Calculation method of long-period multi-source excitation for double helical gears considering asymmetric tooth pitch deviation
By constructing an improved model for the bearing contact analysis of herringbone gears, considering asymmetric pitch deviation and axial movement, the problem of inaccurate vibration excitation calculation in existing herringbone gear transmission systems is solved, and accurate calculation of multi-source excitation and accurate prediction of dynamic models are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHOUKOU NORMAL UNIV
- Filing Date
- 2026-04-02
- Publication Date
- 2026-06-19
AI Technical Summary
Existing research methods fail to effectively consider the asymmetric pitch deviation and axial movement excitation in herringbone gear transmission systems, resulting in inaccurate vibration excitation calculations and affecting the accuracy of the dynamic model.
By constructing an improved model for the load-bearing contact analysis of herringbone gears, considering asymmetric pitch deviation, calculating the comprehensive meshing stiffness, axial movement, and comprehensive meshing error, and using the improved simplex method to solve the model, differentiated calculations of multi-source excitation are achieved.
It achieves accurate calculation of vibration excitation of herringbone gears over long periods, provides more comprehensive vibration excitation input, and provides higher accuracy for predicting the dynamic characteristics of the dynamic model.
Smart Images
Figure CN122241876A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aviation and ship gear transmission technology, specifically to a long-cycle multi-source excitation calculation method for herringbone gears that considers asymmetric pitch deviation. Background Technology
[0002] Herringbone gear drives possess advantages such as high overlap ratio, high load-bearing capacity, smooth operation, and self-balancing axial force, making them widely used in important power transmission devices in aviation, ships, and other fields. Accurately calculating the vibration excitation of a herringbone gear drive system is crucial for predicting its vibration response. The combined meshing stiffness excitation and combined meshing error excitation are important vibration excitations for gear drive systems. However, existing research methods typically assume that the combined meshing stiffness excitation and combined meshing error excitation are the same for each meshing cycle, neglecting the influence of manufacturing deviations. Manufacturing deviations are inevitable during gear manufacturing, such as cumulative pitch deviations, which are long-period deviations. For herringbone gears, the left and right helical gears are machined separately, resulting in differences in cumulative pitch deviations. After assembly, the left and right helical gear pairs will form different relative pitch deviations, leading to asymmetrical pitch deviations in the herringbone gear pair. Considering these asymmetrical pitch deviations, the combined meshing stiffness excitation and combined meshing error excitation for each meshing cycle are no longer the same. Furthermore, in engineering, to address the off-center loading of herringbone gears, a support configuration with the pinion axially floating is typically employed. This generates a unique axial movement excitation in herringbone gear transmissions, and existing research methods rarely address the calculation of long-cycle axial movement excitation in herringbone gears. This invention proposes a long-cycle multi-source excitation calculation method for herringbone gears that considers asymmetrical pitch deviation. By constructing an improved model for herringbone gear load-bearing contact analysis, it can quickly solve for the comprehensive meshing stiffness, axial movement, and comprehensive meshing error in a single meshing cycle. Through multiple iterative calculations, the long-cycle multi-source excitation of the herringbone gear can be obtained, providing comprehensive vibration excitation for the dynamic model of the herringbone gear transmission system, enabling more accurate prediction of the dynamic characteristics of the herringbone gear transmission system. Summary of the Invention
[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a long-cycle multi-source excitation calculation method for herringbone gears that considers asymmetric pitch deviation. By constructing an improved model for herringbone gear bearing contact analysis, the multi-source excitations, such as comprehensive meshing stiffness, axial movement, and comprehensive meshing error, can be quickly solved in a single meshing cycle. After multiple cyclic calculations, the long-cycle multi-source excitations of the herringbone gear can be further obtained, providing a comprehensive vibration excitation basis for the accurate prediction of the dynamic characteristics of the herringbone gear transmission system.
[0004] To solve the above-mentioned technical problems, the technical solution provided by the present invention is as follows: A calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation includes the following steps: Step S1: Derive the tooth surface equations of the herringbone gear and the gear pinion: Based on the gear generating principle, the theoretical tooth surface equations of the pinion and gear pinion are obtained by generating the tooth surface of the rack cutter conjugate with the helical gear. The tooth surface of the pinion is modified in two directions. The theoretical tooth surface of the pinion is superimposed with the modified surface to obtain the position vector and normal vector of the two-way modified tooth surface of the pinion. Step S2: Establish the herringbone gear geometric contact analysis TCA model: Decompose the geometric contact analysis of the herringbone gear pair into independent geometric contact analyses of the left and right helical gear pairs, using the fixed coordinate system of the left helical gear pair fixed to the left helical gear of the herringbone pinion. A geometric contact analysis sub-model is established, taking the rotation angle of the left small wheel. The input quantity is changed in a certain step size, and the equation system is solved repeatedly to obtain all contact points on the tooth surface. The geometric contact analysis sub-model of the right helical gear pair is established and solved in the same way. The simulation data of the left and right helical gear pairs at the same meshing position within one meshing cycle are reordered and output to obtain the tooth surface contact trajectory, initial tooth surface clearance and geometric transmission error of the herringbone gear pair. Step S3: Construct the displacement compatibility conditions for the herringbone gear: Calculate the relative tooth pitch deviation of the left and right helical gear pairs of the herringbone gear pair, convert the relative tooth pitch deviation to the tooth surface normal, define the long period of the herringbone gear, and create a new axial movement amount. Variables, deriving axial displacement The resulting increase in normal clearance of the left and right helical gear pairs is classified according to the degree of overlap into multiple gear meshing states. and For two simultaneous meshing states, For the integer part of the overlap, the initial tooth surface clearance at discrete points on the instantaneous contact line of the tooth surface, the meshing clearance caused by the asymmetrical tooth pitch deviation, and the normal clearance increment caused by the axial movement are superimposed to construct the displacement coordination condition of the herringbone gear. Step S4: Construct the constraint equation for equal axial force of the left and right helical gear pairs: Based on the installation characteristics of the axial floating of the pinion of the herringbone gear, the constraint equation for equal axial force of the left and right helical gear pairs is constructed. Step S5: Establish and solve the improved model for the bearing contact analysis of the herringbone gear: Based on the tooth surface coordinates and initial tooth surface clearance at a finite number of discrete points on the tooth surface calculated by geometric contact analysis, the normal comprehensive compliance matrix is obtained by compliance interpolation using the finite element method. The force balance condition, non-embedding condition, and axial force equality constraint equations are established simultaneously. Combined with the displacement compatibility condition, an improved model for the bearing contact analysis of the herringbone gear is established. The improved simplex method is used to solve the improved model, obtaining the comprehensive meshing stiffness and axial movement of the herringbone gear in a single meshing cycle. and overall meshing error; Step S6: Calculate the multi-source excitation of the long period of the herringbone gear: Decompose the long period of the herringbone gear into... One meshing cycle, after The next iteration executes steps S3 to S5 to solve the improved model of the herringbone gear bearing contact analysis, obtaining the comprehensive meshing stiffness, axial movement and comprehensive meshing error of the herringbone gear over the long period; The number of teeth on the pinion of a herringbone gear; The number of teeth on the large gear of a herringbone gear; and The least common multiple of .
[0005] Furthermore, in step S1, when deriving the tooth surface equations of the large and small gears and performing bidirectional tooth surface modification on the small gear, the theoretical tooth surface equations of the large and small gears are: ; in, Indicates a small wheel; Indicates a large wheel; The position vector of the large and small gear tooth surfaces; It is the normal vector of the gear tooth surfaces; From coordinate system arrive The coordinate transformation matrix; for submatrices; This is the position vector of the rack cutter tooth surface; This is the normal vector of the rack cutter tooth surface; =0 represents the meshing equation; θ i The rotation angle of the gear being machined. For tooth surface parameters; For tooth surface parameters; The rotation angle of the gear being machined; For vector cross product; It is a vector dot product; The expressions for the position vector and normal vector of the bidirectional modified tooth surface of the pinion are: ; in, This is the position vector of the modified tooth surface of the small gear; This is the normal vector of the modified tooth surface of the small gear; For the modified surface data of the rotating projection plane; The position vector of the theoretical tooth surface of the pinion; This is the normal vector of the theoretical tooth surface of the pinion.
[0006] Furthermore, in step S2, the left helical gear pair is in a fixed coordinate system. The geometric contact analysis sub-model established in the model is as follows: ; in, The surface parameters for generating the tooth surface of the left pinion using a rack cutter; The surface parameters for generating the tooth surface of the left pinion using a rack cutter; This refers to the angle of the small left wheel; From coordinate system arrive The coordinate transformation matrix; for submatrices; The surface parameters for generating the tooth surface of the large gear on the left side of the rack cutter; The surface parameters for generating the tooth surface of the large gear on the left side of the rack cutter; This refers to the turning angle of the large left wheel; From coordinate system arrive The coordinate transformation matrix; for submatrices; The small wheel on the left in a fixed coordinate system The lower tooth surface position vector; For the large wheel on the left in a fixed coordinate system The lower tooth surface position vector; The small wheel on the left in a fixed coordinate system The normal vector of the tooth surface below; For the large wheel on the left in a fixed coordinate system The normal vector of the tooth surface below; This is the position vector of the modified tooth surface of the small gear; This is the normal vector of the modified tooth surface of the small gear; This is the position vector of the theoretical tooth surface of the large wheel; This is the normal vector of the theoretical tooth surface of the large gear.
[0007] Further, in step S3, the relative pitch deviation of the helical gear pairs on the left and right sides of the herringbone gear pair is the difference between the cumulative pitch deviations of the pinion and the large gear. The relative pitch deviation of the helical gear pairs on the left and right sides is converted to the tooth surface normal direction, and the conversion relationship is as follows: ; in, This refers to the cumulative deviation of the pinion tooth pitch. This refers to the cumulative deviation of the large gear tooth pitch; This refers to the deviation of the tooth surface from the relative tooth pitch in the normal direction. The base circle helix angle; This is the end face pressure angle.
[0008] Herringbone gear long cycle for: ; in, This is the meshing cycle; The number of teeth on the pinion of a herringbone gear; The number of teeth on the large gear of a herringbone gear; and The least common multiple of .
[0009] Furthermore, in step S3, when establishing a new axial movement variable and deriving the resulting increase in the normal clearance of the left and right helical gear pairs, the axial movement... The resulting increase in normal clearance of the left and right helical gear pairs is: ; in, The helix angle; This represents the normal clearance increment of the meshing gear pair on the left side of the helical gear pair; This represents the normal clearance increment of the meshing gear pair on the right side of the helical gear. The end face pressure angle; This represents the axial displacement.
[0010] Furthermore, when dividing multiple pairs of teeth into meshing states according to their overlap ratio and superimposing various clearances to construct displacement compatibility conditions, the expression for the displacement compatibility conditions is: ; in, A pair of teeth that engage at a specific meshing position; for The normal synthesis compliance matrix of order; for The normal load matrix at discrete points on the contact line of the meshing tooth surface of the order; for An identity matrix of order 1; This represents the normal displacement of the gear teeth; for An identity diagonal matrix of order 1; for The tooth surface clearance matrix after deformation of discrete points on the contact line of the meshing tooth surface; for A matrix of order 1; This refers to the axial displacement. The initial tooth clearance is calculated using geometric contact analysis of the herringbone gear; This is the meshing clearance matrix of simultaneously meshing tooth pairs caused by relative tooth pitch deviation.
[0011] Furthermore, in step S4, the constraint equation for the equal axial forces of the left and right helical gear pairs is: ; in, The normal load at the discrete point of the major axis of the ellipse where the left meshing teeth are in instantaneous contact. The normal load at the discrete point of the major axis of the ellipse where the right meshing teeth are in instantaneous contact; The angle between the left-side normal load and the axis of the small wheel; The angle between the right-side normal load and the axis of the small wheel; , This represents the number of discrete points on the left. This represents the number of discrete points on the right.
[0012] Furthermore, in step S5, when establishing the improved model for bearing contact analysis by combining the force equilibrium condition, the non-embedded condition, the constraint equations for equal axial force, and the displacement compatibility condition, the improved model for bearing contact analysis of the herringbone gear is as follows: ; in, δ represents the normal displacement of the gear teeth. p This represents the axial displacement.
[0013] Furthermore, in step S5, when calculating the comprehensive elastic deformation and comprehensive meshing stiffness of the left and right helical gear pairs after solving the improved model, the formula for calculating the comprehensive elastic deformation of the left and right helical gear pairs is as follows: ; in, This represents the combined elastic deformation of the left helical gear pair; This represents the combined elastic deformation of the right-side helical gear pair; This represents the normal displacement of the gear teeth; This represents the overall meshing error of the left helical gear pair; This represents the overall meshing error of the right-side helical gear pair; The formula for calculating the combined meshing stiffness of the left and right helical gear pairs is: ; in, This represents the overall meshing stiffness of the left helical gear pair; The combined meshing stiffness of the right-side helical gear pair; For the load torque of the large wheel; The pitch circle radius of the large wheel; Normal pressure angle; It is the helix angle.
[0014] The technical effects of this invention are as follows: This invention breaks through the original calculation method that defaults to consistent excitation in each meshing cycle by considering the asymmetric pitch deviation of the herringbone gear pair and establishing a dedicated improved model for load-bearing contact analysis. It achieves differentiated and accurate calculation of the comprehensive meshing stiffness excitation and comprehensive meshing error excitation in each meshing cycle of the herringbone gear over a long period.
[0015] This invention achieves effective calculation of long-period axial movement excitation of herringbone gears by creating a new axial movement variable in the improved model of load-bearing contact analysis and completing its quantitative derivation, thus filling the gap in the calculation of this type of excitation for herringbone gears.
[0016] This invention obtains multi-source excitations such as the comprehensive meshing stiffness, axial movement, and comprehensive meshing error of the herringbone gear in a single solution by improving the model. This achieves comprehensive capture of the vibration excitation of the herringbone gear and provides a more complete vibration excitation input for the dynamic model of the herringbone gear transmission system. Attached Figure Description
[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application.
[0018] In the attached diagram: Figure 1 Let be the coordinate system for the tooth profile of the rack cutter and its generated helical gear tooth surface.
[0019] Figure 2 This is a schematic diagram of the two-way profile modification curve for the tooth surface.
[0020] Figure 3 The coordinate system is the meshing coordinate system of a herringbone gear.
[0021] Figure 4 This is a schematic diagram of the end face showing the cumulative pitch deviation.
[0022] Figure 5 A schematic diagram of the improved model for bearing contact analysis of herringbone gears.
[0023] Figure 6 This refers to the increase in the normal clearance of the left and right helical gear pairs caused by the axial movement of the small gear.
[0024] Figure 7 The flowchart shows the calculation process for long-cycle multi-source excitation of herringbone gears.
[0025] Figure 8 It is a two-way profile modification curve for the small gear tooth surface.
[0026] Figure 9 The contact path sequence of the left and right tooth surfaces of the herringbone gear and the geometric transmission error.
[0027] Figure 10 The cumulative pitch deviation of a herringbone gear pair.
[0028] Figure 11 This refers to the asymmetrical pitch deviation of a herringbone gear pair.
[0029] Figure 12 The tooth surface clearance of multiple pairs of teeth that are simultaneously meshing at the first meshing position of meshing cycle 1 is calculated.
[0030] Figure 13 To provide comprehensive meshing stiffness excitation for herringbone gears under different loads over long periods.
[0031] Figure 14 To excite the axial movement of the herringbone gear during long periods under different loads.
[0032] Figure 15 This is to provide a comprehensive meshing error excitation for herringbone gears over long periods under different loads. Detailed Implementation
[0033] The detailed description of the following embodiments is used to illustrate the principles of this application, but should not be used to limit the scope of this application. That is, the method and system for generating multilingual code based on domain rules of a large language model in this application are not limited to the described embodiments.
[0034] The present invention will be further described below with reference to embodiments.
[0035] Example 1 A calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation includes the following steps: Step S1: Derive the tooth surface equations of the herringbone gear and the gear pinion: Based on the gear generating principle, the theoretical tooth surface equations of the pinion and gear pinion are obtained by generating the tooth surface of the rack cutter conjugate with the helical gear. The tooth surface of the pinion is modified in two directions. The theoretical tooth surface of the pinion is superimposed with the modified surface to obtain the position vector and normal vector of the two-way modified tooth surface of the pinion. In step S1, when deriving the tooth surface equations of the large and small gears and performing bidirectional tooth surface modification on the small gear, the theoretical tooth surface equations of the large and small gears are: ; in, Indicates a small wheel; Indicates a large wheel; The position vector of the large and small gear tooth surfaces; It is the normal vector of the gear tooth surfaces; From coordinate system arrive The coordinate transformation matrix; for submatrices; This is the position vector of the rack cutter tooth surface; This is the normal vector of the rack cutter tooth surface; =0 represents the meshing equation; θ i The rotation angle of the gear being machined. For tooth surface parameters; For tooth surface parameters; The rotation angle of the gear being machined; For vector cross product; It is a vector dot product; The expressions for the position vector and normal vector of the bidirectional modified tooth surface of the pinion are: ; in, This is the position vector of the modified tooth surface of the small gear; This is the normal vector of the modified tooth surface of the small gear; For the modified surface data of the rotating projection plane; The position vector of the theoretical tooth surface of the pinion; This is the normal vector of the theoretical tooth surface of the pinion.
[0036] The basic parameters of the herringbone gear pair used in this embodiment are shown in Table 1. The herringbone gear is composed of two symmetrical helical gears. The tooth surfaces of both the large and small gears are based on the gear generating principle and are generated by the rack cutter tooth surface conjugate with the helical gear. The tooth surface equation is in the follower coordinate system fixed to the gear being machined. The characteristics were then analyzed. In engineering applications, to optimize the meshing performance of the herringbone gear, this embodiment performed bidirectional tooth surface modification on the pinion. The modified surface was modeled using data from a rotating projection plane. The modified tooth surface is obtained by superimposing the theoretical tooth surface of the pinion with the modified curved surface. The corresponding two-way modification curve of the tooth surface is as follows: Figure 8 As shown.
[0037] Table 1 Basic parameters of herringbone gear pairs Step S2: Establish the herringbone gear geometric contact analysis TCA model: Decompose the geometric contact analysis of the herringbone gear pair into independent geometric contact analyses of the left and right helical gear pairs, using the fixed coordinate system of the left helical gear pair fixed to the left helical gear of the herringbone pinion. A geometric contact analysis sub-model is established, taking the rotation angle of the left small wheel. The input quantity is changed in a certain step size, and the equation system is solved repeatedly to obtain all contact points on the tooth surface. The geometric contact analysis sub-model of the right helical gear pair is established and solved in the same way. The simulation data of the left and right helical gear pairs at the same meshing position within one meshing cycle are reordered and output to obtain the tooth surface contact trajectory, initial tooth surface clearance and geometric transmission error of the herringbone gear pair. In step S2, the left helical gear pair is in a fixed coordinate system The geometric contact analysis sub-model established in the model is as follows: ; in, The surface parameters for generating the tooth surface of the left pinion using a rack cutter; The surface parameters for generating the tooth surface of the left pinion using a rack cutter; This refers to the angle of the small left wheel; From coordinate system arrive The coordinate transformation matrix; for submatrices; The surface parameters for generating the tooth surface of the large gear on the left side of the rack cutter; The surface parameters for generating the tooth surface of the large gear on the left side of the rack cutter; This refers to the turning angle of the large left wheel; From coordinate system arrive The coordinate transformation matrix; for submatrices; The small wheel on the left in a fixed coordinate system The lower tooth surface position vector; For the large wheel on the left in a fixed coordinate system The lower tooth surface position vector; The small wheel on the left in a fixed coordinate system The normal vector of the tooth surface below; For the large wheel on the left in a fixed coordinate system The normal vector of the tooth surface below; This is the position vector of the modified tooth surface of the small gear; This is the normal vector of the modified tooth surface of the small gear; This is the position vector of the theoretical tooth surface of the large wheel; This is the normal vector of the theoretical tooth surface of the large gear.
[0038] In a specific embodiment, the geometric contact analysis of the herringbone gear pair can be decomposed into independent geometric contact analyses of the left and right helical gear pairs. Based on the fundamental meshing principle that the two tooth surfaces of the large and small gears are in continuous tangential contact during meshing, and that there is a common contact point and a common normal at any given moment, in this embodiment, for the left helical gear pair, the rotation angle of the left small gear is used as the input quantity. The rotation angle is changed by a fixed step size, and the equation system is solved repeatedly to obtain all contact points on the tooth surface of the left helical gear pair. The geometric contact analysis process of the right helical gear pair is completely consistent with that of the left. After completing the geometric contact analysis of the left and right helical gear pairs respectively, the simulation data of the left and right helical gear pairs at the same meshing position within one meshing cycle are reordered and output. Finally, the tooth surface contact trajectory, initial tooth surface clearance, and geometric transmission error of the herringbone gear pair are obtained. The corresponding herringbone gear left and right tooth surface contact path sequence and geometric transmission error are as follows: Figure 9 As shown.
[0039] Step S3: Construct the displacement compatibility conditions for the herringbone gear: Calculate the relative tooth pitch deviation of the left and right helical gear pairs of the herringbone gear pair, convert the relative tooth pitch deviation to the tooth surface normal, define the long period of the herringbone gear, and create a new axial movement amount. Variables, deriving axial displacement The resulting increase in normal clearance of the left and right helical gear pairs is classified according to the degree of overlap into multiple gear meshing states. and For two simultaneous meshing states, For the integer part of the overlap, the initial tooth surface clearance at discrete points on the instantaneous contact line of the tooth surface, the meshing clearance caused by the asymmetrical tooth pitch deviation, and the normal clearance increment caused by the axial movement are superimposed to construct the displacement coordination condition of the herringbone gear. In step S3, the relative pitch deviation of the helical gear pairs on the left and right sides of the herringbone gear pair is the difference between the cumulative pitch deviations of the pinion and the large gear. The relative pitch deviation of the helical gear pairs on the left and right sides is converted to the tooth surface normal direction, and the conversion relationship is as follows: ; in, This refers to the cumulative deviation of the pinion tooth pitch. This refers to the cumulative deviation of the large gear tooth pitch; This refers to the deviation of the tooth surface from the relative tooth pitch in the normal direction. The base circle helix angle; This is the end face pressure angle.
[0040] Herringbone gear long cycle for: ; in, This is the meshing cycle; The number of teeth on the pinion of a herringbone gear; The number of teeth on the large gear of a herringbone gear; and The least common multiple of .
[0041] In step S3, when creating a new axial movement variable and deriving the resulting increase in the normal clearance of the left and right helical gear pairs, the axial movement... The resulting increase in normal clearance of the left and right helical gear pairs is: ; in, The helix angle; This represents the normal clearance increment of the meshing gear pair on the left side of the helical gear pair; This represents the normal clearance increment of the meshing gear pair on the right side of the helical gear. The end face pressure angle; This represents the axial displacement.
[0042] When dividing multiple pairs of teeth into meshing states according to the degree of overlap and superimposing various clearances to construct displacement compatibility conditions, the expression for the displacement compatibility conditions is: ; in, A pair of teeth that engage at a specific meshing position; for The normal synthesis compliance matrix of order; for The normal load matrix at discrete points on the contact line of the meshing tooth surface of the order; for An identity matrix of order 1; This represents the normal displacement of the gear teeth; for An identity diagonal matrix of order 1; for The tooth surface clearance matrix after deformation of discrete points on the contact line of the meshing tooth surface; for A matrix of order 1; This refers to the axial displacement. The initial tooth clearance is calculated using geometric contact analysis of the herringbone gear; This is the meshing clearance matrix of simultaneously meshing tooth pairs caused by relative tooth pitch deviation.
[0043] In this embodiment, the measured cumulative pitch deviation of the herringbone gear pair is as follows: Figure 10 As shown, the corresponding asymmetric tooth pitch deviation is as follows: Figure 11 As shown, the fundamental periodicity of the asymmetric pitch deviation of the herringbone gear pair is determined by the gear meshing period. The rotation period of the small wheel and the large wheel is jointly determined. In this embodiment, the number of teeth on the small wheel is... The number of teeth on the large gear is Since the number of teeth of both is coprime, a long period Total of In each meshing cycle, all meshing tooth pairs in the left and right helical gear pairs are numbered according to the meshing sequence. The meshing tooth pairs of the left and right helical gear pairs are numbered from tooth pair 1 to tooth pair 748. In this embodiment, one meshing cycle is divided into 5 meshing positions. During the process of the bidirectional modified herringbone gear from meshing in to meshing out, 14 contact lines are formed on each of the left and right tooth surfaces. The theoretical overlap of the gear pair is 2.64. The 14 meshing lines are arranged in the combination of 3, 3, 3, 3, 2. The contact sequence of multiple pairs of teeth meshing simultaneously in four meshing cycles is shown in Table 2. Taking the first meshing position of meshing cycle 1 as an example, three pairs of teeth are meshing simultaneously at this position. Specifically, tooth pair 1 meshes at the 6th contact line, tooth pair 2 meshes at the 1st contact line, and tooth pair 748 meshes at the 11th contact line. The remaining meshing positions are deduced by the same logic.
[0044] Table 2 Contact sequence of multiple pairs of teeth meshing simultaneously in four meshing cycles The geometric contact analysis simulation of herringbone gears simulates the entire process from engagement to disengagement of a single pair of teeth in a left and right helical gear pair. The initial tooth surface clearance of the single pair of teeth obtained can be applied to other tooth pairs under multiple meshing conditions. In this embodiment, a meshing cycle is divided into [number] parts based on the overlap ratio. teeth and Two states of simultaneous meshing of teeth ( (where the integer part is the overlap ratio), using the meshing cycle as the calculation unit, the meshing clearance generated by the relative tooth pitch deviation of the corresponding meshing tooth pair is superimposed on the initial tooth surface clearance at the discrete points of the corresponding contact line, until the corresponding tooth pair completes the calculation of all meshing positions and exits meshing. This clearance superposition process is as follows: Figure 12 As shown. Under quasi-static conditions, at any meshing position, the left and right helical gear pairs simultaneously mesh with the contact lines of the gear pairs respectively. One and There are discrete points, and a total of [number] meshing tooth surfaces on both sides. discrete points ( (This refers to the number of discrete points on the major axis of the instantaneous meshing ellipse at this meshing position). When considering asymmetrical tooth pitch deviation, the tooth surface clearance of the simultaneously meshing gear pairs on the left and right helical gear pairs is no longer the same. The form of axial floating support for the pinion will cause axial movement of the pinion and generate axial movement amount. At this time, the tooth surface clearance of multiple meshing pairs of teeth in a single meshing cycle consists of three parts: the initial tooth surface clearance, the meshing clearance caused by the asymmetrical tooth pitch deviation, and the normal clearance increment caused by the axial movement of the pinion. Among them, the normal load matrix The former The order is the normal load at the discrete points of the left helical gear pair, and then... The order is the normal load at the discrete points of the right helical gear pair, and the matrix is... The former Column elements are ,back Column elements are .
[0045] Step S4: Construct the constraint equation for equal axial force of the left and right helical gear pairs: Based on the installation characteristics of the axial floating of the pinion of the herringbone gear, the constraint equation for equal axial force of the left and right helical gear pairs is constructed. In step S4, the constraint equation for equal axial forces on the left and right helical gear pairs is: ; in, The normal load at the discrete point of the major axis of the ellipse where the left meshing teeth are in instantaneous contact. The normal load at the discrete point of the major axis of the ellipse where the right meshing teeth are in instantaneous contact; The angle between the left-side normal load and the axis of the small wheel; The angle between the right-side normal load and the axis of the small wheel; , This represents the number of discrete points on the left. This represents the number of discrete points on the right.
[0046] In this embodiment, the shaft containing the pinion of the herringbone gear transmission adopts an axially floating installation. Based on this installation characteristic, theoretically, the axial forces generated by the simultaneous meshing of the left and right helical gear pairs can be automatically canceled out. Therefore, when constructing the constraint equations, the core principle is that the axial forces borne by the simultaneously meshing teeth of the left and right helical gear pairs are completely equal. The normal load in the equations... , Angle with the direction of the pinion axis , All of these can be obtained through the calculation results of the aforementioned geometric contact analysis of herringbone gears.
[0047] Step S5: Establish and solve the improved model for the bearing contact analysis of the herringbone gear: Based on the tooth surface coordinates and initial tooth surface clearance at a finite number of discrete points on the tooth surface calculated by geometric contact analysis, the normal comprehensive compliance matrix is obtained by compliance interpolation using the finite element method. The force balance condition, non-embedding condition, and axial force equality constraint equations are established simultaneously. Combined with the displacement compatibility condition, an improved model for the bearing contact analysis of the herringbone gear is established. The improved simplex method is used to solve the improved model, obtaining the comprehensive meshing stiffness and axial movement of the herringbone gear in a single meshing cycle. and overall meshing error; In step S5, when establishing the improved model for bearing contact analysis by combining the force equilibrium condition, the non-embedded condition, the constraint equations for axial force equality, and the displacement compatibility condition, the improved model for bearing contact analysis of the herringbone gear is as follows: ; in, δ represents the normal displacement of the gear teeth. p This represents the axial displacement.
[0048] In step S5, when calculating the comprehensive elastic deformation and comprehensive meshing stiffness of the left and right helical gear pairs after solving the improved model, the formula for calculating the comprehensive elastic deformation of the left and right helical gear pairs is as follows: ; in, This represents the combined elastic deformation of the left helical gear pair; This represents the combined elastic deformation of the right-side helical gear pair; This represents the normal displacement of the gear teeth; This represents the overall meshing error of the left helical gear pair; This represents the overall meshing error of the right-side helical gear pair; The formula for calculating the combined meshing stiffness of the left and right helical gear pairs is: ; in, This represents the overall meshing stiffness of the left helical gear pair; The combined meshing stiffness of the right-side helical gear pair; For the load torque of the large wheel; The pitch circle radius of the large wheel; Normal pressure angle; It is the helix angle.
[0049] In this embodiment, based on the coordinates of a finite number of discrete points on the tooth surface and the initial tooth surface clearance obtained from the aforementioned geometric contact analysis, the finite element method is applied to perform compliance interpolation, resulting in a normal composite compliance matrix composed of the corresponding discrete points. After establishing an improved model for the bearing contact analysis of the herringbone gear under the combined conditions, the improved simplex method is used to solve the model, thereby obtaining the normal bearing transmission error of the herringbone gear pair. Overall meshing stiffness , Axial movement and overall meshing error , Key parameters, including the normal load transmission error. The comprehensive meshing stiffness of the left and right helical gear pairs includes two parts: the normal elastic deformation of the gear teeth and the comprehensive meshing error. When calculating the comprehensive meshing stiffness of the left and right helical gear pairs, the influence of the corresponding gear pair's comprehensive meshing error must be eliminated. , All of these results were obtained by improving the model after considering the asymmetrical pitch deviation of the herringbone gear pair and the change in normal clearance caused by the axial movement of the pinion.
[0050] Step S6: Calculate the multi-source excitation of the long period of the herringbone gear: Decompose the long period of the herringbone gear into... One meshing cycle, after The next iteration executes steps S3 to S5 to solve the improved model of the herringbone gear bearing contact analysis, obtaining the comprehensive meshing stiffness, axial movement and comprehensive meshing error of the herringbone gear over the long period; The number of teeth on the pinion of a herringbone gear; The number of teeth on the large gear of a herringbone gear; and The least common multiple of .
[0051] In this embodiment, a long cycle of the herringbone gear is used. Split into Each meshing cycle, through a corresponding number of iterations, repeatedly executes the entire process of constructing displacement compatibility conditions, constructing axial force equality constraint equations, and establishing and solving the improved load-bearing contact analysis model within each meshing cycle. This ultimately yields multi-source excitations such as comprehensive meshing stiffness, axial movement, and comprehensive meshing error over the long-cycle range of the herringbone gear. This is achieved under different large wheel load torques. Under the conditions, the comprehensive meshing stiffness excitation of the long-period left and right helical gear pairs of the herringbone gear calculated in this embodiment is as follows: Figure 13 (a) and Figure 13 As shown in (b), the long-period axial displacement excitation is as follows: Figure 14 As shown, the long-period comprehensive meshing error excitation of the left and right helical gear pairs is as follows: Figure 15 (a) and Figure 15 As shown in (b).
[0052] Based on the calculation results of this embodiment, three core conclusions can be drawn. First, within each meshing cycle over a long period, the comprehensive meshing stiffness excitation and comprehensive meshing error excitation of the herringbone gear differ. Therefore, when calculating the vibration excitation of the herringbone gear transmission system, the influence of manufacturing deviations cannot be ignored, and it cannot be simply assumed that the excitations of the left and right helical gear pairs are completely identical in each meshing cycle. Second, the axial movement excitation of the herringbone gear over a long period is on the same order of magnitude as the comprehensive meshing error excitation over a long period. In the dynamic characteristic analysis of the herringbone gear transmission system, the influence of axial movement excitation cannot be ignored. Third, the core of long-cycle multi-source excitation calculation lies in introducing the cumulative pitch deviation into the load-bearing contact analysis model. Therefore, the method proposed in this invention has good versatility and is not only applicable to herringbone gear transmissions but can also be extended to other types of gear transmissions.
[0053] It should be noted that the combination of the technical features in this case is not limited to the combination methods described in the claims of this case or the combination methods described in the specific embodiments. All technical features described in this case can be freely combined or combined in any way, unless they contradict each other.
[0054] It should also be noted that the embodiments listed above are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments, and similar changes or modifications made thereto are those that can be directly derived or easily conceived by those skilled in the art from the content disclosed in the present invention, and should all fall within the protection scope of the present invention.
Claims
1. A calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation, characterized in that, Includes the following steps: Step S1: Derive the tooth surface equations of the herringbone gear and the gear pinion: Based on the gear generating principle, the theoretical tooth surface equations of the pinion and gear pinion are obtained by generating the tooth surface of the rack cutter conjugate with the helical gear. The tooth surface of the pinion is modified in two directions. The theoretical tooth surface of the pinion is superimposed with the modified surface to obtain the position vector and normal vector of the two-way modified tooth surface of the pinion. Step S2: Establish the herringbone gear geometric contact analysis TCA model: Decompose the geometric contact analysis of the herringbone gear pair into independent geometric contact analyses of the left and right helical gear pairs, using the fixed coordinate system of the left helical gear pair fixed to the left helical gear of the herringbone pinion. A geometric contact analysis sub-model is established, taking the rotation angle of the left small wheel. The input quantity is changed in a certain step size, and the equation system is solved repeatedly to obtain all contact points on the tooth surface. The geometric contact analysis sub-model of the right helical gear pair is established and solved in the same way. The simulation data of the left and right helical gear pairs at the same meshing position within one meshing cycle are reordered and output to obtain the tooth surface contact trajectory, initial tooth surface clearance and geometric transmission error of the herringbone gear pair. Step S3: Construct the displacement coordination conditions for the herringbone gear: Calculate the relative tooth pitch deviation of the left and right helical gear pairs of the herringbone gear pair, convert the relative tooth pitch deviation to the tooth surface normal, define the long period of the herringbone gear, and create a new axial movement amount. Variables, deriving the axial displacement The resulting increase in normal clearance of the left and right helical gear pairs is classified according to the degree of overlap into multiple gear meshing states. and For two simultaneous meshing states, For the integer part of the overlap, the initial tooth surface clearance at discrete points on the instantaneous contact line of the tooth surface, the meshing clearance caused by the asymmetrical tooth pitch deviation, and the normal clearance increment caused by the axial movement are superimposed to construct the displacement coordination condition of the herringbone gear. Step S4: Construct the constraint equation for equal axial force of the left and right helical gear pairs: Based on the installation characteristics of the axial floating of the pinion of the herringbone gear, the constraint equation for equal axial force of the left and right helical gear pairs is constructed. Step S5: Establish and solve the improved model for the bearing contact analysis of the herringbone gear: Based on the tooth surface coordinates and initial tooth surface clearance at a finite number of discrete points on the tooth surface calculated by geometric contact analysis, the normal comprehensive compliance matrix is obtained by compliance interpolation using the finite element method. The force balance condition, non-embedding condition, and axial force equality constraint equations are established simultaneously. Combined with the displacement compatibility condition, an improved model for the bearing contact analysis of the herringbone gear is established. The improved simplex method is used to solve the improved model to obtain the comprehensive meshing stiffness and axial movement of the herringbone gear in a single meshing cycle. and overall meshing error; Step S6: Calculate the multi-source excitation of the long period of the herringbone gear: Decompose the long period of the herringbone gear into... One meshing cycle, after The next iteration executes steps S3 to S5 to solve the improved model of the herringbone gear bearing contact analysis, obtaining the comprehensive meshing stiffness, axial movement and comprehensive meshing error of the herringbone gear over the long period; The number of teeth on the pinion of a herringbone gear; The number of teeth on the large gear of a herringbone gear; and The least common multiple of .
2. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation as described in claim 1, characterized in that: In step S1, when deriving the tooth surface equations of the large and small gears and performing bidirectional tooth surface modification on the small gear, the theoretical tooth surface equations of the large and small gears are: ； in, Indicates a small wheel; Indicates a large wheel; The position vector of the large and small gear tooth surfaces; It is the normal vector of the tooth surfaces of the large and small gears; From coordinate system arrive The coordinate transformation matrix; for The submatrix; This is the position vector of the rack cutter tooth surface; This is the normal vector of the rack cutter tooth surface; =0 represents the meshing equation; θ i The rotation angle of the gear being machined. For tooth surface parameters; For tooth surface parameters; The rotation angle of the gear being machined; For vector cross product; It is a vector dot product; The expressions for the position vector and normal vector of the bidirectional modified tooth surface of the pinion are: ; in, This is the position vector of the modified tooth surface of the small gear; This is the normal vector of the modified tooth surface of the small gear; For the modified surface data of the rotating projection plane; The position vector of the theoretical tooth surface of the pinion; This is the normal vector of the theoretical tooth surface of the pinion.
3. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 2, characterized in that: In step S2, the left helical gear pair is in a fixed coordinate system The geometric contact analysis sub-model established in the model is as follows: ； in, The surface parameters for generating the tooth surface of the left pinion using a rack cutter; The surface parameters for generating the tooth surface of the left pinion using a rack cutter; This refers to the angle of the small left wheel; From coordinate system arrive The coordinate transformation matrix; for The submatrix; The surface parameters for generating the tooth surface of the large gear on the left side of the rack cutter; The surface parameters for generating the tooth surface of the large gear on the left side of the rack cutter; This refers to the turning angle of the large left wheel; From coordinate system arrive The coordinate transformation matrix; for The submatrix; The small wheel on the left in a fixed coordinate system The lower tooth surface position vector; For the large wheel on the left in a fixed coordinate system The lower tooth surface position vector; The small wheel on the left in a fixed coordinate system The normal vector of the tooth surface below; For the large wheel on the left in a fixed coordinate system The normal vector of the tooth surface below; This is the position vector of the modified tooth surface of the small gear; This is the normal vector of the modified tooth surface of the small gear; This is the position vector of the theoretical tooth surface of the large wheel; This is the normal vector of the theoretical tooth surface of the large gear.
4. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 3, characterized in that: In step S3, the relative pitch deviation of the helical gear pairs on the left and right sides of the herringbone gear pair is the difference between the cumulative pitch deviations of the pinion and the large gear. The relative pitch deviation of the helical gear pairs on the left and right sides is converted to the tooth surface normal direction, and the conversion relationship is as follows: ； in, This refers to the cumulative deviation of the pinion tooth pitch. This refers to the cumulative deviation of the large gear tooth pitch; This refers to the deviation of the tooth surface from the relative tooth pitch in the normal direction. The base circle helix angle; The end face pressure angle; Herringbone gear long cycle for: ； in, This is the meshing cycle; The number of teeth on the pinion of a herringbone gear; The number of teeth on the large gear of a herringbone gear; and The least common multiple of .
5. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 4, characterized in that: In step S3, when creating a new axial movement variable and deriving the resulting increase in the normal clearance of the left and right helical gear pairs, the axial movement variable... The resulting increase in normal clearance of the left and right helical gear pairs is: ； in, The helix angle; This represents the normal clearance increment of the meshing gear pair on the left side of the helical gear pair; This represents the normal clearance increment of the meshing gear pair on the right side of the helical gear. The end face pressure angle; This represents the axial displacement.
6. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 5, characterized in that: When dividing multiple pairs of teeth into meshing states according to the degree of overlap and superimposing various clearances to construct displacement compatibility conditions, the expression for the displacement compatibility conditions is: ； in, A pair of teeth that engage at a specific meshing position; for The normal synthesis compliance matrix of order; for The normal load matrix at discrete points on the contact line of the meshing tooth surface of the order; for An identity matrix of order 1; This represents the normal displacement of the gear teeth; for An identity diagonal matrix of order 1; for The tooth surface clearance matrix after deformation of discrete points on the contact line of the meshing tooth surface; for A matrix of order 1; This refers to the axial displacement. The initial tooth clearance is calculated using geometric contact analysis of the herringbone gear; This is the meshing clearance matrix of simultaneously meshing tooth pairs caused by relative tooth pitch deviation.
7. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 6, characterized in that: In step S4, the constraint equation for the equal axial force of the left and right helical gear pairs is: ； in, The normal load at the discrete point of the major axis of the ellipse where the left meshing teeth are in instantaneous contact; The normal load at the discrete point of the major axis of the ellipse where the right meshing teeth are in instantaneous contact; The angle between the left-side normal load and the axis of the small wheel; The angle between the right-side normal load and the axis of the small wheel; , This represents the number of discrete points on the left. This represents the number of discrete points on the right.
8. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 7, characterized in that: In step S5, when establishing the improved model for bearing contact analysis by combining the force equilibrium condition, the non-embedded condition, the constraint equations for axial force equality, and the displacement compatibility condition, the improved model for bearing contact analysis of the herringbone gear is as follows: ； in, δ represents the normal displacement of the gear teeth. p This represents the axial displacement.
9. The calculation method for long-period multi-source excitation of herringbone gears considering asymmetric pitch deviation according to claim 8, characterized in that: In step S5, when calculating the comprehensive elastic deformation and comprehensive meshing stiffness of the left and right helical gear pairs after solving the improved model, the formula for calculating the comprehensive elastic deformation of the left and right helical gear pairs is as follows: ； in, This represents the combined elastic deformation of the left helical gear pair; This represents the combined elastic deformation of the right-side helical gear pair; This represents the normal displacement of the gear teeth; This represents the overall meshing error of the left helical gear pair; This represents the overall meshing error of the right-side helical gear pair; The formula for calculating the combined meshing stiffness of the left and right helical gear pairs is: ； in, This represents the overall meshing stiffness of the left helical gear pair; The combined meshing stiffness of the right-side helical gear pair; For the load torque of the large wheel; The pitch circle radius of the large wheel; Normal pressure angle; It is the helix angle.