Gear transmission system dynamics modeling method containing cumulative effects of system errors

Abstract

The present application relates to the technical field of mechanical dynamics, and particularly relates to a kind of dynamics modeling method of gear transmission system containing system error cumulative influence, comprising: the assembly body size chain diagram of gear transmission system is constructed;Corresponding jacobian spinor model is established based on assembly body size chain diagram;Using jacobian spinor model, the spinor of each gear node in gear transmission system under the influence of system cumulative error is obtained;The dynamic error of gear pair normal meshing line direction under the influence of cumulative error of gear transmission system is obtained;The dynamic response of gear transmission system is obtained by solving the dynamic equation and solving the dynamic equation.The present application considers the influence of cumulative error in gear transmission system due to manufacturing installation on system response, realizes the combination of dynamics model and three-dimensional tolerance analysis technology, fills the current technical blank of gear transmission system dynamics modeling, and provides a theoretical basis for accurate analysis of dynamic characteristics of gear transmission system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical dynamics, and particularly relates to a dynamic modeling method of a gear transmission system with cumulative effects of system errors. BACKGROUND

[0002] Gear transmission is widely used in the fields of aviation, aerospace and ship. With the continuous development of science and technology, in order to meet the more stringent performance requirements of the above-mentioned fields, the state development puts forward higher requirements for the performance of the gear transmission system, and how to more accurately predict and grasp the vibration response of the gear transmission system is very important to improve the performance of the gear transmission system. The cumulative effects of various manufacturing and installation errors in the system are closely related to the dynamic performance of the gear transmission system, which will change the relative pose of the meshing gear pair through the cumulative effects, and finally affect the dynamic performance of the gear transmission system. Therefore, how to more accurately and practically consider the cumulative error effects caused by various manufacturing and installation errors in the gear system dynamic model is of great significance to the research and further improvement of the performance of the gear transmission system.

[0003] At present, there are two ways to consider the manufacturing and installation errors of components in the dynamics of the gear transmission system. The first way is to artificially give the amplitude and phase angle of the manufacturing or installation error of a component, and to write the corresponding error excitation by using the trigonometric function according to the theoretical speed of the component; the second way is to calculate the error amplitude and phase by two-dimensional dimension chain, and further write the error excitation in the form of trigonometric function.

[0004] The existing consideration of transmission system errors cannot express the cumulative error effects of the manufacturing and installation errors of the related components in the system, and the consideration of form error and fitting error between components is also ignored, so that the dynamic response of the system is not accurate. In addition, the existing method has a single consideration of errors, ignores the influence of axial error when considering the influence of error, and expresses the error by obtaining the error amplitude and phase and writing the result in the form of trigonometric function. However, theoretically, after the assembly of the system is completed, the cumulative error effects of the manufacturing and installation errors of the components in the system are only an initial motion position of the components in the system, not an amplitude, which leads to inaccurate analysis and research on the dynamic performance of the system, thereby affecting the subsequent research on the gear transmission system.

[0005] Therefore, it is necessary to provide a dynamic modeling method of a gear transmission system with cumulative effects of system errors to solve the above problems. SUMMARY

[0006] The present application provides a dynamic modeling method of a gear transmission system with cumulative effects of system errors to solve the existing problems.

[0007] The present invention provides a method for dynamic modeling of a gear transmission system including the cumulative effects of system errors, which adopts the following technical solution:

[0008] Construct the assembly dimension chain diagram of the gear transmission system;

[0009] Establish the corresponding Jacobian spinor model based on the assembly dimension chain diagram;

[0010] Using the Jacobi spinor model, the spinor of each gear node in the gear transmission system under the influence of cumulative system error is obtained;

[0011] Based on the projection vector of each gear node position in the normal meshing direction, the theoretical direction of rotation and theoretical speed of each gear, and the rotation of each gear node under the influence of the cumulative error of the gear transmission system, the dynamic error of the gear pair in the normal meshing direction under the influence of the cumulative error of the gear transmission system is obtained.

[0012] The dynamic equations of the gear transmission system affected by cumulative error are constructed based on dynamic error.

[0013] The dynamic response of the gear transmission system is obtained by solving the dynamic equations.

[0014] Preferably, the steps for constructing the assembly dimension chain diagram of the gear transmission system are as follows:

[0015] Based on the assembly drawing of the gear transmission system assembly and the part drawings of each related component, establish a dimension chain diagram that reflects the functional characteristics involved in each functional requirement of the gear transmission system assembly.

[0016] The functional features include: internal functional features, connection functional features, and parallel functional features.

[0017] Preferably, the steps for establishing the corresponding Jacobi spinor model are as follows:

[0018] Based on the tolerances, dimensions, and position information of each functional feature in the assembly dimension chain diagram, determine the screw amount corresponding to each functional feature; and establish the corresponding Jacobian screw amount model with the pose deviation of each gear node relative to the theoretical position as the functional requirement.

[0019] Preferably, the expression for the Jacobi spinor model is:

[0020]

[0021] In the formula, FR i For gear nodes i Functional requirements; T FRi Gear nodes in a gear transmission system affected by cumulative system errors i spinor; ni is the function requirement FR i the total number of function features contained in the function requirement FR is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the Jacobian matrix between the function requirement FR and the function feature is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the movement vector of the first function feature in the function requirement of the pinion node along the axis of the local coordinate system in which the function feature is located x is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the movement vector of the first function feature in the function requirement of the pinion node along the axis of the local coordinate system in which the function feature is located y is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the movement vector of the first function feature in the function requirement of the pinion node along the axis of the local coordinate system in which the function feature is located z is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the rotation vector of the first function feature in the function requirement of the pinion node around the axis of the local coordinate system in which the function feature is located x is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the rotation vector of the first function feature in the function requirement of the pinion node around the axis of the local coordinate system in which the function feature is located y is the function requirement of the pinion node i is the first function feature in the function requirement of the pinion node is the rotation vector of the first function feature in the function requirement of the pinion node around the axis of the local coordinate system in which the function feature is located z i =( p , g ), p is the driving pinion node g is the driven pinion node.

[0022] Preferably, the screw rotation of the pinion node i in the gear transmission system affected by the system cumulative error according to the Jacobian rotation model is the cumulative position and posture variable of the position of each pinion node in the gear transmission system affected by the system cumulative error relative to the theoretical position.

[0023] Preferably, the step of obtaining the projection vector of the position of each pinion node in the normal meshing line direction is:

[0024] ​​​​​​​The gear axis direction is z axis, and the coordinate system of each gear node in the gear transmission system is established according to the right-hand rule;

[0025] According to the basic parameters of the gear pair and the relative position relationship among the coordinate systems of the gear nodes, the projection vector of the translation coordinates of each gear node in the normal meshing line direction is obtained.

[0026] Preferably, the expression of the dynamic error of the gear pair in the normal meshing line direction under the cumulative error of the gear transmission system is:

[0027]

[0028] In the formula, is the dynamic error of the gear pair in the normal meshing line direction under the cumulative error of the gear transmission system; is the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; x 、 y 、 z is the homogeneous expression of the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; is the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; x 、 y 、 z is the homogeneous expression of the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; is the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; x 、 y 、 z is the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; is the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; x 、 y 、 z is the dynamic error of the driven gear node in the direction under the cumulative error of the gear transmission system; is the attitude transformation matrix of the node of the driving gear corresponding to the time t; is the attitude transformation matrix of the node of the driven gear corresponding to the time t; V p is the projection vector of the translation coordinates of the node of the driving gear of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driving gear; V g is the projection vector of the translation coordinates of the node of the driven gear of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driven gear; is the homogeneous expression of the screw generated by the node of the driving gear in the gear transmission system under the cumulative error of the system; is the homogeneous expression of the translation direction screw generated by the node of the driven gear in the gear transmission system under the cumulative error of the system; i =( p , g ), pis a driven gear node. g is a driven gear node.

[0029] Preferably, the expression of the dynamic equation of the gear transmission system affected by the cumulative error is:

[0030]

[0031] In the formula, is a system mass matrix; is a system damping matrix; is a system stiffness matrix; is a generalized coordinate vector of each node of the system; is a system external load vector; is a system cumulative error excitation force at the gear node caused by the cumulative error of the system; V p is a projection vector of the translational coordinates of the driving gear node of the gear pair in the coordinate system corresponding to the driving gear in the normal meshing line direction; V g is a projection vector of the translational coordinates of the driven gear node of the gear pair in the coordinate system corresponding to the driven gear in the normal meshing line direction.

[0032] Preferably, the dynamic response of the gear transmission system is obtained by solving the dynamic equation by using the Fourier series method.

[0033] A gear transmission system dynamics modeling system containing system error cumulative effect, comprising:

[0034] A Jacobian spinor model construction module is configured to construct an assembly size chain graph of the gear transmission system; and a corresponding Jacobian spinor model is established based on the assembly size chain graph;

[0035] A parameter acquisition module is configured to acquire the spinor of each gear node in the gear transmission system affected by the system cumulative error by using the Jacobian spinor model;

[0036] A dynamic error acquisition module is configured to project the spinor of each gear node affected by the cumulative error of the gear transmission system to the meshing line direction of the gear pair to obtain the dynamic error of the gear pair in the normal meshing line direction under the cumulative error of the gear transmission system according to the projection vector of the position of each gear node in the normal meshing line direction and the theoretical turning direction and the theoretical rotating speed of each gear;

[0037] A dynamics module is configured to construct the dynamic equation of the gear transmission system affected by the cumulative error based on the dynamic error; and obtain the dynamic response of the gear transmission system by solving the dynamic equation.

[0038] The beneficial effects of the present application are:

[0039] The present application obtains the dynamic error of the normal meshing line direction of the gear pair under the influence of the cumulative error of the gear transmission system, then constructs the dynamic equation of the gear transmission system under the influence of the cumulative error based on the dynamic error, and solves the dynamic equation to obtain the dynamic response of the gear transmission system, that is, the present application considers the influence of the cumulative error caused by the manufacturing and installation of the gear transmission system on the system response in the process of solving the dynamic response, realizes the combination of the dynamic model and the three-dimensional tolerance analysis technology, fills the gap of the related technology of the dynamic modeling of the gear transmission system, and provides a theoretical basis for the accurate analysis of the dynamic characteristics of the gear transmission system.

[0040] Secondly, the dynamic error is obtained according to the projection vector of the position of each gear node in the normal meshing line direction and the theoretical rotation direction and the theoretical rotating speed of each gear, and the rotation of each gear node under the influence of the cumulative error of the gear transmission system, that is, the calculation of the dynamic error considers the form error, the matching error and the axial error, which provides technical support for more accurate research and analysis of the dynamic performance of the gear transmission system. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0042] Figure 1 The flow chart of the present application is a kind of system error cumulative influence of gear transmission system dynamics modeling method;

[0043] Figure 2 The structure diagram of the single herringbone gear reducer in the embodiment of the present application is shown in the figure;

[0044] Figure 3 The assembly size chain diagram of the single herringbone gear reducer in the embodiment of the present application is shown in the figure;

[0045] Figure 4 The Jacobian rotation modeling coordinate system diagram corresponding to the single herringbone gear reducer in the embodiment of the present application is shown in the figure;

[0046] Figure 5 The gear pair dynamic meshing force time domain graph under the condition of not considering the system cumulative error in the embodiment of the present application is shown in the figure;

[0047] Figure 6 The gear pair dynamic meshing force frequency domain graph under the condition of not considering the system cumulative error in the embodiment of the present application is shown in the figure;

[0048] Figure 7A time-domain diagram of dynamic meshing force of a gear pair considering system cumulative error in the embodiment of the present application;

[0049] Figure 8 A frequency-domain diagram of dynamic meshing force of a gear pair considering system cumulative error in the embodiment of the present application.

[0050] Figure 2 Fig. 1 is a schematic diagram of a gear pair, wherein 1 represents a driving gear, 2 represents a driven gear, 3 represents an input shaft, and 4 represents an output shaft. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0052] An embodiment of the present application is shown in Fig. 1, which is a schematic diagram of a gear pair, wherein 1 represents a driving gear, 2 represents a driven gear, 3 represents an input shaft, and 4 represents an output shaft. Figure 1 The embodiment of the present application comprises the following steps:

[0053] S1, constructing an assembly size chain diagram of the gear transmission system;

[0054] S2, establishing a corresponding Jacobian screw model based on the assembly size chain diagram;

[0055] S3, obtaining screws of each gear node in the gear transmission system affected by system cumulative error by using the Jacobian screw model;

[0056] S4, obtaining dynamic error of a normal meshing line direction of a gear pair affected by cumulative error of the gear transmission system;

[0057] Specifically, the dynamic error of the normal meshing line direction of the gear pair affected by the cumulative error of the gear transmission system is obtained according to a projection vector of each gear node position in the normal meshing line direction, a theoretical turning direction and a theoretical rotating speed of each gear, and the screws of each gear node affected by the cumulative error of the gear transmission system.

[0058] S5, obtaining a dynamic equation and solving to obtain a dynamic response of the gear transmission system;

[0059] Specifically, a dynamic equation of the gear transmission system affected by the cumulative error is constructed based on the dynamic error; and the dynamic response of the gear transmission system obtained by solving the dynamic equation.

[0060] The steps of the gear transmission system dynamic modeling method with system error cumulative influence in the present example embodiment will be described in more detail below with reference to the drawings and embodiments.

[0061] In step S1, an assembly dimension chain diagram of the gear transmission system is constructed.

[0062] For example, in step S1 above, the step of constructing the assembly dimension chain diagram of the gear transmission system includes: according to... Figure 2 The assembly drawing of the gear transmission system assembly and the part drawings of each related component are shown below, establishing a system as follows: Figure 3 The diagram shown represents the dimensional chain of functional features involved in the functional requirements FR of each component in the gear transmission system assembly; among which, the functional features include: internal functional features (IFE), connection functional features (CFE), and parallel functional features (PFE).

[0063] In step S2, the Jacobi spinor model is established.

[0064] For example, based on the tolerances, dimensions, and other parameters of each functional feature in the assembly dimension chain diagram determined in step S1... Figure 4 The position information of each local coordinate system is shown to determine the screw quantity corresponding to each functional feature; taking the housing reference as the theoretical position, the deviation from the theoretical position to the pose of each driving gear and driven gear node is the functional requirement FR. i Establish the corresponding Jacobi spinor model.

[0065] The expression for the Jacobi spinor model is as follows:

[0066]

[0067] In the formula, FR i For gear nodes i Functional requirements; T FRi Gear nodes in a gear transmission system affected by cumulative system errors i spinor; n i For functional requirements FR i The total number of functional features contained therein; For gear nodes i The first of the functional requirements Functional features Jacobian matrix between functional requirements; For gear nodes i The first of the functional requirements A functional feature along the local coordinate system where the functional feature is located x The vector of movement of the axis; For gear nodes i The first of the functional requirements A functional feature along the local coordinate system where the functional feature is located y The vector of movement of the axis; the movement vector of the first functional feature in the functional requirements of the gear node along the axis of the local coordinate system in which the functional feature is located; i the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; z the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; i the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; x the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; i the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; y the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; i the rotation vector of the first functional feature in the functional requirements of the gear node around the axis of the local coordinate system in which the functional feature is located; z i , p g is a driving gear node; p is a driven gear node. g

[0068] It should be noted that the Jacobian matrix is constructed according to the position information of each local coordinate system of each functional feature in the assembly body size chain diagram.

[0069] In the S3 step, the screw of each gear node in the gear transmission system under the influence of the system cumulative error is obtained.

[0070] For example, in step S2, the screw of each gear node in the gear transmission system under the influence of the system cumulative error calculated by the Jacobian screw model is the cumulative pose variable of the position of each gear node in the gear transmission system under the influence of the system cumulative error relative to the theoretical position.

[0071] The expression of the cumulative pose variable is as follows:

[0072]

[0073] In the formula, the movement vector of the gear node along the axis; i the movement vector of the gear node along the axis; x the movement vector of the gear node along the axis; the movement vector of the gear node along the axis; i the movement vector of the gear node along the axis; y the movement vector of the gear node along the axis; the movement vector of the gear node along the axis; i the movement vector of the gear node along the axis; z the movement vector of the gear node along the axis; ​​​​​​​​​​for the gear node i the rotation vector around x the axis of rotation; for the gear node i the rotation vector around y the axis of rotation; for the gear node i the rotation vector around z the axis of rotation.

[0074] In step S4, the dynamic error of the gear pair normal meshing line direction under the influence of the cumulative error of the gear transmission system is obtained.

[0075] For example, according to the projection vector of each gear node position in the normal meshing line direction, the theoretical rotation and the theoretical rotation speed of each gear, and the screw of each gear node under the influence of the cumulative error of the gear transmission system, the dynamic error of the gear pair normal meshing line direction under the influence of the cumulative error of the gear transmission system is obtained.

[0076] For example, in step S4, the step of obtaining the projection vector of the translation coordinates of each gear node in the normal meshing line direction is: taking the gear axis direction as z the axis, the coordinate system of each gear node in the gear transmission system is established according to the right-hand rule. On this basis, combined with the basic parameters of each gear pair and the relative position relationship between the coordinate systems of each gear node, the projection vector of the translation coordinates of each gear node in the normal meshing line direction is obtained.

[0077] Among them, the projection vector of the translation coordinates of the driven gear node of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driven gear is V p ; the projection vector of the translation coordinates of the driven gear node of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driven gear is V g .

[0078] For example, in step S4, the step of obtaining the dynamic error of the gear pair normal meshing line direction under the influence of the cumulative error of the gear transmission system is: in the projection vector of the translation coordinates of each gear node in the normal meshing line direction, the rotation speed w i and the rotation direction d i of the rotation axis where each gear node is located, and the screw of each gear node under the influence of the cumulative error of the gear transmission system, the dynamic error along the normal meshing line direction of the gear pair caused by the dynamic pose change of each gear node under the influence of the system cumulative error at each moment .

[0079] Among them, the expression of the dynamic error is:

[0080]

[0081] In the formula, is the dynamic error of the normal meshing line direction of the gear pair under the cumulative error of the gear transmission system; is the dynamic error of the direction of the node of the driving gear under the cumulative error of the gear transmission system; x , y , z is the homogeneous expression of the dynamic error of the direction of the node of the driving gear under the cumulative error of the gear transmission system; is the dynamic error of the direction of the node of the driven gear under the cumulative error of the gear transmission system; x , y , z is the homogeneous expression of the dynamic error of the direction of the node of the driven gear under the cumulative error of the gear transmission system; is the dynamic error of the direction of the node of the driving gear under the cumulative error of the gear transmission system; x , y , z is the dynamic error of the direction of the node of the driving gear under the cumulative error of the gear transmission system; is the dynamic error of the direction of the node of the driven gear under the cumulative error of the gear transmission system; x , y , z is the homogeneous expression of the dynamic error of the direction of the node of the driven gear under the cumulative error of the gear transmission system; is the posture transformation matrix of the node of the driving gear at t corresponding to the coordinate system; is the posture transformation matrix of the node of the driven gear at t corresponding to the coordinate system; V p is the projection vector of the translation coordinates of the node of the driving gear of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driving gear; V g is the projection vector of the translation coordinates of the node of the driven gear of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driven gear; is the homogeneous expression of the screw generated by the node of the driving gear in the gear transmission system under the cumulative error of the system; is the homogeneous expression of the screw generated by the node of the driven gear in the gear transmission system under the cumulative error of the system; i =( p , g ), p is the node of the driving gear; g is the node of the driven gear.

[0082] It should be noted that, the result is a 4x1 homogeneous vector, and represents the values of the first three translation directions, that is, a 3x1 vector; the posture transformation matrix is constructed according to the rotation speed and rotation direction of the rotation shaft of each gear node; the dynamic pose of the node of the driving gear and the node of the driven gear generated by the cumulative error of the system and is not a fixed value, but a real dynamic variation quantity varying with time t and the corresponding error along the meshing line direction of the gear pair is also a dynamic variable, so it does not need to be written in the form of a trigonometric function and does not need to artificially give phase angle information.

[0083] In step S5, the dynamic equation is obtained and the dynamic response of the gear transmission system is solved; that is, the dynamic equation of the gear transmission system affected by the cumulative error is constructed based on the dynamic error; and the dynamic response of the gear transmission system solved by solving the dynamic equation is obtained.

[0084] For example, in step S5, the step of constructing the dynamic equation of the gear transmission system affected by the cumulative error is: when considering the influence of the system cumulative error, the initial position of the gear node in the gear transmission system will change relative to the theoretical position and change with the rotation time of the gear, thereby introducing corresponding dynamic error changes in each generalized coordinate direction of the gear node and causing dynamic errors in the meshing line direction of the gear pair , which ultimately affects the system response. Based on the dynamic error of the gear pair along the meshing line direction after considering the influence of the system cumulative error , the system dynamic equation is established, wherein the expression of the system dynamic equation is:

[0085]

[0086] In the formula, is the system mass matrix; is the system damping matrix; is the system stiffness matrix; is the generalized coordinate vector of each node of the system; is the system external load vector; is the system cumulative error excitation force at the gear node due to the system cumulative error, and the excitation force corresponding to the non-gear node is 0; V p is the projection vector of the translational coordinates of the driving gear node of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driving gear; V g is the projection vector of the translational coordinates of the driven gear node of the gear pair in the normal meshing line direction in the coordinate system corresponding to the driven gear.

[0087] For example, in the dynamic response of the gear transmission system solved by solving the dynamic equation in step S5, the Fourier series method is used to solve the dynamic response of the gear transmission system solved by solving the dynamic equation.

[0088] The application discloses a kind of system error cumulative influence containing gear transmission system dynamics modeling system, comprising: Jacobian spin model construction module, parameter acquisition module, dynamic error acquisition module and dynamics module, Jacobian spin model construction module is used to construct the assembly body size chain graph of gear transmission system;Corresponding Jacobian spin model is established based on assembly body size chain graph;Parameter acquisition module is used to obtain the spin of each gear node in gear transmission system under the influence of system cumulative error using Jacobian spin model;Dynamic error acquisition module is used according to the projection vector of each gear node position in normal meshing line direction and the theoretical turning of each gear and theoretical rotating speed;The spin of each gear node under the influence of cumulative error of gear transmission system is projected to gear pair meshing line direction, and the dynamic error of gear pair normal meshing line direction under the cumulative error of gear transmission system is obtained;Dynamics module is used to construct the dynamics equation of gear transmission system under the influence of cumulative error based on dynamic error;And the dynamic response of gear transmission system obtained by solving dynamics equation.

[0089] The following will be specifically described in combination with specific simulation test a kind of system error cumulative influence containing gear transmission system dynamics modeling method provided in the embodiment:

[0090] The basic parameters of gear pair in table 1 are used for simulation calculation.

[0091] Table 1

[0092]

[0093] Figure 5 For gear pair dynamic meshing force time-domain diagram calculated based on the parameters in table 1 without considering system cumulative error, Figure 6 For gear pair dynamic meshing force frequency-domain diagram calculated based on the parameters in table 1 without considering system cumulative error; Figure 7 For gear pair dynamic meshing force time-domain diagram calculated based on the parameters in table 1 considering system cumulative error, Figure 8 For gear pair dynamic meshing force frequency-domain diagram calculated based on the parameters in table 1 considering system cumulative error;From Figures 5 to 8 It can be seen that, under the comprehensive influence of manufacturing error of each component of system and installation error between components, gear pair dynamic meshing force changes from being composed of many periodic regular fluctuations to being composed of only one minimum cycle of 0.06s T m =0.06s fluctuation within 0.06s;At the same time, corresponding to dynamic meshing force spectrum, it also changes from original frequency spectrum only existing multiple of meshing frequency to simultaneously existing rotating frequency of main gear and driven gear f s1 、 f s2 and multiple of meshing frequencynf m and because nf m subjected to f s1 , f s2 the rich modulation frequency nf m ± f s1 , nf m ± f s2 .

[0094] The above description is merely that of the preferred embodiments of the application and is not to be taken in a limiting sense but is made merely for the purpose of providing some preferred embodiments of the application and the full scope of the application should be determined by the appended claims.

Claims

1. A method for dynamic modeling of a gear transmission system including the cumulative effects of systematic errors, characterized in that, include: Construct the assembly dimension chain diagram of the gear transmission system; Establish the corresponding Jacobian spinor model based on the assembly dimension chain diagram; Using the Jacobi spinor model, the spinor of each gear node in the gear transmission system under the influence of cumulative system error is obtained; Based on the projection vectors of each gear node position in the normal meshing direction, the theoretical direction of rotation and theoretical speed of each gear, and the rotational displacement of each gear node under the influence of cumulative errors in the gear transmission system, the dynamic error of the gear pair in the normal meshing direction under the influence of cumulative errors in the gear transmission system is obtained; the expression for the dynamic error of the gear pair in the normal meshing direction under the cumulative errors of the gear transmission system is: In the formula, The dynamic error in the direction of the gear pair's normal meshing line is caused by the cumulative error of the gear transmission system. For the driving gear node affected by the cumulative error of the gear transmission system x , y , z Homogeneous expression of dynamic error in direction; For the driven gear node to be affected by the cumulative error of the gear transmission system along the path x , y , z Homogeneous expression of dynamic error in direction; For the driving gear node affected by the cumulative error of the gear transmission system x , y , z Dynamic error in direction; For the driven gear node to be affected by the cumulative error of the gear transmission system along the path x , y , z Dynamic error in direction; Let be the attitude transformation matrix of the node of the driving gear at time t; Let be the attitude transformation matrix of the node of the driven gear at time t; V p It is the projection vector of the translation coordinates of the driving gear node in the coordinate system corresponding to the driving gear in the direction of the normal meshing line; V g The projection vector of the translation coordinates of the driven gear node in the coordinate system corresponding to the driven gear in the gear pair onto the normal meshing line direction; This is a homogeneous expression for the rotational rotation in the translational direction of the node of the driving gear in a gear transmission system caused by the cumulative error of the system. This is a homogeneous expression for the rotational rotation in the translational direction of the node of the driven gear in a gear transmission system caused by the cumulative error of the system. =( p , g ), p For the driving gear node; g For the driven gear node; The dynamic equations of a gear transmission system affected by cumulative error are constructed based on dynamic error; the dynamic response of the gear transmission system is obtained by solving the dynamic equations; the expression of the dynamic equations of the gear transmission system affected by cumulative error is as follows: In the formula, The system quality matrix; Here is the system damping matrix; Here is the system stiffness matrix; For each node in the system, there is a generalized coordinate vector. This represents the system's external load vector. The cumulative error excitation force at the gear node caused by the cumulative error of the system; V p It is the projection vector of the translation coordinates of the driving gear node in the coordinate system corresponding to the driving gear in the direction of the normal meshing line; V g It is the projection vector of the translation coordinates of the driven gear node in the coordinate system corresponding to the driven gear in the direction of the normal meshing line.

2. The method for dynamic modeling of a gear transmission system including the cumulative effect of system errors according to claim 1, characterized in that, The steps for constructing the assembly dimension chain diagram of a gear transmission system are as follows: Based on the assembly drawing of the gear transmission system assembly and the part drawings of each related component, establish a dimension chain diagram that reflects the functional characteristics involved in each functional requirement of the gear transmission system assembly. The functional features include: internal functional features, connection functional features, and parallel functional features.

3. The method for dynamic modeling of a gear transmission system including the cumulative effect of system errors according to claim 2, characterized in that, The steps to establish the corresponding Jacobi spinor model are as follows: Based on the tolerances, dimensions, and position information of each functional feature in the assembly dimension chain diagram, the screw volume corresponding to each functional feature is determined; and the screw volume corresponding to the pose deviation of each gear node from the theoretical position is used as the functional requirement to establish the corresponding Jacobian screw volume model.

4. The method for dynamic modeling of a gear transmission system including the cumulative effect of system errors according to claim 3, characterized in that, The expression for the Jacobi spinor model is: In the formula, For gear nodes Functional requirements; Gear nodes in a gear transmission system affected by cumulative system errors spinor; For functional requirements The total number of functional features contained therein; For gear nodes The first of the functional requirements Functional features Jacobian matrix between functional requirements; For gear nodes The first of the functional requirements A functional feature along the local coordinate system where the functional feature is located x The vector of movement of the axis; For gear nodes The first of the functional requirements A functional feature along the local coordinate system where the functional feature is located y The vector of movement of the axis; For gear nodes The first of the functional requirements A functional feature along the local coordinate system where the functional feature is located z The vector of movement of the axis; For gear nodes The first of the functional requirements Each functional feature revolves around the local coordinate system in which it resides. x The rotation vector of the axis; For gear nodes The first of the functional requirements Each functional feature is located along the local coordinate system of that functional feature. y The rotation vector of the axis; For gear nodes The first of the functional requirements Each functional feature is located along the local coordinate system of that functional feature. z The rotation vector of the axis; =( p , g ), p For the driving gear node; g This is the node of the driven gear.

5. The method for dynamic modeling of a gear transmission system including the cumulative effect of system errors according to claim 4, characterized in that, Based on the Jacobi spinor model, gear nodes in a gear transmission system affected by cumulative system errors are obtained. i The spinor is the cumulative pose variable of each gear node position in the gear transmission system relative to its theoretical position under the influence of the system's cumulative error.

6. The method for dynamic modeling of a gear transmission system including the cumulative effect of system errors according to claim 1, characterized in that, The steps to obtain the projection vector of each gear node position in the normal meshing direction are as follows: With the gear axis direction as the z-axis, establish the coordinate system of each gear node in the gear transmission system according to the right-hand rule; Based on the basic parameters of the gear pair and the relative positional relationship between the coordinate systems of each gear node, the projection vector of the translation coordinates of each gear node in the direction of the normal meshing line is obtained.

7. The method for dynamic modeling of a gear transmission system including the cumulative effect of system errors according to claim 1, characterized in that, The dynamic response of the gear transmission system is obtained by solving the dynamic equations using the Fourier series method.

8. A dynamic modeling system for a gear transmission system including the cumulative effects of systematic errors, characterized in that, include: The Jacobi spinor model building module is used to construct the assembly dimension chain diagram of a gear transmission system. Establish the corresponding Jacobian spinor model based on the assembly dimension chain diagram; The parameter acquisition module is used to obtain the screw of each gear node in the gear transmission system under the influence of the cumulative error of the system using the Jacobi screw model. The dynamic error acquisition module is used to obtain the projection vector of each gear node position in the normal meshing line direction, as well as the theoretical direction of rotation and theoretical speed of each gear. Projecting the screw force of each gear node under the influence of the cumulative error of the gear transmission system onto the direction of the gear pair meshing line, we obtain the dynamic error of the gear pair in the normal meshing line direction under the cumulative error of the gear transmission system; the expression for the dynamic error of the gear pair in the normal meshing line direction under the cumulative error of the gear transmission system is: In the formula, The dynamic error in the direction of the gear pair's normal meshing line is caused by the cumulative error of the gear transmission system. For the driving gear node affected by the cumulative error of the gear transmission system x , y , z Homogeneous expression of dynamic error in direction; For the driven gear node to be affected by the cumulative error of the gear transmission system along the path x , y , z Homogeneous expression of dynamic error in direction; For the driving gear node affected by the cumulative error of the gear transmission system x , y , z Dynamic error in direction; For the driven gear node to be affected by the cumulative error of the gear transmission system along the path x , y , z Dynamic error in direction; Let be the attitude transformation matrix of the node of the driving gear at time t; Let be the attitude transformation matrix of the node of the driven gear at time t; V p It is the projection vector of the translation coordinates of the driving gear node in the coordinate system corresponding to the driving gear in the direction of the normal meshing line; V g The projection vector of the translation coordinates of the driven gear node in the coordinate system corresponding to the driven gear in the gear pair onto the normal meshing line direction; This is a homogeneous expression for the rotational rotation in the translational direction of the node of the driving gear in a gear transmission system caused by the cumulative error of the system. This is a homogeneous expression for the rotational rotation in the translational direction of the node of the driven gear in a gear transmission system caused by the cumulative error of the system. =( p , g ), p For the driving gear node; g For the driven gear node; The dynamics module is used to construct the dynamic equations of a gear transmission system affected by cumulative errors based on dynamic errors; and to solve the dynamic equations to obtain the dynamic response of the gear transmission system. The expression for the dynamic equations of the gear transmission system affected by cumulative errors is as follows: In the formula, The system quality matrix; Here is the system damping matrix; Here is the system stiffness matrix; For each node in the system, there is a generalized coordinate vector. This represents the system's external load vector. The cumulative error excitation force at the gear node caused by the cumulative error of the system; V p It is the projection vector of the translation coordinates of the driving gear node in the coordinate system corresponding to the driving gear in the direction of the normal meshing line; V g It is the projection vector of the translation coordinates of the driven gear node in the coordinate system corresponding to the driven gear in the direction of the normal meshing line.

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