Parallel shaft gear transmission system kinetic model construction method

Abstract

The invention provides a parallel shaft gear transmission system kinetic model construction method, which comprises the steps of constructing a parallel shaft gear transmission system model, and constructing a multi-body kinetic equation according to a parallel shaft gear transmission system, the parallel shaft gear transmission system model comprising a driving gear, a driven gear and a rolling bearing; carrying out dynamic modeling analysis on a rolling bearing in the parallel shaft gear transmission system to obtain a bearing force; the gear teeth of the driving gear and the gear teeth of the driven gear are subjected to contact analysis, and gear pair dynamic contact force is obtained; and combining the bearing force and the gear pair dynamic contact force into a system generalized force, and substituting the system generalized force into the multi-body kinetic equation to obtain a system kinetic model. The parallel shaft gear transmission system dynamic modeling method solves the problems that in the prior art, a parallel shaft gear transmission system dynamic modeling method cannot consider the dynamic contact influence of a bearing rolling body and gear teeth, the dynamic performance of a parallel shaft gear transmission system cannot be comprehensively reflected, and the influence of bearing parameters on the dynamic characteristics of the system cannot be researched.

Description

Technical Field

[0001] The present invention relates to the technical field of the dynamics of a parallel-axis gear transmission system, and particularly to a method for constructing a dynamics model of a parallel-axis gear transmission system. Background Art

[0002] Parallel-axis gear transmission systems are widely used in many fields such as automobiles, aerospace, energy, and transportation. Gears and rolling bearings are the core components of a parallel-axis gear transmission system, and the dynamic contacts between the rolling elements and the bearing raceways, as well as between the meshing teeth of the gear pair, are the main excitation sources that cause system vibration. However, due to the complex structure and modeling of rolling bearings, it is difficult to simulate the dynamic contacts of the bearing rolling elements and gear teeth. The existing dynamics modeling methods for parallel-axis gear transmission systems cannot consider the influence of the dynamic contacts of the bearing rolling elements and gear teeth, making it difficult to comprehensively reflect the dynamic performance of the parallel-axis gear transmission system and study the influence of bearing parameters on the dynamic characteristics of the system. Summary of the Invention

[0003] In view of the deficiencies in the prior art, the present invention provides a method for constructing a dynamics model of a parallel-axis gear transmission system, which solves the problems in the prior art that the dynamics modeling method of the parallel-axis gear transmission system cannot consider the influence of the dynamic contacts of the bearing rolling elements and gear teeth, making it difficult to comprehensively reflect the dynamic performance of the parallel-axis gear transmission system and study the influence of bearing parameters on the dynamic characteristics of the system.

[0004] According to an embodiment of the present invention, a method for constructing a dynamics model of a parallel-axis gear transmission system includes:

[0005] Construct a parallel-axis gear transmission system model, and establish a multi-body dynamics equation based on the parallel-axis gear transmission system. The parallel-axis gear transmission system model includes a driving gear, a driven gear, and a rolling bearing;

[0006] Perform dynamics modeling and analysis on the rolling bearing in the parallel-axis gear transmission system using the Hertz contact theory to obtain the bearing force;

[0007] Perform contact analysis between the teeth of the driving gear and the teeth of the driven gear to obtain the dynamic contact force of the gear pair;

[0008] Combine the bearing force and the dynamic contact force of the gear pair into the system generalized force and substitute it into the multi-body dynamics equation to obtain the system dynamics model, and calculate the dynamic characteristics of the parallel-axis gear transmission system at any time according to the dynamics model.

[0009] Preferably, the parallel-axis gear transmission system model further includes a driving shaft and a driven shaft, and one of the rolling bearings is provided on each of the driving shaft and the driven shaft;

[0010] The rolling bearing includes an inner bearing ring, an outer bearing ring, and a plurality of rolling elements. The rolling elements are arranged between the inner bearing ring and the outer bearing ring. The driving gear or the driven gear is fixedly connected to the outer bearing ring, and the driving shaft or the driven shaft is fixedly connected to the inner bearing ring.

[0011] Preferably, the Hertz contact theory is used to perform dynamic modeling and analysis on the rolling bearing in the parallel-axis gear transmission system. The method for obtaining the bearing force includes:

[0012] Establish a generalized coordinate system, locate the positions of the rolling elements, the inner bearing ring, and the outer bearing ring in the generalized coordinate system. Use the Hertz contact theory to establish the contact relationships between each rolling element and the inner bearing ring and the outer bearing ring respectively, and calculate the bearing eccentricity vectors between the inner bearing ring and the outer bearing ring respectively.

[0013] Combine the bearing eccentricity vectors to obtain the dynamic contact forces of each rolling element inside the rolling bearing, and superimpose the dynamic contact forces of each rolling element to obtain the bearing force.

[0014] Preferably, the contact analysis is performed between the teeth of the driving gear and the teeth of the driven gear. The method for obtaining the dynamic contact force of the gear pair includes:

[0015] Discretize the tooth profile curves of the driving gear and the driven gear to obtain the discrete point set of the driving gear and the discrete point set of the driven gear.

[0016] Determine the position vectors of all discrete points in the discrete point set of the driving gear and the discrete point set of the driven gear, find the possible contact points according to the position vectors of the discrete points, and judge whether they are real contact points according to the relationship between the tangential vector and the normal vector between the possible contact points and calculate the maximum contact depth between the teeth.

[0017] Perform a force analysis on the gear pair in the generalized coordinate system, and calculate the dynamic contact force of the gear pair in combination with the maximum contact depth.

[0018] Preferably, the method for determining the position vector of the discrete point is as follows:

[0019] Establish a first coordinate system and a second coordinate system at the geometric centers of the driving gear and the driven gear respectively in the generalized coordinate system, and select a discrete point from the discrete point set of the driving gear and the discrete point set of the driven gear respectively to establish a driving coordinate system and a driven coordinate system.

[0020] Calculate the position vectors of the discrete points in the discrete point set of the driving gear / the discrete point set of the driven gear in the driving coordinate system / the driven coordinate system, and convert them to the generalized coordinate system, so as to obtain the position vectors of the discrete points in the discrete point set of the driving gear / the discrete point set of the driven gear in the generalized coordinate system.

[0021] Preferably, the discrete points that satisfy the following equation are possible contact points:

[0022]

[0023] wherein, and are the normal vector and the tangent vector of the discrete points of the driving gear respectively, and are the normal vector and the tangent vector of the discrete points of the driven gear respectively, and are the velocity vectors of the discrete points of the driving gear and the driven gear in the generalized coordinate system respectively.

[0024] Preferably, the system dynamics model is as follows:

[0025]

[0026] wherein, M is the mass and inertia vector of the parallel-axis gear transmission system, Φ q is the Jacobian matrix of the system, and are the system acceleration vector and the velocity vector respectively; λ is the Lagrange multiplier, which is a constant; and are the X-component and the Y-component of the bearing force of the driving gear respectively; and are the X-component and the Y-component of the dynamic contact force of the gear pair of the driven gear respectively; T bp and T mp are the torques generated by the bearing force and the dynamic contact force of the gear pair on the driving gear respectively; and are the X-component and the Y-component of the bearing force of the driven gear respectively; and are the X-component and the Y-component of the dynamic contact force of the gear pair of the driving gear respectively; T q is the load.

[0027] Preferably, when calculating the dynamic characteristics, it is necessary to determine whether each rolling element inside the corresponding rolling bearing of the driving gear or the driven gear is in contact with the raceway. If not, the bearing force of the rolling element is 0; in addition, it is also necessary to determine whether the teeth between the driving gear and the driven gear are in contact. If not, the dynamic contact force of the gear pair is 0.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] By performing a dynamic contact impact analysis between the rolling elements and the raceways inside the rolling bearings corresponding to the driving gear and the driven gear, the respective bearing forces are obtained. Then, a dynamic contact analysis is carried out between the teeth of the driving gear and the driven gear to obtain the dynamic contact force between the gear pairs. By combining these two forces, the generalized force of the system is obtained and substituted into the multi-body dynamics equation to calculate the dynamic characteristics of the parallel-axis gear transmission system at any moment. The obtained results can provide a scientific basis and effective guidance for the dynamic design of the parallel-axis gear transmission system. Brief Description of the Drawings

[0030] Figure 1 It is a flowchart of the construction method of the embodiment of the present invention.

[0031] Figure 2 It is a dynamic model diagram of the transmission system of the embodiment of the present invention.

[0032] Figure 3 It is a model diagram of the driving gear or the driven gear of the embodiment of the present invention.

[0033] Figure 4 It is a force analysis diagram of the driving gear or the driven gear under the generalized coordinate system of the embodiment of the present invention.

[0034] Figure 5 It is a tooth contact modeling diagram of the driving gear and the driven gear of the embodiment of the present invention.

[0035] Figure 6 It is a tooth contact force analysis diagram of the driving gear and the driven gear of the embodiment of the present invention. Detailed Embodiment

[0036] The technical solutions in the present invention will be further described below with reference to the drawings and embodiments.

[0037] As Figure 1 shown, the embodiment of the present invention proposes a method for constructing a dynamic model of a parallel-axis gear transmission system, including:

[0038] Construct a parallel-axis gear transmission system model, and establish a multi-body dynamics equation according to the parallel-axis gear transmission system. The parallel-axis gear transmission system model includes a driving gear, a driven gear, a driving shaft, a driven shaft, and rolling bearings;

[0039] One of the rolling bearings is provided on each of the driving shaft and the driven shaft. The rolling bearing includes an inner bearing ring, an outer bearing ring, and a plurality of rolling elements. The rolling elements are arranged between the inner bearing ring and the outer bearing ring. The driving gear or the driven gear is fixedly connected to the outer bearing ring, and the driving shaft or the driven shaft is fixedly connected to the inner bearing ring.

[0040] As Figure 2As shown in the figure, a dynamic model of a parallel-axis gear transmission system is established. In the model, it is assumed that the gears and the outer rings of the bearings are fixedly connected by interference fit and their geometric centers coincide, and the shafts and the inner rings of the bearings are fixedly connected by interference fit and their geometric centers coincide. In the figure, the subscripts p, q, a, and b represent the driving gear, the driven gear, the driving shaft, and the driven shaft in sequence.

[0041] The model has three coordinate systems: 1) the generalized coordinate system OXY; 2) the local coordinate system o i x i y i (i = p, q); 3) the local coordinate system o j x j y j (j = a, b); The origins of the local coordinate systems are all located at the geometric centers of the components.

[0042] Each component in the system model has three degrees of freedom, and the expressions of its generalized coordinate vectors are as follows:

[0043]

[0044] In the formula, x and y represent the generalized displacements of the component, and θ represents the rotation angle of the component.

[0045] The expressions for the mass and inertia of the parallel-axis gear transmission system are as follows:

[0046]

[0047] In the formula, I and m represent the moment of inertia and mass of the component.

[0048] The Jacobian matrix of the constraint equations of the system model is:

[0049]

[0050] The expression for the generalized force vector of the system is as follows:

[0051]

[0052] In the formula, F x , F y and T represent the generalized force in the x direction, the generalized force in the y direction, and the torque of component k in sequence.

[0053] Substitute equations (1) to (4) into equation (5) to establish the dynamic model of the parallel-axis gear transmission system as shown below:

[0054]

[0055] In the formula, the vector and They respectively represent the system acceleration and velocity vectors; α and β represent the stability parameters; λ represents the Lagrange multiplier; the load vector F of the parallel-axis gear transmission system is mainly composed of bearing forces, gear pair contact forces, gravity, and loads. To establish the system model, it is necessary to derive the load vector F of the parallel-axis gear transmission system.

[0056] The Hertz contact theory is used to conduct dynamic modeling and analysis of the rolling bearings in the parallel-axis gear transmission system to obtain the bearing forces;

[0057] As Figure 3 shown, during the operation of the rolling bearing (the driving gear or the driven gear), the inner ring of the bearing will be eccentric relative to the outer ring of the bearing, and the bearing eccentricity vector e i and the eccentricity velocity ν i are expressed as follows:

[0058]

[0059] In the formula, r i and respectively represent the position and velocity vectors of the outer ring of the bearing in the generalized coordinate system.

[0060] The magnitude e i of the eccentricity of the inner ring of the bearing relative to the outer ring is expressed as:

[0061]

[0062] The expression of the bearing eccentricity unit vector n i is as follows:

[0063] n i = e i / e i (8)

[0064] As shown by Figure 4 shown, represents the intersection point of the outer ring of the bearing and the gear in the bearing eccentricity direction. In the generalized coordinate system the expression of the position vector is as follows:

[0065]

[0066] In the formula, R i represents the outer diameter of the outer ring of the bearing.

[0067] represents the intersection point of the inner ring of the bearing and the shaft in the bearing eccentricity direction. In the generalized coordinate system the expression of the position vector is:

[0068]

[0069] In the formula, R j represents the inner diameter of the bearing inner ring.

[0070] Assuming that the rotational speeds of each rolling element are the same and evenly distributed, the rotational angle φ of the rolling element r in bearing i at time t is ir expressed as follows:

[0071]

[0072] In the formula, N b represents the total number of bearing rolling elements; ω ir represents the common angular velocity of the rolling element r in bearing i.

[0073] The radial offset δ of the rolling element r of the rolling bearing at the position angle φ ir and the relative eccentric velocity ν ir are expressed as follows ir

[0074] δ ir = e ix cosφ ir + e iy sinφ ir - P d / 2 (12)

[0075] v ir = v ix cosφ ir + v iy sinφ ir (13)

[0076] In the formula, ν ix and ν iy represent the components of ν i along the X-axis and Y-axis directions in the generalized coordinate system; e ix and e iy represent the components of e i along the X-axis and Y-axis directions in the generalized coordinate system; P d is the bearing clearance.

[0077] The formula for the contact force of the rolling element r in bearing i is as follows:

[0078]

[0079] In the formula, τ is the force-deformation coefficient; C ir and K ir represent the contact damping and stiffness of the rolling element r of bearing i.

[0080] The generalized bearing forces and of the rolling bearing are calculated and expressed as follows: ​

[0081]

[0082] From Figure 5 it can be seen that and will generate torque on the gear, and its calculation expression is as follows:

[0083]

[0084] In the formula, and successively represent the generalized distances relative to the gear center in the generalized coordinate system respectively.

[0085] Conduct contact analysis between the teeth of the driving gear and the teeth of the driven gear to obtain the dynamic contact force of the gear pair;

[0086] As Figure 5 shown, use the gear meshing principle to establish an involute tooth profile, and discretize the tooth profiles of the driving gear and the driven gear into uniformly discrete points to obtain the driving gear discrete point set and the driven gear discrete point set. Then, select a discrete point from each of the driving gear discrete point set and the driven gear discrete point set to construct a local coordinate system, obtaining the driving coordinate system and the driven coordinate system. At the same time, the two coordinate axes of the driving coordinate system and the driven coordinate system coincide / are perpendicular to the tangent of the tooth profile curve of the gear respectively.

[0087] And respectively represent the driving coordinate system and the driven coordinate system at the discrete points of the tooth profiles of the driving gear and the driven gear; n and t represent the normal and tangential vectors of each discrete point.

[0088] The position vector of the discrete point a on the tooth profile of the driving gear in the parallel-axis gear transmission system and the position vector

[0089]

[0090] of the discrete point b on the tooth profile of the driven gear are as follows successively: p and r q are successively the position vectors of the geometric centers of the driving gear and the driven gear; and represent that the discrete point a on the tooth profile of the driving gear and the discrete point b on the tooth profile of the driven gear are respectively located at o p x p y p (driving coordinate system) and o q x q y q (driven coordinate system) of the position vectors; A p and Aq successively represent and from o p x p y p and o q x q y q the transformation vector transformed to OXY.

[0091] The velocity vectors of the discrete points on the profiles of the driving gear and the driven gear in the generalized coordinate system are successively

[0092]

[0093] wherein, and respectively represent the velocity vectors of the driving gear and the driven gear; and successively represent and the derivatives with respect to time; and respectively represent A p and A q the derivatives with respect to time.

[0094] After obtaining the discrete point position vector, if the discrete points on the gear pair conform to formulas (19) and (20), they are represented as possible contact points.

[0095] The normal vector and the tangent vector of the potential tooth profile contact point a of the driving gear and the normal vector and the tangent vector of the potential tooth profile contact point b of the sun gear need to satisfy the following equation:

[0096]

[0097] The position vector between the possible contact points of the driving gear and the driven gear and the tangent vector t also need to conform to the following relationship:

[0098]

[0099] Subsequently, the real contact points are found from the possible contact points. The expression of the normal relative distance between the possible contact points is as follows:

[0100]

[0101] If it means that the possible contact points are not in contact; if it indicates that the possible contact points are in contact; if it represents that the teeth are in contact and the contact depth The calculation formula is as follows:

[0102]

[0103] The relative velocity vector between the true contact points The vectors along the normal and tangential directions are

[0104]

[0105] Given and The normal contact force of the contact gear teeth can be calculated as:

[0106]

[0107] In the formula, k qp and c qp represent the tooth meshing stiffness and damping respectively; where k qp The calculation expression is as follows:

[0108]

[0109] In the formula, ν and E represent the Poisson's ratio and elastic modulus of the material in sequence; and represent the radii of curvature at the meshing positions of the driving gear and the driven gear in sequence.

[0110] Given and After that, the tangential meshing force of the contact gear teeth is

[0111]

[0112] In the formula, represents scalar; μ qp represents the friction coefficient; c d is the correction coefficient, and its expression is as follows:

[0113]

[0114] In the formula, ν 0 and ν 1 are the given velocity deviations.

[0115] See Figure 6 , the normal meshing force and the tangential meshing force The generalized forces and can be obtained along the generalized coordinate directions, and the calculation formula for the torque caused by the generalized forces applied to the center of the driving gear is as follows

[0116]

[0117] In the formula, and represent the distance from the true contact point along the direction of the generalized coordinate axis to the center of the driving gear.

[0118] When the parallel-axis gear transmission system is working, the driving gear meshes with the driven gear. The driving gear is subjected to the generalized meshing force and and the torque T mp The expressions are as follows

[0119]

[0120] In the formula, and represent the contact force of the l-th pair of meshing teeth of the driving gear and the driven gear pair; a N represents the number of tooth contacts; and represent the generalized distance from the contact point of the l-th pair of meshing teeth of the driving gear to the geometric center of the driving gear.

[0121] The driven gear is subjected to the generalized meshing force and and the torque T mq The expressions are as follows

[0122]

[0123] In the formula, and represent the contact force of the l-th pair of meshing teeth of the driving gear and the driven gear pair; and represent the generalized distance from the contact point of the l-th pair of meshing teeth of the driving gear to the geometric center of the driving gear.

[0124] The bearing force and the dynamic contact force of the gear pair are combined as the system generalized force and substituted into the multi-body dynamics equation to obtain the system dynamics model, and the dynamic characteristics of the parallel-axis gear transmission system at any time are calculated according to the dynamics model.

[0125] After calculating each component force, the system load vector F can be obtained as follows

[0126]

[0127] In the formula, g represents the acceleration due to gravity; T q represents the load.

[0128] The system dynamics model can be combined from formula (5) and formula (36) as follows:

[0129]

[0130] where, M is the mass and inertia vector of the parallel-axis gear transmission system, and Φ q is the Jacobian matrix of the system, and are the system acceleration vector and velocity vector respectively; λ is the Lagrange multiplier and is a constant; and are the X - component and Y - component of the bearing force of the driving gear respectively; and are the X - component and Y - component of the dynamic contact force of the gear pair of the driven gear respectively; T bp and T mp are the torques generated by the bearing force and the dynamic contact force of the gear pair on the driving gear respectively; and are the X - component and Y - component of the bearing force of the driven gear respectively; and are the X - component and Y - component of the dynamic contact force of the gear pair of the driving gear respectively; T q is the load.

[0131] After that, for the state of the transmission system at any moment, record the velocity at its initial position, and at the same time determine whether each rolling element inside the corresponding rolling bearing of the driving gear or the driven gear is in contact with the raceway. If not, the bearing force of the rolling element is 0; in addition, it is also necessary to determine whether the teeth between the driving gear and the driven gear are in contact. If not, the dynamic contact force of the gear pair is 0. Then, the dynamic characteristics of the parallel-axis gear transmission system can be calculated according to formula (5).

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for constructing a dynamic model of a parallel axis gear transmission system, characterized in that: include: Constructing a parallel axis gear transmission system model, and constructing a multi-body dynamics equation based on the parallel axis gear transmission system, wherein the parallel axis gear transmission system model includes a driving gear, a driven gear and a rolling bearing; The Hertz contact theory is used to conduct dynamic modeling analysis on the rolling bearing in the parallel axis gear transmission system to obtain the bearing force; Conduct contact analysis between the gear teeth of the driving gear and the gear teeth of the driven gear to obtain the dynamic contact force of the gear pair; The bearing force and the dynamic contact force of the gear pair are combined into the generalized force of the system and substituted into the multi-body dynamics equation to obtain the system dynamics model. The dynamic characteristics of the parallel axis gear transmission system at any time are calculated based on the dynamics model.

2. A method for constructing a dynamic model of a parallel axis gear transmission system according to claim 1, characterized in that: The parallel axis gear transmission system model also includes a driving shaft and a driven shaft, and each of the driving shaft and the driven shaft is provided with a rolling bearing; The rolling bearing comprises a bearing inner ring, a bearing outer ring and a plurality of rolling bodies, wherein the rolling bodies are arranged between the bearing inner ring and the bearing outer ring, the driving gear or the driven gear is fixedly connected to the bearing outer ring, and the driving shaft or the driven shaft is fixedly connected to the bearing inner ring.

3. A method for constructing a dynamic model of a parallel axis gear transmission system according to claim 2, characterized in that: The Hertz contact theory is used to conduct dynamic modeling analysis on rolling bearings in parallel axis gear transmission systems. The methods for obtaining bearing forces include: Establish a generalized coordinate system, locate the positions of the rolling elements, the inner ring of the bearing and the outer ring of the bearing in the generalized coordinate system, use the Hertz contact theory to establish the contact relationship between each rolling element and the inner ring of the bearing and the outer ring of the bearing, and calculate the bearing eccentricity vector between the inner ring of the bearing and the outer ring of the bearing; The dynamic contact force of each rolling element inside the rolling bearing is obtained in combination with the bearing eccentricity vector, and the dynamic contact force of each rolling element is superimposed to obtain the bearing force.

4. A method for constructing a dynamic model of a parallel axis gear transmission system according to claim 1, characterized in that: The contact analysis between the gear teeth of the driving gear and the gear teeth of the driven gear is performed to obtain the dynamic contact force of the gear pair, including: Discrete the tooth profile curves of the driving gear and the driven gear to obtain a discrete point set of the driving gear and a discrete point set of the driven gear; Determine the position vectors of all discrete points in the discrete point set of all active gears and the discrete point set of all driven gears, and find possible contact points based on the position vectors of the discrete points, and determine whether they are real contact points based on the relationship between the tangential vectors and the normal vectors between the possible contact points and calculate the maximum contact depth between the gear teeth; The force analysis of the gear pair is carried out in the generalized coordinate system, and the dynamic contact force of the gear pair is calculated in combination with the maximum contact depth.

5. A method for constructing a dynamic model of a parallel axis gear transmission system according to claim 4, characterized in that: The method for determining the position vector of a discrete point is as follows: In the generalized coordinate system, a first coordinate system and a second coordinate system are respectively established at the geometric centers of the driving gear and the driven gear, and a discrete point is respectively selected from the discrete point set of the driving gear and the discrete point set of the driven gear to establish the active coordinate system and the driven coordinate system; The position vectors of the discrete points in the active gear discrete point set / driven gear discrete point set in the active coordinate system / driven coordinate system are calculated and converted to the generalized coordinate system, thereby obtaining the position vectors of the discrete points in the active gear discrete point set / driven gear discrete point set in the generalized coordinate system.

6. A method for constructing a dynamic model of a parallel axis gear transmission system according to claim 4, characterized in that: Discrete points that satisfy the following equation are possible contact points: in, and are the normal vector and tangent vector of the discrete points of the active gear respectively, and are the normal vector and tangent vector of the discrete point of the driven gear, and are the velocity vectors of the discrete points of the driving gear and the discrete points of the driven gear in the generalized coordinate system respectively.

7. A method for constructing a dynamic model of a parallel axis gear transmission system according to claim 1, characterized in that: The system dynamics model is as follows: Where M is the mass and inertia vector of the parallel axis gear transmission system, Φ q is the Jacobian matrix of the system, and are the acceleration vector and velocity vector of the system respectively; λ is the Lagrange multiplier, which is a constant; and They are the X-direction component and the Y-direction component of the bearing force of the driving gear respectively; and are the X-direction component and Y-direction component of the gear pair dynamic contact force of the driven gear respectively; T bp and T mp are the torques on the driving gear generated by the bearing force and the dynamic contact force of the gear pair; and They are the X-direction component and the Y-direction component of the bearing force of the driven gear respectively; and are the X-direction component and Y-direction component of the gear pair dynamic contact force of the driving gear respectively; T q For load.

8. The method for constructing a dynamic model of a parallel axis gear transmission system according to claim 1, characterized in that: When calculating the dynamic characteristics, it is necessary to determine whether the rolling elements inside the rolling bearing corresponding to the driving gear or the driven gear are in contact with the raceway. If not, the bearing force of the rolling elements is 0. In addition, it is also necessary to determine whether the gear teeth between the driving gear and the driven gear are in contact. If not, the dynamic contact force of the gear pair is 0.

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