Plastic worm gear tooth thickness optimization design method, device and equipment and storage medium

Abstract

The application provides a plastic worm gear tooth thickness optimization design method, device, equipment and storage medium, and the method comprises the following steps: calculating geometric parameters according to the number of teeth, modulus, pressure angle and input torque of worm gear transmission; a first functional relationship between worm gear shearing stress and tooth thickness displacement coefficient is established; a second functional relationship between worm gear root bending stress and tooth thickness displacement coefficient is established through root dangerous section analysis; the optimal tooth thickness displacement coefficient is solved and the best tooth thickness is obtained by taking the minimum worm gear shearing stress as the target and the worm gear root bending stress not exceeding the allowable stress as the constraint. The plastic worm gear shearing stress model and the metal worm gear root bending stress model are established, and both are included in the unified optimization framework, the optimal design of the worm gear tooth thickness is realized under the premise of ensuring the strength of the worm gear, the limitation that the prior art only focuses on the strength of a single part is overcome, the blindness of the experience design is avoided, and the design efficiency and quality are improved.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method, apparatus, device, and storage medium for optimizing the tooth thickness of a plastic worm gear. Background Technology

[0002] Plastic worm gears paired with metal worms offer advantages such as low noise, self-lubrication, and lightweight construction, making them widely used in automobiles, home appliances, and precision instruments. During the design process, tooth thickness is a key parameter affecting transmission performance and service life. The mechanical properties of plastic materials differ significantly from those of metal materials; plastic failure primarily manifests as shear failure, and traditional metal gear design methods are difficult to directly apply to the tooth thickness design of plastic worm gears.

[0003] In existing technologies, the design of plastic worm gear tooth thickness mainly relies on empirical formulas and trial-and-error methods. Designers typically refer to the design standards for metal gears and then adjust the tooth thickness appropriately based on experience. This method lacks theoretical basis and is inefficient. More importantly, existing design methods only focus on the strength verification of the plastic worm gear, ignoring the impact of tooth thickness variations on the strength of the metal worm. This often leads to overly conservative design results or potential safety hazards, failing to achieve the optimal design of the plastic worm gear tooth thickness while ensuring the strength of the worm. Summary of the Invention

[0004] The main objective of this invention is to solve the technical problem that existing plastic worm gear tooth thickness design methods only focus on the strength of the worm gear and ignore the strength constraints of the worm, resulting in the inability to achieve optimal system design; This invention provides a method for optimizing the tooth thickness of a plastic worm gear, the method comprising: Calculate the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle, and input torque of the worm gear drive; Based on the geometric parameters, a first functional relationship is established between the worm gear shear stress and the tooth thickness displacement coefficient. Based on the geometric parameters, a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient is established through tooth root critical section analysis. Based on the first and second functional relationships, with the minimum shear stress of the worm gear as the objective function and the bending stress at the root of the worm tooth not exceeding the allowable stress as the constraint condition, the optimal tooth thickness displacement coefficient is solved, and the optimal tooth thickness of the plastic worm gear is obtained based on the optimal tooth thickness displacement coefficient.

[0005] The present invention also provides a plastic worm gear tooth thickness optimization design device, the plastic worm gear tooth thickness optimization design device comprising: The geometric parameter calculation module is used to calculate the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle and input torque of the worm gear drive. The worm gear stress modeling module is used to establish a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient based on the geometric parameters. The worm stress modeling module is used to establish a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient based on the geometric parameters and through tooth root critical section analysis. The optimization solution module is used to solve for the optimal tooth thickness displacement coefficient based on the first functional relationship and the second functional relationship, with the objective function being the minimum shear stress of the worm gear and the constraint condition being that the bending stress at the root of the worm tooth does not exceed the allowable stress. The optimal tooth thickness of the plastic worm gear is then obtained based on the optimal tooth thickness displacement coefficient.

[0006] The present invention also provides a plastic worm gear tooth thickness optimization design device, comprising: a memory and at least one processor, wherein the memory stores instructions, and the memory and the at least one processor are interconnected by a circuit; the at least one processor calls the instructions in the memory to cause the plastic worm gear tooth thickness optimization design device to perform the steps of the above-described plastic worm gear tooth thickness optimization design method.

[0007] The present invention also provides a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the steps of the above-described plastic worm gear tooth thickness optimization design method.

[0008] The aforementioned method, apparatus, equipment, and storage medium for optimizing the tooth thickness of plastic worm gears calculate geometric parameters based on the number of teeth, module, pressure angle, and input torque of the worm gear drive; establishes a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient; establishes a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient through tooth root critical section analysis; and solves for the optimal tooth thickness displacement coefficient and obtains the optimal tooth thickness by taking the minimum worm gear shear stress as the objective and the worm tooth root bending stress not exceeding the allowable stress as the constraint. This invention establishes a plastic worm gear shear stress model and a metal worm tooth root bending stress model, incorporating both into a unified optimization framework. This achieves optimal worm gear tooth thickness design while ensuring worm strength, overcoming the limitations of existing technologies that only focus on the strength of a single component, avoiding the blindness of empirical design, and improving design efficiency and quality.

[0009] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0010] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of an embodiment of the plastic worm gear tooth thickness optimization design method in this invention; Figure 2 This is a schematic diagram of one embodiment of the plastic worm gear tooth thickness optimization design device in this invention; Figure 3 This is a schematic diagram of one embodiment of the plastic worm gear tooth thickness optimization design device in this invention; Figure 4 This is a schematic diagram illustrating the determination of the critical section at the root of the worm gear in an embodiment of the present invention; Figure 5 This is a schematic diagram comparing the tooth profiles of the plastic worm gear and the metal worm before optimization in an embodiment of the present invention; Figure 6 This is a schematic diagram comparing the tooth profiles of the optimized plastic worm gear and the metal worm in an embodiment of the present invention. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions 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, 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.

[0013] The terms "comprising" and "having," and any variations thereof, used in the embodiments of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the steps or units listed, but may optionally include other steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0014] To facilitate understanding of this embodiment, a detailed description of the plastic worm gear tooth thickness optimization design method disclosed in this embodiment of the invention will be provided first. For example... Figure 1 As shown, this method includes the following steps: 101. Calculate the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle, and input torque of the worm gear drive; In this embodiment, calculating the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle, and input torque of the worm gear drive includes: calculating the pitch circle diameter of the worm and the pitch circle diameter of the worm wheel based on the number of teeth and module; calculating the center distance based on the pitch circle diameter of the worm and the pitch circle diameter of the worm wheel; calculating the addendum circle diameter and base circle diameter of the worm and worm wheel based on the pitch circle diameter, module, and number of teeth; and calculating the pitch circle helix angle, the worm base circle helix angle, and the worm wheel base circle helix angle based on the pressure angle and helix parameters.

[0015] Specifically, based on the basic design parameters of the worm gear transmission system, the various geometric parameters required for subsequent stress analysis can be calculated. For example, when optimizing the tooth thickness of a plastic worm gear and a metal worm, it is necessary to obtain the number of worm threads z1, the number of worm gear teeth z2, and the normal module m in advance. n The known conditions include the end face module mt, pressure angle α, input torque T1, and output torque T2. Among these, the number of worm threads z1 can be understood as the number of spiral lines in the worm, and the number of worm wheel teeth z2 represents the number of teeth on the worm wheel circumference. These parameters are typically determined by the transmission ratio and load requirements.

[0016] It should be noted that in this embodiment, the input torque T1 acts on the worm gear, and the output torque T2 acts on the worm wheel; there is a transmission ratio between them. The pressure angle α is generally taken as a standard value and is not specifically limited thereto.

[0017] Based on this, the pitch circle diameter d1 of the worm can be calculated using the following formula: ; Where mt is the end face module and q is the worm diameter coefficient. It should be noted that the selection of this worm diameter coefficient q will affect the stiffness and strength of the worm, and it usually needs to be reasonably selected according to the transmission requirements and stress conditions. Generally speaking, a larger diameter coefficient can improve the bending stiffness of the worm, but it will also increase the overall size of the transmission device. No specific limit is made on this.

[0018] The pitch circle diameter d2 of the worm gear can be calculated using the following formula: ; Where z2 is the number of teeth on the worm gear. It can be understood that the pitch circle diameter of the worm gear is the benchmark for its geometric design, determining its pitch circle position. The pitch circle diameter is directly proportional to the number of teeth and the module, a relationship that reflects the fundamental geometric principle of gear transmission. Furthermore, based on the aforementioned worm pitch circle diameter d1 and worm gear pitch circle diameter d2, the center distance a of the worm gear transmission can be calculated: ; The center distance 'a' represents the perpendicular distance between the worm gear axis and the worm wheel axis. Deviations in the center distance will cause changes in tooth backlash, thus affecting transmission accuracy.

[0019] In this embodiment, it is also necessary to obtain the addendum circle diameter and base circle diameter of the worm and worm wheel, including the addendum circle diameter of the worm. worm base circle diameter worm gear tooth tip circle diameter worm gear base circle diameter These geometric parameters can be calculated using standard gear design methods based on the pitch circle diameter, module, number of teeth, and pressure angle, without any specific limitations.

[0020] It should be noted that the tooth thickness displacement coefficient affects the tip circle diameter. In the optimization method of this invention, the tooth thickness displacement coefficient achieves the coordination of the strength of the worm gear and the worm by changing the tooth thickness distribution, which will be described in detail in subsequent embodiments and will not be repeated here.

[0021] In this embodiment, the helix angle parameter is used to calculate the meshing efficiency. The size of the helix angle is related to the inclination of the worm helix, affecting the self-locking performance and efficiency of the transmission.

[0022] The pitch circle helix angle and base circle helix angle can be calculated based on the pressure angle and helix parameters. For example, the pitch circle helix angle β represents the inclination angle of the worm helix on the pitch cylinder surface, and the worm base circle helix angle... and the helix angle of the worm gear base circle These represent the helix angle on the base circle. The more threads a worm has or the smaller the pitch circle diameter, the larger the helix angle, which improves transmission efficiency but reduces self-locking performance.

[0023] In worm gear drives, there is a geometric relationship between the helix angle of the worm and the helix angle of the worm wheel, which affects the contact state between the worm wheel and the worm during meshing.

[0024] 102. Based on the aforementioned geometric parameters, establish a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient; In this embodiment, establishing the first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient based on the geometric parameters includes: calculating the transmission meshing efficiency and friction angle based on the input torque, pitch circle helix angle, and friction coefficient; calculating the functional relationship between the worm gear shear area and the tooth thickness displacement coefficient based on the geometric parameters; and establishing the first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient based on the input torque, meshing efficiency, friction angle, and the functional relationship between the shear area and the tooth thickness displacement coefficient.

[0025] Specifically, in this embodiment, the main failure mode of the plastic worm gear is shear failure, therefore it is necessary to establish a functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient. Establishing this functional relationship involves calculating the transmission meshing efficiency, friction angle, and shear area.

[0026] Specifically, when calculating the shear stress of the worm gear, it is first necessary to determine the shear force acting on the worm gear. This shear force can be calculated using the following formula: ; Where T2 is the output torque. This is the pitch circle diameter of the worm gear. It should be noted that this shear force... This represents the tangential force acting on the worm gear tooth surface; it is directly proportional to the output torque and inversely proportional to the pitch circle diameter. T1 is the input torque. The value is the staggered shaft meshing efficiency, and u is the transmission ratio.

[0027] In this embodiment, the staggered shaft meshing efficiency The following formula can be used for calculation: ; in, The pitch circle helix angle, Let be the friction angle. This formula illustrates the influence of the helix angle and the friction angle on transmission efficiency. The larger the helix angle, the higher the transmission efficiency, but the friction angle will reduce the transmission efficiency.

[0028] Friction angle The following formula can be used for calculation: ; Where u is the coefficient of friction. The friction angle is the normal pitch circle pressure angle. The friction angle reflects the frictional characteristics between the meshing surfaces of the worm gear and worm. A larger coefficient of friction results in a larger friction angle and lower transmission efficiency. The coefficient of friction is typically taken as 0.1, without specific limitations.

[0029] Based on this, the worm gear shear stress It can be represented as: ; in, K A This is a usage factor, typically ranging from 1 to 1.25. This is the overlap coefficient. This represents the shear area.

[0030] It should be noted that this shear area There is a functional relationship between the tooth thickness displacement coefficient x and the shear area. The larger the tooth thickness displacement coefficient x, the larger the worm gear tooth thickness and the shear area. This also increases accordingly, leading to shear stress. Decrease. This shear area. The specific calculations involve parameters such as the overlap of the normal plane, the length of the meshing line, and the maximum load-bearing tooth width, which will be explained in detail in subsequent embodiments and will not be repeated here.

[0031] Furthermore, the aforementioned shear force and shear area Substituting the expression into the shear stress formula, we can obtain the worm gear shear stress. The first functional relationship between the worm gear and the tooth thickness displacement coefficient x. This functional relationship shows that as the tooth thickness displacement coefficient x increases, the worm gear shear stress... Gradually decrease, that is, increasing the tooth thickness of the worm gear can reduce shear stress and improve the shear resistance of the worm gear.

[0032] Furthermore, the step of calculating the functional relationship between the worm gear shear area and the tooth thickness displacement coefficient based on the geometric parameters includes: calculating the normal plane overlap and the length of the tooth tip contact line based on the tooth tip circle diameter, base circle diameter, pitch circle diameter, and base circle helix angle of the worm and worm gear; calculating the overlap coefficient based on the normal plane overlap and the length of the tooth tip contact line; and calculating the maximum load-bearing tooth width based on the overlap coefficient; and establishing the functional relationship between the worm gear shear area and the tooth thickness displacement coefficient based on the maximum load-bearing tooth width.

[0033] Specifically, the functional relationship between the shear area of ​​the worm gear and the tooth thickness displacement coefficient is calculated based on the geometric parameters.

[0034] In this embodiment, the calculation of the worm gear shear area requires first determining the normal plane overlap and the length of the meshing line, and then calculating the overlap coefficient and the maximum load-bearing tooth width.

[0035] Specifically, the degree of overlap of the normal plane The following formula can be used for calculation: ; in, The length of the worm gear tooth tip engagement line. The length of the worm gear tooth tip meshing line, in meters. n Normal modulus, This is the normal pressure angle. The normal plane overlap reflects the number of gear teeth pairs that participate in meshing simultaneously during the meshing process. The greater the overlap, the smoother the transmission.

[0036] In this embodiment, the length of the worm gear tooth tip meshing line... The following formula can be used for calculation: ; in, The diameter of the worm gear tip circle is... The base circle diameter of the worm gear. The pitch circle diameter of the worm gear. Let be the helix angle of the worm's base circle. This formula calculates the length of the meshing line at the worm's tooth tip using the geometric relationship between the addendum circle, base circle, and pitch circle.

[0037] Similarly, the length of the worm gear tooth tip meshing line g_m2 can be calculated using the following formula: ; in, The diameter of the worm gear tooth tip circle is... The base circle diameter of the worm gear is... The pitch circle diameter of the worm gear. The helix angle is the base circle angle of the worm gear.

[0038] Furthermore, based on the coincidence of the normal plane It can calculate the overlap coefficient. : ; This overlap factor is used to correct the load distribution in shear stress calculations.

[0039] Based on this, the maximum load-bearing tooth width can be calculated. The maximum load-bearing tooth width is limited by the geometric relationship between the tooth tip circle and the center distance, and can be calculated using the following formula: ; Where 'a' is the center distance and 'b2' is the actual tooth width of the worm gear. This formula shows that the maximum load-bearing tooth width is the smaller of the geometrically constrained calculated value and the actual tooth width. Geometrically, once the positional relationship between the worm tooth tip circle and the worm gear tooth tip circle is determined, the width of the effective meshing area is finite.

[0040] It should be noted that the shear area It is also related to the tooth thickness. In this embodiment, the shear area... The following formula can be used for calculation: ; in, The thickness of the end face tooth at the tip circle of the worm gear tooth. Let be the tooth thickness at the tip circle of the worm gear. This formula uses a weighted average method to comprehensively consider the contribution of the tooth thickness of the worm and worm gear at the tip circle to the shear area.

[0041] In this embodiment, the end face tooth thickness at the tip circle of the worm gear tooth The calculation of involute functions can be determined using the following formula: ; in, Let s2 be the intermediate calculated diameter, and s2 be the tooth thickness of the worm gear end face. Let be the involute function value of the pressure angle on the worm gear end face. The involute function inv(α) is defined as inv(α) = tan(α) - α (in radians), x3 is the tooth thickness displacement coefficient, and m2 is the worm gear module. This is the normal pressure angle.

[0042] Similarly, the end face tooth thickness at the tip circle of the worm gear tooth The following formula can be used for calculation: ; It is understandable that the above and The calculation formulas all include the tooth thickness displacement coefficient x, therefore the shear area It is a function of the tooth thickness displacement coefficient x. As the tooth thickness displacement coefficient x increases, the end face tooth thickness... and Increase, which in turn leads to shear area Increased, ultimately leading to shear stress This reduces the shear area of ​​the worm gear. Thus, the above calculations establish a functional relationship between the shear area of ​​the worm gear and the tooth thickness displacement coefficient. 103. Based on the aforementioned geometric parameters, a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient is established through tooth root critical section analysis. In this embodiment, establishing a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient based on the geometric parameters and through analysis of the critical section of the tooth root includes: determining the coordinates of the tangent point of the critical section of the tooth root using the transition curve analytical method and the tangent method; calculating the distance from the tooth root to the coordinates of the tangent point and the tooth thickness at the coordinates of the tangent point, and calculating the normal force acting at the coordinates of the tangent point based on the input torque and the normal force angle; treating the worm tooth as a cantilever beam, and establishing a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient using the cantilever beam bending stress formula based on the normal force, the distance from the tooth root to the coordinates of the tangent point, and the tooth thickness at the coordinates of the tangent point.

[0043] Specifically, in this embodiment, the main failure mode of the metal worm gear is tooth root bending fatigue failure. Therefore, it is necessary to establish a functional relationship between the tooth root bending stress and the tooth thickness displacement coefficient. Unlike traditional empirical methods, this embodiment uses the cantilever beam 30° tangent method to accurately determine the location of the critical section at the tooth root.

[0044] Specifically, such as Figure 4 As shown, the worm gear tooth is considered as a cantilever beam, and the bending stress at the root of the worm gear tooth is... The following formula can be used for calculation: ; in, α is the normal force acting on the tooth surface. F The angle of application of the normal force. hF denoted by , where is the distance from the tooth root to the critical section, and b is the tooth width. s F The tooth thickness is at the critical section. This formula is the classic stress formula for cantilever beams under bending, simplifying the worm gear tooth into a cantilever beam model with one end fixed and the other end under stress.

[0045] It should be noted that the location of the critical section is not at the root circle, but needs to be precisely determined using the analytical method of the transition curve and the 30° tangent method. The critical section is located at the point where the tangent on the root transition curve forms a 30° angle with the horizontal direction; the bending stress is greatest at this location. Solving for the transition curve involves tool parameters and geometric parameters, which will be explained in detail in subsequent embodiments and will not be repeated here.

[0046] In this embodiment, normal force The tangential component can be calculated using the following formula: ; in, Let α be the tangential force, β be the pressure angle, β be the helix angle, T1 be the input torque, and d2 be the pitch circle diameter of the worm gear. This formula calculates the normal force component acting at the critical section by inputting the torque and geometric parameters.

[0047] In this embodiment, the normal force action angle α F The approximate value is the pressure angle α, which is usually about 10°, and no specific limit is made on this.

[0048] Based on this, the key to determining the critical section lies in calculating the tooth thickness sF at the tangent point coordinates and the distance hF from the tooth root to the tangent point. When the tangent point coordinates are determined using the analytical method of the transition curve ( x s , y s After that, the tooth thickness sF at the critical section can be determined according to the following relationship: ; This relationship is based on the symmetry of the tooth thickness, and the horizontal coordinate of the tangent point. x s That is, half the thickness of the tooth.

[0049] The distance hF from the tooth root to the critical section can be calculated using the following formula: This formula is based on the geometric relationship of a 30° tangent, and the vertical distance from the root circle to the point of tangency. y s The ratio of the tangent value to the tangent angle of 30° is the distance from the critical section to the tooth root.

[0050] It should be noted that the tooth thickness sF at the critical section has a functional relationship with the tooth thickness displacement coefficient x. When the tooth thickness displacement coefficient x increases, the worm gear tooth thickness increases while the worm tooth thickness decreases accordingly, resulting in a decrease in the tooth thickness sF at the critical section of the worm, which in turn leads to an increase in the bending stress at the worm tooth root. This is opposite to the changing trend of the worm gear shear stress, and it is precisely this opposite trend that makes the optimization problem necessary.

[0051] Furthermore, substituting the expressions for the normal force, tooth thickness sF, and distance hF into the bending stress formula, we can obtain the second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient x. This functional relationship shows that as the tooth thickness displacement coefficient x increases, the worm tooth root bending stress... Gradually increase, when When the allowable stress of the worm material is exceeded, the worm will fail.

[0052] It is understandable that within this functional relationship, there exists a critical tooth thickness displacement coefficient value that causes the worm tooth root bending stress to reach a certain level. It is exactly equal to the allowable stress. This critical value is the constraint boundary in the optimization solution. The tooth thickness displacement coefficient x cannot exceed this critical value, otherwise the worm gear strength will be insufficient.

[0053] Furthermore, determining the coordinates of the tangent point of the critical section of the tooth root using the transition curve analytical method and the tangent method includes: establishing the tooth root transition curve equation based on the tool parameters and geometric parameters, and differentiating the transition curve equation to obtain the expression for the tangent slope of the transition curve; based on the tangent slope expression, using the tangent method to iteratively solve for the coordinates of the tangent point on the transition curve that satisfies the preset angle condition through a preset angle determination condition.

[0054] Specifically, in this embodiment, the location of the critical section at the tooth root needs to be determined by establishing the tooth root transition curve equation and solving for the tangent point that satisfies the 30° tangent condition. The tooth root transition curve is the transition region curve connecting the tooth root and the tooth profile, and the shape of this curve is determined by the tooth profile of the machining tool.

[0055] Specifically, the equation for the tooth root transition curve can be established in the following form: ; Where r is the pitch circle radius, ψ is the tool tooth profile angle, φ is the rotation angle parameter, a is the distance from the center of the tool tip arc to the critical section, and ρ is the tool fillet radius. This set of equations describes the relationship between the coordinates of any point on the transition curve and the parameter φ.

[0056] In this embodiment, the calculation of tool-related parameters involves the addendum coefficient and clearance coefficient. The distance a1 from the center of the tool tip arc to the centerline can be calculated using the following formula: in, This is the tooth tip height coefficient. ρ is the clearance coefficient, and ρ is the tool fillet radius.

[0057] The distance b from the center of the tip arc of the tool to the center line of the tool teeth can be calculated using the following formula: in, Let be the end face pressure angle, and x be the tooth thickness displacement coefficient. It should be noted that this formula includes the tooth thickness displacement coefficient x; therefore, the shape of the transition curve will change with the displacement coefficient.

[0058] The fillet radius ρ of the cutting tool can be calculated using the following formula: Based on this, it is also necessary to calculate the relationship between the rotation angle parameter φ and the tool tooth profile angle ψ: Furthermore, to determine the location of the tangent point at the critical section, it is necessary to differentiate the transition curve equation to obtain the expression for the tangent slope. Differentiating the above transition curve equation with respect to ψ yields: The slope of the tangent line to the transition curve can be expressed as: ; This condition determines the location of the critical section. From a mechanical perspective, the 30° tangent position corresponds to the section where the stress is greatest when the cantilever beam is subjected to bending.

[0059] Based on this, a numerical iterative method can be used to solve for the coordinates of the tangent point that satisfies the above-mentioned tangent slope condition. Specifically, Newton's iteration method can be used, by continuously adjusting the parameter ψ, so that the calculated tangent slope dy / dx gradually approaches tan(30°) until the accuracy requirement is met. When the iteration converges, the parameter value corresponding to the tangent point can be obtained, and then the coordinates of the tangent point can be calculated according to the transition curve equation. x s , y s ).

[0060] It should be noted that, since the transition curve equation includes the tooth thickness displacement coefficient x, the coordinates of the tangent point ( x s , y sIt is also a function of the tooth thickness displacement coefficient x. When the tooth thickness displacement coefficient x changes, the shape of the transition curve changes, and the position of the tangent point also changes accordingly, which in turn affects the tooth thickness sF and distance hF at the critical section, and ultimately affects the bending stress at the worm tooth root. .

[0061] Thus, by using the analytical method of transition curves and the 30° tangent method, the coordinates of the tangent point of the critical section of the tooth root can be accurately determined. These coordinates are key parameters for subsequent calculation of the bending stress at the worm tooth root.

[0062] 104. Based on the first functional relationship and the second functional relationship, with the minimum shear stress of the worm gear as the objective function and the bending stress at the root of the worm tooth not exceeding the allowable stress as the constraint condition, solve for the optimal tooth thickness displacement coefficient, and obtain the optimal tooth thickness of the plastic worm gear based on the optimal tooth thickness displacement coefficient.

[0063] In this embodiment, the step of solving for the optimal tooth thickness displacement coefficient based on the first and second functional relationships, with the goal of minimizing the worm gear shear stress and the constraint that the worm tooth root bending stress does not exceed the allowable stress, and obtaining the optimal tooth thickness of the plastic worm gear based on the optimal tooth thickness displacement coefficient includes: establishing an objective function based on the first functional relationship with the goal of minimizing the worm gear shear stress; establishing a constraint condition for the worm tooth root bending stress based on the second functional relationship and the allowable stress of the worm material; constructing a constraint optimization model based on the objective function and the constraint condition, and solving the constraint optimization model using a numerical optimization algorithm to obtain the optimal tooth thickness displacement coefficient; and calculating the optimal tooth thickness of the plastic worm gear based on the optimal tooth thickness displacement coefficient, the module, and the pressure angle.

[0064] Specifically, such as Figure 5 As shown, when using traditional design methods, plastic worm gear teeth are relatively thin, making them prone to shear failure, while metal worm gear teeth are relatively thick. In this embodiment, the worm gear shear stress has been established through the aforementioned steps. The first functional relationship between the tooth thickness displacement coefficient x and the worm tooth root bending stress. The second functional relationship between the tooth thickness displacement coefficient x and the tooth thickness displacement coefficient. Based on these two functional relationships, a constrained optimization model can be constructed to solve for the optimal tooth thickness displacement coefficient.

[0065] Specifically, based on the first functional relationship, an objective function can be established with the goal of minimizing the shear stress of the worm gear: ; The objective function indicates the need to find a suitable tooth thickness displacement coefficient x to minimize the shear stress of the worm gear. The minimum value is reached. As the previous analysis shows, the larger the tooth thickness displacement coefficient x, the larger the worm gear tooth thickness, and the higher the shear stress. The smaller the value, the better. Therefore, the objective function is essentially to maximize the tooth thickness displacement coefficient x within the limits allowed by the constraints.

[0066] Based on this, according to the second functional relationship and the allowable stress of the worm material, the constraint conditions for the bending stress at the root of the worm can be established: ; in,[ [ ] represents the allowable stress of the worm material, which is determined based on the material's mechanical properties and safety factor. The constraints indicate that the tooth thickness displacement coefficient x must be selected to ensure that the bending stress at the worm tooth root does not exceed the allowable stress; otherwise, the worm will fail.

[0067] It should be noted that an increase in the tooth thickness displacement coefficient x leads to a decrease in the worm tooth thickness, which in turn increases the bending stress at the worm tooth root. The constraint increases, thus limiting the upper limit of the tooth thickness displacement coefficient x. The essence of the optimization problem is to maximize the shear resistance of the worm gear while meeting the strength requirements of the worm.

[0068] Furthermore, based on the above objective function and constraints, a constrained optimization model can be constructed: ; This optimization model unifies the strength requirements of the worm gear and worm into the same mathematical framework. By solving this optimization model, the optimal tooth thickness displacement coefficient can be obtained.

[0069] In this embodiment, a numerical optimization algorithm can be used to solve the constrained optimization model. Specifically, the solution steps include: First, initialize the range of values ​​for the tooth thickness displacement coefficient x. Based on engineering experience and geometric constraints, the tooth thickness displacement coefficient x usually takes values ​​within a certain range, and no specific limitation is made on this.

[0070] Secondly, given the tooth thickness displacement coefficient x, the worm gear shear stress τF(x) and the worm tooth root bending stress σF(x) are calculated respectively. The calculation process involves the formulas established in the preceding steps, including geometric parameter calculation, meshing efficiency calculation, shear area calculation, and transition curve solution.

[0071] Then, check if the constraints are met. If the calculated worm tooth root bending stress σF(x) is less than or equal to the allowable stress [ If σF(x) is greater than [ ], it means that the current tooth thickness displacement coefficient x satisfies the constraint condition; if σF(x) is greater than [ If the value is ], it means that the current x value is too large and needs to be reduced.

[0072] Based on this, the value of the tooth thickness displacement coefficient x is gradually adjusted, while satisfying the constraint condition σF(x) ≤ [ Under the premise of […], find the value of x that minimizes the shear stress τF(x) of the worm gear. Since τF(x) decreases as x increases, the optimal solution corresponds to the boundary of the constraint conditions, i.e., σF(x) = […]. The tooth thickness displacement coefficient x at that time.

[0073] Understandably, this optimization process can be implemented using an iterative method. Starting with a small value of x, x is gradually increased while monitoring the change in σF(x). When σF(x) approaches but does not exceed [ When the optimal tooth thickness displacement coefficient is found, the optimal tooth thickness displacement coefficient is found.

[0074] Once the optimal tooth thickness displacement coefficient is obtained, the optimal tooth thickness of the plastic worm gear can be calculated based on this displacement coefficient, module, and pressure angle. The relationship between the worm gear tooth thickness and the tooth thickness displacement coefficient can be determined using the standard gear displacement design formula. Once the tooth thickness displacement coefficient is determined, the tooth thickness of the worm gear at the pitch circle is also determined.

[0075] It should be noted that, compared with traditional empirical design methods, this embodiment, through establishing a precise mechanical model and optimizing the solution, can obtain the optimal tooth thickness in a single calculation, avoiding repeated trial and error and improving design efficiency. Simultaneously, the optimization result satisfies both the shear strength requirements of the worm gear and the bending strength requirements of the worm, achieving strength matching between the plastic worm gear and the metal worm. Figure 6 As shown, after adopting the optimization method of the present invention, the thickness of the plastic worm gear tooth increases and the shear stress decreases, while the thickness of the metal worm tooth decreases accordingly but still meets the constraint condition of tooth root bending stress, thus achieving a coordinated design between the two.

[0076] Thus, by solving the above-mentioned constraint optimization model, the optimal tooth thickness of the plastic worm gear can be obtained. This tooth thickness ensures the shear resistance of the worm gear itself, while preventing the worm from becoming too strong due to excessive increase.

[0077] In this embodiment, geometric parameters are calculated based on the number of teeth, module, pressure angle, and input torque of the worm gear drive; a first functional relationship is established between the worm gear shear stress and the tooth thickness displacement coefficient; a second functional relationship is established between the worm tooth root bending stress and the tooth thickness displacement coefficient through tooth root critical section analysis; with the goal of minimizing worm gear shear stress and the constraint that the worm tooth root bending stress does not exceed the allowable stress, the optimal tooth thickness displacement coefficient is solved to obtain the optimal tooth thickness. This invention establishes a plastic worm gear shear stress model and a metal worm tooth root bending stress model, incorporating both into a unified optimization framework. This achieves optimal worm gear tooth thickness design while ensuring worm strength, overcoming the limitations of existing technologies that only focus on the strength of a single component, avoiding the blindness of empirical design, and improving design efficiency and quality.

[0078] The above describes the method for optimizing the tooth thickness of plastic worm gears in embodiments of the present invention. The following describes the apparatus for optimizing the tooth thickness of plastic worm gears in embodiments of the present invention. Please refer to [link to apparatus description] for details. Figure 2 One embodiment of the plastic worm gear tooth thickness optimization design device of the present invention includes: The geometric parameter calculation module 201 is used to calculate the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle and input torque of the worm gear drive. The worm gear stress modeling module 202 is used to establish a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient based on the geometric parameters. The worm stress modeling module 203 is used to establish a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient based on the geometric parameters and through tooth root critical section analysis. The optimization solution module 204 is used to solve for the optimal tooth thickness displacement coefficient based on the first functional relationship and the second functional relationship, with the minimum shear stress of the worm wheel as the objective function and the bending stress at the root of the worm tooth not exceeding the allowable stress as the constraint condition, and to obtain the optimal tooth thickness of the plastic worm wheel based on the optimal tooth thickness displacement coefficient.

[0079] In this embodiment of the invention, the plastic worm gear tooth thickness optimization design device operates the aforementioned plastic worm gear tooth thickness optimization design method. The device calculates geometric parameters based on the number of teeth, module, pressure angle, and input torque of the worm gear drive; establishes a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient; establishes a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient through tooth root critical section analysis; and solves for the optimal tooth thickness displacement coefficient and obtains the optimal tooth thickness by taking the minimum worm gear shear stress as the objective and the worm tooth root bending stress not exceeding the allowable stress as the constraint. This invention establishes a plastic worm gear shear stress model and a metal worm tooth root bending stress model, incorporating both into a unified optimization framework. This achieves optimal worm gear tooth thickness design while ensuring worm strength, overcoming the limitations of existing technologies that only focus on the strength of a single component, avoiding the blindness of experience-based design, and improving design efficiency and quality.

[0080] above Figure 2 The plastic worm gear tooth thickness optimization design device in this embodiment of the invention is described in detail from the perspective of unitized functional entities. The plastic worm gear tooth thickness optimization design device in this embodiment of the invention is described in detail from the perspective of hardware processing.

[0081] Figure 3This is a schematic diagram of a plastic worm gear tooth thickness optimization design device 300 provided in an embodiment of the present invention. The plastic worm gear tooth thickness optimization design device 300 can vary significantly due to different configurations or performance. It may include one or more central processing units (CPUs) 310 (e.g., one or more processors) and a memory 320, and one or more storage media 330 (e.g., one or more mass storage devices) storing application programs 334 or data 332. The memory 320 and storage media 330 can be temporary or persistent storage. The program stored in the storage media 330 may include one or more units (not shown in the diagram), each unit may include a series of instruction operations on the plastic worm gear tooth thickness optimization design device 300. Furthermore, the processor 310 may be configured to communicate with the storage media 330 and execute the series of instruction operations in the storage media 330 on the plastic worm gear tooth thickness optimization design device 300 to implement the steps of the aforementioned plastic worm gear tooth thickness optimization design method.

[0082] The plastic worm gear tooth thickness optimization design device 300 may also include one or more power supplies 340, one or more wired or wireless network interfaces 350, one or more input / output interfaces 360, and / or one or more operating systems 331, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 3 The illustrated structure of the plastic worm gear tooth thickness optimization design device does not constitute a limitation on the plastic worm gear tooth thickness optimization design device provided by the present invention. It may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0083] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the plastic worm gear tooth thickness optimization design method.

[0084] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0085] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0086] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the tooth thickness of a plastic worm gear, characterized in that, The method for optimizing the tooth thickness of the plastic worm gear includes: Calculate the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle, and input torque of the worm gear drive; Based on the geometric parameters, a first functional relationship is established between the worm gear shear stress and the tooth thickness displacement coefficient. Based on the geometric parameters, a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient is established through tooth root critical section analysis. Based on the first and second functional relationships, with the minimum shear stress of the worm gear as the objective function and the bending stress at the root of the worm tooth not exceeding the allowable stress as the constraint condition, the optimal tooth thickness displacement coefficient is solved, and the optimal tooth thickness of the plastic worm gear is obtained based on the optimal tooth thickness displacement coefficient.

2. The method for optimizing the tooth thickness of a plastic worm gear according to claim 1, characterized in that, The calculation of the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle, and input torque of the worm gear drive includes: Calculate the worm gear pitch circle diameter and the worm wheel pitch circle diameter based on the number of teeth and module. Calculate the center distance based on the worm gear pitch circle diameter and the worm wheel pitch circle diameter; Calculate the addendum circle diameter and base circle diameter of the worm and worm wheel based on the pitch circle diameter, module, and number of teeth. Based on the pressure angle and helix parameters, calculate the pitch circle helix angle, worm base circle helix angle, and worm wheel base circle helix angle.

3. The method for optimizing the tooth thickness of a plastic worm gear according to claim 2, characterized in that, The step of establishing the first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient based on the geometric parameters includes: Calculate the transmission meshing efficiency and friction angle based on the input torque, pitch circle helix angle, and friction coefficient; Based on the aforementioned geometric parameters, calculate the functional relationship between the worm gear shear area and the tooth thickness displacement coefficient; Based on the functional relationship between the input torque, meshing efficiency, friction angle, shear area, and tooth thickness displacement coefficient, a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient is established.

4. The method for optimizing the tooth thickness of a plastic worm gear according to claim 3, characterized in that, The step of calculating the functional relationship between the worm gear shear area and the tooth thickness displacement coefficient based on the geometric parameters includes: Based on the addendum circle diameter, base circle diameter, pitch circle diameter, and base circle helix angle of the worm and worm wheel, the planar overlap ratio and the length of the addendum meshing line are calculated. Based on the normal plane overlap ratio and the length of the tooth tip contact line, calculate the overlap ratio coefficient, and based on the overlap ratio, calculate the maximum load-bearing tooth width; Based on the maximum load-bearing tooth width, a functional relationship is established between the worm gear shear area and the tooth thickness displacement coefficient.

5. The method for optimizing the tooth thickness of a plastic worm gear according to claim 1, characterized in that, The step of establishing a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient through tooth root critical section analysis based on the geometric parameters includes: The coordinates of the tangent point of the critical section at the tooth root are determined by the analytical method of transition curve and the tangent method. Calculate the distance from the tooth root to the coordinates of the tangent point and the tooth thickness at the coordinates of the tangent point, and calculate the normal force acting at the coordinates of the tangent point based on the input torque and the angle of action of the normal force; Treating the worm gear tooth as a cantilever beam, and based on the normal force, the distance from the tooth root to the tangent point coordinates, and the tooth thickness at the tangent point coordinates, the cantilever beam bending stress formula is used to establish a second functional relationship between the worm gear tooth root bending stress and the tooth thickness displacement coefficient.

6. The method for optimizing the tooth thickness of a plastic worm gear according to claim 5, characterized in that, The determination of the tangent point coordinates of the critical section at the tooth root using the transition curve analytical method and the tangent method includes: Based on the tool parameters and geometric parameters, the equation of the tooth root transition curve is established, and the derivative of the transition curve equation is obtained to obtain the expression of the tangent slope of the transition curve. Based on the expression for the tangent slope, the coordinates of the tangent points on the transition curve that satisfy the preset angle conditions are iteratively solved using the tangent method and the preset angle determination conditions.

7. The method for optimizing the tooth thickness of a plastic worm gear according to claim 1, characterized in that, The process of determining the optimal tooth thickness displacement coefficient based on the first and second functional relationships, with the objective function being the minimum shear stress of the worm gear and the constraint that the bending stress at the worm tooth root does not exceed the allowable stress, and obtaining the optimal tooth thickness of the plastic worm gear based on the optimal tooth thickness displacement coefficient includes: Based on the first functional relationship, an objective function is established with the goal of minimizing the shear stress of the worm gear. Based on the second functional relationship and the allowable stress of the worm material, the constraint conditions for the bending stress at the root of the worm tooth are established. Based on the objective function and constraints, a constrained optimization model is constructed, and a numerical optimization algorithm is used to solve the constrained optimization model to obtain the optimal tooth thickness displacement coefficient. The optimal tooth thickness of the plastic worm gear is calculated based on the optimal tooth thickness displacement coefficient, module, and pressure angle.

8. A device for optimizing the tooth thickness of a plastic worm gear, characterized in that, The plastic worm gear tooth thickness optimization design device includes: The geometric parameter calculation module is used to calculate the geometric parameters of the worm and worm wheel based on the number of teeth, module, pressure angle and input torque of the worm gear drive. The worm gear stress modeling module is used to establish a first functional relationship between the worm gear shear stress and the tooth thickness displacement coefficient based on the geometric parameters. The worm stress modeling module is used to establish a second functional relationship between the worm tooth root bending stress and the tooth thickness displacement coefficient based on the geometric parameters and through tooth root critical section analysis. The optimization solution module is used to solve for the optimal tooth thickness displacement coefficient based on the first functional relationship and the second functional relationship, with the objective function being the minimum shear stress of the worm gear and the constraint condition being that the bending stress at the root of the worm tooth does not exceed the allowable stress. The optimal tooth thickness of the plastic worm gear is then obtained based on the optimal tooth thickness displacement coefficient.

9. A device for optimizing the tooth thickness of a plastic worm gear, characterized in that, The plastic worm gear tooth thickness optimization design device includes: a memory and at least one processor, wherein the memory stores instructions; The at least one processor invokes the instructions in the memory to cause the plastic worm gear tooth thickness optimization design device to perform the steps of the plastic worm gear tooth thickness optimization design method as described in any one of claims 1-7.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instruction is executed by the processor, it implements the steps of the plastic worm gear tooth thickness optimization design method as described in any one of claims 1-7.

Images