as backup initial values; for subsequent nodes of the rotation projection discrete grid, grouping is performed by column, and the converged solution of the last adjacent node is used as the iteration initial value of the current node; the starting nodes of different groups use the converged solution of the adjacent group starting node as the iteration initial value; a nonlinear optimization solver is called to find the optimal solution that minimizes the objective function value within the preset parameter boundary constraint range. Second level solution: if the state returned by the first level solution is successful and the error value is less than the preset tolerance, the result is directly output; If the first level solution fails, that is, it does not converge, falls into a local minimum value or the error is too large, the grid remediation mechanism is triggered, the parameter value range is divided into a rough discrete grid, each grid intersection point is taken as an initial guess value, is substituted into the objective function, and a fast trial calculation is performed with a specified allowable error, the point with the smallest residual in the trial calculation result is selected as a new initial value, and the nonlinear optimization solver is called again for fine calculation; Based on the convergence solution, the discrete grid nodes are calculated again, and in the calculation process, it is judged whether the current point is located in the transition fillet line to the tooth root line area, if it is determined that the point is located in the transition fillet area, the transition fillet surface equation is called to replace the working tooth surface equation for coordinate recalculation, so as to ensure the geometric continuity of the transition fillet area; Finally, all the results of the computing nodes are substituted into the tooth surface equation to obtain complete discrete point cloud data of the three-dimensional tooth surface of the pinion of the quasi-hypoid gear.

9. A digital design system for a hypoid gear, characterized by The application discloses a digital design method of a quasi-hypoid gear. The parameter calculation module is used for receiving initial design parameters and calculating the tooth blank parameters and corresponding machining parameters of the hypoid gear pair. The discrete grid node division module is connected with the parameter calculation module and is used for determining the discrete grid nodes of the rotary projection tooth surface. The digital tooth surface generation module is connected with the discrete grid node division module and is used for generating the discrete point cloud data of the tooth surfaces of the big gear and the pinion. The automatic modeling module is connected with the digital tooth surface generation module and is used for generating a three-dimensional entity model of the quasi-hypoid gear and completing the construction of a multi-body dynamics simulation model.

Images