Design method of multi-stage fixed-axis helical gear transmission system

Abstract

The invention discloses a design method of a multi-stage fixed-axis helical gear transmission system, and relates to the technical field of mechanical design, and the design method comprises the following steps: establishing a bearing internal deformation coordination equation and a rolling body stress balance equation; solving the internal deformation coordination equation of the bearing and the stress balance equation of the rolling body, and determining a bearing rigidity curve considering the play and friction influence; determining a meshing stiffness curve of the helical gear pair; establishing a multi-body model; introducing the bearing rigidity curve and the meshing rigidity curve into a gear force element and a bearing force element of the multi-body model, and establishing a multi-body dynamic model; solving the multi-body dynamic model to obtain the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system; and adjusting the structural parameters, and comparing the dynamic characteristics after parameter adjustment to obtain optimized structural design parameters. According to the method, the influence of the bearing clearance and friction on the dynamic characteristics of the gear transmission system can be accurately considered, and rapid modeling can be carried out according to the increase and decrease of the components of the multistage fixed-axis helical gear transmission system.

Description

Technical Field

[0001] The present application relates to the technical field of mechanical design, and in particular to a design method for a multi-stage fixed-axis helical gear transmission system. Background Art

[0002] The gear transmission system is a key component in the mechanical system and one of the main sources of vibration and noise in the mechanical system. Understanding the vibration response characteristics of the gear transmission system is of vital importance for the vibration reduction and noise reduction design of the mechanical system and its stable and reliable operation. In order to avoid the system vibration caused by the large fluctuation of the meshing stiffness of the spur gears and to meet the requirements of the mechanical system for large transmission ratios and multi-path power splitting, complex multi-stage fixed-axis helical gear transmission systems are widely used. Therefore, it is of great significance to accurately obtain the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system and carry out low-vibration structural optimization design.

[0003] In the prior art, the patent publication number CN117669329A "Dynamic Modeling Method of Rigid-Flexible Coupling Planetary Gear and Rotor System" obtains the mass and stiffness matrix of the input shaft and planetary carrier through the finite element analysis software Ansys, and brings it into the dynamic equation established by Matlab, thereby establishing a rigid-flexible coupling dynamic model of the planetary gear and rotor system. The above method uses a modeling method that combines finite elements with numerical methods. Although it solves the time-consuming characteristics of pure finite element modeling methods to a certain extent, it still needs to obtain the mass and stiffness matrix through finite element software calculations and transmit data across Ansys and Matlab platforms, which is not conducive to the frequent and rapid design of gear transmission systems.

[0004] The structure of the multi-stage fixed-axis helical gear transmission system is complex, and it is difficult to model and calculate its dynamic characteristics using numerical calculation methods. In addition, the system needs to be remodeled according to the increase or decrease of components in the multi-stage fixed-axis helical gear transmission system, which is not conducive to the rapid design of the system. In addition, most of the current research on gear transmission system modeling ignores the influence of bearing clearance and friction on bearing contact stiffness, which results in the above technology being unable to accurately consider the influence of bearing clearance and friction on the dynamic characteristics of the gear transmission system, and unable to correctly guide the low-vibration design of the multi-stage fixed-axis helical gear transmission system. Summary of the invention

[0005] An embodiment of the present application provides a design method for a multi-stage fixed-axis helical gear transmission system, which is used to solve the problem that the simulation method in the prior art is difficult to calculate the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system, and does not consider the influence of bearing clearance and friction on the dynamic characteristics of the gear transmission system, and cannot correctly guide the design of the multi-stage fixed-axis helical gear transmission system.

[0006] The embodiment of the present application provides a design method for a multi-stage fixed-axis helical gear transmission system, comprising: Establish the bearing internal deformation coordination equation and rolling element force balance equation; Solve the bearing internal deformation coordination equation and rolling element force balance equation to obtain the contact force between the bearing and the raceway, and the rolling element contact force, friction force and friction torque respectively; Determine the bearing stiffness considering the effects of clearance and friction based on the contact force between the bearing and the raceway, the rolling element contact force, the friction force and the friction torque; Combining the radial deformation and clearance under different conditions, the bearing stiffness is fitted to obtain the bearing stiffness curve; Determine the mesh stiffness curve of the helical gear pair; According to the geometric information of the multi-stage fixed-axis helical gear transmission system, a multi-body model of each component in the system is established; According to the force transmission relationship between the multi-body models, the gear force element and the bearing force element are defined; The bearing stiffness curve and meshing stiffness curve are introduced into the gear force element and the bearing force element to establish the multi-body dynamics model of the multi-stage fixed-axis helical gear transmission system. Solve the multi-body dynamics model to obtain the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system; The structural parameters of the multi-stage fixed-axis helical gear transmission system are adjusted, and the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system after the adjustment of the structural parameters are compared to obtain the optimized structural design parameters.

[0007] A design method for a multi-stage fixed-axis helical gear transmission system in this application has the following advantages: Compared with the existing technology, the influence of bearing clearance and friction on bearing stiffness is considered, and the influence of bearing clearance and friction on the dynamic characteristics of the gear transmission system can be considered more accurately. In addition, it takes less time to calculate the system dynamic characteristics than the finite element modeling method, and is simpler to operate than the numerical modeling calculation method. It can also be quickly modeled according to the increase or decrease of components in the multi-stage fixed-axis helical gear transmission system, which is conducive to the rapid design of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0009] Figure 1 It is a flow chart of a design method of a multi-stage fixed-axis helical gear transmission system provided in an embodiment of the present application.

[0010] Figure 2It is a three-dimensional schematic diagram of a multi-stage fixed-axis helical gear transmission system provided in an embodiment of the present application.

[0011] Figure 3 It is a side schematic diagram of a multi-stage fixed-axis helical gear transmission system provided in an embodiment of the present application.

[0012] Figure 4 It is a schematic diagram of the displacement-deformation relationship of a bearing element provided in an embodiment of the present application.

[0013] Figure 5 It is a schematic diagram of the relative sliding speed relationship between the rolling element and the outer ring raceway of the bearing element provided in an embodiment of the present application.

[0014] Figure 6 It is a schematic diagram of the relative sliding speed relationship between the rolling element and the inner ring raceway of the bearing element provided in an embodiment of the present application.

[0015] Figure 7 It is a schematic diagram of the force analysis of the rolling element of the bearing element in the xz direction provided in the embodiment of the present application.

[0016] Figure 8 It is a schematic diagram of the force analysis of the rolling element of the bearing element in the yz direction provided in the embodiment of the present application.

[0017] Fig. 9 It is a schematic diagram of the force analysis of the rolling element of the bearing element in the xy direction provided in the embodiment of the present application.

[0018] Fig.10 It is a schematic diagram of a single tooth slice of a helical gear provided in an embodiment of the present application.

[0019] Fig.11 This is a schematic diagram of the maximum contact line length of the helical gear in the first case provided in an embodiment of the present application.

[0020] Fig.12 This is a schematic diagram of the maximum contact line length of the helical gear in the second case provided in an embodiment of the present application.

[0021] Fig.13 This is a schematic diagram of the time-varying contact line length of the helical gear in the first case provided in an embodiment of the present application.

[0022] Fig.14 This is a schematic diagram of the time-varying contact line length of the helical gear in the second case provided in an embodiment of the present application.

[0023] Fig.15 It is a block diagram of a multi-body dynamics model of a multi-stage fixed-axis helical gear transmission system in the Simpack simulation platform provided in an embodiment of the present application.

[0024] Fig.16The bearing stiffness of the gear shaft Z4-1 support in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application is K xx The changing law of bearing clearance and bearing radial deformation.

[0025] Fig.17 The bearing stiffness of the gear shaft Z4-1 support in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application is K θxθx The changing law of bearing clearance and bearing radial deformation.

[0026] Fig.18 This is the law of change of the gear tooth meshing stiffness between the gear axis Z3 and the gear axis Z4-1 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application as the gear rotation angle changes.

[0027] Fig.19 It is the root mean square value of the vibration acceleration of the gear shafts Z2 and Z3 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0028] Fig. 20 It is the root mean square value of the vibration acceleration of the gear shaft Z4-1 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0029] Fig.21 It is the root mean square value of the vibration acceleration of the gear shaft Z4-2 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0030] Fig. 22 It is the root mean square value of the vibration acceleration of the gear shaft Z4-3 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0031] Fig.23 It is the root mean square value of the vibration acceleration of the gear shaft Z5-1 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0032] Fig.24 It is the root mean square value of the vibration acceleration of the gear shaft Z5-2 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0033] Fig.25It is the root mean square value of the vibration acceleration of the gear shaft Z5-3 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3.

[0034] Fig.26 It is the root mean square value of the vibration acceleration of the gear shaft Z6 in the multi-stage fixed-axis helical gear transmission system provided in the embodiment of the present application accompanied by the changes in the bearing support positions of the gear shafts Z4-1, Z4-2, and Z4-3. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0036] Figure 1 A flowchart of a design method for a multi-stage fixed-axis helical gear transmission system provided in an embodiment of the present application. An embodiment of the present application provides a design method for a multi-stage fixed-axis helical gear transmission system, comprising: S100, establish the bearing internal deformation coordination equation and rolling element force balance equation.

[0037] For example, Figure 2 and 3 The figure shows a schematic diagram of a multi-stage fixed-axis helical gear transmission system, which consists of 10 gear shafts, namely Z1, Z2, Z3, Z4-1, Z4-2, Z4-3, Z5-1, Z5-2, Z5-3 and Z6, of which Z1 is the input shaft and Z6 is the output shaft. Each gear shaft is supported by two angular contact ball bearings.

[0038] Furthermore, when establishing the bearing internal deformation coordination equation and the rolling element force balance equation, the bearing geometric dimension parameters and the rolling element force analysis conditions are first obtained, and then the bearing internal deformation coordination equation and the rolling element force balance equation are respectively established based on the geometric dimension parameters and the force analysis conditions.

[0039] Specifically, the internal deformation coordination equation of the bearing is established based on the geometric size parameters of the bearing, and the rolling element force balance equation is established based on the force analysis of the rolling element. The bearing mentioned here is an angular contact bearing supporting the gear shaft.

[0040] When establishing the bearing internal deformation coordination equation, the bearing radial clearance size needs to be introduced into the equation. Specifically, Figure 4 As shown, the established bearing internal deformation coordination equations are shown in equations (1) and (2): (1) (2) In the formula, δ ik and δ ok are the contact deformation of the inner and outer ring raceways of the bearing, r i and r o are the curvature radii of the inner and outer ring raceways of the bearing, D is the diameter of the steel ball. X 1k and X 2k are the distances between the geometric center of the deformed rolling element in the bearing and the center of curvature of the inner ring raceway of the bearing and the center of curvature of the outer ring raceway of the bearing, respectively. A 1k and A 2k are the lateral and vertical distances between the centers of curvature of the inner and outer ring raceways of the bearing after deformation, respectively, as shown in equations (3) and (4): (3) (4) In the formula, δ x , δ y and δ z The inner ring of the bearing is x , y and z Displacement in three directions, θ y and θ z The inner ring of the bearing is y Axis and z Angular displacement of the shaft, α 0 is the initial contact angle, φ k For the k The position angle of the rolling element, c 0 is the radial clearance of the bearing, ℜ i is the radial position of the contact point between the bearing inner ring raceway and the steel ball, which can be expressed by formula (5): (5) In the formula, d m is the bearing pitch diameter.

[0041] The method of establishing the rolling element force balance equation includes determining the rolling element contact force, friction force and friction torque in sequence. Specifically, the contact force between the rolling element and the inner ring raceway and the outer ring raceway can be expressed by equations (6) and (7): (6) (7) In the formula, Q ik and Q ok are the contact forces between the rolling element and the inner ring raceway and the outer ring raceway, respectively. K i and K o are the Hertzian contact stiffness of the inner ring raceway and the outer ring raceway, respectively.

[0042] The friction force and friction torque applied by the inner ring raceway and the outer ring raceway of the bearing to the rolling element can be obtained by Coulomb's law. Specifically, the elliptical contact area between the rolling element and the raceway is divided into v × w square contact units, where v is the row number of the block contact unit, w is the column number of the block contact unit. The friction force and friction torque of each block contact unit are accumulated respectively to obtain the friction force and friction torque applied by the inner ring raceway and the outer ring raceway to the rolling element, which are expressed by equations (8) and (9): (8) (9) In the formula, f ix / iy and f ox / oy are the friction forces exerted on the rolling elements by the inner raceway and the outer raceway respectively; S i and S o are the Hertzian contact ellipse areas of the rolling element and the inner ring raceway and the outer ring raceway respectively; τ ix / iy ( x c , y c )and τ ox / oy ( x c , y c ) are the friction stresses between the rolling element and the inner ring raceway and the outer ring raceway respectively; sign () is a symbol function; u ix / iy (x v , y w )and u ox / oy ( x v , y w ) are the relative sliding speeds of the rolling element and the inner ring raceway and the outer ring raceway respectively; P i ( x v , y w )and P o ( x v , y w ) are rolling element and inner ring raceway and outer ring raceway square block contact unit ( x v , y w ) of the Hertzian contact pressure; A i ( x v , y w )and A o ( x v , y w ) are the areas of each square contact unit on the inner raceway and the outer raceway respectively; m i and m o are the friction distances applied by the inner ring raceway and the outer ring raceway to the rolling element respectively; x v and y w The contact units of each block are along the coordinate axis x c and y c location; u ix ( x v , y w ), u iy ( x v , y w ) is the rolling element and the inner ring raceway along the coordinate axis x c andy c The relative sliding speed, u ox ( x v , y w )and u oy ( x v , y w ) is the rolling element and outer ring raceway along the coordinate axis x c and y c The relative sliding speed; μ ic and μ oc are the Coulomb friction coefficients of the inner ring raceway and the outer ring raceway, respectively, which can be expressed by formula (10): (10) In the formula, μ yes μ ic and μ oc A general term for A L , B L , C L and D L is the fitting coefficient of friction coefficient that varies with load, temperature and relative sliding speed; SR is the rolling-slip ratio of the rolling element. The corresponding fitting coefficient is solved according to the load, temperature and relative sliding speed of the rolling element and the inner ring raceway and outer ring raceway. A L , B L , C L and D L , then the parameters can be obtained according to formula (10) μ ic and μ oc .

[0043] like Figure 5 , Figure 6 As shown, the rolling element is in contact with the inner ring raceway and the outer ring raceway ( x c , y c ) is expressed by formula (11): (11) In the formula, for u ix ( x c , y c )and u ox ( x c , y c ), for u iy ( x c , y c )and u oy ( x c , y c ), u ix ( x c , y c ), u iy ( x c , y c ), u ox ( x c , y c )and u oy ( x c , y c ) are the contact positions of the rolling element and the inner ring raceway x c and y c The relative sliding speed at the contact position between the rolling element and the outer ring raceway x c and y c The relative sliding velocity at For two parameters and A general term for and The inner ring raceway and outer ring raceway surfaces are along the coordinate axis x cDirection of linear velocity vector; For two parameters and A general term for and The contact surfaces between the rolling element and the inner ring raceway and the outer ring raceway are along the coordinate axis. x c Direction of linear velocity vector; For two parameters and A general term for and The inner ring raceway and outer ring raceway surfaces are along the coordinate axis y c Direction of linear velocity vector; For two parameters and A general term for and The contact surfaces between the rolling element and the inner ring raceway and the outer ring raceway are along the coordinate axis. y c Direction of linear velocity vector; For two parameters and A general term for and The inner ring raceway and outer ring raceway surfaces are respectively around the coordinate axis z c Angular velocity vector; For two parameters and A general term for and The contact surfaces between the rolling element and the inner ring raceway and the outer ring raceway are around the coordinate axis. z c The angular velocity vector of the rolling element and the raceway surface is expressed by equation (12) and equation (13) respectively: (12) (13) In the formula, ω xj , ω yj and ω zj The rolling elements are x , y and z The angular velocity component of the rotation direction; α j For the j The contact angle between the rolling element and the raceway; ω i / o For two parameters ω i and ω o A general term for ω i and ω o are the rotational angular velocities of the inner and outer rings of the bearing respectively; ω cj is the angular velocity of the rolling body; d bi / bo For two parameters d bi and d bo A general term for d bi and d bo The contact points between the rolling element geometric center and the inner and outer ring raceways are ( x c , y c ) distance; d zi / zo For two parameters d zi and d zo A general term for d zi and d zo They are the distances between the rolling element contact point and the inner ring raceway and outer ring raceway bearing rotation axis respectively: (14) In the formula, r ie / oe For two parameters r ie and r oe A general term for r ie and r oe are the equivalent radius of curvature between the rolling element and the inner ring raceway and the outer ring raceway, respectively. r ie / oe =2 r i / o d b / (2 r i / o + d b ); r i / o For two parameters r i and r o A general term ford b is the rolling element diameter; a i / o For two parameters a i and a o A general term for a i and a o are the major semi-axis lengths of the elliptical contact areas between the rolling element and the inner and outer ring raceways, d is the bearing inner ring diameter.

[0044] The rolling element force is as follows Figure 7-9 As shown in the figure, the established rolling element force balance equation is expressed by equations (15) to (19): (15) (16) (17) (18) (19) In the formula, α ik and α ok are the contact angles between the rolling element and the inner ring raceway and the outer ring raceway respectively; f ix and f ox The rolling element and the inner ring raceway and the outer ring raceway are along the coordinate axis. x c Directional friction; f iy and f oy The coordinate axes of the rolling element, inner ring raceway and outer ring raceway are y c Directional friction; F c is the centrifugal force of the rolling element; F d is the fluid resistance of the rolling element; m ix and m ox They are the friction moments between the rolling element and the inner ring raceway and the outer ring raceway around the coordinate axis. x c Directional component; m iy and m oyThey are the friction moments between the rolling element and the inner ring raceway and the outer ring raceway around the coordinate axis. y c Directional component; M gy’ for y The gyroscopic moment about the axis, Fig. 9 middle M gz’ for z Gyroscopic torque about the axis.

[0045] S110, solving the bearing internal deformation coordination equation and the rolling element force balance equation, and obtaining the contact force between the bearing and the raceway and the rolling element contact force, friction force and friction torque respectively.

[0046] Exemplarily, when solving the bearing internal deformation coordination equation and the rolling element force balance equation, the Newton-Raphson method is used to iteratively solve the bearing internal deformation coordination equation and the rolling element force balance equation based on the given external load conditions and the iteratively updated bearing displacement.

[0047] Specifically, when iteratively updating the bearing displacement, an iterative equation is defined according to the force balance equation of the bearing inner ring. If the iterative equation does not meet the convergence constraint, the increment of the bearing displacement is calculated, and the initial value of the bearing displacement is updated based on the increment. The initial value is substituted into the rolling element force balance equation, and the updating process is repeated until the iterative equation meets the convergence constraint to obtain the final bearing displacement.

[0048] The iterative equations are expressed by equations (20) to (24): (20) (twenty one) (twenty two) (twenty three) (twenty four) In the formula, H 1. H 2. H 3. H 4 and H 5. Composition of iterative equations H g , F x , F y and F z Along the coordinate axes x , y and z External loads in the direction of N bis the number of rolling elements; M x and M y Around the coordinate axis x , y of external torque.

[0049] If the iterative equation H g If the convergence constraint is not met, the bearing displacement increment {Δ δ}, expressed by formula (25): (25) In the formula, the superscript T represents transpose, θ x For the inner ring of the bearing x Angular displacement of the shaft. Based on the bearing displacement increment {Δ δ Update the initial value of the bearing displacement, substitute the updated initial value into equations (15) to (19), and repeat the above solution process until the iterative equation H g Satisfy the convergence constraints.

[0050] S120, determining the bearing stiffness considering the effects of clearance and friction based on the contact force between the bearing and the raceway, the rolling element contact force, the friction force and the friction torque.

[0051] For example, according to the relationship between the bearing inner ring force and displacement, the bearing stiffness considering the effects of clearance and friction is obtained, as shown in formula (26): (26) In the formula, K xx 、K yy 、K zz 、 and is the main stiffness of the bearing, and the remaining matrix elements are cross stiffnesses.

[0052] S130, combining radial deformation and clearance under different conditions, the bearing stiffness is fitted to obtain the bearing stiffness curve.

[0053] S140, determining the meshing stiffness curve of the helical gear pair.

[0054] Exemplarily, when determining the meshing stiffness curve of the helical gear pair, the gear teeth are first divided into multiple spur gear elements along the tooth thickness direction, the meshing stiffness of each spur gear element is calculated, and then the meshing stiffness of each spur gear element is connected in parallel to obtain the meshing stiffness curve of the helical gear pair.

[0055] like Fig.10 The helical gear shown can be equivalent to countless widths db The spur gear differential element. db The width is infinitesimal, so the width is db The meshing stiffness of the spur gear microelement can be expressed by formula (27): (27) In the formula, K d is the meshing stiffness of the spur gear microelement, K i The tooth width is db The time-varying meshing stiffness of the spur gear microelement is K i It can be simply obtained by conventional calculation methods such as energy method or material mechanics method. The meshing stiffness of the helical gear pair can be obtained by connecting the meshing stiffness of all spur gear micro-elements involved in the meshing in parallel. In order to determine the spur gear micro-element involved in the meshing, it is necessary to calculate the time-varying contact line length of the helical gear. Figure 11-12 According to the geometric relationship shown in Figure 2, the maximum length of the contact line can be expressed by formula (28): (28) In the formula, L tmax is the maximum length of the contact line, L cd is the transverse length of the meshing plane, that is, the involute length from the tooth root to the tooth top, and its expression is L cd = ε a · pbt ,in ε a is the helical gear end face overlap, pbt is the base circle pitch of the driving wheel end face, β is the helical angle of the helical gear, b is the tooth width of the helical gear.

[0056] like Figure 13-14 As shown in Figure 2, the contact line length of the helical gear changes continuously with the gear rotation angle. Corresponding to the two cases of the maximum contact line length shown in equation (28), the time-varying contact line length of the helical gear is expressed by equation (29): (29) In the formula, L t1 and L t2 are the time-varying contact line lengths of the helical gears in the first and second cases, respectively. θ is the gear angle, θ1 is the gear rotation angle corresponding to the time-varying contact line length of the helical gear reaching the maximum value in the first case, θ 2 is the gear rotation angle corresponding to the time-varying contact line length of the helical gear reaching its maximum value in the second case.

[0057] With the angle between 0≤ θ ≤ θ 2 interval as an example, n The meshing stiffness expression of the helical gear pair is expressed by equation (30): (30) In the formula, For the n Meshing stiffness of helical gear pairs, θ is is the gear rolling angle corresponding to the starting point of the contact line, θ if is the rolling angle corresponding to the end point of the contact line.

[0058] Therefore, the meshing stiffness of the helical gear pair is expressed by equation (31): (31) In the formula, K h is the meshing stiffness of the helical gear pair, m is the maximum number of teeth that mesh simultaneously, and its expression is m =ceil( ε a + ε b ), ceil() is rounded up, ε a and ε b It is the overlap between the end faces of two meshing helical gears.

[0059] S150, establishing a multi-body model of each component in the system according to geometric information of the multi-stage fixed-axis helical gear transmission system.

[0060] For example, after establishing the multi-body model of each component in the system, the motion state of each component in the system is analyzed, and the corresponding motion freedom of the corresponding component is restricted. Specifically, the motion freedom of each component can be restricted by using a kinematic pair.

[0061] like Fig.15As shown, based on the Simpack multi-body dynamics simulation platform, the geometric information such as the mass and moment of inertia of each gear shaft in the multi-stage fixed-axis helical gear transmission system is defined, and a multi-body model of each gear shaft component is established. According to the motion state of each component of the multi-stage fixed-axis helical gear transmission system, the corresponding kinematic pair is used to limit the motion freedom of the component. The usage of the kinematic pair of the multi-stage fixed-axis helical gear transmission system provided in this embodiment is shown in Table 1. In Table 1, the component earth is a fixed coordinate system of the Simpack simulation platform. In order to facilitate modeling, a fictitious component box is added, which is fixedly connected to the earth through the kinematic pair Joint #0, and its motion freedom is 0.

[0062] Table 1 The usage of kinematic pairs in multi-stage fixed-axis helical gear transmission system

[0063] S160, define gear force elements and bearing force elements according to the force transmission relationship between the multi-body models.

[0064] For example, Fig.15 As shown in the figure, each gear shaft is supported by two bearings. The bearing force element in the Simpack multi-body dynamics simulation platform is 88: Rolling bearing. The gear force element 225: Gear pair is used to represent the meshing force between the two meshing helical gears.

[0065] S170, introducing the bearing stiffness curve and the meshing stiffness curve into the gear force element and the bearing force element, and establishing a multi-body dynamics model of the multi-stage fixed-axis helical gear transmission system.

[0066] S180, solve the multi-body dynamics model and obtain the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system.

[0067] For example, the solver of the Simpack simulation platform can be used to simulate and solve the multi-body dynamics model. The simulation step size and simulation time can be adjusted according to actual needs. The smaller the simulation step size, the better the convergence of the results, but the simulation time will increase accordingly. It is recommended that the simulation solution time step size be Δ t =1×10 -5 s, and the kinematic and dynamic states of each component of the gear transmission system are obtained by solving the multi-body dynamics model.

[0068] S190, adjusting structural parameters of the multi-stage fixed-axis helical gear transmission system, comparing dynamic characteristics of the multi-stage fixed-axis helical gear transmission system after adjusting the structural parameters, and obtaining optimized structural design parameters.

[0069] Exemplarily, the distance between the gear shaft support bearings can be adjusted in batches through the DoE (Design of Experiments, parametric design) module of the Simpack simulation platform to obtain the influence of the bearing support position on the system vibration level, thereby obtaining the optimal support position parameters of the gear shaft. Taking the multi-stage fixed-axis helical gear transmission system provided in this embodiment as an example, the bearing movement distance conditions are shown in Table 2. Table 2 shows that there are a total of 4096 calculation conditions for the multi-stage fixed-axis helical gear transmission system provided in this embodiment. The calculation using the finite element method or the finite element method-numerical method combination method has the problem of huge workload. The method adopted in this application can use the DoE module to automatically adjust the parameters and calculate the 4096 calculation conditions.

[0070] Table 2 Gear shaft bearing movement distance conditions of multi-stage fixed-axis helical gear transmission system

[0071] Support bearing stiffness of gear shaft Z4-1 K xx and The change law of bearing clearance and bearing radial deformation, such as Fig.16 , Fig.17 The results show that the bearing stiffness K xx and As the bearing clearance increases, it decreases, and with the continuous increase of the radial deformation of the bearing, the influence of the clearance on the bearing stiffness gradually decreases.

[0072] The variation law of the gear meshing stiffness between gear axis Z3 and gear axis Z4-1 with the gear rotation angle is as follows: Fig.18 The results show that the meshing stiffness of helical gears fluctuates less than that of spur gears, which is beneficial to improving the vibration level of the multi-stage fixed-axis helical gear transmission system.

[0073] Figures 19 to 26 The results show that the changes in the root mean square value of the vibration acceleration of gear shafts Z2 and Z3, gear shafts Z4-1 to Z4-3, gear shafts Z5-1 to Z5-3 and gear shaft Z6 are accompanied by the changes in the bearing support positions of gear shafts Z4-1, Z4-2 and Z4-3. The results show that increasing the bearing support position of the shunt gear shaft Z4 has a significant inhibitory effect on the vibration levels of other gear shaft components. When the rear bearing movement distance is -15mm and the front bearing movement distance is 15mm, it is the optimal bearing support position of the shunt gear shaft Z4.

[0074] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0075] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A design method for a multi-stage fixed-axis helical gear transmission system, characterized in that: include: Establish the bearing internal deformation coordination equation and rolling element force balance equation; Solving the bearing internal deformation coordination equation and the rolling element force balance equation to obtain the contact force between the bearing and the raceway and the rolling element contact force, friction force and friction torque respectively; Determine the bearing stiffness considering the effects of clearance and friction based on the contact force between the bearing and the raceway, the rolling element contact force, the friction force and the friction torque; The bearing stiffness is fitted based on the radial deformation and clearance under different conditions to obtain a bearing stiffness curve; Determine the mesh stiffness curve of the helical gear pair; According to the geometric information of the multi-stage fixed-axis helical gear transmission system, a multi-body model of each component in the system is established; According to the force transmission relationship between the multi-body models, a gear force element and a bearing force element are defined; Introducing the bearing stiffness curve and the meshing stiffness curve into the gear force element and the bearing force element to establish a multi-body dynamics model of a multi-stage fixed-axis helical gear transmission system; Solving the multi-body dynamics model to obtain the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system; The structural parameters of the multi-stage fixed-axis helical gear transmission system are adjusted, and the dynamic characteristics of the multi-stage fixed-axis helical gear transmission system after the structural parameters are adjusted are compared to obtain optimized structural design parameters.

2. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 1, characterized in that: When establishing the bearing internal deformation coordination equation and the rolling element force balance equation, first obtain the bearing geometric dimension parameters and the rolling element force analysis conditions, and then establish the bearing internal deformation coordination equation and the rolling element force balance equation based on the geometric dimension parameters and the force analysis conditions.

3. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 1, characterized in that: When establishing the force balance equation of the rolling body, the elliptical contact area between the rolling body and the raceway is divided into a plurality of square contact units, and the friction force and friction torque of each square contact unit are accumulated respectively to obtain the friction force and friction torque applied to the rolling body by the inner ring raceway and the outer ring raceway.

4. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 1, characterized in that: When solving the bearing internal deformation coordination equation and the rolling element force balance equation, the Newton-Raphson method is used to iteratively solve the bearing internal deformation coordination equation and the rolling element force balance equation based on the given external load conditions and the iteratively updated bearing displacement.

5. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 4, characterized in that: When iteratively updating the bearing displacement, an iterative equation is defined according to the force balance equation of the bearing inner ring. If the iterative equation does not satisfy the convergence constraint, the increment of the bearing displacement is calculated, and the initial value of the bearing displacement is updated based on the increment. The initial value is substituted into the rolling element force balance equation, and the updating process is repeated until the iterative equation satisfies the convergence constraint to obtain the final bearing displacement.

6. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 1, characterized in that: When determining the meshing stiffness curve of the helical gear pair, the gear teeth are first divided into a plurality of spur gear elements along the tooth thickness direction, the meshing stiffness of each spur gear element is calculated, and then the meshing stiffness of each spur gear element is connected in parallel to obtain the meshing stiffness curve of the helical gear pair.

7. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 1, characterized in that: After the multi-body model of each component in the system is established, the motion state of each component in the system is analyzed, and the corresponding motion freedom of the corresponding component is restricted.

8. The design method of a multi-stage fixed-axis helical gear transmission system according to claim 7, characterized in that: Kinematic pairs are used to limit the freedom of movement of each component.

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