Gear design method and computer product based on reverse engineering of composite tooth profile parameters

Abstract

This invention relates to the field of gear reverse engineering technology, and more particularly to a gear design method and computer product based on reverse construction using composite tooth profile parameters. The gear design method based on reverse construction using composite tooth profile parameters of this invention, for the first time, constructs the centers of the addendum and root arcs as functions that dynamically shift with the displacement coefficient. At the microscopic level, the precise tangent points B and C between the involute and the addendum / root arcs are automatically searched to ensure a strictly smooth and interference-free tooth profile. At the macroscopic level, global optimization using the Jacobian matrix is ​​employed until the three strong constraints of equal addendum diameter, root diameter, and arc radius are satisfied, and the optimal module, displacement coefficient, and pressure angle are output. This allows for tooth profile generation simply by inputting the "addendum diameter, root diameter, and number of teeth." This process eliminates the need for repeated manual calculations, making it more direct, concise, and accurate, thus solving the technical problems of cumbersome operation and low accuracy of generated tooth profiles in existing reverse construction methods.

Description

Technical Field

[0001] This invention relates to the field of gear reverse engineering technology, and in particular to a tooth profile construction method based on reverse construction of composite tooth profile parameters, a gear design method, a computer system, a computer-readable storage medium, and a computer program product. Background Technology

[0002] When performing reverse engineering or non-standard design of gears, it is necessary to deduce the tooth profile from the finished gear. For example, using a standard involute tooth profile, the tooth profile is calculated using parametric formulas such as module and pressure angle, and the tooth tip is achieved by using radial truncation or a simple circular arc transition.

[0003] In existing reverse engineering or non-standard design, for composite tooth profiles composed of "circular arc-involute-circular arc," three strong geometric constraints must be met: the predetermined addendum circle diameter, the root circle diameter, and the equal radii of the addendum and root arcs. Existing methods typically assume a fixed arc center or approximate solutions through simple geometric constructions, resulting in the following drawbacks: 1. Extensive reverse engineering is required, involving repeatedly substituting extracted parameters such as module and pressure angle, leading to complex, tedious, and labor-intensive operations. 2. Since the extracted module and pressure angle are based on product measurements, errors exist, resulting in unsolvable problems when reverse engineering the extracted module and pressure angle, leading to a final tooth profile that does not meet the requirements. Summary of the Invention

[0004] To address the technical problems of existing reverse engineering methods being cumbersome and having large errors in the extracted gear parameters, resulting in low accuracy of the generated tooth profile, this invention provides a gear design method and computer product based on reverse engineering using composite tooth profile parameters.

[0005] The first aspect of this invention provides a tooth profile construction method based on reverse construction using composite tooth profile parameters, comprising:

[0006] Through the target modulus m Target displacement coefficient x n Target pressure angle α Design a semi-tooth profile of the target gear; rotate and copy the semi-tooth profile to generate the tooth profile;

[0007] m x n α Constructed using the reverse construction method based on composite tooth profile parameters:

[0008] Based on the known tooth tip circle diameter Root circle diameter Given the number of teeth z, a set of constraint equations is constructed based on the addendum circle function, involute function, and root circle function. :

[0009] ;

[0010] in, Constraints on the tooth tip circle diameter; Constraints the root circle diameter; For isotopic fillet constraints; , These are the currently preset modulus, displacement coefficient, and pressure angle, respectively. For a moving circle center model, ; The current tooth tip radius, based on the current... Determine the center of the current tooth tip arc. Iteratively find the optimal tangent point B between the involute and the tooth tip arc, where the normal to tangent point B passes through... Determine the current time value; The current tooth root radius, based on the current... Determine the center of the current tooth root arc. Iteratively find the optimal tangent point C between the involute and the tooth tip arc, where the normal to tangent point C passes through... Determine the current time value;

[0011] Based on the current value, The value is iterated until X satisfies the system of constraint equations. m x n α These are X at this time. The value of .

[0012] Furthermore, the tooth tip arc function is:

[0013]

[0014] Among them, the tooth tip arc is based on With center at and radius at, The arc; ; u The angle parameter of the tooth tip arc function; u B Let u be the value of the angle parameter at the tangent point B; the coordinates of the tooth tip arc function are... .

[0015] Furthermore, the involute function is:

[0016]

[0017] in, The radius of the base circle; ; This represents the offset of the initial phase of the involute. ; The pressure angle; , For the involute development angle, For the tooth tip tangent point parameters, Here are the parameters for the tooth root tangent point; the coordinates of the involute function are... .

[0018] Furthermore, the root radius function is:

[0019]

[0020] Among them, the root arc is based on With center at and radius at, The arc; the center yes Rotate around the origin The position after; ; ; θ The angle parameter of the tooth root arc function; the center of the circle. The coordinates are ; θ C Let be the value of the angle parameter of the tooth root arc function at the tangency point C; the coordinates of the tooth root arc function are... .

[0021] Furthermore, , The same iterative algorithm is used for iteration, which can be the Newton-Raphson iterative algorithm, or the bisection method, or the secant method, or the Brent method.

[0022] Furthermore, X is iterated using an iterative algorithm two, which can be the LM iterative algorithm, the trust region dogleg method, the Gauss-Newton method, the genetic algorithm, or the sequential quadratic programming algorithm.

[0023] A second aspect of the present invention provides a gear design method, wherein the gear is designed by means of a tooth profile; the tooth profile is obtained by means of the tooth profile construction method described above, which is based on the reverse construction of composite tooth profile parameters.

[0024] A third aspect of the present invention provides a computer system including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the tooth profile construction method based on the reverse construction of composite tooth profile parameters described above.

[0025] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the tooth profile construction method described above based on the reverse construction of composite tooth profile parameters.

[0026] The fifth aspect of the present invention provides a computer program product, including a computer program / instruction that, when executed by a processor, implements the steps of the tooth profile construction method described above based on the reverse construction of composite tooth profile parameters.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. The reverse construction method for composite tooth profile parameters of this invention proposes for the first time a "following center" model, constructing the centers of the tooth tip arc and tooth root arc as functions that dynamically shift with the displacement coefficient. Based on this, a "macro-micro" double-layer nested numerical iterative algorithm is designed: the micro layer automatically searches for the precise tangent points B and C between the involute and the tooth tip / root arc connection points, ensuring a strictly smooth and interference-free tooth profile; the macro layer uses the Jacobian matrix for global optimization until the three strong constraints of equal tooth tip diameter, tooth root diameter, and arc radius are satisfied, and outputs the optimal module, displacement coefficient, and pressure angle. This invention breaks through the traditional trial-and-error mode that requires pre-setting the module and pressure angle, realizing automatic reverse calculation of optimal parameters and outputting the optimal module, displacement coefficient, and pressure angle that meet the requirements, thereby generating the tooth profile, by only inputting three intuitive geometric quantities: "tooth tip diameter, tooth root diameter, and number of teeth". Compared to traditional methods, this process eliminates the need for manual and repeated data matching, making it more direct, concise, and accurate. This solves the technical problems of existing reverse engineering methods, such as cumbersome operations and large errors in the extracted gear parameters, which lead to low accuracy in the generated tooth profile.

[0029] 2. It changes the traditional method of relying on manual trial and error to adjust parameters, and can automatically find methods that simultaneously satisfy dimensional constraints and geometric constraints (such as...). = This provides the only solution to reduce the complexity of manual intervention. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating the reverse construction method for composite tooth profile parameters of the present invention.

[0031] Figure 2 This is a schematic diagram of a semi-tooth-shaped profile;

[0032] Figure 3 This is a schematic diagram of the full tooth profile. Detailed Implementation

[0033] 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.

[0034] Embodiments of the present invention provide a gear design method, wherein the gear is designed by means of a tooth profile; the tooth profile is obtained by a tooth profile construction method based on the reverse construction of composite tooth profile parameters. The tooth profile construction method based on the reverse construction of composite tooth profile parameters is implemented based on the reverse construction method of composite tooth profile parameters, and its core point is that only the tip circle diameter needs to be input. Root circle diameter and number of teeth Therefore, the accurate target module m can be obtained based on the reverse construction method of composite tooth profile parameters. Target displacement coefficient x n Target pressure angle α Then, based on the target module, target displacement coefficient, and target pressure angle, the tooth profile of the target gear can be calculated (e.g., Figure 2 , Figure 3 As shown), where the tooth tip circle diameter is... Root circle diameter and number of teeth This refers to the data of the target gear being reverse-engineered, which are the intuitive parameters of the gear to be designed. It eliminates the need to extract parameters such as the module, displacement coefficient, and pressure angle of the gear being imitated, thus avoiding errors caused by traditional methods in extracting these parameters. This improves the accuracy of the gear profile after reverse engineering, solving the technical problems of cumbersome operation and large errors in extracted gear parameters leading to low accuracy of the generated tooth profile in existing reverse engineering methods. This tooth profile construction method based on composite tooth profile parameters can also be edited into a computer program / instruction and embedded in a computer system, computer-readable storage medium, or computer program product, thus becoming an intelligent reverse engineering tool that only requires inputting the target tooth tip circle diameter. Target tooth root circle diameter and number of teeth This allows us to obtain the target module, target displacement coefficient, and target pressure angle, and even further generate the gear profile required for machining based on the target module, target displacement coefficient, and target pressure angle.

[0035] The thought process of the reverse construction method for composite tooth profile parameters is as follows: Figure 1 As shown:

[0036] Build Step 1:

[0037] Preset / Known Tooth Tip Circle Diameter Root circle diameter And the number of teeth z.

[0038] In this step, we only need to provide the addendum circle diameter, dedendum circle diameter, and number of teeth of the gear we want to reverse engineer. These three parameters are much easier to obtain intuitively than the module, displacement coefficient, and pressure angle. For example, the number of teeth can be observed directly by the human eye, and existing measuring tools can also measure the addendum circle diameter and dedendum circle diameter very intuitively. In contrast, the module, displacement coefficient, and pressure angle need to be calculated multiple times based on manually measured parameters. It can be seen that the data input in this case is obviously more accurate, with virtually no data errors. This greatly improves the accuracy of the final module, displacement coefficient, pressure angle, and gear profile, and significantly reduces the computational intensity of manual intervention.

[0039] Step 2 of the construction process:

[0040] Define / use three separate functions for the addendum arc, involute, and root arc;

[0041] Based on three functions and a preset tooth tip circle diameter Root circle diameter Given the number of teeth z, construct a system of constraint equations. :

[0042] ;

[0043] in, Constraints on the tip circle diameter. This is the current radius of the tooth tip arc; Constraints based on the root circle diameter. This is the current radius of the tooth root arc; For isotopic fillet constraints; , These are the currently preset modulus, displacement coefficient, and pressure angle, respectively. For a moving circle center model,

[0044] In this step, Equivalent to , This refers to the reference center position of the tooth profile arc segment, which is determined by the distance from the follower center to the gear rotation center. Quantify, It's not fixed. The purpose of setting up three functions is to... , Subsequent iterative optimizations are performed to select the optimal one. value, Value. The isotopic fillet constraint refers to the fact that the radius of the tooth tip radius is equal to the radius of the tooth root radius. This constraint equation system... Essentially, it uses a follower-centered model to define the center positions of the tooth tip arc and tooth root arc in order to find the corresponding optimal module, displacement coefficient, and pressure angle.

[0045] Step 3 of the construction process:

[0046] Based on the current Determine the center of the current tooth tip arc. The optimal tangent point B between the involute and the tooth tip arc is found through iterative algorithm one, i.e., the normal to tangent point B passes through... Determine the current time value.

[0047] This step involves the constraint equation system. middle The iterative steps are to iteratively and automatically search for the optimal point of tangency B between the tooth tip arc and the involute, where the normal to tangency B passes through... At this point, the tangent point B is the current optimal tangent point, and thus the most suitable radius of the tooth tip arc can be obtained. .

[0048] Step 4 of the construction process:

[0049] Based on the current Determine the center of the current tooth root arc. The optimal tangent point C between the involute and the tooth tip arc is found through iterative algorithm one, i.e., the normal to tangent point C passes through... Determine the current time value.

[0050] This step involves the constraint equation system. middle The iterative steps are to automatically search for the optimal point of tangency C between the tooth tip arc and the involute, where the normal to tangency C passes through... When this point C is the optimal point of tangency, the most suitable radius of the tooth tip arc can be obtained. .

[0051] Step 5 of the construction process:

[0052] Based on the current value, The value is obtained through a two-step iterative algorithm. The value is iterated to X. When the constraint equations are satisfied .

[0053] This step involves macro-level iterations, which can be obtained from previous steps. , This reduces the number of unknowns, allowing for the formulation of a system of constraint equations. This iteration differs from the previous two not only in its algorithm but also in its purpose. The primary goal is to iterate over the overall geometric constraints of the tooth tip arc, involute, and tooth root arc, continuously reducing the errors between the tooth tip arc and the target value, the involute and the target value, and the tooth root arc and the target value, thus intelligently adjusting the algorithm. If any parameter value has a non-zero error, the first two iterations are repeated until all errors are zero, finally yielding a result that meets the requirements. The parameter value, i.e., X .

[0054] Step 6 of the construction process:

[0055] At this time, X The value is the target parameter (target modulus m) constructed in reverse. Target displacement coefficient x n Target pressure angle α ).

[0056] In summary, the reverse construction method for composite tooth profile parameters of this invention proposes for the first time a "following center" model, constructing the arc center as a function that dynamically shifts with the displacement coefficient. Based on this, a "macro-micro" double-layer nested numerical iterative algorithm is designed: the micro layer automatically searches for the precise tangent points B and C between the involute and the tooth tip / root arc connection points, ensuring a strictly smooth and interference-free tooth profile; the macro layer utilizes the Jacobian matrix for global optimization until the three strong constraints of equal tooth tip diameter, tooth root diameter, and arc radius are satisfied. This invention breaks through the traditional trial-and-error mode that requires pre-setting the module and pressure angle, achieving automatic inverse calculation of optimal parameters and output of a tooth profile that meets the requirements by only inputting three intuitive geometric quantities: "tooth tip diameter, tooth root diameter, and number of teeth." Compared to traditional methods, this process eliminates the need for manual and repeated parameter adjustments, making it more direct, concise, and accurate.

[0057] The complete implementation scheme of this invention is as follows:

[0058] Implementation Step 1: Define the design goals and initial assumptions.

[0059] Define the rigid boundary conditions for the gear design: target tooth tip circle diameter Target tooth root circle diameter and number of teeth Define the initial value vector for the solution variables. =[m0, x n0 ,α0].

[0060] m0 is the initial guessed modulus.

[0061] x n0 These are the initial guesses for the displacement coefficients.

[0062] α0 is the initial guessed pressure angle.

[0063] This step describes the input data; the initial value vector is the one mentioned above. The parameter value is arbitrarily given and belongs to the starting point of the iteration.

[0064] Step 2: Construct the geometric model of the "following circle center".

[0065] This is the core step of the invention. In the reverse design of non-standard gears, a fixed center cannot simultaneously satisfy the requirements of the tooth tip / root circle diameter and equal radius. To address the challenge of strong constraints, this invention proposes for the first time a "following center" model, constructing the arc center as a function that dynamically shifts with the displacement coefficient. In each iterative calculation, based on the current modulus... and displacement coefficient Define the reference center position of the tooth profile arc segment. Its mathematical expression is:

[0066]

[0067] It is the distance (mm) from the center of the following circle (the center of the arc of the tooth tip and the tooth root) to the center of rotation of the gear.

[0068] The physical meaning of this formula is that in standard gears, the addendum / root radius is usually positioned based on the pitch circle. However, when a displacement coefficient is introduced... If the center of the arc is fixed in its original position, it will lead to tooth mismatch. The "following center" concept proposed in this invention allows the center of the arc to shift radially synchronously with the displacement. This allows the ideal circular arc-involute tangent relationship to be maintained even under displacement conditions.

[0069] High-precision parameter reverse calculation capability: By introducing the "following circle center" geometric model, it is possible to accurately describe the coupling effect of the displacement coefficient on the tooth profile arc position, thus ensuring the theoretical correctness of the tooth profile while meeting the actual tooth tip / tooth root circle diameter.

[0070] Automated fulfillment of multiple constraints: This method changes the traditional reliance on manual trial and error to adjust parameters, automatically finding ways to simultaneously satisfy dimensional and geometric constraints (such as...). = The only solution to ).

[0071] Step 3: Establish the geometric relationship between the involute and the tooth tip arc and tooth root arc.

[0072] 1. Define the tooth tip radius function:

[0073] Description: with With center at and radius at, The arc.

[0074]

[0075] Parameter variables: ; u The angle parameter of the tooth tip arc function; u B Let u be the value of the angle parameter at the tangent point B; the coordinates of the tooth tip arc function are... .

[0076] Note: The corresponding highest point A of the tooth tip (on the Y-axis), The point of tangency with the involute is B.

[0077] 2. Define the involute function:

[0078] Description: Base circle is And includes phase shift The equation of the involute.

[0079]

[0080] Parameter variables: .

[0081] For the involute development angle, For the tooth tip tangent point parameters, These are the parameters for the tooth root tangent point.

[0082] The base circle radius (in mm). .

[0083] This represents the offset of the involute's initial phase. .

[0084] θ is the pressure angle. z is the number of teeth. m is the module. The coefficients are the displacement coefficients; the coordinates of the involute function are... .

[0085] 3. Define the tooth root circular arc function:

[0086] Description: with With center at and radius at, The arc. Center of the circle. yes Rotate around the origin The position after.

[0087] Center coordinates: .

[0088]

[0089] Parameter variables: ; θ The angle parameter of the tooth root arc function; the center of the circle. The coordinates are ; θ C Let be the value of the angle parameter of the tooth root arc function at the tangency point C; the coordinates of the tooth root arc function are... .

[0090] Note: The lowest point D of the tooth root arc (the connection point with the adjacent tooth) corresponds to this.

[0091] Step 4: Nonlinear inverse function finding of three variables and three constraints.

[0092] Based on the above three functions, i.e., the geometric definitions, the final optimization equation system (constraint equation system) is constructed. =0. .

[0093] Tooth tip circle diameter constraint: .

[0094] Tooth root circle diameter constraint: .

[0095] Topological fillet constraints: .

[0096] in It is not a simple analytical variable, but a geometric value obtained in real time through the inner iteration in step five below, based on the three functions mentioned above.

[0097] Step 5: Implement a "macro-micro" double-layer nested numerical iterative solution.

[0098] To solve the aforementioned highly nonlinear system of equations, this embodiment employs a "double-nested, three-iteration" numerical solution strategy. This strategy includes a macroscopic main loop and two microscopic sub-loops, ensuring both geometric smoothness and physical dimensional accuracy when inversely solving for gears of arbitrary sizes.

[0099] The following is an analysis of the specific execution logic and function of the three iterations:

[0100] 1. First iteration (micro sub-loop ①): Tooth tip geometry locking.

[0101] Its goal is to find the precise tangent point B between the involute and the tooth tip arc, given the module, displacement coefficient, and pressure angle, and the center of the moving circle. The location has been determined. The algorithm searches for the involute's development angle through numerical approximation. Continue until a point is found such that the normal to that point passes precisely through the center of the circle. Calculate the actual tooth tip radius under the current design parameters. (Right now The value ensures a smooth transition at the tooth tip, significantly reducing the risk of tooth tip interference and ensuring that the theoretical tooth profile is free from geometric interference.

[0102] 2. Second iteration (micro sub-cycle ②): tooth root geometric locking.

[0103] Its goal is to find the precise tangent point C between the involute and the tooth tip arc, based on the coordinates after rotating the center of rotation. The algorithm restarts the numerical search, looking for a point deep within the involute such that the normal at that point passes precisely through the center of the circle. Calculate the actual tooth root fillet radius under the current design parameters. (Right now The value ensures a smooth transition at the tooth tip, significantly reducing the risk of tooth tip interference and ensuring that the theoretical tooth profile is free from geometric interference.

[0104] 3. Third iteration (macro main loop): global inverse calculation of all parameters.

[0105] An iterative algorithm is employed, continuously receiving three error values ​​(tooth tip error, tooth root error, and arc radius error) returned from the inner iteration. The error gradient is analyzed using the Jacobian matrix, and adjustments are made intelligently. The algorithm calculates the value of the parameter and triggers the inner iteration again until all errors are zero. Under the premise of satisfying the basic geometric conditions for gear forming, this algorithm can efficiently converge to the parameter set that satisfies the design constraints.

[0106] The iterative algorithms used in the above three iterations are shown in Table 1 below:

[0107] Table 1 shows the iterative algorithms used in the three iterations.

[0108]

[0109] In addition, the above iterative algorithm can be replaced by other iterative algorithms. For example, the first and second iterations are both micro-sub-iterations. The main purpose of the micro-sub-iterations is to smoothly connect points B and C. Originally, the Newton-Raphson method was used, but other algorithms such as 1. Bisection Method, 2. Secant Method, and 3. Brent's Method can also be used.

[0110] The third iteration is a macroscopic main iteration. The main function of the macroscopic main iteration is to perform a global iteration from a global perspective until a value that meets the overall requirements is found. This is both the implementation level and the intuitive level. Originally, the Levenberg-Marquardt (LM) iterative algorithm was used, but other algorithms that can be used include: 1. Trust-Region Dogleg; 2. Gauss-Newton method; 3. Genetic Algorithm / Particle Swarm Optimization (GA / PSO); 4. Sequential Quadratic Programming (SQP), etc.

[0111] Based on the above description, the mechanism of the three iterations is clarified, and the constraint equations in step four are solved through numerical iteration. Then we can obtain a unique solution that satisfies the constraints of the space. Ultimately, a semi-tooth profile that meets the design requirements can be output using general programming methods, such as... Figure 2 The full tooth profile is generated by rotation, such as... Figure 3 , Figure 3 The blue line represents the tooth profile (gear outline), the red dashed line represents the pitch circle of the gear, and the green dashed line represents the base circle of the gear.

[0112] In summary, this invention constructs a ternary nonlinear equation system with constraints including the equality of the addendum circle diameter with a preset addendum circle diameter, the dedendum circle diameter with a preset dedendum circle diameter, and the addendum arc radius with the dedendum arc radius, and performs a full-parameter inverse calculation. The abstract problem of the constraints obtained from the above full-parameter inverse calculation is transformed into a numerical iteration problem through a "following center" model, whereby the center radius of the arc segment is defined as a function of the module and the displacement coefficient. This is used as the core variable of the constraint equation, and the optimal solution (i.e., optimal module, optimal displacement coefficient, and optimal pressure angle) is automatically found by using a two-level iteration method. With the help of the optimal solution, the tooth profile of the reverse-constructed near-perfect gear can be calculated almost perfectly. This achieves high-precision gear reverse construction using only intuitive data, thereby solving the technical problems of existing reverse construction methods being cumbersome to operate and having large errors in the extracted gear parameters, resulting in low accuracy of the generated tooth profile.

[0113] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0114] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A tooth profile construction method based on reverse construction using composite tooth profile parameters, comprising: Through the target modulus m Target displacement coefficient x n Target pressure angle α Design a semi-tooth profile of the target gear; rotate and copy the semi-tooth profile to generate the tooth profile; Its characteristic is that m x n α Constructed using the reverse construction method based on composite tooth profile parameters: Based on the known tooth tip circle diameter Root circle diameter Given the number of teeth z, a set of constraint equations is constructed based on the addendum circle function, involute function, and root circle function. : ； in, Constraints on the tip circle diameter; Constraints the root circle diameter; For equal topological fillet constraints; , These are the currently preset modulus, displacement coefficient, and pressure angle, respectively. For a moving center model, ; The current tooth tip radius, based on the current... Determine the center of the current tooth tip arc. Iteratively find the optimal tangent point B between the involute and the tooth tip arc, where the normal to tangent point B passes through... Determine the current time value; The current root radius, based on the current... Determine the center of the current tooth root arc. Iteratively find the optimal tangent point C between the involute and the tooth tip arc, where the normal to tangent point C passes through... Determine the current time value; Based on the current value, The value is iterated until X satisfies the system of constraint equations. m x n α These are X at this time. The value of .

2. The tooth profile construction method based on reverse construction of composite tooth profile parameters according to claim 1, characterized in that, The tooth tip arc function is: Among them, the tooth tip arc is based on With center at and radius at, The arc; ; u The angle parameter of the tooth tip arc function; u B Let u be the value of the angle parameter at the tangent point B; the coordinates of the tooth tip arc function are... .

3. The tooth profile construction method based on reverse construction of composite tooth profile parameters according to claim 1, characterized in that, The involute function is: in, The radius of the base circle; ; This represents the offset of the initial phase of the involute. ; The pressure angle; , For the involute development angle, For the tooth tip tangent point parameters, Here are the parameters for the tooth root tangent point; the coordinates of the involute function are... .

4. The tooth profile construction method based on reverse construction of composite tooth profile parameters according to claim 1, characterized in that, The root arc function is: Among them, the root arc is based on With center at and radius at, The arc; the center yes Rotate around the origin The position after; ; ; θ The angle parameter of the tooth root arc function; the center of the circle. The coordinates are ; θ C The angle parameter of the tooth root arc function at the tangent point C The value at the location; the coordinates of the tooth root circular arc function are .

5. The tooth profile construction method based on reverse construction of composite tooth profile parameters according to claim 1, characterized in that, , The same iterative algorithm is used for iteration, which can be the Newton-Raphson iterative algorithm, or the bisection method, or the secant method, or the Brent method.

6. The tooth profile construction method based on reverse construction of composite tooth profile parameters according to claim 1, characterized in that, X is iterated using an iterative algorithm two, which can be the LM iterative algorithm, the trust region dogleg method, the Gauss-Newton method, the genetic algorithm, or the sequential quadratic programming algorithm.

7. A gear design method, wherein the gear is obtained by designing its tooth profile; Its features are: The tooth profile is obtained by the tooth profile construction method based on the reverse construction of composite tooth profile parameters as described in any one of claims 1 to 6.

8. A computer system comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the tooth profile construction method based on reverse construction of composite tooth profile parameters as described in claim 1.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the tooth profile construction method based on the reverse construction of composite tooth profile parameters as described in claim 1.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the tooth profile construction method based on the reverse construction of composite tooth profile parameters as described in claim 1.

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