Multi-objective optimization method for off-road vehicle automatic transmission considering dynamic characteristics and fatigue life

Abstract

This invention discloses a multi-objective optimization method for off-road vehicle automated transmission (AT) systems that considers dynamic characteristics and fatigue life. The method comprises: using a multi-objective optimization model for off-road vehicle AT systems, using gear parameters as optimization variables, and utilizing a multi-objective genetic algorithm to iteratively optimize gear parameter design solutions corresponding to the optimization objectives of maximizing transmission efficiency, minimizing system mass, and minimizing meshing torque fluctuation, subject to gear geometry constraints, static load capacity constraints, and fatigue life constraints. The multi-objective optimization model for off-road vehicle AT systems is based on an established gear tooth profile model, a rigid-flexible coupling dynamics model for the transmission system, and a fatigue life prediction model for key components. The method utilizes multi-objective optimization design to optimize a high-performance transmission with low vibration, high efficiency, lightweight design, and a satisfactory service life.

Description

Technical Field

[0001] The present invention relates to the technical field of transmissions, and in particular to a multi-objective optimization method for off-road vehicle automatic transmissions (ATs) considering dynamic characteristics and fatigue life. Background Art

[0002] Off-road vehicles primarily include loaders, excavators, bulldozers, forklifts, and more. With the rapid development of the infrastructure and mining industries, off-road vehicles are becoming increasingly versatile. The automatic transmission (AT), a core component of off-road vehicle powertrains, directly determines the vehicle's transmission stability and reliability due to its dynamic characteristics and fatigue life, which in turn impacts the driving experience for drivers and passengers.

[0003] The transmission systems of off-road vehicles are repeatedly subjected to highly unstable loads, which can lead to poor transmission vibration and noise performance, reduced reliability, and shortened service life, ultimately reducing the service life of the vehicle. Transmissions are characterized by complex structures, high levels of integration, strong coupling between multiple components, and time-varying loads. These characteristics result in high vibration and complex and unpredictable dynamic characteristics. Traditional empirical formulas make it difficult to analyze transmission fatigue characteristics and optimize them to achieve low-vibration, high-efficiency, lightweight, and high-performance transmissions that meet service life requirements. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a multi-objective optimization method for off-road vehicle automatic transmissions (ATs) that takes into account dynamic characteristics and fatigue life, so as to solve the problem that traditional empirical formulas are difficult to analyze the fatigue characteristics of the transmission and optimize to obtain a high-performance transmission with low vibration, high efficiency, lightweight and sufficient service life.

[0005] To solve the above technical problems, the present invention is implemented by adopting the following solutions:

[0006] The present invention provides a multi-objective optimization method for off-road vehicle automated driving (AT) considering dynamic characteristics and fatigue life, comprising:

[0007] Based on the multi-objective optimization model of off-road vehicle automatic transmission (AT), with gear parameters as optimization variables, a multi-objective genetic algorithm is used to iteratively optimize the gear parameter design solution corresponding to the optimization objectives of maximizing transmission efficiency, minimizing system mass, and minimizing meshing torque fluctuation under the constraints of gear geometry, static load capacity, and fatigue life.

[0008] Among them, the multi-objective optimization model of off-road vehicle AT is established based on the established gear tooth profile model, transmission system rigid-flexible coupling dynamic model and key component fatigue life prediction model.

[0009] Compared with the existing technology, the beneficial effects achieved by the present invention are as follows: the present invention takes into account the precise modeling of the tooth profile, the internal and external excitations of the transmission system, the flexibility of the key components of the system and the coupling between the components, establishes a rigid-flexible coupling dynamic model of the transmission, uses dynamic simulation to obtain dynamic loads, evaluates the dynamic characteristics of the system, and uses this as the load spectrum to calculate the fatigue life of key components. On this basis, multi-objective optimization design is carried out to optimize a high-performance transmission with low vibration, high efficiency, lightweight and meeting service life requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 The tooth profile of a single arc universal rack tool provided by an embodiment of the present invention;

[0011] Figure 2 The generating processing principle and the established coordinate system provided by the embodiment of the present invention;

[0012] Figure 3 The end face tooth profile points and tooth shape provided by the embodiment of the present invention;

[0013] Figure 4 A gear slice meshing model provided by an embodiment of the present invention;

[0014] Figure 5 A schematic diagram of the movement of the contact line on the meshing plane provided by an embodiment of the present invention;

[0015] Figure 6 The slicing wheel tooth cantilever beam provided in the embodiment of the present invention;

[0016] Figure 7 The gear concentrated mass model provided by the embodiment of the present invention;

[0017] Figure 8 A three-dimensional diagram of a transmission provided by an embodiment of the present invention;

[0018] Figure 9 A three-dimensional diagram of a transmission case provided by an embodiment of the present invention;

[0019] Figure 10 A bearing sub-model provided in an embodiment of the present invention;

[0020] Figure 11 A flow chart of the dynamic model coupling provided by an embodiment of the present invention;

[0021] Figure 12 The finite element calculation of bending stress load and constraint setting provided in the embodiment of the present invention;

[0022] Figure 13 A finite element processing flow chart provided for an embodiment of the present invention;

[0023] Figure 14A flow chart for evaluating contact fatigue and bending fatigue life of gears provided in an embodiment of the present invention;

[0024] Figure 15 A flowchart of the multi-objective optimization design of an off-road vehicle AT considering dynamic characteristics and fatigue life provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0025] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0026] This embodiment provides a multi-objective optimization method for an off-road vehicle automatic transmission (AT) that takes into account dynamic characteristics and fatigue life. The method first derives the tooth surface equation based on the gear meshing principle and the rack tool equation, and then derives the gear pair meshing efficiency and time-varying meshing stiffness based on the precise tooth surface equation. Then, a gear lumped parameter model, a bearing sub-model, and a housing and shaft system finite element reduction model are coupled to establish a rigid-flexible coupling model of the transmission drive system. Gear contact fatigue life, bending fatigue life, and bearing fatigue life are evaluated based on the load spectrum obtained from the dynamic model. Finally, multi-objective optimization is performed using gear parameters as design variables, gear geometry constraints, static load capacity constraints, and fatigue life constraints as constraints, with the optimization objectives of minimizing meshing torque fluctuation in each gear, minimizing system mass, and maximizing transmission efficiency in each gear. The result is a high-performance transmission with low vibration, high efficiency, lightweight, and sufficient service life.

[0027] The multi-objective optimization method for off-road vehicle AT considering dynamic characteristics and fatigue life includes the following steps:

[0028] S1: Establishing gear tooth profile model

[0029] Based on the seven basic parameters of gears, namely the number of teeth, module, driving side pressure angle, non-driving side pressure angle, helix angle, tooth width, tooth top height coefficient and modification coefficient, the rack tool tooth profile equation applicable to symmetric gears and asymmetric gears was derived; based on the principle of generating processing, the gear meshing equation was derived, and the tooth profile curve was generated and the gear three-dimensional model was established; the gear was sliced ​​along the tooth width direction to obtain the gear slice meshing model; the time-varying meshing stiffness was solved based on the helical gear slicing method and the potential energy method, and the gear transmission efficiency was solved based on the slicing method and the empirical formula method.

[0030] S2: Establishing a rigid-flexible coupling dynamic model of the transmission system

[0031] A rigid-flexible coupling dynamic model of the transmission system is established, including a gear lumped parameter sub-model, a bearing sub-model, and a flexible component shrinkage model (housing and shaft system). Nonlinear factors such as time-varying meshing stiffness and meshing damping are considered. By combining the interaction relationship between displacement and force with the dynamic equation, the sub-models are coupled to establish a rigid-flexible and dynamic model of the system. The meshing force and bearing force of each gear pair are obtained through simulation, and the dynamic characteristics of the system are analyzed.

[0032] S3: Establishing a fatigue life prediction model for key components

[0033] Calculate contact stress based on the gear slicing method and Hertz contact theory; calculate gear bending stress using finite element software; combine the gear and bearing load spectra obtained from the rigid-flexible coupling dynamic model of the transmission system to calculate the gear contact stress spectrum and bending stress spectrum, and use the linear cumulative damage criterion and gear SN curve to predict the gear contact fatigue life and bending fatigue life; use the bearing load spectrum combined with LP theory to predict bearing fatigue life;

[0034] S4: Conduct multi-objective optimization of transmissions considering dynamic characteristics and fatigue life

[0035] Taking gear parameters as design variables, gear geometry constraints and performance constraints as constraints, and minimizing meshing torque fluctuation, minimizing system mass, and maximizing transmission efficiency as optimization goals, multi-objective optimization of the transmission is carried out considering dynamic characteristics and fatigue life. The result is a high-performance transmission with low vibration, high efficiency, lightweight, and sufficient service life.

[0036] Step S1 includes the following sub-steps:

[0037] refer to Figure 1 Schematic diagram of the rack tool. The rack tool tooth profile suitable for symmetrical and asymmetrical gears is established, including four parts: the driving side straight line part AB, the driving side transition curve part BC, the non-driving side transition area line part CD, and the non-driving side straight line part DE. The equations of each segment of the tool and the tangent vector and normal vector of each segment are as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] in, and The rack tool tooth profile equations are the driving side straight line part AB, the driving side transition curve part BC, the non-driving side transition area line part CD and the non-driving side straight line part DE, respectively. and They are the tangent vectors of the driving side straight line part AB, the driving side transition curve part BC, the non-driving side transition area line part CD and the non-driving side straight line part DE, and are the normal vectors of the driving side straight line part AB, the driving side transition curve part BC, the non-driving side transition area line part CD, and the non-driving side straight line part DE respectively; m is the module, unit is mm; α d , α c is the pressure angle between the drive side and the non-drive side of the rack tool, in rad. d ≠α c When h ad * 、h ac * c is the tooth addendum coefficient of the rack tool drive side and non-drive side; d * 、c c * is the top clearance coefficient between the driving side and the non-driving side of the rack; x * is the displacement coefficient; R f is the tool tip arc radius, unit is mm.

[0051] refer to Figure 2 Schematic diagram of the generating processing principle and the established coordinate system. Two coordinate systems are established: the rotating coordinate system S1 fixed on the gear blank and the translation coordinate system S2 fixed on the rack tool.

[0052] As the rack moves, several envelopes are generated in the gear blank coordinate system, which are expressed as follows:

[0053]

[0054]

[0055]

[0056] in, is the coordinate of each point on the envelope in the rotating coordinate system S1, M 12 is the coordinate transformation from S2 to S1, The coordinates of each point of the tool in the translation coordinate system S2; the meanings of u and θ refer to Figure 1 , x2, y2 and z2 are the coordinate values ​​of each point of the tool in the x, y and z directions in the translation coordinate system S2 respectively; is the rotation arc of the gear blank, unit is rad, r is the pitch circle radius of the gear blank, unit is mm.

[0057] According to the meshing principle, the condition for any point on the rack cutter tooth profile to be tangent to the tooth blank is that the relative motion velocity vector of the point should be in the direction of the common tangent of the two tooth profiles passing through the point:

[0058]

[0059] Among them, X2 and Y2 are the horizontal and vertical coordinates of each point of the tool in the translation coordinate system S2, x l 、y l N is the horizontal and vertical coordinates of the contact point in the translation coordinate system S2, lx 、N ly The components of the normal vector at the tool contact point along the x2 and y2 axes.

[0060] The gear meshing equation derived from the meshing principle is as follows. The meshing equation consists of four sections:

[0061]

[0062]

[0063]

[0064]

[0065] refer to Figure 3 The end face tooth profile points and tooth shape diagram, envelope equation and meshing equation are combined to obtain the points of the tooth profile. The precise tooth profile is obtained by connecting the points into lines. The precise gear tooth profile points are imported into the 3D software to build a 3D model of the gear.

[0066] refer to Figure 4 Gear Slice Meshing Model and Figure 5Schematic diagram of the movement of the contact line on the meshing plane; based on the precise tooth profile of the gear, a gear slice meshing model can be established. The method is to cut the gear into several thin slices along the tooth width direction, so that the geometric parameters at any position on the tooth surface can be obtained, such as the normal curvature radius of each point on the involute line, the tangential velocity of each point, load distribution, etc.

[0067] refer to Figure 6 The schematic diagram of the cantilever beam of the gear teeth is sliced, and a model for solving the time-varying meshing stiffness of the gear is established, including the gear tooth stiffness, contact stiffness and gear body stiffness. The gear teeth are regarded as cantilever beams, and the gear tooth stiffness of each slice (including the bending stiffness k b , shear stiffness k s and compressive stiffness k a ). The meshing contact point will produce contact deformation, and the Hertz contact stiffness k is calculated based on the Hertz contact theory. h The equivalent stiffness caused by the deformation of the gear matrix is ​​the wheel body stiffness. The wheel body stiffness k can be obtained using the empirical formula f .

[0068] The instantaneous meshing stiffness of a pair of gears is obtained by summing up the stiffness of each slice, as shown in the following formula:

[0069]

[0070] The complete time-varying mesh stiffness of the gear pair can be obtained by calculating the mesh stiffness of one cycle.

[0071] The established gear transmission efficiency solution model includes the calculation of meshing power loss based on the slice meshing model, and the calculation of oil stirring power loss, sealing power loss and bearing power loss based on empirical formulas.

[0072] The meshing power loss includes rolling friction power loss and sliding friction power loss. The rolling friction power loss and sliding friction power loss of each slice can be calculated using the slice meshing model. Then, the meshing power loss of the meshing pair can be obtained by adding them up. Finally, the meshing power loss of the entire meshing cycle is calculated. The average meshing power loss of the entire meshing cycle is used as the meshing power loss:

[0073]

[0074] Among them, P mesh is the meshing power loss, p slide 、p roll is the contact element M j Sliding friction power loss and rolling friction power loss at p θis the meshing power loss at the moment of rotation angle θ, unit is W; mean is the averaging function; i represents the i-th contact line, j is the j-th contact unit, m is the total number of gear teeth at the meshing moment, and N is the total number of units in the i-th contact line.

[0075] The power loss caused by friction torque and drag torque due to bearing rotation is calculated as follows:

[0076]

[0077] Among them, P bearing is the bearing power loss, n b Bearing operating speed, unit r / min, T b 、T drag 、T sl 、T rr and T seal They are bearing friction torque, drag torque, sliding friction torque, rolling friction torque and seal friction torque, with the unit of N·mm.

[0078] The oil stirring power loss includes: the oil stirring loss P related to the outer diameter of the optical axis c1 , oil churning loss related to gear end face P c2 Oil churning loss P related to the gear surface c3 , the calculation formula is as follows:

[0079]

[0080] Among them, f g is the gear oil immersion factor (completely immersed in oil f g =1, oil-free f g = 0, when only a part is immersed, the value is linearly checked between 0 and 1); R f is the roughness factor, which is related to the modulus, R f =7.93-4.648 / m; n c , D and L are the working speed (r / min), outer diameter and length (mm) of the stirring element respectively; ν0 is the kinematic viscosity of the lubricating oil, unit is cSt; A g is the arrangement constant; B and β are the tooth width and the helical angle of the helical gear. When β<10°, the β value is 10°

[0081] The friction power loss between the seal and the housing shaft system to maintain the sealing is calculated as follows:

[0082]

[0083] Among them, P sealing is the sealing power loss, unit W; T s is the friction torque of the seal, in N·m; ns is the shaft speed in r / min.

[0084] The transmission power loss of a pair of meshing pairs includes: gear meshing power loss P mesh , Sealing power loss P sealing , oil stirring power loss P churing =P c1 +P c2 +P c3 And the bearing power loss P bearing , the transmission efficiency is calculated as follows:

[0085]

[0086] Step S2 specifically includes the following sub-steps:

[0087] refer to Figure 7 Schematic diagram of the gear concentrated mass model; the established rigid-flexible coupling dynamic model of the AT transmission system. In the gear concentrated parameter model, the gear is considered rigid, and its mass is concentrated at the center of the gear. Each gear has six degrees of freedom, and its dynamic equation is as follows:

[0088]

[0089] Among them, m, J x 、J y and J z are the gear mass and the moment of inertia in the x, y, and z directions respectively; F x 、F y 、F z and T x 、T y 、T z are the forces and moments acting on the gear in the x, y, and z directions respectively; and are the translational acceleration and angular acceleration of the gear in the x, y, and z directions respectively. The integral of these is the velocity, and the quadratic integral is the displacement. x 、k y 、k z and c x 、c y 、c z are the stiffness and damping of the gear support bearing in the x, y, and z directions respectively; k tx 、k ty 、k tz and c tx 、c ty 、c tz are the torsional stiffness and torsional damping of the gear support bearing in the x, y, and z directions respectively; δ x , δ y , δ z and δθx , δ θy , δ θz are the relative translational displacement and relative angular displacement in the x, y, and z directions at the gear and shaft nodes, respectively.

[0090] The relative displacement of the two gears along the meshing line in the meshing pair is calculated using the center of mass displacement as follows:

[0091]

[0092] Among them, x, y, z and θ x ,θ y ,θ z is the x, y, z direction displacement and angular displacement of the gear, is the angle between the radius of gear 1 perpendicular to the meshing plane and the positive direction of the x-axis, φ is the angle between the centerline of the gear and the positive direction of the x-axis, r b1 、r b2 are the base circle radii of gear 1 and gear 2, β b Base circle helix angle, e m is the meshing error.

[0093] The normal force can be calculated using the relative displacement and meshing stiffness:

[0094] F n =k m Δδ+c m Δv

[0095] Among them, k m is the meshing stiffness, c m is the meshing damping, Δv is the relative motion speed along the meshing line, and Δv can be obtained by differentiating the relative displacement.

[0096] The normal force is decomposed into the directions of the gear, and the force calculations of the six degrees of freedom are as follows:

[0097]

[0098] Among them, F x1 、F y1 、F z1 is the contact force of gear 1 along the x, y, and z directions, T x1 、T y1 、T z1 The torque of gear 1 around the x, y, and z directions, r b1 、r b2 are the base circle radii of gear 1 and gear 2, β b Base circle helix angle, F n is the overall normal force of the gear, φ is the angle between the center line of the gear and the positive direction of the x-axis, is the angle between the radius of gear 1 perpendicular to the meshing plane and the positive direction of the x-axis, α t is the end pressure angle.

[0099] The theoretical basis of the flexible component polycondensation model is as follows: the dynamic equation of any system can be expressed as:

[0100]

[0101] M, C d and K are the mass matrix, damping matrix, and stiffness matrix respectively, u is the displacement vector, and F is the load vector.

[0102] Decouple the dynamic equations into m independent differential equations:

[0103]

[0104] Among them, Φ j is the jth mode vector, y i is the modal coordinate, ξ j is the j-th order modal damping, ω j is the j-th natural frequency.

[0105] The influence of high-order vibration is relatively small. The first n equations in the above formula are used to calculate the system vibration to reduce the amount of calculation and transform it into the following state equation:

[0106]

[0107] in w is the displacement of each point, y is the modal coordinate vector, and A, B, C, and D are the state equation matrices respectively.

[0108] refer to Figure 8 Transmission 3D diagram and Figure 9 A 3D diagram of the transmission case; the condensed components include the case condensed model and the shaft system condensed model. The process flow is as follows: constraints are set in the finite element software, with fixed constraints set on both sides of the case and remote nodes set for the case bearing holes. Remote nodes are set at the bearing locations and gear positions of each shaft component to calculate the action and reaction forces using the displacement velocities of the bearing inner and outer rings. Finite element software is used to process the obtained vibration modal data and generate the A, B, and C matrices to complete the condensed modeling.

[0109] Figure 10Schematic diagram of the bearing submodel. During installation, the inner ring of the bearing is fixed to the shaft, and the outer ring is fixed to the housing. Therefore, the displacements and velocities of the inner and outer ring nodes are derived using a contraction model of the shafting and housing. Based on geometric relationships, each displacement is equated to the normal displacement at the contact point between the roller and the outer ring. Combined with the normal contact stiffness and contact damping of each roller, the normal force on each roller is calculated, and then the overall dynamic load of the bearing is calculated by summing them.

[0110] The normal force of a single roller is calculated as follows:

[0111]

[0112] Among them, Q ei is the normal force of the ith roller, δ ni is the normal displacement of a single roller, K ne is the contact stiffness coefficient of the outer raceway:

[0113] K ne =6.24×10 4 l 0.82 D w 0.11 [1+c i 0.9 cos(α e -α i )] -1.11

[0114] Where, l is the contact line length of the tapered roller, in m; D w is the average diameter of the tapered roller, in m; c i =sin(α e+ α f ) / sin(α i+ α f ), α e , α i and α f are the contact angles of the tapered roller with the outer race, inner race and bearing retaining ring respectively.

[0115] The axial and radial forces of each roller can be obtained by decomposing the normal force according to the geometric relationship. The total axial and radial forces of the bearing can then be obtained by adding up the forces on each roller:

[0116]

[0117] Among them, F r 、F a is the total radial force and total axial force of the bearing, i represents the i-th tapered roller, there are z tapered rollers in total, Q ri , Q ai are the radial force and axial force of the i-th tapered roller.

[0118] refer to Figure 11 Dynamic model coupling flow chart; a rigid-flexible coupling dynamic model for the AT transmission system is established, with the following coupling relationship: Force is transmitted between the housing and the shafting through bearings. The inner ring is fixed to the shaft, and the outer ring is fixed to the housing. The relative displacement of the inner and outer rings is used to calculate the bearing force acting on the housing and shafting. The corresponding node displacements and velocities can be calculated using the condensation models of the housing and shafting, respectively. Similarly, force is transmitted between the shaft and gears through bearings. The gears are subjected to meshing forces and bearing forces. The motion displacements and velocities are calculated using their dynamic equations. The meshing forces between the gear pairs are calculated using the relative displacements.

[0119] Step S3 specifically includes the following sub-steps:

[0120] A gear contact stress calculation model is established. The contact stress of the gear teeth on all meshing slices is calculated based on the Hertz contact formula and the gear slice meshing model, and the contact stress at the maximum slice is taken as the tooth surface contact stress.

[0121] The contact stress of a single gear tooth slice is:

[0122]

[0123] Among them, F ni is the normal force of each slice, unit N; R is the integrated curvature radius at the meshing point, unit mm; L is the contact line length, unit mm; μ1, μ2 and E1, E2 are the Poisson's ratio and elastic modulus (pa) of the two gears respectively.

[0124] The irregularly varying contact stresses on the gears are then statistically analyzed, and the complex load is decomposed into multiple groups of load half-cycles and load cycles using the rainflow counting method. The load mean, amplitude, and corresponding cycle number data for each load cycle are obtained. The asymmetric cyclic loads obtained from the rainflow counting method are corrected to symmetric cyclic loads using the Goodman correction method, allowing fatigue life to be calculated using the material's contact SN curve.

[0125] refer to Figure 12 Finite element calculation of bending stress load and constraint setting diagram, Figure 13 Finite element processing flow chart and Figure 14Gear contact fatigue and bending fatigue life assessment flow chart; establish a gear bending stress calculation model, and use Ansys software to automatically analyze gear bending stress. First, input the generated tooth profile points into the SCDM three-dimensional software under Ansys, and then establish a three-tooth model (a simplified processing of gear finite element analysis. In practice, a gear circle is all gear teeth, but the finite element processing speed is too slow, so three adjacent gear teeth are used to establish the finite element model), and apply loads and constraints, set materials, and output the tooth root bending stress calculation results. Similarly, the rain flow counting method is used to decompose complex loads into multiple groups of load half cycles and load cycles. The Goodman correction method is used to correct the asymmetric cyclic loads obtained by the rain flow counting method to symmetric cyclic loads, and the fatigue life is calculated in combination with the bending SN curve of the material.

[0126] Establish bearing service life based on the LP bearing rating life formula:

[0127]

[0128] a1 is the reliability coefficient; a2 is the performance correction coefficient; a3 is the lubrication condition coefficient; C r is the rated dynamic load; ε is the life index; the calculation formula for the equivalent dynamic load P is as follows:

[0129] P=f t (XF r +YF a )

[0130] F r and F a Refers to radial force and axial force, f t is the load factor, f t Take 2.0, X and Y are the radial dynamic load distribution coefficient and axial dynamic load distribution coefficient respectively, which can be obtained by referring to the mechanical design manual.

[0131] The equivalent dynamic load can be calculated by using the dynamic radial force and axial force of the bearing obtained by dynamic simulation. After obtaining the dynamic load of each bearing, combined with the rated dynamic load C of each model of bearing r , calculate the service life of the bearing under the current working conditions through the formula.

[0132] Step S4 specifically includes the following sub-steps:

[0133] refer to Figure 15 AT multi-objective optimization design flow chart considering dynamic characteristics and fatigue life; based on the above-established gear tooth profile model, transmission system rigid-flexible coupling dynamic model and key component fatigue life prediction model, a non-road vehicle AT multi-objective optimization model is established.

[0134] The number of teeth z, module m, pressure angle α, helix angle β, tooth width B, tooth top height coefficient h of each gear a , the modification coefficient x is used as the multi-objective optimization design variable in this section, including the nine gears included in the V-type working condition.

[0135] To ensure machining and meshing accuracy, tooth profile constraints such as no over-pointing of the tooth tips and no meshing interference were set based on the principle of gear meshing. To ensure installation and transmission ratio accuracy, center distance and transmission ratio constraints were set. To ensure tooth surface contact and tooth root bending load capacity, static load capacity constraints were set. To ensure the designed transmission achieves a reasonable service life, gear contact fatigue constraints, tooth root bending fatigue constraints, and bearing fatigue life constraints were set.

[0136] The optimization design starts with the gear parameters. First, it is determined whether the gear geometric constraints (including the above-mentioned tooth shape constraints, center distance constraints and transmission ratio constraints) are met. If the gear geometric constraints are met, the precise gear tooth profile is obtained according to the tool tooth profile and a gear slice meshing model is generated to solve the transmission efficiency of each gear. The gear slice meshing model can be combined with the nominal load to calculate the tooth surface contact stress and tooth root bending stress to determine whether the static load capacity constraints are met. At the same time, the bending stress finite element analysis can obtain the gear tooth quality, which is one of the optimization targets. If the static load capacity constraints are met, the gear slice model and potential energy method are used to calculate the time-varying meshing stiffness of the gear, establish a gear concentrated mass model, and couple the box finite element reduction model, shaft system finite element reduction model and bearing sub-model established based on the transmission structural parameters. A rigid-flexible coupling dynamic model of the AT transmission system is established. Dynamic simulation is carried out by inputting the working parameters of each gear. The dynamic load of each key component is obtained by reading the operation results, and the meshing torque fluctuation coefficient is calculated. The bearing fatigue life, gear contact fatigue life and gear bending fatigue life are calculated in combination with the linear cumulative damage criterion to evaluate whether the life of the above components meets the fatigue life constraints; if one of the above gear geometric constraints, static load capacity constraints and fatigue life constraints is not met, the next set of gear parameters is iterated; finally, a comprehensive performance evaluation is performed on the optimization target, including system quality, meshing torque fluctuation of each gear and transmission efficiency of each gear. The highest transmission efficiency, minimum system quality and minimum meshing torque fluctuation are taken as the objective functions, and the optimal gear design parameters are output according to the ranking of the system comprehensive trade-off solution.

[0137] The meshing torque fluctuation is expressed by the meshing torque fluctuation coefficient, which is calculated as follows:

[0138]

[0139] Among them, T max 、T min Refers to the maximum and minimum values ​​of the meshing torque.

[0140] The transmission efficiency is calculated by multiplying the meshing efficiencies of all meshing pairs in the gear to obtain the transmission efficiency of the gear.

[0141] Genetic algorithm (NSGA-Ⅱ) is used as a multi-objective optimization algorithm. In order to comprehensively evaluate the pros and cons of each design solution, the normalization method is used to adjust each objective function to 0-1, and then the linear weighted method is used to comprehensively evaluate each solution. The formula is as follows:

[0142]

[0143] Among them, w1...w7 are the weights of each target, f1(x)...f7(x) are the objective functions; since there are three gears, there are seven objective functions in total, including the transmission efficiency under three gears, the meshing torque fluctuation under three gears, and the system quality.

[0144] Finally, the multi-objective trade-off solution with the highest comprehensive ranking is output as the result of the transmission optimization design.

[0145] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life, characterized in that: include: Based on the multi-objective optimization model of off-road vehicle automatic transmission (AT), with gear parameters as optimization variables, a multi-objective genetic algorithm is used to iteratively optimize the gear parameter design solution corresponding to the optimization objectives of maximizing transmission efficiency, minimizing system mass, and minimizing meshing torque fluctuation under the constraints of gear geometry, static load capacity, and fatigue life. Among them, gear geometric constraints include tooth shape constraints, center distance constraints, and transmission ratio constraints; the multi-objective optimization model for off-road vehicle AT is established based on the established gear tooth profile model, the rigid-flexible coupling dynamic model of the transmission system, and the fatigue life prediction model of key components; The establishment of the rigid-flexible coupling dynamic model of the transmission system includes: establishing a gear lumped parameter sub-model, a bearing sub-model and a flexible component condensation model; considering the nonlinear factors of time-varying meshing stiffness and meshing damping, the interaction relationship between displacement and force is combined with the dynamic equation, and the gear lumped parameter sub-model, the bearing sub-model and the flexible component condensation model are coupled to establish the rigid-flexible coupling dynamic model of the transmission system; the coupling relationship between the gear lumped parameter sub-model, the bearing sub-model and the flexible component condensation model is as follows: the force is transmitted between the housing and the shaft system through the bearing, the inner ring is fixed to the shaft, and the outer ring is fixed to the housing, and the relative displacement of the inner and outer rings is used to calculate the bearing force acting on the housing and the shaft system, and the corresponding node displacement and velocity are calculated using the condensation model of the housing and the shaft system respectively; the force is transmitted between the shaft and the gear through the bearing, and the gear is subjected to meshing force and bearing force, and the motion displacement and velocity are calculated using the gear dynamics equation; the meshing force between the gear pairs is calculated using the relative displacement; The gear concentration model is established by treating the gears as rigid and concentrating the mass at the center of the gears. Each gear has six degrees of freedom. The relative displacement of the two gears along the meshing line in the meshing pair is calculated using the displacement of the center of mass. The normal force is calculated using the relative displacement and the meshing stiffness. Based on the decomposition of the normal force into various directions of the gear, the forces of the six degrees of freedom of the gear are calculated. The establishment of the fatigue life prediction model for key components includes: using the contact SN curve of the material to calculate the contact fatigue life of the gear, combining the bending SN curve of the material to calculate the bending fatigue life of the gear, and calculating the fatigue life of the bearing under the current working conditions based on the LP bearing rated life formula.

2. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 1, characterized in that: The establishment of the gear tooth profile model includes: The rack cutter tooth profile equations applicable to symmetrical and asymmetrical gears are derived based on the basic parameters of the gears. Based on the principles of generating and meshing, the gear meshing equation is derived, and the tooth profile and gear 3D model are generated. Slice the gear along the tooth width direction to obtain the gear slice meshing model; A solution model for the time-varying meshing stiffness of gears is established based on the helical gear slicing method and the potential energy method, and a solution model for the gear transmission efficiency is established based on the slicing method and the empirical formula method.

3. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 2, characterized in that: The tooth profile of the rack tool applicable to symmetrical and asymmetrical gears includes a driving side straight line portion, a driving side transition curve portion, a non-driving side transition curve portion, and a non-driving side straight line portion. The equations and corresponding tangent vectors and normal vectors are as follows: Where, and The tooth profile equations of the rack tool are the straight line part of the driving side, the transition curve part of the driving side, the transition line part of the non-driving side, and the straight line part of the non-driving side. and They are the tangent vectors of the driving side straight line part, the driving side transition curve part, the non-driving side transition area line part and the non-driving side straight line part, and are the normal vectors of the driving side straight line part, the driving side transition curve part, the non-driving side transition area line part and the non-driving side straight line part respectively; m is the modulus; α d , α c are the pressure angles on the driving side and non-driving side of the rack tool, respectively. d ≠α c When h ad * 、h ac * are the tooth addendum coefficients of the drive side and non-drive side of the rack tool respectively; c d * 、c c * are the top clearance coefficients of the rack drive side and non-drive side respectively; x * is the displacement coefficient; R f is the tool tip arc radius; Based on the principles of generating and meshing, the gear meshing equation is derived, and the tooth profile and gear 3D model are generated, including: Establish a rotation coordinate system S1 fixed on the gear blank and a translation coordinate system S2 fixed on the rack tool; As the rack moves, the rotating coordinate system S1 generates several envelopes, and the envelope equations are obtained; The gear meshing equation is derived based on the meshing principle; The envelope equation and the gear meshing equation are used together to obtain the points on the tooth profile, and the tooth profile is obtained by connecting the points into lines; Import the gear tooth profile points in the tooth profile line into the 3D software to build a 3D gear model; The envelope equation is: Where, is the coordinate of each point on the envelope in the rotating coordinate system S1, M 12 is the coordinate transformation from S2 to S1, are the coordinates of each point of the tool in the translation coordinate system S2, x2, y2 and z2 are the coordinate values ​​of each point of the tool in the translation coordinate system S2 in the x, y and z directions respectively; is the rotation arc of the gear blank, r is the pitch circle radius of the gear blank; The meshing equations include:

4. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 2, characterized in that: A gear time-varying mesh stiffness solution model is established based on the helical gear slicing method and potential energy method, and a gear transmission efficiency solution model is established based on the slicing method and empirical formula method, including: The gear teeth are regarded as cantilever beams, and the gear tooth stiffness of each slice is solved based on the potential energy method and the slice method. The Hertz contact stiffness k is calculated based on the contact deformation generated by the meshing contact point and the Hertz contact theory. h ; Based on the equivalent stiffness caused by the deformation of the gear matrix as the wheel body stiffness, the wheel body stiffness k is solved using the empirical formula f ; The instantaneous meshing stiffness of a pair of gears is obtained by summing up the stiffness of each slice, and the time-varying meshing stiffness of the gears is obtained by solving the meshing stiffness of the gears for one cycle. Based on the slice meshing model, the rolling friction power loss and sliding friction power loss of each slice are calculated and accumulated to obtain the meshing power loss of the meshing pair. The average meshing power loss of the meshing pair in the entire meshing cycle is calculated and taken as the gear meshing power loss. Calculate the oil stirring power loss, seal power loss and bearing power loss based on empirical formulas; The gear transmission efficiency is solved by gear meshing power loss, oil stirring power loss, sealing power loss and bearing power loss; Among them, the time-varying meshing stiffness of gears includes tooth stiffness, contact stiffness and wheel body stiffness; tooth stiffness includes bending stiffness k b , shear stiffness k s and compressive stiffness k a The cumulative calculation formula for each slice's stiffness is: The gear transmission efficiency solution model is: Where, is the gear meshing power loss, p slide 、p roll is the contact element M j Sliding friction power loss and rolling friction power loss at p θ is the meshing power loss at the moment of rotation angle θ, mean is the averaging function, i represents the i-th contact line, j is the j-th contact unit, m is the total number of gear teeth at the meshing moment, and N is the total number of units in the i-th contact line; is the bearing power loss, n b is the bearing operating speed, T b =T rr +T sl +T drag +T seal , T b 、T drag 、T sl 、T rr and T seal They are bearing friction torque, drag torque, sliding friction torque, rolling friction torque and seal friction torque; is the oil stirring power loss, f g is the gear immersion factor, completely immersed in oil f g =1, oil-free f g =0, when only a part is immersed, the value is linearly checked between 0 and 1, R f is the roughness factor, which is related to the modulus, R f =7.93-4.648 / m,n c , D and L are the working speed, outer diameter and length of the oil stirring element respectively, ν0 is the kinematic viscosity of the lubricating oil, A g is the arrangement constant, B and β are the tooth width and the helix angle of the helical gear. When β<10°, the β value is 10°; is the sealing power loss, T s is the seal friction torque, n s is the shaft speed.

5. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 1, characterized in that: The gear dynamics equation is: Where m, J x 、J y and J z are the gear mass and the moment of inertia in the x, y, and z directions respectively; F x 、F y 、F z and T x 、T y 、T z are the forces and moments acting on the gear in the x, y, and z directions respectively; and are the translational acceleration and angular acceleration of the gear in the x, y, and z directions respectively. The integral of these is the velocity, and the quadratic integral is the displacement. x 、k y 、k z and c x 、c y 、c z are the stiffness and damping of the gear support bearing in the x, y, and z directions respectively; k tx 、k ty 、k tz and c tx 、c ty 、c tz are the torsional stiffness and torsional damping of the gear support bearing in the x, y, and z directions respectively; δ x , δ y , δ z and δ θx , δ θy , δ θz are the relative translation displacement and relative angular displacement in the x, y, and z directions at the gear and shaft nodes, respectively; The calculation formula for the relative displacement of two gears along the meshing line in a meshing pair is: Where x, y, z and θ x ,θ y ,θ z is the x, y, z direction displacement and angular displacement of the gear, is the angle between the radius of gear 1 perpendicular to the meshing plane and the positive direction of the x-axis, φ is the angle between the centerline of the gear and the positive direction of the x-axis, r b1 、r b2 are the base circle radii of gear 1 and gear 2, β b Base circle helix angle, e m is the meshing error; The formula for calculating the normal force is: F n =k m Δδ+c m Δv Where k m is the meshing stiffness, c m is the meshing damping, Δv is the relative motion speed along the meshing line; The formula for calculating the force of the six degrees of freedom of the gear is: Where, F x1 、F y1 、F z1 is the contact force of gear 1 along the x, y, and z directions, T x1 、T y1 、T z1 The torque of gear 1 in the x, y, and z directions, F n is the overall normal force of the gear, α t is the end pressure angle.

6. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 1, characterized in that: The establishment of the flexible component polycondensation model includes: Decouple the system dynamics equations into m independent differential equations; Take the first n differential equations and convert them into state equations to calculate the system vibration; Set constraints in the finite element software. Set fixed constraints on both sides of the box, set remote nodes on the box bearing holes, and set remote nodes at the bearing positions and gear positions of each shaft component. Calculate the action and reaction forces using the displacement speed of the inner and outer rings of the bearings. Use the finite element software to process the obtained vibration modal data of each order and create the A, B, and C matrices. The system dynamics equation is: Where, M, C d and K are the mass matrix, damping matrix, and stiffness matrix respectively, u is the displacement vector, and F is the load vector; The m independent differential equations are: Where, Φ j is the jth mode vector, y i is the modal coordinate, ξ j is the j-th order modal damping, ω j is the j-th order natural frequency; The state equation is: Where, w is the displacement of each point, y is the modal coordinate vector, and A, B, C, and D are the state equation matrices.

7. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 1, characterized in that: The establishment of the bearing sub-model includes: Based on the geometric relationship, each displacement is equivalent to the normal displacement at the contact point between the roller and the outer ring. The normal force of each roller of the bearing is calculated by combining the normal contact stiffness and contact damping of each roller. The normal force of each roller of the bearing is accumulated to obtain the overall dynamic load of the bearing. Decompose the normal force according to the geometric relationship to solve the axial force and radial force of each roller, and accumulate the forces on each roller to obtain the total axial force and radial force of the bearing; The calculation formula of the normal force of a single roller is: Where Q ei is the normal force of the ith roller, δ ni is the normal displacement of a single roller, K ne =6.24×10 4 l 0.82 D w 0.11 [1+c i 0.9 cos(α e -α i )] -1.11 is the contact stiffness coefficient of the outer raceway, l is the contact line length of the tapered roller,; D w is the average diameter of the tapered roller, c i =sin(α e+ α f ) / sin(α i+ α f ), α e , α i and α f are the contact angles between the tapered roller and the outer race, inner race and bearing retaining ring respectively; The calculation formula for the total axial force and radial force of the bearing is: Where, F r 、F a is the total radial force and total axial force of the bearing, i represents the i-th tapered roller, there are z tapered rollers in total, Q ri , Q ai are the radial force and axial force of the i-th tapered roller.

8. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 1, characterized in that: The establishment of fatigue life prediction model for key components includes: The contact stress of the gear teeth on all meshing slices is calculated based on the Hertz contact formula and the gear slice meshing model, and the contact stress at the maximum slice is taken as the tooth surface contact stress; The irregularly changing contact stress on the gear is statistically analyzed. The complex load is decomposed into multiple groups of load half-cycles and load cycles using the rain flow counting method. The load mean, amplitude, and corresponding number of cycles under different load cycles are obtained. The asymmetric cyclic load obtained by the rain flow counting method is corrected to a symmetric cyclic load using the Goodman correction method. The contact SN curve of the material is used to calculate the gear contact fatigue life. The generated tooth profile points are input into the SCDM 3D software under Ansys. A three-tooth model is established and loads and constraints are applied. The material is set and the tooth root bending stress calculation results are output. The complex load is decomposed into multiple groups of load half cycles and load cycles using the rain flow counting method. The asymmetric cyclic load obtained by the rain flow counting method is corrected to a symmetric cyclic load using the Goodman correction method. The bending fatigue life of the gear is calculated based on the material's bending SN curve. Based on the LP bearing rating life formula, the dynamic radial force and axial force of the bearing obtained by dynamic simulation are used to calculate the equivalent dynamic load of each bearing. According to the equivalent dynamic load of each bearing and the rated dynamic load C of each model of bearing r , calculate the fatigue life of the bearing under the current working conditions through the formula; Among them, the contact stress of a single gear tooth slice is: Where, F ni is the normal force of each slice, R is the integrated curvature radius at the meshing point, L is the length of the contact line, μ1, μ2 and E1, E2 are the Poisson's ratio and elastic modulus of the two gears respectively; The rating life formula for LP bearings is: Where a1 is the reliability coefficient, a2 is the performance correction coefficient, a3 is the lubrication state coefficient, C r is the rated dynamic load, ε is the life index, P = f t (XF r +YF a ) is the equivalent dynamic load, F r and F a Refers to radial force and axial force, f t is the load factor, f t Take 2.0, X and Y are the radial dynamic load distribution coefficient and axial dynamic load distribution coefficient respectively.

9. The multi-objective optimization method for off-road vehicle automatic transmission (AT) considering dynamic characteristics and fatigue life according to claim 1, characterized in that: Based on the multi-objective optimization model of off-road vehicle automatic transmission (AT), with gear parameters as optimization variables, a multi-objective genetic algorithm is used to iteratively optimize the gear parameter design solutions corresponding to the optimization objectives of maximizing transmission efficiency, minimizing system mass, and minimizing meshing torque fluctuation, under the constraints of gear geometry, static load capacity, and fatigue life. The solutions include: The number of teeth z, module m, pressure angle α, helix angle β, tooth width B, tooth top height coefficient h of each gear a and the modification coefficient x as multi-objective optimization design variables, including the nine gears included in the V-type working condition; Based on the principle of gear meshing, set the gear tooth profile constraints to prevent over-pointing of the tooth top and meshing interference. Based on the installation and transmission ratio, correctly set the center distance constraint and transmission ratio constraint. Based on the gear tooth surface contact and tooth root bending load capacity, set the static load capacity constraint. Based on the expected service life of the transmission system, set the gear contact fatigue constraint, tooth root bending fatigue constraint, and bearing fatigue life constraint. Input gear parameters to determine whether the gear parameters meet the gear geometric constraints. Gear geometric constraints include tooth shape constraints, center distance constraints and transmission ratio constraints. If the constraints are met, the precise gear tooth profile is obtained according to the tool tooth profile and a gear slice meshing model is generated to solve the transmission efficiency of each gear. The gear slice meshing model is combined with the nominal load to calculate the tooth surface contact stress and tooth root bending stress to determine whether the static load-bearing capacity constraint is met. The bending stress finite element analysis is used to obtain the gear tooth quality. If the static load-bearing capacity constraint is met, the gear slice model and potential energy method are used to calculate the time-varying meshing stiffness of the gear, establish a gear concentrated mass model, and couple the housing finite element reduction model, shaft system finite element reduction model and bearing sub-model established based on the transmission structural parameters to establish a rigid-flexible coupling dynamic model of the AT transmission system. By inputting the working condition parameters of each gear, dynamic simulation is carried out, and the running results are read to obtain the dynamic load of each key component, the meshing torque fluctuation coefficient is calculated, and the bearing fatigue life, gear contact fatigue life and gear bending fatigue life are calculated in combination with the linear cumulative damage criterion to evaluate whether the life of the above components meets the fatigue life constraint. If the gear geometric constraints and static load-bearing capacity constraints are not met, the gear geometry constraints and static load-bearing capacity constraints are not met. and one of the fatigue life constraints then iterate the next set of gear parameters; Taking the highest transmission efficiency, the lowest system mass, and the lowest meshing torque fluctuation as the objective functions, a multi-objective genetic algorithm was used for multi-objective optimization. Each objective function was adjusted to a range of 0-1 using a normalization method. A linear weighted method was used to comprehensively evaluate each solution, and the multi-objective trade-off solution with the highest overall ranking was output as the result of the transmission system optimization design. Among them, the meshing torque fluctuation is expressed by the meshing torque fluctuation coefficient, and the calculation formula is: Where, T max 、T min are the maximum and minimum values ​​of the meshing torque; The transmission efficiency is calculated as follows: multiply the meshing efficiencies of all meshing pairs in the gear to obtain the transmission efficiency of the gear; The normalization method is used to adjust each objective function to 0-1, and the formula for comprehensively evaluating each solution using the linear weighted method is: maxF(x)=w1f1(x)+w2f2(x)+w3f3(x)+w4f4(x)+w5f5(x)+w6f6(x)+w7f7(x), Where w1, w2, w3, w4, w5, w6 and w7 are the target weights, and f1(x), f2(x), f3(x), f4(x), f5(x), f6(x) and f7(x) are the target functions.

Images