Parameter design method and system for instantaneous line contact staggered-axis variable-tooth-thickness gear pair

Abstract

The invention discloses a parameter design method and system for an instantaneous line contact staggered-axis variable-tooth-thickness gear pair, and the method comprises the steps: solving a tooth surface equation of a non-involute variable-tooth-thickness gear and a normal vector of the non-involute variable-tooth-thickness gear according to the tooth surface equation of the involute variable-tooth-thickness gear and the normal vector of the involute variable-tooth-thickness gear; based on the tooth surface equation of the involute variable-tooth-thickness gear, a comprehensive modification tooth surface equation of the involute variable-tooth-thickness gear is obtained; according to the comprehensive modification tooth surface equation of the involute variable-tooth-thickness gear, the tooth surface equation of the non-involute variable-tooth-thickness gear and the normal vector of the non-involute variable-tooth-thickness gear, the normal deviation between the involute variable-tooth-thickness gear and the non-involute variable-tooth-thickness gear is obtained; constructing an optimization model according to the normal deviation; and performing parameter optimization on the involute variable-tooth-thickness gear to obtain target parameters of the involute variable-tooth-thickness gear. According to the method, parameter optimization design of the instantaneous line contact staggered-axis variable-tooth-thickness gear pair can be achieved, and the tooth surface utilization rate of the variable-tooth-thickness gear is increased.

Description

Technical Field

[0001] The present application relates to the technical field of gear transmission, and in particular to a parameter design method and system for an instantaneous line contact staggered axis variable tooth thickness gear pair. Background Art

[0002] The involute variable tooth thickness gear is a general case of involute gears, and has obvious advantages in the case of small shaft angles. The traditional design method of the parameters of the staggered axis involute variable tooth thickness gear pair can only achieve instantaneous point contact in theory. Although the tooth surfaces of the two involute variable tooth thickness gears are in line contact with the common rack, the two contact lines do not overlap. There are some disadvantages of point contact variable tooth thickness gears. The tooth surface utilization rate of the variable tooth thickness gear is not high, and only a small part of the tooth surface participates in the meshing, which reduces the load-bearing capacity of the gear. At the same time, the gear pair is prone to wear, which reduces the reliability and service life of the gear.

[0003] The use of involute variable tooth thickness gears and non-involute variable tooth thickness gears can realize line contact transmission of staggered axis variable tooth thickness gears. However, non-involute variable tooth thickness gears have problems such as the inability to express parameterization and difficulty in tooth surface processing, making it difficult to achieve parameter design of instantaneous line contact staggered axis variable tooth thickness gear pairs.

[0004] Therefore, how to achieve parameter optimization design of instantaneous line contact staggered axis variable tooth thickness gear pairs is a problem that needs to be solved urgently. Summary of the invention

[0005] The present application aims to propose a parameter design method and system for an instantaneous line contact staggered axis variable tooth thickness gear pair, which can convert the tooth surface of a non-involute variable tooth thickness gear into the tooth surface of an involute variable tooth thickness gear, thereby realizing the parameter optimization design of the instantaneous line contact staggered axis variable tooth thickness gear pair, thereby improving the tooth surface utilization rate of the variable tooth thickness gear, and improving the load-bearing capacity and service life of the variable tooth thickness gear.

[0006] In a first aspect, an embodiment of the present application provides a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair, the method comprising:

[0007] Construct the normal section equation of the generated rack and the first normal vector of the generated rack;

[0008] According to the normal section equation and the first normal vector of the shaping rack, the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear are obtained;

[0009] When the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear;

[0010] Based on the tooth surface equation of the involute variable tooth thickness gear, a comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained;

[0011] According to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear, the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is obtained;

[0012] constructing an optimization model according to the normal deviation;

[0013] Based on the optimization model, the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear, so as to realize the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

[0014] Compared with the prior art, the first aspect of the present application has the following beneficial effects:

[0015] The method constructs the normal section equation of the forming rack and the first normal vector of the forming rack; according to the normal section equation and the first normal vector of the forming rack, the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear are obtained; when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear; based on the involute variable tooth thickness gear The tooth surface equation is used to obtain the comprehensive modified tooth surface equation of the involute variable tooth thickness gear; the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is obtained according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear; according to the normal deviation, an optimization model is constructed; based on the optimization model, the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear to realize the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair. In this way, the tooth surface of the non-involute variable tooth thickness gear can be converted into the comprehensive modified tooth surface of the involute variable tooth thickness gear, so that the non-involute variable tooth thickness gear is represented by the basic parameters of the involute variable tooth thickness gear after comprehensive modification. By converting the tooth surface of the non-involute variable tooth thickness gear into the tooth surface of the involute variable tooth thickness gear, the parameter optimization design of the instantaneous line contact staggered axis variable tooth thickness gear pair is realized, thereby improving the tooth surface utilization rate of the variable tooth thickness gear and improving the load-bearing capacity and service life of the variable tooth thickness gear.

[0016] In some embodiments, when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear, including:

[0017] When the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, construct the coordinate system of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear;

[0018] In the coordinate system, according to the tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear is obtained as follows:

[0019]

[0020] In the coordinate system, according to the normal vector of the involute variable tooth thickness gear, the normal vector of the non-involute variable tooth thickness gear is obtained as follows:

[0021]

[0022] in, represents the tooth surface equation of the non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M 2j The following coordinate system S represents the involute variable tooth thickness gear j The transformation matrix to the following coordinate system S2 of the non-involute variable tooth thickness gear, r j (l,z n ) represents the tooth surface equation of the involute variable tooth thickness gear, represents the meshing equation of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear, n j (l,z n ) represents the normal vector of the involute variable tooth thickness gear, represents the relative speed of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear at the common contact point, Represents the normal vector of the non-involute variable tooth thickness gear.

[0023] In some embodiments, the step of obtaining the comprehensive modified tooth surface equation of the involute variable tooth thickness gear based on the tooth surface equation of the involute variable tooth thickness gear comprises:

[0024] Constructing a comprehensive modification tooth surface equation of the shaping rack and a comprehensive modification normal vector of the shaping rack;

[0025] Determine the position vector of the shaping rack and the second normal vector of the shaping rack according to the normal section equation of the shaping rack and the first normal vector of the shaping rack;

[0026] Obtaining the position vector of the comprehensive modified tooth surface of the shaping rack through the comprehensive modified tooth surface equation of the shaping rack and the position vector of the shaping rack;

[0027] Obtaining the normal vector of the comprehensive modified tooth surface of the shaping rack through the comprehensive modified normal vector of the shaping rack and the second normal vector of the shaping rack;

[0028] According to the position vector of the comprehensive modified tooth surface of the shaping rack, the normal vector of the comprehensive modified tooth surface of the shaping rack and the tooth surface equation of the involute variable tooth thickness gear, the comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained.

[0029] In some embodiments, the step of constructing the comprehensive modified tooth surface equation of the profiled rack and the comprehensive modified normal vector of the profiled rack includes:

[0030] Using a parabola to modify the tooth profile of the shaping rack, and obtaining a tooth profile modification equation;

[0031] Using a parabola to perform tooth modification on the profiled rack, and obtaining a tooth modification equation;

[0032] Combining the tooth profile modification equation and the tooth guide modification equation, a comprehensive modification tooth surface equation of the shaping rack is obtained;

[0033] The comprehensive shaping normal vector of the shaping rack is obtained by performing partial derivative calculation on the comprehensive shaping tooth surface equation of the shaping rack.

[0034] In some embodiments, the method of obtaining the comprehensive modified tooth surface equation of the involute variable tooth thickness gear according to the position vector of the comprehensive modified tooth surface of the shaping rack, the normal vector of the comprehensive modified tooth surface of the shaping rack, and the tooth surface equation of the involute variable tooth thickness gear comprises:

[0035]

[0036] in, represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, l represents the coordinate axis y n The variable on Z n Represents the coordinate axis z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, Mjc The pitch plane coordinate system S represents the generated rack c To the moving coordinate system S of the involute variable tooth thickness gear j The transformation matrix, r c_c (l,z n ) represents the position vector of the comprehensive modified tooth surface of the shaping rack, n xc_c represents the x-axis direction vector in the normal vector of the comprehensive modified tooth surface of the shaping rack, y c_c The y-axis direction vector of the position vector of the comprehensive modified tooth surface of the shaping rack is represented by n yc_c represents the y-axis direction vector of the normal vector of the comprehensive modified tooth surface of the shaping rack, x c_c represents the x-axis direction vector in the position vector of the comprehensive modified tooth surface of the shaping rack, and r represents the pitch circle radius of the involute variable tooth thickness gear.

[0037] In some embodiments, the method of obtaining the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear, and the normal vector of the non-involute variable tooth thickness gear comprises:

[0038] h i (l,z n , x) = [r j_c (l,z n , x)-r2]·n2

[0039] Among them, h i (l,z n , x) represents the normal deviation of the i-th tooth surface point between the comprehensive modified tooth surface equation of the involute variable tooth thickness gear and the tooth surface equation of the non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , X represents the optimization variable of the involute variable tooth thickness gear, r j_c (l,z n , x) represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, r2 represents the tooth surface equation of the non-involute variable tooth thickness gear, and n2 represents the normal vector of the non-involute variable tooth thickness gear.

[0040] In some embodiments, the step of performing parameter optimization on the involute variable tooth thickness gear based on the optimization model to obtain target parameters of the involute variable tooth thickness gear includes:

[0041] Preset the convergence threshold, and obtain the initial parameters of the involute variable tooth thickness gear, the tooth surface data of the non-involute variable tooth thickness gear, the initial trust region radius, and the translation speed of the generated rack;

[0042] Based on the optimization model, the initial parameters of the involute variable tooth thickness gear, the tooth surface data of the non-involute variable tooth thickness gear, the initial trust region radius and the translation speed of the forming rack, the trust region method is used to optimize the parameters of the involute variable tooth thickness gear to obtain the result of the optimization model;

[0043] The result of the optimization model is compared with the convergence threshold. If the result of the optimization model is less than or equal to the convergence threshold, the parameters of the involute variable tooth thickness gear corresponding to the result of the optimization model are used as target parameters.

[0044] In a second aspect, the embodiment of the present application further provides a parameter design system for an instantaneous line contact staggered axis variable tooth thickness gear pair, the system comprising:

[0045] A first construction unit is used to construct a normal section equation of the generated rack and a first normal vector of the generated rack;

[0046] A first calculation unit is used to obtain the tooth surface equation and the normal vector of the involute variable tooth thickness gear according to the normal section equation and the first normal vector of the profiled rack;

[0047] The second calculation unit is used to obtain the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission;

[0048] A third calculation unit is used to obtain a comprehensive modified tooth surface equation of the involute variable tooth thickness gear based on the tooth surface equation of the involute variable tooth thickness gear;

[0049] a fourth calculation unit, for obtaining a normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear;

[0050] A second construction unit is used to construct an optimization model according to the normal deviation;

[0051] A parameter optimization unit is used to optimize the parameters of the involute variable tooth thickness gear based on the optimization model to obtain the target parameters of the involute variable tooth thickness gear to achieve parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

[0052] In a third aspect, an embodiment of the present application also provides an electronic device comprising at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions executable by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the parameter design method of an instantaneous line contact staggered axis variable tooth thickness gear pair as described above.

[0053] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair as described above.

[0054] It can be understood that the beneficial effects of the second to fourth aspects compared with the related art are the same as the beneficial effects of the first aspect compared with the related art. Please refer to the relevant description in the first aspect, and no further details will be given here. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0056] Figure 1 It is a flow chart of an embodiment of a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0057] Figure 2 It is a schematic diagram of a normal cross section of a generated rack in a best embodiment of a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0058] Figure 3 It is a schematic diagram of the position coordinate relationship between the forming rack and the variable tooth thickness gear in the best embodiment of the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0059] Figure 4 It is a schematic diagram of the position coordinate relationship between the staggered axis involute variable tooth thickness gear and the non-involute variable tooth thickness gear in the best embodiment of the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0060] Figure 5 It is a schematic diagram of comprehensive shaping of the generated rack in the best embodiment of the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0061] Figure 6It is a schematic diagram of the position matching of the involute variable tooth thickness gear tooth surface and the non-involute variable tooth thickness gear tooth surface in the best embodiment of the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0062] Figure 7 It is a schematic diagram of a flow chart for solving an optimization model in a best embodiment of a parameter design method for an instantaneous line contact staggered shaft variable tooth thickness gear pair provided by the present application;

[0063] Figure 8 It is a convergence diagram of the objective function and the number of iterations in the best embodiment of the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application;

[0064] Fig. 9 This is a schematic diagram of the finite element contact simulation results of the variable tooth thickness gear in the best embodiment of the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application

[0065] Fig.10 It is a structural schematic diagram of an embodiment of a parameter design system for an instantaneous line contact staggered axis variable tooth thickness gear pair provided by the present application. DETAILED DESCRIPTION

[0066] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as limiting the present application.

[0067] In the description of this application, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0068] In the description of the present application, it should be understood that the descriptions involving orientation, such as the orientation or positional relationship indicated as up, down, etc., are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0069] In the description of this application, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meaning of the above terms in this application based on the specific content of the technical solution.

[0070] The use of involute variable tooth thickness gears and non-involute variable tooth thickness gears can realize line contact transmission of staggered axis variable tooth thickness gears. However, non-involute variable tooth thickness gears have problems such as the inability to express parameterization and difficulty in tooth surface processing, making it difficult to achieve parameter design of instantaneous line contact staggered axis variable tooth thickness gear pairs.

[0071] In order to solve the above-mentioned problem that the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair is difficult to achieve, the present application proposes a parameter design method and system for the instantaneous line contact staggered axis variable tooth thickness gear pair.

[0072] Reference Figure 1 The embodiment of the present application provides a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair, the method comprising the following steps:

[0073] Step S100, constructing a normal section equation of the shaping rack and a first normal vector of the shaping rack;

[0074] Step S200, according to the normal section equation and the first normal vector of the generated rack, the tooth surface equation and the normal vector of the involute variable tooth thickness gear are obtained;

[0075] Step S300, when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear;

[0076] Step S400, based on the tooth surface equation of the involute variable tooth thickness gear, obtain the comprehensive modified tooth surface equation of the involute variable tooth thickness gear;

[0077] Step S500, according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear, obtain the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear;

[0078] Step S600, constructing an optimization model according to the normal deviation;

[0079] Step S700: Based on the optimization model, the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear, so as to realize the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

[0080] In this embodiment, the normal section equation of the forming rack and the first normal vector of the forming rack are constructed; according to the normal section equation and the first normal vector of the forming rack, the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear are obtained; when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered axis transmission, according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained; based on the involute variable tooth thickness gear The tooth surface equation of the gear is used to obtain the comprehensive modified tooth surface equation of the involute variable tooth thickness gear; the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is obtained according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear; according to the normal deviation, an optimization model is constructed; based on the optimization model, the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear to realize the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair. In this way, the tooth surface of the non-involute variable tooth thickness gear can be converted into the comprehensive modified tooth surface of the involute variable tooth thickness gear, so that the non-involute variable tooth thickness gear is represented by the basic parameters of the involute variable tooth thickness gear after comprehensive modification. By converting the tooth surface of the non-involute variable tooth thickness gear into the tooth surface of the involute variable tooth thickness gear, the parameter optimization design of the instantaneous line contact staggered axis variable tooth thickness gear pair is realized, thereby improving the tooth surface utilization rate of the variable tooth thickness gear and improving the load-bearing capacity and service life of the variable tooth thickness gear.

[0081] The above-mentioned shaped rack can be a rack that can fit with the basic rack, and the teeth of one rack just fill the tooth grooves of the other rack.

[0082] The above-mentioned optimization model is constructed according to the normal deviation, which can be to plan m grid points on the tooth surface points on the non-involute variable tooth thickness gear, take the comprehensive modified tooth surface parameters of the involute variable tooth thickness gear as the optimization target, and establish the optimization model according to the normal deviation.

[0083] The above-mentioned optimization model is based on which the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear. The optimization model can be based on which the trust region method is used to optimize the parameters of the involute variable tooth thickness gear to obtain the target parameters of the involute variable tooth thickness gear, such as the LM (Levenberg-Marquardt) optimization algorithm, which is not specifically limited in this embodiment.

[0084] The parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair can be achieved based on the obtained target parameters of the involute variable tooth thickness gear and the involute variable tooth thickness gear to achieve the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

[0085] In some embodiments, when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear, including:

[0086] When the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the coordinate system of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is constructed;

[0087] In the coordinate system, according to the tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear is obtained as follows:

[0088]

[0089] In the coordinate system, according to the normal vector of the involute variable tooth thickness gear, the normal vector of the non-involute variable tooth thickness gear is obtained as follows:

[0090]

[0091] in, It represents the tooth surface equation of non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M 2j The following coordinate system S represents the involute variable tooth thickness gear j The transformation matrix to the follower coordinate system S2 of the non-involute variable tooth thickness gear, r j (l,z n ) represents the tooth surface equation of the involute variable tooth thickness gear, The meshing equations of involute variable tooth thickness gears and non-involute variable tooth thickness gears, n j (l,z n ) represents the normal vector of the involute variable tooth thickness gear, It represents the relative speed of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear at the common contact point. Represents the normal vector of a non-involute variable tooth thickness gear.

[0092] In this embodiment, when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, a coordinate system of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is constructed; in this coordinate system, the tooth surface equation of the non-involute variable tooth thickness gear is obtained according to the tooth surface equation of the involute variable tooth thickness gear; and in this coordinate system, the normal vector of the non-involute variable tooth thickness gear is obtained according to the normal vector of the involute variable tooth thickness gear. The non-involute variable tooth thickness gear is obtained by enveloping the involute variable tooth thickness gear, so that the tooth surface contact is instantaneous line contact.

[0093] In some embodiments, based on the tooth surface equation of the involute variable tooth thickness gear, the comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained, including:

[0094] Construct the comprehensive modification tooth surface equation of the shaping rack and the comprehensive modification normal vector of the shaping rack;

[0095] According to the normal section equation of the shaping rack and the first normal vector of the shaping rack, the position vector of the shaping rack and the second normal vector of the shaping rack are determined;

[0096] The position vector of the comprehensive modified tooth surface of the shaping rack is obtained through the comprehensive modified tooth surface equation of the shaping rack and the position vector of the shaping rack;

[0097] The normal vector of the comprehensive modified tooth surface of the shaping rack is obtained through the comprehensive modified normal vector of the shaping rack and the second normal vector of the shaping rack;

[0098] According to the position vector of the comprehensive modified tooth surface of the profiling rack, the normal vector of the comprehensive modified tooth surface of the profiling rack and the tooth surface equation of the involute variable tooth thickness gear, the comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained.

[0099] In this embodiment, the comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained according to the position vector of the comprehensive modified tooth surface of the profiling rack, the normal vector of the comprehensive modified tooth surface of the profiling rack and the tooth surface equation of the involute variable tooth thickness gear, thereby laying a good data foundation for later converting the tooth surface of the non-involute variable tooth thickness gear into the comprehensive modified tooth surface of the involute variable tooth thickness gear, so that the non-involute variable tooth thickness gear is represented by the basic parameters of the involute variable tooth thickness gear after comprehensive modification.

[0100] In some embodiments, constructing a comprehensive modified tooth surface equation of a profiled rack and a comprehensive modified normal vector of the profiled rack includes:

[0101] The tooth profile of the gear rack is modified by using a parabola, and the tooth profile modification equation is obtained;

[0102] The tooth profile of the gear rack is modified by using a parabola, and the tooth profile modification equation is obtained;

[0103] Combining the tooth profile modification equation and the tooth guide modification equation, the comprehensive modification tooth surface equation of the generated rack is obtained;

[0104] The comprehensive shaping normal vector of the shaping rack is obtained by performing partial derivative calculation on the comprehensive shaping tooth surface equation of the shaping rack.

[0105] In this embodiment, the tooth profile modification equation and the tooth direction modification equation are combined to obtain the comprehensive modification tooth surface equation of the profiled rack; the comprehensive modification tooth surface equation of the profiled rack is calculated by partial derivative to obtain the comprehensive modification normal vector of the profiled rack, which lays a good data foundation for the subsequent calculation of the comprehensive modification tooth surface equation of the involute variable tooth thickness gear.

[0106] In some embodiments, the comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained according to the position vector of the comprehensive modified tooth surface of the profiled rack, the normal vector of the comprehensive modified tooth surface of the profiled rack, and the tooth surface equation of the involute variable tooth thickness gear, including:

[0107]

[0108] in, It represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, l represents the coordinate axis y n The variable on Z n Represents the coordinate axis z n , It represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M jc The pitch plane coordinate system S represents the generated rack c To the moving coordinate system S of the involute variable tooth thickness gear j The transformation matrix, r c_c (l,z n ) represents the position vector of the comprehensive modified tooth surface of the shaping rack, n xc_c The x-axis direction vector of the normal vector of the comprehensive modified tooth surface of the profiled rack, y c_c Represents the y-axis direction vector in the position vector of the comprehensive modified tooth surface of the shaping rack, n yc_c The y-axis direction vector of the normal vector of the comprehensive modified tooth surface of the profiled rack, x c_c It represents the x-axis direction vector in the position vector of the comprehensive modified tooth surface of the shaping rack, and r represents the pitch circle radius of the involute variable tooth thickness gear.

[0109] In some embodiments, according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear, and the normal vector of the non-involute variable tooth thickness gear, the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is obtained, including:

[0110] h i (l,zn ,x)=[r j _ c (l,z n ,X)-r2]·n2

[0111] Among them, h i (l,z n ,x) represents the normal deviation of the i-th tooth surface point between the comprehensive modified tooth surface equation of the involute variable tooth thickness gear and the tooth surface equation of the non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , x represents the optimization variable of the involute variable tooth thickness gear, r j_c (l,Z n ,x) represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, r2 represents the tooth surface equation of the non-involute variable tooth thickness gear, and n2 represents the normal vector of the non-involute variable tooth thickness gear.

[0112] In this embodiment, in order to facilitate the description of non-involute variable tooth thickness gears by parameters, the tooth surface of the non-involute variable tooth thickness gear is converted into the comprehensive modified tooth surface of the involute variable tooth thickness gear by an optimization method, and the tooth surface of the non-involute variable tooth thickness gear is used as a reference to make the tooth surface of the involute variable tooth thickness gear as close to the tooth surface of the non-involute variable tooth thickness gear as possible. Therefore, the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is calculated, which lays a good data foundation for converting the tooth surface of the non-involute variable tooth thickness gear into the tooth surface of the comprehensive modified involute variable tooth thickness gear by a nonlinear optimization method in the later stage.

[0113] In some embodiments, based on the optimization model, the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear, including:

[0114] Preset the convergence threshold, and obtain the initial parameters of the involute variable tooth thickness gear, the tooth surface data of the non-involute variable tooth thickness gear, the initial trust region radius, and the translation speed of the generated rack;

[0115] Based on the optimization model, the initial parameters of the involute variable tooth thickness gear, the tooth surface data of the non-involute variable tooth thickness gear, the initial trust region radius and the translation speed of the forming rack, the trust region method is used to optimize the parameters of the involute variable tooth thickness gear and the results of the optimization model are obtained;

[0116] The result of the optimization model is compared with the convergence threshold. If the result of the optimization model is less than or equal to the convergence threshold, the parameters of the involute variable tooth thickness gear corresponding to the result of the optimization model are used as target parameters.

[0117] In this embodiment, the result of the optimization model is compared with the convergence threshold. If the result of the optimization model is less than or equal to the convergence threshold, the parameters of the involute variable tooth thickness gear corresponding to the result of the optimization model are used as the target parameters. In this way, when the tooth surface of the non-involute variable tooth thickness gear is converted into the tooth surface of the involute variable tooth thickness gear, the maximum modification interval of the involute variable tooth thickness gear is given to ensure that the tooth surface modification parameters (i.e., target parameters) after conversion are within a reasonable range.

[0118] To facilitate understanding by those skilled in the art, a set of best embodiments is provided below:

[0119] Involute variable tooth thickness gears are the general case of involute gears. The displacement coefficient of the tooth shape along the axial direction changes linearly, and there is a taper in the axial direction. The tooth side clearance of the gear pair can be adjusted by moving the axial relative position of the variable tooth thickness gear pair to improve the transmission accuracy. Involute variable tooth thickness gears can realize power transmission of parallel axes, intersecting axes and staggered axes. They have the advantages of small size, compact structure and high transmission accuracy. They have obvious advantages in small axis angle application scenarios such as artillery aiming systems, ship propulsion systems, helicopter transmission systems and automobile drive systems.

[0120] Theoretically, the staggered axis involute variable tooth thickness gear pair can only achieve point contact. Although the tooth surfaces of the two involute variable tooth thickness gears are in line contact with the common rack, the two contact lines do not overlap. There are some disadvantages of point contact variable tooth thickness gears, because the tooth surface utilization rate of the variable tooth thickness gear is not high, only a few tooth surfaces participate in meshing, which reduces the bearing capacity of the gear. At the same time, the gear pair is easy to wear, which reduces the reliability and service life of the gear.

[0121] The tooth surface modification of variable tooth thickness gears can improve the contact area of ​​variable tooth thickness gears to a certain extent, but the geometric parameters of variable tooth thickness gears are the key factors affecting the line contact of variable tooth thickness gears. The tooth surface modification design method relies on a large number of contact simulation calculations, and it takes a lot of time to get barely satisfactory results.

[0122] The design method of variable tooth thickness gears with approximate line contact has indeed improved the load-bearing capacity, reliability and service life of variable tooth thickness gear transmission, but there are also some limitations. The conditions for approximate line contact of involute variable tooth thickness gears are relatively harsh, and the utilization rate of the tooth surface contact area is not high. If the tooth width of the involute variable tooth thickness gear increases, the utilization rate of the tooth surface will be further reduced; in addition, the involute variable tooth thickness gear pair that achieves approximate line contact is more sensitive to installation errors, and a small installation error will cause a large change in the tooth surface contact area.

[0123] The line contact transmission realized by involute variable tooth thickness gear and non-involute variable tooth thickness gear can theoretically achieve 100% line contact, but there are some problems. First, the parametric model of non-involute variable tooth thickness gear cannot be expressed parametrically, which is not conducive to its engineering application and processing and manufacturing; secondly, the modification value of non-involute variable tooth thickness gear is too large. According to the parameters of the non-involute variable tooth thickness gear forming wheel, its initial parameters are given to obtain the tooth surface deviation between the non-involute variable tooth thickness gear and the involute variable tooth thickness gear with given parameters. The tooth surface deviation is used as the modification value, but as the parameters such as the tooth width, cone angle and helix angle of the gear increase, the modification value will be very large, and even far exceeds the maximum processing allowance. Obviously, this is not conducive to its manufacturing and processing, especially for heat-treated gears.

[0124] In order to solve the above problems, this embodiment proposes a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair, obtains a non-involute variable tooth thickness gear by enveloping an involute variable tooth thickness gear, and then parametrically expresses the tooth surface of the non-involute variable tooth thickness gear, and the designed staggered axis variable tooth thickness gear pair is easy to express and process. The technical solution of this embodiment specifically includes the following contents:

[0125] 1. Construct the tooth surface model of involute variable tooth thickness gear.

[0126] 1. Shape the rack tooth surface.

[0127] The normal section of the shaped rack is as follows Figure 2 As shown, the left and right straight line segments M0M1 and M2M3 are enveloping to obtain the working profile of the involute variable tooth thickness gear, and the point M0 and point M2 are swept to obtain the transition arc of the involute variable tooth thickness gear. Establish the coordinate system S n It is fixedly connected to the normal section of the generated rack. In this coordinate system S n Under this condition, the mathematical equation of the normal section of the generated rack (i.e. the normal section equation) and the normal vector (i.e. the first normal vector) can be expressed as:

[0128]

[0129] Among them, r n (l,z n ) represents the normal section equation of the generated rack, n n Represents the normal vector of the shaping rack. The positive sign in the ± symbol represents the M0M1 segment of the shaping rack, and the negative sign represents the M2M3 segment of the shaping rack. n represents the normal pressure angle of the forming rack, m represents the normal module of the forming rack, h a Denotes the tooth addendum coefficient, c n is the headspace coefficient, p c is the pitch of the gear rack, p c =πm, l is the coordinate axis y nThe variables on the coordinate system S are based on the points M0 and M1 n The geometric relationship between , we can get the interval of variable l as:

[0130]

[0131] 2. Involute variable tooth thickness gear tooth surface.

[0132] Establish the tooth surface equation of the generated rack on the pitch plane, and establish Figure 3 The coordinate system of the generated rack is shown. p (x p ,y p , z p ) is the end face coordinate system of the generated rack, S n (x n ,y n , z n ) is the normal plane coordinate system of the forming rack, S c (x c ,y c , z c ) is the plane coordinate system of the generated rack. The normal plane of the generated rack is p The angle between the pitch plane and the end face of the gear is the pitch cone angle δ. According to the normal plane coordinate system S of the gear n To the section plane coordinate system S c The coordinate transformation relationship of the gear rack is: c It can be expressed as:

[0133] r c (l,z n )=[x c y c z c 1] T =M cp ·M pn ·r n (l,z n ) (4)

[0134] n c =[n xc n yc n zc 1] T =M cp ·M pn ·n n (5)

[0135] in,

[0136]

[0137]

[0138] Among them, M pn is the coordinate system S n To S p The transformation matrix, M cp is the coordinate system S p To S c The transformation matrix of .

[0139] The tooth surface of the involute variable tooth thickness gear is obtained by enveloping the generated rack. Figure 3 The coordinate system position relationship of the profile rack to the involute variable tooth thickness gear is shown in S b (x b ,y b ,z b ) is a fixed coordinate system, S j (x j ,y j ,z j ) is the moving coordinate system of the involute variable tooth thickness gear, S c (x c ,y c ,z c ) is the coordinate system of the pitch plane of the profiling rack. In the process of the profiling rack enveloping the involute variable tooth thickness gear, the wheel blank of the involute variable tooth thickness gear rotates at an angular velocity of ω, and the profiling rack moves in translation at a speed of v=ωr, where r is the pitch circle radius of the involute variable tooth thickness gear. is the rotation angle of the involute variable tooth thickness gear, then the spatial position vector and unit normal vector of the involute variable tooth thickness gear tooth surface can be expressed as:

[0140]

[0141] Among them, M bc is the coordinate system S c To coordinate system S b The coordinate transformation matrix, M jb is the coordinate system S b To coordinate system S j The coordinate transformation matrix can be expressed as:

[0142]

[0143] The common contact point on the tooth surface of the involute variable tooth thickness gear and the profile rack is Q, so the relative motion velocity vector of point Q should be perpendicular to the common normal vector of the involute variable tooth thickness gear and the profile rack passing through point Q. According to this condition, in the coordinate system S c The meshing equation of the involute variable tooth thickness gear and the profiled rack is established in the paper, and the variable l and the rotation angle of the involute variable tooth thickness gear tooth surface equation can be obtained. The relationship is:

[0144]

[0145] According to formula (8) and formula (12), the tooth surface equation of the involute variable tooth thickness gear can be obtained as follows:

[0146]

[0147] According to formula (9) and formula (12), the normal vector of the involute variable tooth thickness gear can be obtained as:

[0148]

[0149] 2. Construct a non-involute variable tooth thickness gear tooth surface model.

[0150] For staggered axis non-involute variable tooth thickness gears, when the involute variable tooth thickness gear envelops the non-involute variable tooth thickness gear, establish Figure 4 The coordinate system position relationship of the involute variable tooth thickness gear to the non-involute variable tooth thickness gear is shown. d (x d ,y d ,z d ) is the fixed coordinate system of the involute variable tooth thickness gear, S j (x j ,y j ,z j ) is the moving coordinate system of the involute variable tooth thickness gear, S f (x f ,y f ,z f ) is the fixed coordinate system of the non-involute variable tooth thickness gear, S2(x2,y2,z2) is the moving coordinate system of the non-involute variable tooth thickness gear, when the involute variable tooth thickness gear envelops the non-involute variable tooth thickness gear, the number of teeth of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are z and z, respectively. s and z2, rotate around their respective axes, with angles of rotation respectively and The numerical relationship of the rotation angle is The angle between the axis of the involute variable tooth thickness gear and the axis of the non-involute variable tooth thickness gear is θ, r s is the pitch circle radius of the involute variable tooth thickness gear, r2 is the pitch circle radius of the non-involute variable tooth thickness gear, then the tooth surface equation of the non-involute variable tooth thickness gear can be expressed as:

[0151]

[0152] Among them, the coordinate system S j To coordinate system S d The coordinate transformation matrix M dj It can be expressed as:

[0153]

[0154] Coordinate system S b To coordinate system S f The coordinate transformation matrix M fb It can be expressed as:

[0155]

[0156] Coordinate system S f To coordinate system S2 coordinate transformation matrix M 2f It can be expressed as:

[0157]

[0158] The angular velocities of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear rotating around their own axes are ω (s) and ω (2) , transmission ratio q2s = z s / z2=ω (2) / ω (s) , then the relative speed of the two gears at the common contact point is in the coordinate system S j In the expression:

[0159]

[0160] The angular velocity of the involute variable tooth thickness gear in the coordinate system S j The following can be expressed as:

[0161]

[0162] The angular velocity of the non-involute variable tooth thickness gear can be expressed in the coordinate system S2 as:

[0163]

[0164] Then the angular velocity of the non-involute variable tooth thickness gear in the coordinate system S j The following can be expressed as:

[0165]

[0166] Coordinate system S d To coordinate system S j The coordinate transformation matrix L jd It can be expressed as:

[0167]

[0168] Coordinate system S f To coordinate system S d The coordinate transformation matrix L df It can be expressed as:

[0169]

[0170] Coordinate system S2 to coordinate system S f The coordinate transformation matrix L f2 It can be expressed as:

[0171]

[0172] According to the positional relationship and meshing equation of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear can be obtained as follows:

[0173]

[0174] Among them, among them, represents the tooth surface equation of the non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M 2j The following coordinate system S represents the involute variable tooth thickness gear j The transformation matrix to the following coordinate system S2 of the non-involute variable tooth thickness gear, r j (l,z n ) represents the tooth surface equation of the involute variable tooth thickness gear, represents the meshing equation of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear, n j (l,z n ) represents the normal vector of the involute variable tooth thickness gear, represents the relative speed of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear at the common contact point, Represents the normal vector of the non-involute variable tooth thickness gear.

[0175] 3. Conversion of non-involute variable tooth thickness gear tooth surface model and involute variable tooth thickness gear tooth surface model.

[0176] 1. Comprehensive shaping model of the produced rack.

[0177] The comprehensive modification of the tooth surface of the gear rack consists of the tooth profile modification and the tooth direction modification. Figure 5 As shown in (a). Figure 5 (b) is a schematic diagram of the use of parabolic shaping to modify the tooth profile of the production rack. p0 is the vertex of the modified parabola. The position of p0 is determined by the parameters (i.e., the starting parameters of the tooth profile modification) u0 and o c The distance l of o0d The parabolic tooth profile shape is obtained by the parabolic coefficient (i.e. tooth profile modification coefficient) a r and parameter u r Determine, when the parabola coefficient a r = 0, the rack tool tooth profile is the standard rack tool shape, and the rack tool pressure angle is α n , in the coordinate system S n Next, a point p on the parabola segment r The coordinates can be written as:

[0178]

[0179] Among them, u r The relationship between and l is:

[0180]

[0181] Among them, in ±, the right tooth profile corresponds to the positive sign in the upper and lower symbols, and the left tooth profile corresponds to the negative sign.

[0182] Figure 5 (c) is a schematic diagram of using a parabola to modify the tooth profile of the production rack. d is the vertex of the modified parabola, p d The position is obtained by the tooth width h and parameter h0 of the tooth profile (i.e. the starting parameter of the tooth profile modification). The parabolic tooth profile shape is determined by the coefficient b (i.e. the tooth profile modification coefficient) and parameter k, k = z n -h0+h / 2, when the parabola coefficient b=0, the gear rack has no tooth modification, in the coordinate system S n Next, a point p on the parabola segment k The coordinates can be written as:

[0183]

[0184] in,

[0185] k=z n -h0+h / 2 (31)

[0186] Combining the tooth profile modification equation (i.e., formula (28)) and the tooth profile modification equation (i.e., formula (30)) of the profiled rack, the comprehensive tooth surface modification equation of the profiled rack can be obtained as follows:

[0187]

[0188] The comprehensive modification normal vector of the shaping rack can be expressed as:

[0189]

[0190] 2. Comprehensive modification model of involute variable tooth thickness gear.

[0191] The generation principle of the comprehensive modified tooth surface of the involute variable tooth thickness gear is the same as that of the unmodified tooth surface of the involute variable tooth thickness gear. c According to formula (4), formula (5), formula (32) and formula (33), the position vector and normal vector (i.e., the second normal vector) of the comprehensive modified tooth surface of the profiled rack are obtained:

[0192] r c_c (l,z n )=[x c_c y c_c z c_c 1] T =M cp ·M pn ·r n_c (l,z n )(34)

[0193] n c_c =[n xc_c n yc_c n zc_c 1] T =M cp ·M pn ·n n_c (35)

[0194] According to formula (13), formula (34) and (35), the comprehensive modified tooth surface equation of the involute variable tooth thickness gear can be obtained:

[0195]

[0196] in, represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, l represents the coordinate axis y n The variable on Z n Represents the coordinate axis Z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M jc The pitch plane coordinate system S represents the generated rack c To the moving coordinate system S of the involute variable tooth thickness gear j The transformation matrix, r c_c (l,z n ) represents the position vector of the comprehensive modified tooth surface of the shaping rack, n xc_c represents the x-axis direction vector in the normal vector of the comprehensive modified tooth surface of the shaping rack, y c_c The y-axis direction vector of the position vector of the comprehensive modified tooth surface of the shaping rack is represented by n yc_c represents the y-axis direction vector of the normal vector of the comprehensive modified tooth surface of the shaping rack, xc_c represents the x-axis direction vector in the position vector of the comprehensive modified tooth surface of the shaping rack, and r represents the pitch circle radius of the involute variable tooth thickness gear.

[0197] 3. Tooth surface model conversion.

[0198] The staggered axis non-involute variable tooth thickness gear obtained by enveloping the involute variable tooth thickness gear has instantaneous line contact on the tooth surfaces, which improves the tooth surface contact area and the gear's load-bearing capacity. However, the tooth surface parameters of the non-involute variable tooth thickness gear are not easy to describe.

[0199] In order to describe the non-involute variable tooth thickness gear by parameters, the tooth surface of the non-involute variable tooth thickness gear is transformed into the comprehensive modified tooth surface of the involute variable tooth thickness gear by optimization method, such as Figure 6 As shown, taking the tooth surface of the non-involute variable tooth thickness gear as a reference, the tooth surface of the involute variable tooth thickness gear is made as close to the tooth surface of the non-involute variable tooth thickness gear as possible.

[0200] According to the tooth surface and normal vector of the non-involute variable tooth thickness gear and the tooth surface of the involute variable tooth thickness gear, the normal deviation of the two tooth surfaces is established as:

[0201] h i (l,z n , X) = [r j_c (l,z n ,x)-r2]·n2 (37)

[0202] Among them, h i (l,z n , X) represents the normal deviation of the i-th tooth surface point between the comprehensive modified tooth surface equation of the involute variable tooth thickness gear and the tooth surface equation of the non-involute variable tooth thickness gear, r j_c (l,z n , x) is the comprehensive modification tooth surface point of the involute variable tooth thickness gear, r2 is the tooth surface point of the non-involute variable tooth thickness gear, n2 is the normal vector of the tooth surface point of the non-involute variable tooth thickness gear, X is the optimization variable of the involute variable tooth thickness gear, including the normal pressure angle α of the involute variable tooth thickness gear n , helix angle β, pitch cone angle δ, tooth profile modification starting parameter u0, tooth profile modification coefficient a r , tooth modification starting parameter h0, tooth modification coefficient b, i represents multiple points on the tooth surface.

[0203] The tooth surface points on the non-involute variable tooth thickness gear are planned to have m grid points, and the optimization model is established with the comprehensive modified tooth surface parameters of the involute variable tooth thickness gear as the optimization target:

[0204]

[0205] in,

[0206]

[0207] Among them, u z is the variable in the tooth direction of the tooth surface equation of the generated rack. The above formula is expanded by first-order Taylor and simplified:

[0208] F(x k +Δx)≈F(x k )+J(x k )·Δx(40)

[0209] Δx is the iteration step size. For each iteration, the optimal Δx is solved, which can be expressed as:

[0210]

[0211] Adding a damping term to the objective function can be expressed as:

[0212]

[0213] Where μ is the damping coefficient, and the damping term is the penalty for excessive Δx. Let the derivative of the objective function be 0, and we get:

[0214] Δx * =-(J(x k ) T ·J(x k )+μI) -1 ·J(x k ) T ·F(x k )(43)

[0215] It can be simplified as:

[0216] Δx * =-(H k +μI) -1 ·g k (44)

[0217] Where H and g can be expressed as:

[0218]

[0219] Define the gain rate ρ, which can be expressed as:

[0220]

[0221] ρ represents the similarity between the first-order Taylor expansion and the true function. When the numerator is larger, it means that the Taylor approximate expansion is more accurate and the damping coefficient should be reduced. When the numerator is smaller, it means that the Taylor approximate expansion is not accurate and the damping coefficient should be increased. The damping coefficient can be expressed as:

[0222]

[0223] Given the initial value X0, the convergence accuracy ε and the initial trust region radius (i.e., the damping coefficient) μ, the optimization objective is solved. The solution steps are as follows: Figure 7 shown.

[0224] Taking the tooth surface of the non-involute variable tooth thickness gear as the reference plane, the seven variables of the involute variable tooth thickness gear are optimized and solved, and the optimal parameters of the involute variable tooth thickness gear are obtained, thus realizing the parameter conversion between the non-involute variable tooth thickness gear and the involute variable tooth thickness gear.

[0225] According to the involute variable tooth thickness gear and the optimized comprehensive modified variable tooth thickness gear (i.e. the optimal parameters (i.e. the target parameters) of the involute variable tooth thickness gear), the parameter design of the staggered axis variable tooth thickness gear pair with instantaneous line contact is realized.

[0226] For better explanation, the following experiments were performed in this embodiment:

[0227] According to the envelope of the involute variable tooth thickness gear tooth surface model, the tooth surface model of the non-involute variable tooth thickness gear is obtained. The only parameters of the non-involute variable tooth thickness gear that can be expressed are the number of teeth, tooth top height coefficient, and top clearance coefficient. Other parameters cannot be expressed. The parameters of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are shown in Table 1.

[0228] Table 1 Parameters of variable tooth thickness gears

[0229]

[0230] The tooth surface of the non-involute variable tooth thickness gear is converted into the tooth surface of the involute variable tooth thickness gear with comprehensive modification. The optimization target is established according to formula (48). The seven optimization parameters are the pressure angle α of the involute variable tooth thickness gear with comprehensive modification. f , helix angle β f , cone angle δ f , tooth profile modification starting point u0, tooth profile modification coefficient a r , tooth modification starting point h0, tooth modification coefficient b; constrain the 7 optimization variables of the comprehensive modification tooth surface of the involute variable tooth thickness gear, and the constraint conditions can be expressed as:

[0231]

[0232] The objective function is iteratively optimized using the LM (Levenberg-Marquardt) optimization algorithm. The convergence diagram of the objective function and the number of iterations is shown in the figure below: Figure 8 As shown in the figure, after 53 iterations, the objective function value no longer decreases significantly, and the convergence condition has been reached.

[0233] The seven parameters of the optimized involute variable tooth thickness gear after comprehensive modification are shown in Table 2. The pressure angle α f is 20.0455°, the helix angle β f is -7.9983°, cone angle δ f is 3.0311°, the tooth profile modification starting point u0 is 0.4691mm, and the tooth profile modification coefficient a r It is -0.000001, the starting point of tooth modification h0 is 0.5941mm, and the tooth profile modification coefficient b is 0.0001.

[0234] Table 2 Parameters of variable tooth thickness gear after comprehensive modification tooth surface optimization

[0235] Parameter name symbol Parameter Value Pressure Angle <![CDATA[α f / °]]> 20.0455 Helix Angle <![CDATA[β f / °]]> -7.9983 Cone Angle <![CDATA[δ f / °]]> 3.0311 Starting point of tooth profile modification <![CDATA[u0 / mm]]> 0.4691 Tooth profile modification coefficient <![CDATA[a r ]]> -0.000001 Starting point of tooth modification <![CDATA[h0]]> 0.5941 Tooth modification coefficient b / mm 0.0001

[0236] According to the involute variable tooth thickness gear parameters in Table 1 and the involute variable tooth thickness gear parameters with comprehensive modification in Table 2, the finite element contact simulation model of the variable tooth thickness gear is established, and the torque is 1000 N·m. Fig. 9 is the finite element contact simulation result of the variable tooth thickness gear, where Fig. 9 (a) is the simulation result of the involute variable tooth thickness gear. Fig. 9 (b) is the simulation result of the parametric non-involute variable tooth thickness gear. The tooth surface contact mark is line contact, which almost covers the entire tooth surface. The maximum contact stress of the involute variable tooth thickness large wheel is 402.1Mpa, and the maximum contact stress of the non-involute variable tooth thickness small wheel is 424.5Mpa. The tooth surfaces of the involute variable tooth thickness gear and the parametric non-involute variable tooth thickness gear are in line contact, which almost covers the entire tooth surface.

[0237] Compared with the prior art, the technical solution of this embodiment has the following advantages:

[0238] 1. Establish the design method of instantaneous line contact staggered axis variable tooth thickness gear pair. The involute variable tooth thickness gear is enveloping to obtain the non-involute variable tooth thickness gear, and the tooth surface contact is instantaneous line contact.

[0239] 2. Establish a parametric model of non-involute variable tooth thickness gears. The tooth surface of non-involute variable tooth thickness gears is transformed into the tooth surface of comprehensive modified involute variable tooth thickness gears through non-linear optimization methods, and the non-involute variable tooth thickness gears are represented by the basic parameters of comprehensive modified involute variable tooth thickness gears.

[0240] 3. Reduce the tooth surface modification value of non-involute variable tooth thickness gears. When converting the tooth surface of a non-involute variable tooth thickness gear to an involute variable tooth thickness gear, give the maximum modification range of the involute variable tooth thickness gear to ensure that the tooth surface modification parameters after conversion are within a reasonable range.

[0241] Reference Fig.10 The embodiment of the present application also provides a parameter design system for an instantaneous line contact staggered axis variable tooth thickness gear pair, the system comprising a first construction unit 100, a first calculation unit 200, a second calculation unit 300, a third calculation unit 400, a fourth calculation unit 500, a second construction unit 600 and a parameter optimization unit 700, wherein:

[0242] A first construction unit 100 is used to construct a normal section equation of the generated rack and a first normal vector of the generated rack;

[0243] The first calculation unit 200 is used to obtain the tooth surface equation and the normal vector of the involute variable tooth thickness gear according to the normal section equation and the first normal vector of the generated rack;

[0244] The second calculation unit 300 is used to obtain the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear;

[0245] The third calculation unit 400 is used to obtain the comprehensive modified tooth surface equation of the involute variable tooth thickness gear based on the tooth surface equation of the involute variable tooth thickness gear;

[0246] The fourth calculation unit 500 is used to obtain the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear;

[0247] A second construction unit 600 is used to construct an optimization model according to the normal deviation;

[0248] The parameter optimization unit 700 is used to optimize the parameters of the involute variable tooth thickness gear based on the optimization model to obtain the target parameters of the involute variable tooth thickness gear to achieve parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

[0249] It should be noted that since the parameter design system of an instantaneous line contact staggered axis variable tooth thickness gear pair in this embodiment and the parameter design method of an instantaneous line contact staggered axis variable tooth thickness gear pair mentioned above are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the present system embodiment and will not be described in detail here.

[0250] An embodiment of the present application also provides an electronic device, comprising: at least one control processor and a memory for communicating with the at least one control processor.

[0251] 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.

[0252] The non-transient software program and instructions required to implement the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair of the above embodiment are stored in the memory. When executed by the processor, the parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair of the above embodiment is executed, for example, the above described Figure 1 The method comprises steps S100 to S700.

[0253] The system 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 units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0254] The present application also provides a computer-readable storage medium storing computer-executable instructions, which are executed by one or more control processors to enable the one or more control processors to execute a parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair in the above method embodiment, for example, to execute the above described Figure 1 The functions of method steps S100 to S700 in the method.

[0255] It will be appreciated by those skilled in the art that all or some of the steps and systems in the disclosed method above may be implemented as software, firmware, hardware and appropriate combinations thereof. Some physical components or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor or a microprocessor, or may be implemented as hardware, or may be implemented as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on a computer-readable medium, which may include a computer storage medium (or a non-transitory medium) and a communication medium (or a temporary medium). As known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, disk storage or other magnetic storage devices, or any other medium that may be used to store desired information and may be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically embodies computer readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0256] The embodiments of the present application are described in detail above in conjunction with the accompanying drawings, but the present application is not limited to the above embodiments. Various changes can be made within the knowledge scope of ordinary technicians in the relevant technical field without departing from the purpose of the present application.

Claims

1. A parameter design method for an instantaneous line contact staggered axis variable tooth thickness gear pair, characterized in that: The method comprises: Construct the normal section equation of the generated rack and the first normal vector of the generated rack; According to the normal section equation and the first normal vector of the shaping rack, the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear are obtained; When the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear; Based on the tooth surface equation of the involute variable tooth thickness gear, a comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained; According to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear, the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear is obtained; constructing an optimization model according to the normal deviation; Based on the optimization model, the parameters of the involute variable tooth thickness gear are optimized to obtain the target parameters of the involute variable tooth thickness gear, so as to realize the parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

2. The parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair according to claim 1 is characterized in that: When the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear are obtained according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear, including: When the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission, construct the coordinate system of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear; In the coordinate system, according to the tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear is obtained as follows: In the coordinate system, according to the normal vector of the involute variable tooth thickness gear, the normal vector of the non-involute variable tooth thickness gear is obtained as follows: in, represents the tooth surface equation of the non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M 2j The following coordinate system S represents the involute variable tooth thickness gear j The transformation matrix to the following coordinate system S2 of the non-involute variable tooth thickness gear, r j (l,z n ) represents the tooth surface equation of the involute variable tooth thickness gear, represents the meshing equation of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear, n j (l,z n ) represents the normal vector of the involute variable tooth thickness gear, represents the relative speed of the involute variable tooth thickness gear and the non-involute variable tooth thickness gear at the common contact point, Represents the normal vector of the non-involute variable tooth thickness gear.

3. The parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair according to claim 1 is characterized in that: The method of obtaining the comprehensive modified tooth surface equation of the involute variable tooth thickness gear based on the tooth surface equation of the involute variable tooth thickness gear comprises: Constructing a comprehensive modification tooth surface equation of the shaping rack and a comprehensive modification normal vector of the shaping rack; Determine the position vector of the shaping rack and the second normal vector of the shaping rack according to the normal section equation of the shaping rack and the first normal vector of the shaping rack; Obtaining the position vector of the comprehensive modified tooth surface of the shaping rack by using the comprehensive modified tooth surface equation of the shaping rack and the position vector of the shaping rack; Obtaining the normal vector of the comprehensive modified tooth surface of the shaping rack through the comprehensive modified normal vector of the shaping rack and the second normal vector of the shaping rack; According to the position vector of the comprehensive modified tooth surface of the shaping rack, the normal vector of the comprehensive modified tooth surface of the shaping rack and the tooth surface equation of the involute variable tooth thickness gear, the comprehensive modified tooth surface equation of the involute variable tooth thickness gear is obtained.

4. The parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair according to claim 3 is characterized in that: The step of constructing the comprehensive modification tooth surface equation of the shaping rack and the comprehensive modification normal vector of the shaping rack includes: Using a parabola to modify the tooth profile of the shaping rack, and obtaining a tooth profile modification equation; Using a parabola to perform tooth modification on the profiled rack, and obtaining a tooth modification equation; Combining the tooth profile modification equation and the tooth guide modification equation, a comprehensive modification tooth surface equation of the shaping rack is obtained; The comprehensive shaping normal vector of the shaping rack is obtained by performing partial derivative calculation on the comprehensive shaping tooth surface equation of the shaping rack.

5. The parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair according to claim 3 is characterized in that: The method of obtaining the comprehensive modified tooth surface equation of the involute variable tooth thickness gear according to the position vector of the comprehensive modified tooth surface of the shaping rack, the normal vector of the comprehensive modified tooth surface of the shaping rack and the tooth surface equation of the involute variable tooth thickness gear comprises: in, represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , represents the rotation angle of the involute variable tooth thickness gear in the follower coordinate system of the involute variable tooth thickness gear, M jc The pitch plane coordinate system S represents the generated rack c To the moving coordinate system S of the involute variable tooth thickness gear j The transformation matrix, r c_c (l,z n ) represents the position vector of the comprehensive modified tooth surface of the shaping rack, n xc_c represents the x-axis direction vector in the normal vector of the comprehensive modified tooth surface of the shaping rack, y c_c The y-axis direction vector of the position vector of the comprehensive modified tooth surface of the shaping rack is represented by n yc_c represents the y-axis direction vector of the normal vector of the comprehensive modified tooth surface of the shaping rack, x c_c represents the x-axis direction vector in the position vector of the comprehensive modified tooth surface of the shaping rack, and r represents the pitch circle radius of the involute variable tooth thickness gear.

6. The parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair according to claim 1 is characterized in that: The method of obtaining the normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear comprises: Among them, h i (l,z n , x) represents the normal deviation of the i-th tooth surface point between the comprehensive modified tooth surface equation of the involute variable tooth thickness gear and the tooth surface equation of the non-involute variable tooth thickness gear, l represents the coordinate axis y n The variable on z n Represents the coordinate axis z n , X represents the optimization variable of the involute variable tooth thickness gear, represents the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, r2 represents the tooth surface equation of the non-involute variable tooth thickness gear, and n2 represents the normal vector of the non-involute variable tooth thickness gear.

7. The parameter design method of the instantaneous line contact staggered axis variable tooth thickness gear pair according to claim 1 is characterized in that: The step of performing parameter optimization on the involute variable tooth thickness gear based on the optimization model to obtain target parameters of the involute variable tooth thickness gear includes: Preset the convergence threshold, and obtain the initial parameters of the involute variable tooth thickness gear, the tooth surface data of the non-involute variable tooth thickness gear, the initial trust region radius, and the translation speed of the generated rack; Based on the optimization model, the initial parameters of the involute variable tooth thickness gear, the tooth surface data of the non-involute variable tooth thickness gear, the initial trust region radius and the translation speed of the forming rack, the trust region method is used to optimize the parameters of the involute variable tooth thickness gear to obtain the result of the optimization model; The result of the optimization model is compared with the convergence threshold. If the result of the optimization model is less than or equal to the convergence threshold, the parameters of the involute variable tooth thickness gear corresponding to the result of the optimization model are used as target parameters.

8. A parameter design system for instantaneous line contact staggered axis variable tooth thickness gear pair, characterized in that: The system comprises: A first construction unit is used to construct a normal section equation of the generated rack and a first normal vector of the generated rack; A first calculation unit is used to obtain the tooth surface equation and the normal vector of the involute variable tooth thickness gear according to the normal section equation and the first normal vector of the profiled rack; The second calculation unit is used to obtain the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear according to the tooth surface equation of the involute variable tooth thickness gear and the normal vector of the involute variable tooth thickness gear when the involute variable tooth thickness gear and the non-involute variable tooth thickness gear are staggered shaft transmission; A third calculation unit is used to obtain a comprehensive modified tooth surface equation of the involute variable tooth thickness gear based on the tooth surface equation of the involute variable tooth thickness gear; a fourth calculation unit, for obtaining a normal deviation between the involute variable tooth thickness gear and the non-involute variable tooth thickness gear according to the comprehensive modified tooth surface equation of the involute variable tooth thickness gear, the tooth surface equation of the non-involute variable tooth thickness gear and the normal vector of the non-involute variable tooth thickness gear; A second construction unit is used to construct an optimization model according to the normal deviation; A parameter optimization unit is used to optimize the parameters of the involute variable tooth thickness gear based on the optimization model to obtain the target parameters of the involute variable tooth thickness gear to achieve parameter design of the instantaneous line contact staggered axis variable tooth thickness gear pair.

9. An electronic device, characterized in that: It comprises at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions executable by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the parameter design method for the instantaneous line contact staggered axis variable tooth thickness gear pair as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the parameter design method for the instantaneous line contact staggered axis variable tooth thickness gear pair as described in any one of claims 1 to 7.

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