Joint calculation method and device for contact stress and bending stress of straight gear

Abstract

The invention provides a joint calculation method and device for contact stress and bending stress of a straight gear. The method comprises the following steps: acquiring gear tooth surface equations of a driving wheel and a driven wheel of the asymmetric straight gear; respectively carrying out derivative calculation on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position; calculating according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel and the force vector on each wheel tooth in the target wheel to obtain the contact stress of the target wheel; and calculating according to the load force on the target wheel, the load angle of the upper bound point of conversion from the three-tooth meshing to the two-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient to obtain the bending stress of the tooth root of the target wheel. According to the method, the contact stress and the bending stress of the asymmetric straight gear can be accurately calculated.

Description

Technical Field

[0001] The present application relates to the field of mechanics, and in particular to a method and device for jointly calculating contact stress and bending stress of spur gears. Background Art

[0002] Most existing contact stress and bending stress calculation methods are based on symmetrical gears or low-contact gears, without considering the impact of asymmetry and high contact of asymmetrical gear tooth profile on stress distribution. Due to the asymmetry of asymmetrical gear tooth profile, the tooth surface load distribution and contact conditions are different from those of symmetrical gears, and a method is urgently needed to calculate the contact stress and bending stress of asymmetrical gear tooth profile. Summary of the invention

[0003] The main purpose of the embodiments of the present application is to propose a method and device for jointly calculating the contact stress and bending stress of spur gears, aiming to solve the problem that the existing stress calculation method cannot calculate the contact stress and bending stress of asymmetric spur gears.

[0004] To achieve the above object, a first aspect of an embodiment of the present application proposes a method for jointly calculating contact stress and bending stress of a spur gear, the method comprising: Obtaining a gear tooth surface equation of a driving wheel of an asymmetric spur gear and a gear tooth surface equation of a driven wheel of the asymmetric spur gear; Performing derivative calculations on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel respectively to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position; Calculating according to the radius of curvature of the driving wheel at the meshing position, the radius of curvature of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, to obtain the contact stress of the target wheel, wherein the contact stress of the target wheel includes the contact stress on each tooth in the target wheel, and the target wheel is the driving wheel or the driven wheel; The bending stress of the tooth root of the target wheel is calculated based on the load force on the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient. The load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing is determined according to the gear tooth surface equation of the target wheel. The first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root.

[0005] In some embodiments, the step of obtaining the gear tooth surface equation of the driving wheel of the asymmetric spur gear and the gear tooth surface equation of the driven wheel of the asymmetric spur gear comprises: Based on the geometric shape of a machining tool for machining the driving wheel, a first tooth profile tooth surface equation is constructed, and based on the geometric shape of a machining tool for machining the driven wheel, a second tooth profile tooth surface equation is constructed; Based on the relative movement of the machining tool during machining of the driving wheel, a first coordinate transformation matrix is ​​constructed, and based on the relative movement of the machining tool during machining of the driven wheel, a second coordinate transformation matrix is ​​constructed; The first tooth profile tooth surface equation is transformed by the first coordinate transformation matrix to obtain the gear tooth surface equation of the driving wheel, and the second tooth profile tooth surface equation is transformed by the second coordinate transformation matrix to obtain the gear tooth surface equation of the driven wheel.

[0006] In some embodiments, the geometric parameters of the driving wheel include the Poisson's ratio of the driving wheel and the elastic modulus of the driving wheel, and the geometric parameters of the driven wheel include the Poisson's ratio of the driven wheel and the elastic modulus of the driven wheel; The contact stress of the target wheel is obtained by calculating according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, including: The sum of the reciprocal of the radius of curvature of the driving wheel at the meshing position and the reciprocal of the radius of curvature of the driven wheel at the meshing position is taken as the first value; Taking the product of the first value and the force vector on each tooth of the target wheel as the second value; taking the ratio of the Poisson's ratio of the driving wheel to the elastic modulus of the driving wheel as the third value; taking a ratio of the Poisson's ratio of the driven wheel to the elastic modulus of the driven wheel as a fourth value; The product of the third value, the fourth value and the first preset coefficient is used as the fifth value; A square root operation is performed on the ratio of the second value to the fifth value to obtain the contact stress of the target wheel.

[0007] In some embodiments, the geometric parameters of the target wheel include: tooth width and module; The method of calculating the bending stress of the tooth root of the target wheel according to the load force on the target wheel, the load angle of the upper limit point of the conversion from the three-tooth meshing to the double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient comprises: The product of the load force on the target wheel, the cosine value of the load angle, the first correction coefficient and the second correction coefficient is used as a sixth value; The product of the tooth width and the module is taken as the seventh value; The sixth value and the seventh value are ratio-calculated to obtain the bending stress of the tooth root of the target wheel.

[0008] In some embodiments, the first correction coefficient is calculated according to the following steps: The ratio of the distance between any plane section of the tooth root of the target wheel and the intersection point of the load midline to the modulus is used as the eighth value; The product of the second preset coefficient, the eighth value and the cosine value of the load angle is used as the ninth value; The ratio of the chordal tooth thickness of any plane section of the tooth root of the target wheel to the module is taken as the tenth value; The product of the square of the tenth value and the cosine value of the driving tooth pressure angle is taken as the eleventh value; A ratio calculation is performed on the ninth value and the eleventh value to obtain the first correction coefficient.

[0009] In some embodiments, the second correction coefficient is calculated according to the following steps: A twelfth value is obtained by calculating according to a distance from an arbitrary plane section of a tooth root of the target wheel to an intersection point of a load midline and a chordal tooth thickness of an arbitrary plane section of a tooth root of the target wheel; A thirteenth value is obtained by calculating according to a chordal tooth thickness of an arbitrary plane section of a tooth root of the target wheel and a radius of curvature of an intersection of an arbitrary plane section of a tooth root of the target wheel and a transition curve on a meshing side; The twelfth value is multiplied by the thirteenth value to obtain the second correction coefficient.

[0010] In some embodiments, the load force on the target wheel is calculated according to the following steps: Obtaining the overlap of the target wheel on the meshing side; Comparing the overlap with a preset value to obtain a comparison result, wherein the comparison result is used to indicate a meshing area of ​​the target wheel, wherein the meshing area includes a three-tooth meshing area and a double-tooth meshing area; The load force on the target wheel is determined according to the load distribution in the meshing area indicated by the comparison result.

[0011] To achieve the above-mentioned purpose, a second aspect of an embodiment of the present application provides a device for jointly calculating contact stress and bending stress of a spur gear, the device comprising: A tooth surface equation acquisition module, used to acquire the gear tooth surface equation of the driving wheel of the asymmetric spur gear and the gear tooth surface equation of the driven wheel of the asymmetric spur gear; A curvature radius calculation module, used to perform derivative calculations on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel, respectively, to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position; a contact stress calculation module, configured to calculate the contact stress of the target wheel according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, wherein the contact stress of the target wheel includes the contact stress on each tooth in the target wheel, and the target wheel is the driving wheel or the driven wheel; A bending stress calculation module is used to calculate the bending stress of the tooth root of the target wheel according to the load force on the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, a first correction coefficient and a second correction coefficient, wherein the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing is determined according to the gear tooth surface equation of the target wheel, the first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root.

[0012] To achieve the above-mentioned purpose, the third aspect of an embodiment of the present application proposes an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the joint calculation method of the contact stress and bending stress of the spur gear described in the first aspect.

[0013] To achieve the above-mentioned purpose, the fourth aspect of an embodiment of the present application proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the joint calculation method of the contact stress and bending stress of the spur gear described in the first aspect above.

[0014] The joint calculation method and device of the contact stress and bending stress of spur gears proposed in the present application obtain the gear tooth surface equations of the driving wheel and the gear tooth surface equations of the driven wheel of the asymmetric spur gear to accurately describe the geometric shape of the asymmetric spur gear, and perform inverse calculations on the gear tooth surface equations of the driving wheel and the gear tooth surface equations of the driven wheel respectively to obtain the curvature radius of the driving wheel and the driven wheel at the meshing point, and obtain the comprehensive curvature radius of the asymmetric spur gear through the curvature radius of the driving wheel and the driven wheel at the meshing point, and then accurately calculate the contact stress between the driving wheel and the driven wheel based on the geometric parameters of the driving wheel and the driven wheel and the force vector on each tooth of the driving wheel or the driven wheel, and correct the bending stress through the first correction coefficient and the second correction coefficient to accurately calculate the bending stress of the tooth root of the driving wheel or the driven wheel. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic flow chart of a method for jointly calculating contact stress and bending stress of spur gears provided in an embodiment of the present application; Figure 2 is a schematic diagram of an asymmetric spur gear meshing partition provided in an embodiment of the present application; Figure 3 is a schematic diagram of a machining tool for machining asymmetric gears provided in an embodiment of the present application; Figure 4 It is a force diagram of the bending stress of the asymmetric high gear provided in the embodiment of the present application; Figure 5 is a schematic structural diagram of a device for jointly calculating contact stress and bending stress of spur gears provided in an embodiment of the present application; Figure 6 It is a schematic diagram of the hardware structure of the electronic device provided in the embodiment of the present application. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0017] It should be noted that, although the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first", "second", etc. in the specification, claims and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0019] Most existing contact stress and bending stress calculation methods are based on symmetrical gears or low-contact gears, without considering the impact of asymmetry and high contact of asymmetrical gear tooth profile on stress distribution. Due to the asymmetry of asymmetrical gear tooth profile, the tooth surface load distribution and contact conditions are different from those of symmetrical gears, and a method is urgently needed to calculate the contact stress and bending stress of asymmetrical gear tooth profile.

[0020] Based on this, an embodiment of the present application provides a method and device for jointly calculating the contact stress and bending stress of spur gears, aiming to solve the problem that the existing stress calculation method cannot calculate the contact stress and bending stress of asymmetric spur gears.

[0021] The combined calculation method, device, electronic device and medium for the contact stress and bending stress of spur gears provided in the embodiments of the present application are specifically illustrated through the following embodiments. First, the combined calculation method for the contact stress and bending stress of spur gears in the embodiments of the present application is described.

[0022] The embodiments of the present application can acquire and process relevant data based on artificial intelligence technology. Artificial Intelligence (AI) is the theory, method, technology and application system that uses digital computers or machines controlled by digital computers to simulate, extend and expand human intelligence, perceive the environment, acquire knowledge and use knowledge to obtain the best results.

[0023] AI basic technologies generally include sensors, dedicated AI chips, cloud computing, distributed storage, big data processing technology, operation / interaction systems, mechatronics, etc. AI software technologies mainly include computer vision technology, robotics technology, biometrics technology, speech processing technology, natural language processing technology, and machine learning / deep learning.

[0024] The embodiments of the present application provide a method and device for the joint calculation of the contact stress and bending stress of spur gears, which relate to the field of machinery. The method for the joint calculation of the contact stress and bending stress of spur gears provided in the embodiments of the present application can be applied to a terminal, or to a server, or can be software running in a terminal or a server. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, etc.; the server can be configured as an independent physical server, or as a server cluster or distributed system composed of multiple physical servers, or as a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application that implements a method for the joint calculation of the contact stress and bending stress of spur gears, etc., but is not limited to the above forms.

[0025] The present application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc. The present application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments, in which tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0026] It should be noted that in each specific implementation of the present application, when it comes to the need to perform relevant processing based on data related to user identity or characteristics such as user information, user behavior data, user historical data, and user location information, the user's permission or consent will be obtained first, and the collection, use, and processing of these data will comply with relevant laws, regulations, and standards. In addition, when the embodiment of the present application needs to obtain the user's sensitive personal information, the user's separate permission or consent will be obtained through a pop-up window or by jumping to a confirmation page. After clearly obtaining the user's separate permission or consent, the necessary user-related data for the normal operation of the embodiment of the present application will be obtained.

[0027] Figure 1 is a flow chart of a method for jointly calculating contact stress and bending stress of a spur gear provided in an embodiment of the present application, see Figure 1 A method for jointly calculating contact stress and bending stress of a spur gear provided in an embodiment of the present application may include but is not limited to steps S101 to S104.

[0028] Step S101, obtaining a gear tooth surface equation of a driving wheel of an asymmetric spur gear and a gear tooth surface equation of a driven wheel of the asymmetric spur gear.

[0029] In this step, the gear pair includes a driving wheel and a driven wheel, both of which are asymmetric spur gears. According to the tooth surface geometry of the driving wheel, the gear tooth surface equation of the driving wheel is constructed, and according to the tooth surface geometry of the driven wheel, the gear tooth surface equation of the driven wheel is constructed.

[0030] In some embodiments, the asymmetric spur gears are asymmetric high contact spur gears.

[0031] Step S102, respectively performing derivative calculations on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position.

[0032] In this step, the first-order derivatives of the gear tooth surface equations of the driving wheel and the driven wheel are calculated respectively, and the first-order derivatives of the gear tooth surface equations are used to characterize the tangent vectors of the tooth surfaces. Then, the second-order derivatives of the gear tooth surface equations of the driving wheel and the driven wheel are calculated respectively, and the second-order derivatives of the gear tooth surface equations are used to characterize the curvature of the gears. According to the first-order derivatives of the driving wheel and the driven wheel, and the second-order derivatives of the driving wheel and the driven wheel, the curvature radius of the driving wheel at the meshing point and the curvature radius of the driven wheel at the meshing point are obtained.

[0033] For example, the curvature radius of the driving wheel and the driven wheel at the meshing position can be calculated by the following formula 1: (1); In the formula, express Parameters t The first derivative of express Parameters t The first derivative of express Parameters t The second-order derivative of express Parameters t The second-order derivative of Represents the tooth root transition curve in the rectangular coordinate system x Direction coordinates, Represents the tooth root transition curve in the rectangular coordinate system y Direction coordinates.

[0034] Combining the gear tooth surface equation of the driving wheel and Formula 1, the curvature radius of the driving wheel at the meshing position is obtained. Combining the gear tooth surface equation of the driven wheel and Formula 1, the curvature radius of the driven wheel at the meshing position is obtained.

[0035] Step S103, calculating according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the value of the force vector on each tooth in the target wheel, to obtain the contact stress of the target wheel, wherein the contact stress of the target wheel includes the contact stress on each tooth in the target wheel, and the target wheel is the driving wheel or the driven wheel.

[0036] In this step, the combined curvature radius is calculated based on the curvature radius of the driving wheel at the meshing point and the curvature radius of the driven wheel at the meshing point, and then the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the value of the force vector on each tooth in the target wheel are substituted into the Hertz contact theory for calculation to obtain the contact stress on each tooth of the target wheel.

[0037] It should be noted that the target wheel can be a driving wheel or a driven wheel. In practical applications, because the contact stress is mutual, when calculating the contact stress on a certain tooth of the driving wheel, the value of the contact stress on the corresponding tooth of the driven wheel is the same as the value of the contact stress on the tooth of the driving wheel.

[0038] Step S104, calculating according to the load force on the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient, to obtain the bending stress of the tooth root of the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing is determined according to the gear tooth surface equation of the target wheel, the first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root.

[0039] In this step, the first correction coefficient is used to characterize the influence of the tooth profile shape of the asymmetric spur gear on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect at the tooth root of the asymmetric spur gear; the bending stress at the tooth root of the target wheel is calculated by the first correction coefficient, the second correction coefficient, the load force on the target wheel, the load angle of the upper limit point of the conversion from three-tooth meshing to double-tooth meshing, and the geometric parameters of the target wheel.

[0040] It should be noted that the upper limit of the double-tooth meshing area is the point where the last gear tooth is about to disengage and the new gear tooth is about to enter the meshing. The load direction at this time can be determined by the pressure angles on the driving and non-driving sides of the asymmetric spur gear, as well as the angle between the normal directions of the tooth surface. The direction of the load angle is determined according to the direction of the contact force and the local curvature of the tooth surface, and the direction of the tooth surface is determined according to the gear tooth surface equation, tooth profile curve and pressure angle. Among them, the pressure angle is a geometric parameter of the asymmetric spur gear, which directly affects the transmission direction of the contact load.

[0041] In other implementations, the load force on the target wheel can be calculated by the following steps: Step S201, obtaining the overlap degree of the target wheel on the meshing side; Step S202, comparing the overlap degree with a preset value to obtain a comparison result, wherein the comparison result is used to indicate a meshing area of ​​the target wheel, wherein the meshing area includes a three-tooth meshing area and a double-tooth meshing area; Step S203: Determine the load force on the target wheel according to the load distribution in the meshing area indicated by the comparison result.

[0042] In some implementations, the preset value may be set to 2, such as Figure 2 As shown in the figure, when the overlap of the meshing side of the asymmetric spur gear is greater than 2, the meshing area of ​​the asymmetric spur gear is divided into a three-tooth meshing area and a two-tooth meshing area alternating with each other along the meshing line direction. Indicates the degree of overlap, represents the base circle pitch, represents the base circle radius of the driving wheel, represents the node radius of point F in the gear contact area, represents the node radius of point A in the gear contact area, Indicates the base circle radius of the driven wheel, such as AB is a three-tooth area and BC is a two-tooth area.

[0043] Furthermore, the length of the three-tooth meshing area along the meshing line direction can be expressed by the following formula 2: (2); In the formula, It represents the length of the three-tooth area along the meshing line. Indicates the degree of overlap, Indicates the base circle pitch.

[0044] The length of the meshing area of ​​two teeth along the meshing line can be expressed by the following formula 3: (3); In the formula, It represents the length of the two tooth areas along the meshing line. Indicates the degree of overlap, Indicates the base circle pitch.

[0045] During the meshing process, the effective length of different contact areas can be calculated by the trajectory of the contact point. According to the Hertz contact theory, the load per unit length can be determined by the pressure distribution in the contact area. The meshing stiffness of the gears is calculated by combining the Weber-Banaschek method, and the load force on the target wheel is further obtained. In addition, the accuracy of the load distribution can be verified by finite element analysis (FEA).

[0046] In this implementation, the gear tooth surface equations of the driving wheel and the driven wheel of the asymmetric spur gear are obtained to accurately describe the geometric shape of the asymmetric spur gear, and the gear tooth surface equations of the driving wheel and the driven wheel are respectively calculated by inverse calculation to obtain the curvature radius of the driving wheel and the driven wheel at the meshing point. The comprehensive curvature radius of the asymmetric spur gear is obtained by the curvature radius of the driving wheel and the driven wheel at the meshing point, and then based on the geometric parameters of the driving wheel and the driven wheel and the force vector on each tooth of the driving wheel or the driven wheel, the contact stress between the driving wheel and the driven wheel is accurately calculated, and the bending stress is corrected by the first correction coefficient and the second correction coefficient to accurately calculate the bending stress of the tooth root of the driving wheel or the driven wheel.

[0047] In some embodiments, obtaining the gear tooth surface equation of the driving wheel of the asymmetric spur gear and the gear tooth surface equation of the driven wheel of the asymmetric spur gear in step S101 may include but is not limited to steps S1011 to S1013.

[0048] Step S1021: construct a first tooth profile and tooth surface equation based on the geometric shape of a machining tool for machining the driving wheel, and construct a second tooth profile and tooth surface equation based on the geometric shape of a machining tool for machining the driven wheel.

[0049] Step S1012: constructing a first coordinate transformation matrix based on the relative motion of the machining tool during machining of the driving wheel, and constructing a second coordinate transformation matrix based on the relative motion of the machining tool during machining of the driven wheel.

[0050] Step S1013, performing coordinate transformation on the first tooth profile tooth surface equation by using the first coordinate transformation matrix to obtain the gear tooth surface equation of the driving wheel, and performing coordinate transformation on the second tooth profile tooth surface equation by using the second coordinate transformation matrix to obtain the gear tooth surface equation of the driven wheel.

[0051] In this implementation, both the driving wheel and the driven wheel are asymmetric spur gears, and the end face tooth profile of the tool for machining the asymmetric spur gear is as follows: Figure 3 As shown, half of the tooth profile is divided into three segments: AB, BC, and CD. The AB segment is the tooth top straight line segment, and the parameters of the tooth profile and tooth surface equation are BC segment is the tooth top arc, and the parameters of its tooth profile and tooth surface equation are ; CD segment is the involute segment of the tooth profile, and the parameters of its tooth profile and tooth surface equation are , Figure 3 middle, is the pressure angle, is the tooth pitch, is a radial variable, is the radius of the tooth tip fillet, is the tooth top height, The tooth root height is Indicates the distance between the tool centerline and the center point of the tooth root arc. Indicates the distance between the center point of the tooth root arc and the tool symmetry line.

[0052] Specifically, the tooth profile and tooth surface equation of the AB segment can be expressed by the following formula 4: (4); In the formula, The tooth profile and tooth surface equation of segment AB is: represents the parameter variable of segment AB, represents radial variables, Indicates tooth root height, Indicates the distance between the center point of the tooth root arc and the tool symmetry line.

[0053] The tooth profile and tooth surface equation of the BC segment can be expressed by the following formula 5: (5); In the formula, Tooth profile and tooth surface equation of BC segment, Indicates the distance between the center point of the tooth root arc and the tool symmetry line. Indicates the distance between the tool centerline and the center point of the tooth root arc. Indicates the parameter variable of the BC segment, represents the radius of the tooth tip fillet, Represents the pressure angle.

[0054] The tooth profile and tooth surface equation of the CD segment can be expressed by the following equation 6: (6); In the formula, The tooth profile and tooth surface equation of CD segment: represents the parameter variable of the CD segment, Indicates tooth top height, Indicates the tooth pitch.

[0055] Similarly, by adding a negative sign to the above tooth profile and tooth surface equation, we can obtain the tooth profile and tooth surface equation of the other half of the tooth profile of the tool for machining asymmetric spur gears.

[0056] Furthermore, during the processing of the asymmetric gear, when the processed gear rotates counterclockwise relative to the initial position After that, the machining tool moves to the left relative to the initial position ,in, is the pitch circle radius of the processed gear, from which the parameter variables of the tooth surface equation can be derived Gear Angle relationship.

[0057] Specifically, the parameter variables of the tooth profile and tooth surface equations are Gear Angle The relationship can be expressed by the following formula 7: (7); In the formula, represents the parameter variables of the tooth profile and tooth surface equations, represents the gear angle, Indicates the pitch circle radius of the gear being processed. represents the normal vector of the tooth profile curve, Represents the tooth profile and tooth surface curve.

[0058] Furthermore, the tool coordinate system and the gear coordinate system are rigidly connected to the tool and the gear that move and rotate relative to the fixed coordinate system, and the tooth profile and tooth surface equations are transformed from the tool coordinate system to the gear coordinate system through the coordinate transformation matrix.

[0059] Specifically, the coordinate transformation matrix can be expressed by the following formula 8: (8); In the formula, represents the coordinate transformation matrix, Indicates the gear angle. Furthermore, the tooth top straight line segment AB of the machining tool envelops the tooth root arc segment AB, the tooth top arc segment BC of the machining tool envelops the tooth root transition curve segment BC, and the tooth profile involute segment CD of the machining tool envelops the gear transition curve segment CD. Since the gear tooth profile of the asymmetric spur gear is formed by the machining of the machining tool, the tooth profile tooth surface equations of the AB, BC, and CD segments are respectively transformed by coordinates through the above formula 8 and the following formula 9 to obtain the gear tooth surface equations corresponding to the AB, BC, and CD segments.

[0060] (9); In the formula, represents the gear tooth surface equation of segment j, represents the coordinate transformation matrix, Represents the tooth profile and tooth surface equation of segment j.

[0061] Specifically, the gear tooth surface equation of the AB segment can be expressed by the following equation 10: (10); (11); In the formula, The gear tooth surface equation representing the AB segment is: represents the parameter variable of segment AB, represents radial variables, represents the gear rotation angle of segment AB, Indicates tooth root height, Indicates the pitch circle radius of the gear being machined.

[0062] The gear tooth surface equation of the BC segment can be expressed by the following equation 12: (12); (13); In the formula, The gear tooth surface equation representing the BC segment is: Indicates the parameter variable of the BC segment, represents the radius of the tooth tip fillet, express, express, The gear angle of the BC segment, Indicates the pitch circle radius of the gear being machined.

[0063] The gear tooth surface equation of the CD segment can be expressed by the following equation 14: (14); (15); in, The gear tooth surface equation representing the BC segment is: Indicates the parameter variable of the BC segment, represents the pressure angle, Indicates the tooth pitch, represents radial variables, Indicates the gear rotation angle of the CD segment.

[0064] Similarly, by adding a negative sign to the above gear tooth surface equation, we can obtain the gear tooth surface equation of the other half of the asymmetric spur gear.

[0065] In this implementation, through the above method, based on the geometric shape of the machining tool for machining the driving wheel, the first tooth profile tooth surface equation is constructed, and based on the geometric shape of the machining tool for machining the driven wheel, the second tooth profile tooth surface equation is constructed; then based on the relative movement of the machining tool during the machining of the driving wheel, a first coordinate transformation matrix is ​​constructed, and based on the relative movement of the machining tool during the machining of the driven wheel, a second coordinate transformation matrix is ​​constructed; the first tooth profile tooth surface equation is coordinate transformed through the first coordinate transformation matrix to obtain the gear tooth surface equation of the driving wheel, and the second tooth profile tooth surface equation is coordinate transformed through the second coordinate transformation matrix to obtain the gear tooth surface equation of the driven wheel.

[0066] In this embodiment, the tooth profile and tooth surface equations are constructed based on the geometric shape of the machining tool to more accurately simulate the actual tooth surface of the gear. The relative motion of the tool and the gear during the machining process is simulated by the coordinate transformation matrix to accurately convert the tooth profile and tooth surface equations into the gear tooth surface equations, thereby accurately describing the geometric shape of the gear, facilitating the subsequent accurate calculation of the curvature radius of the gear, thereby improving the calculation accuracy of contact stress and bending stress.

[0067] In some embodiments, the contact stress of the target wheel is obtained by calculating in step S103 according to the radius of curvature of the driving wheel at the meshing point, the radius of curvature of the driven wheel at the meshing point, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, which may include but is not limited to steps S1031 to S1036.

[0068] Step S1031: taking the sum of the reciprocal of the radius of curvature of the driving wheel at the meshing position and the reciprocal of the radius of curvature of the driven wheel at the meshing position as the first value.

[0069] Step S1032: taking the product of the first value and the force vector on each tooth in the target wheel as the second value.

[0070] Step S1033: taking the ratio of the Poisson's ratio of the driving wheel to the elastic modulus of the driving wheel as the third value.

[0071] Step S1034: taking the ratio of the Poisson's ratio of the driven wheel to the elastic modulus of the driven wheel as the fourth value.

[0072] Step S1035: taking the product of the third value, the fourth value and the first preset coefficient as the fifth value.

[0073] Step S1036: Perform a square root operation on the ratio of the second value to the fifth value to obtain the contact stress of the target wheel.

[0074] In this implementation, the geometric parameters of the driving wheel include the Poisson's ratio and the elastic modulus of the driving wheel, and the geometric parameters of the driven wheel include the Poisson's ratio and the elastic modulus of the driven wheel. According to the curvature radius of the driving wheel at the meshing point and the curvature radius of the driven wheel at the meshing point, a comprehensive curvature radius is obtained, and the comprehensive curvature radius replaces the curvature radius in the Hertz contact theory, and then combines the material elastic modulus, Poisson's ratio and other factors of the asymmetric spur gear to calculate the contact stress of the driving wheel or the driven wheel; because the contact stress distribution of the asymmetric spur gear is affected by the asymmetry and high overlap of the tooth shape, the contact stress acting on each tooth is obtained by integration through the Hertz contact theory and the load distribution of the tooth surface.

[0075] Specifically, the contact stress can be calculated by the following formula 16: (16); In the formula, represents the contact stress on each gear tooth, Represents the value of the force vector on each gear tooth, It represents the radius of curvature of the driving wheel at the meshing point. It represents the radius of curvature of the driven wheel at the meshing point, represents the Poisson's ratio of the driving wheel, is the Poisson's ratio of the driven wheel, represents the elastic modulus of the driving wheel, Represents the elastic modulus of the driven wheel.

[0076] in, Recorded as the first value, Recorded as the second value, The third value is Recorded as the fourth value, is the first preset coefficient, Recorded as the fifth value.

[0077] In this embodiment, the contact stress on each gear tooth in the asymmetric spur gear is accurately calculated through the above steps, and the tooth profile parameters can be optimized through the contact stress to reduce the stress concentration effect, thereby improving the durability of the gear.

[0078] In some embodiments, in step S104, the bending stress of the tooth root of the target wheel is obtained by calculation based on the load force on the target wheel, the load angle of the upper limit point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient, which may include but is not limited to steps S1041 to S1043.

[0079] Step S1041: taking the product of the load force on the target wheel, the cosine value of the load angle, the first correction coefficient and the second correction coefficient as the sixth value.

[0080] Step S1042: taking the product of the tooth width and the module as the seventh value.

[0081] Step S1043: Calculate the ratio of the sixth value to the seventh value to obtain the bending stress of the tooth root of the target wheel.

[0082] In traditional bending stress calculation practices, conventional calculation formulas often ignore the unique properties of asymmetric gears. Given that the tooth addendum coefficient and pressure angle of asymmetric gears are different from those of spur gears, the evaluation of their load-bearing capacity should not simply follow the bending strength calculation method of spur gears.

[0083] During the meshing process of an asymmetric gear pair, the stress state on the tooth surface changes with the meshing position, which makes it difficult to accurately calculate the bending stress at the tooth root. Therefore, an approximate method is usually used, which is to regard it as a normal equivalent spur gear for calculation, and introduce a correction coefficient to reflect some potential factors that affect the bending stress of the asymmetric spur gear.

[0084] In this implementation, in order to simplify the calculation of the bending stress of the asymmetric spur gear, the friction force during the gear meshing process will not be considered, such as Figure 4 As shown, the load force Move along the meshing line to the gear symmetry line and decompose it into tangential components and radial force . Tangential force The gears are subjected to bending stress and shear stress, and the radial force produces compressive stress on the gears. Since the bending stress on the gears is much greater than the shear stress and compressive stress, the fatigue crack of the gears first occurs on the tensile side of the gear teeth. The bending stress on the tensile side of the dangerous section is used as the bending stress of the tooth root of the asymmetric spur gear. Figure 4 middle, It represents the chordal tooth thickness of any plane section of the tooth root, in mm; It represents the chordal tooth thickness of any plane section on the meshing side, in mm; It represents the chordal tooth thickness of any plane section on the non-meshing side, in mm; Indicates the radius of curvature of the intersection of any plane section of the target gear tooth root and the transition curve on the meshing side, in mm. is the load angle of the upper limit point of the transition from double-tooth meshing to single-tooth meshing, Indicates the pitch circle radius.

[0085] It should be noted that , , The tooth profile coordinates on the cross section can be calculated using the gear tooth surface equation, and the chordal tooth thickness can be calculated using the distance formula between two points.

[0086] In this implementation, the geometric parameters of the target wheel include the tooth width and the module, the target wheel is an asymmetric spur gear, and the target wheel can be either a driving wheel or a driven wheel.

[0087] Furthermore, the bending stress at the tooth root of the asymmetric high spur gear can be expressed by the following formula 17: (17); In the formula, represents the bending stress at the tooth root of an asymmetric high spur gear, represents the load force, The load angle representing the upper limit point of the transition from double tooth meshing to single tooth meshing, represents the first correction coefficient, represents the second correction coefficient, Indicates tooth width, Indicates the modulus.

[0088] in, Recorded as the sixth value, Recorded as the seventh value.

[0089] In this implementation, the first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root. The bending stress is corrected by the first correction coefficient and the second correction coefficient to improve the calculation accuracy of the bending stress.

[0090] Furthermore, the first correction coefficient can be calculated through the following steps S1044 to S1048: Step S1044, taking the ratio of the distance between any plane section of the tooth root of the target wheel and the intersection point of the load midline to the modulus as the eighth value; Step S1045, taking the product of the second preset coefficient, the eighth value and the cosine value of the load angle as the ninth value; Step S1046, taking the ratio of the chordal tooth thickness of any plane section of the tooth root of the target wheel to the module as the tenth value; Step S1047, taking the product of the square of the tenth value and the cosine value of the driving tooth pressure angle as the eleventh value; Step S1048, calculate the ratio of the ninth value and the eleventh value to obtain the first correction coefficient.

[0091] Specifically, the first correction coefficient can be expressed by the following formula 18: (18); In the formula, represents the first correction coefficient; represents a second preset coefficient; It represents the distance between any plane section of the tooth root of the target wheel and the intersection point of the load centerline, in mm; represents the modulus of the target wheel; The load angle representing the upper limit point of the transition from double tooth meshing to single tooth meshing; is the driving side pressure angle; It represents the chordal tooth thickness of any plane section at the root of the gear tooth in the target wheel, in mm.

[0092] in, Recorded as the eighth value, Recorded as the ninth value, represents the tenth value, Recorded as the eleventh value.

[0093] Furthermore, the second correction coefficient can be calculated through the following steps S1049 to S1051: Step S1049, calculating according to the distance between the arbitrary plane section of the tooth root of the target wheel and the intersection point of the load midline and the chordal tooth thickness of the arbitrary plane section of the tooth root of the target wheel, to obtain a twelfth value; Step S1050, calculating according to the chordal tooth thickness of any plane section of the tooth root of the target wheel, the radius of curvature of the intersection of any plane section of the tooth root of the target wheel and the meshing side transition curve, and the distance between any plane section of the tooth root of the target wheel and the intersection of the load centerline, to obtain a thirteenth value; Step S1051, multiply the twelfth value by the thirteenth value to obtain the second correction coefficient.

[0094] Specifically, the second correction coefficient can be expressed by the following formula 19: (19); In the formula, represents the second correction coefficient, It represents the distance between any plane section of the tooth root of the target wheel and the intersection point of the load centerline, in mm; It represents the chordal thickness of any plane section of the tooth root in the target wheel, in mm; It represents the radius of curvature of the intersection of any plane section of the target gear tooth root and the transition curve on the meshing side, in mm.

[0095] in, Recorded as the twelfth value, Recorded as the thirteenth value.

[0096] It should be noted that the second preset coefficient It can be set according to actual conditions, usually taking a value between 0.7 and 0.8. The target wheel can be any one of the driving wheel and the driven wheel. The target wheel is an asymmetric right-angle wheel.

[0097] In this embodiment, since the force on the tooth surface of the asymmetric gear changes continuously during the meshing process, an approximate normal equivalent spur gear model is used, and a first correction coefficient and a second correction coefficient are introduced to correct the calculation of the bending stress to improve the calculation accuracy of the bending stress. It is also convenient to optimize the tooth profile parameters through the bending stress to reduce the tooth root bending stress and improve the gear's bending resistance.

[0098] Figure 5 This is a schematic diagram of the structure of a device for jointly calculating contact stress and bending stress of a spur gear provided in an embodiment of the present application. Figure 5The embodiment of the present application further provides a device 800 for jointly calculating the contact stress and bending stress of a spur gear, which can implement the above-mentioned method for jointly calculating the contact stress and bending stress of a spur gear. The device 800 for jointly calculating the contact stress and bending stress of a spur gear includes: A tooth surface equation acquisition module 801 is used to acquire the gear tooth surface equation of the driving wheel of the asymmetric spur gear and the gear tooth surface equation of the driven wheel of the asymmetric spur gear; The curvature radius calculation module 802 is used to perform derivative calculations on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel, respectively, to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position; A contact stress calculation module 803 is used to calculate the contact stress of the target wheel according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, wherein the contact stress of the target wheel includes the contact stress on each tooth in the target wheel, and the target wheel is the driving wheel or the driven wheel; The bending stress calculation module 804 is used to calculate the bending stress of the tooth root of the target wheel according to the load force on the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient. The load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing is determined according to the gear tooth surface equation of the target wheel. The first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root.

[0099] In some implementations, the tooth surface equation acquisition module 801 includes: A first construction submodule is used to construct a first tooth profile and tooth surface equation based on a geometric shape of a machining tool for machining the driving wheel, and to construct a second tooth profile and tooth surface equation based on a geometric shape of a machining tool for machining the driven wheel; A second construction submodule, configured to construct a first coordinate transformation matrix based on the relative motion of the machining tool during machining of the driving wheel, and to construct a second coordinate transformation matrix based on the relative motion of the machining tool during machining of the driven wheel; A coordinate conversion submodule is used to perform coordinate conversion on the first tooth profile tooth surface equation through the first coordinate conversion matrix to obtain the gear tooth surface equation of the driving wheel, and to perform coordinate conversion on the second tooth profile tooth surface equation through the second coordinate conversion matrix to obtain the gear tooth surface equation of the driven wheel.

[0100] In some embodiments, the geometric parameters of the driving wheel include the Poisson's ratio of the driving wheel and the elastic modulus of the driving wheel, and the geometric parameters of the driven wheel include the Poisson's ratio of the driven wheel and the elastic modulus of the driven wheel; The contact stress calculation module 803 includes: a first calculation submodule, configured to take the sum of the reciprocal of the radius of curvature of the driving wheel at the meshing position and the reciprocal of the radius of curvature of the driven wheel at the meshing position as a first value; A second calculation submodule, configured to obtain a product of the first value and the force vector on each tooth of the target wheel as a second value; a third calculation submodule, configured to take a ratio of the Poisson's ratio of the driving wheel to the elastic modulus of the driving wheel as a third value; a fourth calculation submodule, configured to take a ratio of the Poisson's ratio of the driven wheel to the elastic modulus of the driven wheel as a fourth value; a fifth calculation submodule, configured to obtain a fifth value by multiplying the third value, the fourth value and the first preset coefficient; The sixth calculation submodule is used to perform a square root operation on the ratio of the second value to the fifth value to obtain the contact stress of the target wheel.

[0101] In some embodiments, the geometric parameters of the target wheel include: tooth width and module; The bending stress calculation module 804 includes: a seventh calculation submodule, configured to take the product of the load force on the target wheel, the cosine value of the load angle, the first correction coefficient and the second correction coefficient as a sixth value; an eighth calculation submodule, configured to take the product of the tooth width and the module as a seventh value; The ninth calculation submodule is used to calculate the ratio of the sixth value to the seventh value to obtain the bending stress of the tooth root of the target wheel.

[0102] In some embodiments, the first correction coefficient is calculated according to the following steps: The ratio of the distance between any plane section of the tooth root of the target wheel and the intersection point of the load midline to the modulus is used as the eighth value; The product of the second preset coefficient, the eighth value and the cosine value of the load angle is used as the ninth value; The ratio of the chordal tooth thickness of any plane section of the tooth root of the target wheel to the module is taken as the tenth value; The product of the square of the tenth value and the cosine value of the driving tooth pressure angle is taken as the eleventh value; A ratio calculation is performed on the ninth value and the eleventh value to obtain the first correction coefficient.

[0103] In some embodiments, the second correction coefficient is calculated according to the following steps: A twelfth value is obtained by calculating according to a distance from an arbitrary plane section of a tooth root of the target wheel to an intersection point of a load midline and a chordal tooth thickness of an arbitrary plane section of a tooth root of the target wheel; The thirteenth value is calculated according to the chordal tooth thickness of any plane section of the tooth root of the target wheel, the radius of curvature of the intersection of any plane section of the tooth root of the target wheel and the meshing side transition curve, and the distance between any plane section of the tooth root of the target wheel and the intersection of the load center line; The twelfth value is multiplied by the thirteenth value to obtain the second correction coefficient.

[0104] In some embodiments, the load force on the target wheel is calculated according to the following steps: Obtaining the overlap of the target wheel on the meshing side; Comparing the overlap with a preset value to obtain a comparison result, wherein the comparison result is used to indicate a meshing area of ​​the target wheel, wherein the meshing area includes a three-tooth meshing area and a double-tooth meshing area; The load force on the target wheel is determined according to the load distribution in the meshing area indicated by the comparison result.

[0105] The specific implementation of the device 800 for jointly calculating the contact stress and bending stress of a spur gear is substantially the same as the specific implementation of the method for jointly calculating the contact stress and bending stress of a spur gear described above, and will not be described in detail herein.

[0106] The embodiment of the present application also provides an electronic device, the electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the above-mentioned joint calculation method of the contact stress and bending stress of the spur gear when executing the computer program. The electronic device can be any intelligent terminal including a desktop computer, a tablet computer, a mobile phone, and a car computer.

[0107] See also Figure 6 , Figure 6 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application, wherein the electronic device includes: The processor 901 may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present application; The memory 902 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 902 can store an operating system and other application programs. When the technical solution provided in the embodiment of this specification is implemented by software or firmware, the relevant program code is stored in the memory 902, and the processor 901 calls and executes the joint calculation method of the contact stress and bending stress of the spur gear in the embodiment of this application; Input / output interface 903, used to implement information input and output; Communication interface 904, used to realize communication interaction between the device and other devices, which can be realized through wired mode (such as USB, network cable, etc.) or wireless mode (such as mobile network, WIFI, Bluetooth, etc.); A bus 905 that transmits information between various components of the device (e.g., the processor 901, the memory 902, the input / output interface 903, and the communication interface 904); The processor 901 , the memory 902 , the input / output interface 903 and the communication interface 904 are connected to each other in communication within the device via a bus 905 .

[0108] An embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned method for jointly calculating the contact stress and bending stress of a spur gear.

[0109] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0110] The embodiments of the present application provide a method and device for jointly calculating the contact stress and bending stress of a spur gear. The method and device obtain the gear tooth surface equations of the driving wheel and the driven wheel of the asymmetric spur gear to accurately describe the geometric shape of the asymmetric spur gear, and perform inverse calculations on the gear tooth surface equations of the driving wheel and the driven wheel respectively to obtain the curvature radius of the driving wheel and the driven wheel at the meshing point. The comprehensive curvature radius of the asymmetric spur gear is obtained by the curvature radius of the driving wheel and the driven wheel at the meshing point. The contact stress between the driving wheel and the driven wheel is accurately calculated by the geometric parameters of the driving wheel and the driven wheel and the force vector on each tooth of the driving wheel or the driven wheel. The bending stress is corrected by the first correction coefficient and the second correction coefficient to accurately calculate the bending stress at the tooth root of the driving wheel or the driven wheel.

[0111] The embodiments described in the embodiments of the present application are intended to more clearly illustrate the technical solutions of the embodiments of the present application and do not constitute a limitation on the technical solutions provided in the embodiments of the present application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

[0112] Those skilled in the art will appreciate that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present application, and may include more or fewer steps than shown in the figures, or a combination of certain steps, or different steps.

[0113] The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0114] Those skilled in the art will appreciate that all or some of the steps in the methods disclosed above, and the functional modules / units in the systems and devices may be implemented as software, firmware, hardware, or a suitable combination thereof.

[0115] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0116] It should be understood that in the present application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0117] In the several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the above units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0118] The units described above as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0119] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0120] If the integrated unit is implemented in the form of 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 application, 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, and the computer software product is stored in a storage medium, including multiple instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, referred to as ROM), random access memory (Random Access Memory, referred to as RAM), disk or optical disk and other media that can store programs.

[0121] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. A joint calculation method for contact stress and bending stress of spur gears, characterized in that: The method comprises: Obtaining a gear tooth surface equation of a driving wheel of an asymmetric spur gear and a gear tooth surface equation of a driven wheel of the asymmetric spur gear; Performing derivative calculations on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel respectively to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position; Calculating according to the radius of curvature of the driving wheel at the meshing position, the radius of curvature of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, to obtain the contact stress of the target wheel, wherein the contact stress of the target wheel includes the contact stress on each tooth in the target wheel, and the target wheel is the driving wheel or the driven wheel; The bending stress of the tooth root of the target wheel is calculated based on the load force on the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient. The load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing is determined according to the gear tooth surface equation of the target wheel. The first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root.

2. The method according to claim 1, characterized in that The step of obtaining the gear tooth surface equation of the driving wheel of the asymmetric spur gear and the gear tooth surface equation of the driven wheel of the asymmetric spur gear comprises: Based on the geometric shape of a machining tool for machining the driving wheel, a first tooth profile tooth surface equation is constructed, and based on the geometric shape of a machining tool for machining the driven wheel, a second tooth profile tooth surface equation is constructed; Based on the relative movement of the machining tool during machining of the driving wheel, a first coordinate transformation matrix is ​​constructed, and based on the relative movement of the machining tool during machining of the driven wheel, a second coordinate transformation matrix is ​​constructed; The first tooth profile tooth surface equation is transformed by the first coordinate transformation matrix to obtain the gear tooth surface equation of the driving wheel, and the second tooth profile tooth surface equation is transformed by the second coordinate transformation matrix to obtain the gear tooth surface equation of the driven wheel.

3. The method according to claim 1, characterized in that The geometric parameters of the driving wheel include the Poisson's ratio of the driving wheel and the elastic modulus of the driving wheel, and the geometric parameters of the driven wheel include the Poisson's ratio of the driven wheel and the elastic modulus of the driven wheel; The contact stress of the target wheel is obtained by calculating according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, including: The sum of the reciprocal of the radius of curvature of the driving wheel at the meshing position and the reciprocal of the radius of curvature of the driven wheel at the meshing position is taken as the first value; Taking the product of the first value and the force vector on each tooth of the target wheel as the second value; taking the ratio of the Poisson's ratio of the driving wheel to the elastic modulus of the driving wheel as the third value; taking a ratio of the Poisson's ratio of the driven wheel to the elastic modulus of the driven wheel as a fourth value; The product of the third value, the fourth value and the first preset coefficient is used as the fifth value; A square root operation is performed on the ratio of the second value to the fifth value to obtain the contact stress of the target wheel.

4. The method according to claim 1, characterized in that: The geometric parameters of the target wheel include: tooth width and module; The method of calculating the bending stress of the tooth root of the target wheel according to the load force on the target wheel, the load angle of the upper limit point of the conversion from the three-tooth meshing to the double-tooth meshing, the geometric parameters of the target wheel, the first correction coefficient and the second correction coefficient comprises: The product of the load force on the target wheel, the cosine value of the load angle, the first correction coefficient and the second correction coefficient is used as a sixth value; The product of the tooth width and the module is taken as the seventh value; The sixth value and the seventh value are ratio-calculated to obtain the bending stress of the tooth root of the target wheel.

5. The method according to claim 4, characterized in that The first correction coefficient is calculated according to the following steps: The ratio of the distance between any plane section of the tooth root of the target wheel and the intersection point of the load midline to the modulus is used as the eighth value; The product of the second preset coefficient, the eighth value and the cosine value of the load angle is used as the ninth value; The ratio of the chordal tooth thickness of any plane section of the tooth root of the target wheel to the module is taken as the tenth value; The product of the square of the tenth value and the cosine value of the driving tooth pressure angle is taken as the eleventh value; A ratio calculation is performed on the ninth value and the eleventh value to obtain the first correction coefficient.

6. The method according to claim 4, characterized in that The second correction coefficient is calculated according to the following steps: A twelfth value is obtained by calculating according to a distance from an arbitrary plane section of a tooth root of the target wheel to an intersection point of a load midline and a chordal tooth thickness of an arbitrary plane section of a tooth root of the target wheel; A thirteenth value is obtained by calculating according to a chordal tooth thickness of an arbitrary plane section of a tooth root of the target wheel and a radius of curvature of an intersection of an arbitrary plane section of a tooth root of the target wheel and a transition curve on a meshing side; The twelfth value is multiplied by the thirteenth value to obtain the second correction coefficient.

7. The method according to any one of claims 1 to 6, characterized in that The load force on the target wheel is calculated according to the following steps: Obtaining the overlap of the target wheel on the meshing side; Comparing the overlap with a preset value to obtain a comparison result, wherein the comparison result is used to indicate a meshing area of ​​the target wheel, wherein the meshing area includes a three-tooth meshing area and a double-tooth meshing area; The load force on the target wheel is determined according to the load distribution in the meshing area indicated by the comparison result.

8. A device for jointly calculating contact stress and bending stress of spur gears, characterized in that: The device comprises: A tooth surface equation acquisition module, used to acquire the gear tooth surface equation of the driving wheel of the asymmetric spur gear and the gear tooth surface equation of the driven wheel of the asymmetric spur gear; A curvature radius calculation module, used to perform derivative calculations on the gear tooth surface equation of the driving wheel and the gear tooth surface equation of the driven wheel, respectively, to obtain the curvature radius of the driving wheel at the meshing position and the curvature radius of the driven wheel at the meshing position; a contact stress calculation module, configured to calculate the contact stress of the target wheel according to the curvature radius of the driving wheel at the meshing position, the curvature radius of the driven wheel at the meshing position, the geometric parameters of the driving wheel, the geometric parameters of the driven wheel, and the force vector on each tooth in the target wheel, wherein the contact stress of the target wheel includes the contact stress on each tooth in the target wheel, and the target wheel is the driving wheel or the driven wheel; A bending stress calculation module is used to calculate the bending stress of the tooth root of the target wheel according to the load force on the target wheel, the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing, the geometric parameters of the target wheel, a first correction coefficient and a second correction coefficient, wherein the load angle of the upper boundary point of the conversion from three-tooth meshing to double-tooth meshing is determined according to the gear tooth surface equation of the target wheel, the first correction coefficient is used to characterize the influence of the tooth profile shape on the bending stress, and the second correction coefficient is used to characterize the stress concentration effect of the tooth root.

9. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the method for jointly calculating the contact stress and bending stress of spur gears as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for jointly calculating the contact stress and bending stress of a spur gear according to any one of claims 1 to 7 is implemented.

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