Dynamic modeling and dynamic performance analysis method for curve type meshing line gear planetary gear train

Abstract

The invention provides a dynamic modeling and dynamic performance analysis method for a curve type meshing line gear planetary gear train, and the method comprises the steps: carrying out the derivation of a meshing line equation based on an S-shaped gear meshing line equation, obtaining a slope change rule, deducing a U-shaped periodic change function an (t) of a pressure angle in a single-tooth and double-tooth alternate meshing region, and carrying out the calculation of a pressure angle in a double-tooth meshing region, the pressure angle average value of the meshing starting point and the meshing ending point is taken, and the pressure angle periodic change rule of the single-tooth and double-tooth alternating meshing area is synthesized; and fitting the time-varying pressure angle function ar (t) through a fourth-order Fourier series. By accurately representing the time-varying pressure angle of the curve type meshing line gear, key excitation input is provided for subsequent dynamic modeling and dynamic performance analysis, and high-precision vibration and bearing characteristic prediction are ensured.

Description

Technical Field

[0001] The present invention belongs to the technical fields such as gear dynamics analysis, and particularly relates to a method for dynamic modeling and dynamic performance analysis of a planetary gear train of a gear with a curved meshing line. Background Art

[0002] Planetary gear trains are key basic components with a large quantity and wide application in mechanical equipment, and are widely used in important fields such as metallurgy, petroleum, coal mines, wind power, aviation, ships, locomotives, etc. With the rapid development of various fields, such as high-end mechanical equipment like helicopters, high-power wind turbines, earth pressure balance shield machines, and large tunneling machines, the demand for the load-bearing capacity of planetary gear trains is increasing day by day. At present, the most commonly used planetary gear train in the market is the involute planetary gear train. However, restricted by the geometric characteristics of the involute, the sun gear and the planetary gear are in convex-to-convex tooth meshing transmission, the tooth surface contact strength is low, and the load-bearing capacity is limited to a certain extent. Problems such as tooth surface pitting and gluing under high loads are becoming increasingly prominent. As is well known, the geometric shape of the tooth can, to a certain extent, determine the performance of the planetary gear train. To meet the new requirements put forward by the new generation of equipment for the load-bearing capacity and other aspects of the transmission system, researchers have gradually designed a variety of new non-involute gears. The concave-convex contact S-shaped gear is a new type of gear with a curved meshing line. Compared with the involute gear transmission, the contact form of the S-shaped gear transmission is concave-convex contact, and the problem of insufficient contact strength under large load conditions has been greatly improved. At the same time, the S-shaped gear transmission has a small sliding rate, strong anti-pitting and anti-wear capabilities, and is more suitable for the design of small-volume precision and high-ratio planetary gear trains. With the increasingly high requirements of modern industry for the performance of gear systems, it is of great significance to develop new tooth profile planetary gear trains, comprehensively consider the influence of multiple excitations, establish a more refined dynamic model, and analyze the dynamic performance of new gear systems. The existing literature has relatively complete research on the dynamics of involute planetary gear trains, but the research on the dynamics of planetary gear trains with a curved meshing line remains to be improved. Summary of the Invention

[0003] Aiming at the blank and deficiency of the existing technology, the present invention provides a method for dynamic modeling and dynamic performance analysis of a planetary gear train of a gear with a curved meshing line, filling the blank in the research on the dynamic characteristics of curved gears, and specifically realizing through the following hierarchical innovations:

[0004] 1. Pressure angle dynamic modeling method:

[0005] Aiming at the defect that the existing model ignores the non-constant change of the pressure angle of the gear with a curved meshing line, the periodic change law of the U-shaped pressure angle in the single and double tooth alternating meshing areas is derived for the first time, and the time-varying function is fitted by a fourth-order Fourier series, providing the core excitation input for high-precision dynamic modeling.

[0006] Even if this dynamic modeling scheme of pressure angle is implemented independently, this method can optimize the internal excitation of the curvilinear gear planetary gear train and improve the accuracy of the dynamic model.

[0007] 2. Dynamic modeling method:

[0008] Based on the dynamic modeling of the pressure angle, a multi-excitation coupling nonlinear model is proposed. By comprehensively considering the time-varying meshing stiffness, static transmission error, backlash, and pressure angle change, a multi-degree-of-freedom dynamic equation of bending-torsion-axis-pendulum is established, breaking through the limitations of the traditional model in simplifying the uneven load distribution and single-double tooth meshing effect.

[0009] Furthermore, the solution is simplified through dimensionless processing to ensure the engineering applicability of the model.

[0010] 3. Dynamic performance analysis method:

[0011] Based on the dynamic model, the fourth-order variable-step Runge-Kutta method (MATLAB ode45) is used to solve the dynamic response and quantify the fluctuation range of the meshing force.

[0012] The technical solution specifically adopted by the present invention to solve its technical problems is:

[0013] A dynamic modeling method of pressure angle for a curvilinear meshing line gear planetary gear train: Derive the slope change law by differentiating the meshing line equation based on the S-shaped gear meshing line equation, and deduce the U-shaped periodic change function a n (t) of the pressure angle in the single-double tooth alternating meshing area. In the double-tooth meshing area, take the average value of the pressure angles at the starting and ending points of meshing, and synthesize the periodic change law of the pressure angle in the single-double tooth alternating meshing area; fit the time-varying pressure angle function a r (t) through the fourth-order Fourier series.

[0014] Furthermore, the derivation of the pressure angle function a n (t) includes:

[0015] Calculate the U-shaped periodic change law of the pressure angle with the meshing position through the inverse trigonometric function α n =arctan(y a '), where y a ' is the first derivative of the meshing position variable;

[0016] The meshing line equation is a p =tan(90° - α n ) / n c , where n c is the parameter controlling the curve shape, and α n is the pitch circle pressure angle.

[0017] Furthermore, the pressure angle function a n(t) is derived by combining the helix angle β to correct the direction of the line of action and the contact area.

[0018] Furthermore, the harmonic coefficients of the Fourier series fitting are obtained based on the Abaqus finite element simulation data by establishing a five-tooth finite element model of internal and external meshing, extracting the time-varying mesh stiffness and static transmission error data.

[0019] And, a dynamic modeling method for a planetary gear train with a curved line of action gear, based on the pressure angle dynamic modeling method as described above, couples the time-varying pressure angle function a r (t) with the time-varying mesh stiffness, static transmission error, and backlash nonlinear function of the helical planetary gear train to establish a multi-degree-of-freedom bending-torsion-shaft-pendulum dynamic model; the dynamic equation is simplified to a matrix form through non-dimensionalization.

[0020] Furthermore, the multi-degree-of-freedom bending-torsion-shaft-pendulum dynamic model is constructed in the following way:

[0021] Define the relative displacement equation of the external and internal meshing gear pairs along the line of action direction, and the equation includes the coordinate transformation relationship of the linear displacement and angular displacement of the sun gear, planet carrier, internal gear ring, and planet gear;

[0022] Introduce the backlash nonlinear function, and the function defines the contact state in segments according to the relationship between the relative displacement δ hn of the meshing pair and the backlash b hn .

[0023] Furthermore, the coordinate transformation relationship is based on the position angle of the planet gear, and the linear displacement and angular displacement of each component are converted into the relative displacement along the line of action direction; the non-dimensionalization process introduces b a = b s1 / 2 and the time scale where b s1 is the backlash of the external meshing pair of the planetary gear train; is the average mesh stiffness of the external meshing pair of the planetary gear train; m s and m1 are the masses of the sun gear and planet gear respectively; the damping matrix adopts the Rayleigh formula; the time-varying mesh stiffness and static transmission error are fitted by a fourth-order Fourier series.

[0024] And, a dynamic performance analysis method for a planetary gear train with a curved line of action gear, based on the dynamic modeling method as described above, uses the ode45 solver of MATLAB to perform dynamic response analysis on the non-dimensionalized nonlinear motion differential equation, and verifies the engineering applicability of the model according to the dynamic response results.

[0025] In addition, an electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the method described above are implemented.

[0026] A non-transitory computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described above are implemented.

[0027] Compared with the prior art, the beneficial effects of the present invention and its preferred solutions at least include:

[0028] High-precision pressure angle dynamic modeling: For the first time, the periodic variation law of the time-varying pressure angle is established for gears with a curved meshing line, breaking through the limitations of the constant pressure angle assumption of traditional models and improving the prediction accuracy of contact stress and transmission error.

[0029] Refined multi-excitation coupling model: Based on Lagrange's equation, a multi-degree-of-freedom model of bending-torsion-axis-pendulum is constructed, comprehensively considering the coupling effects of multiple factors such as component deformation coordination, time-varying meshing stiffness, static transmission error, and backlash, and more realistically reflecting the dynamic characteristics under actual working conditions.

[0030] Efficient dynamic response solution: The fourth-order variable-step Runge-Kutta method is used to solve the nonlinear motion differential equation, quantifying the dynamic response of the meshing force and transmission error, and providing a theoretical basis for the dynamic design and vibration control of the curved gear system. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The present invention will be further described in detail below with reference to the drawings and specific embodiments:

[0032] Figure 1 It is a graph of the periodic change law of the pressure angle of the S-shaped gear in the embodiment of the present invention;

[0033] Figure 2 It is a graph of the nonlinear dynamics model of the S-shaped helical planetary gear train in the embodiment of the present invention;

[0034] Figure 3 It is a graph of the internal meshing five-tooth model of the S-shaped helical planetary gear train in the embodiment of the present invention;

[0035] Figure 4 It is a graph of the external meshing five-tooth model of the S-shaped helical planetary gear train in the embodiment of the present invention;

[0036] Figure 5 It is a graph of the time-varying meshing stiffness of the internal and external meshing pairs of the S-shaped gear planetary gear train in the embodiment of the present invention;

[0037] Figure 6 It is a graph of the static transmission error of the internal and external meshing pairs of the S-shaped gear planetary gear train in the embodiment of the present invention;

[0038] Figure 7 The time-varying pressure angle diagram of the external meshing pair of the S-shaped gear planetary gear in the embodiment of the present invention;

[0039] Figure 8 The time-varying pressure angle diagram of the internal meshing pair of the S-shaped planetary gear train in the embodiment of the present invention;

[0040] Figure 9 The dynamic meshing force diagram of the external meshing pair of the S-shaped planetary gear train in the embodiment of the present invention;

[0041] Figure 10 The dynamic meshing force diagram of the internal meshing pair of the S-shaped planetary gear train in the embodiment of the present invention;

[0042] Figure 11 The dynamic transmission error diagram of the external meshing pair of the S-shaped planetary gear train in the embodiment of the present invention;

[0043] Figure 12 The dynamic transmission error diagram of the internal meshing pair of the S-shaped planetary gear train in the embodiment of the present invention. Detailed implementation manners

[0044] To make the features and advantages of this patent more obvious and understandable, specific embodiments are given below and described in detail as follows:

[0045] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further descriptions of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those of ordinary skill in the technical field to which this application belongs.

[0046] It should be noted that the terms used here are only for describing specific implementation manners and are not intended to limit the exemplary implementation manners according to this application. As used here, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should also be understood that when the terms "include" and / or "comprise" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or their combinations.

[0047] The specific modeling and implementation process of the dynamic modeling and dynamic performance analysis method for a curve-shaped meshing line gear planetary gear train provided by the embodiment of the present invention is referred to Figures 1 to 12 , and includes the following steps:

[0048] Step 1: Deduction of the pressure angle change law of the S-shaped gear

[0049] Involute gears have a constant pressure angle. However, as a curve-shaped meshing line gear, due to the tooth profile shape, the pressure angle of the S-shaped gear is not constant along the contact path. The meshing line equation of the S-shaped gear is:

[0050]

[0051] where: m is the module of the gear, a p and n c are the parameters of the S-shaped curve, a p and n c are related as a p = tan(90° - α n ) / n c , where α n is the pressure angle of the pitch circle of the gear. Take the S-shaped gear tooth profile parameter n c = 2, and α n is taken as 20°. According to the fact that the pressure angle is equal to the meshing angle under the standard center distance installation, the derivative of the meshing line equation is obtained to get its slope change, and then the inverse trigonometric function α n = arctan(y a '), from which the change law of the pressure angle in a meshing cycle can be obtained: first it becomes smaller and then larger, showing a U-shaped change law. Four pairs of gear pairs are used to represent the time-varying pressure angle of the gear in a meshing cycle. As Figure 1 shown, the gear pair 2 enters meshing at point B1 and exits meshing at point B2. When the gear pair 2 moves to point C1, the previous gear pair 1 disengages at point C1, and the gear pair 2 enters the single-tooth meshing area. When the gear pair 2 moves to point C2, the gear pair 3 starts to enter meshing at point C2, and the gear pair 2 enters the double-tooth meshing area. When the gear pair 2 moves to point B2, the gear pair 2 officially disengages, and the gear pair 3 enters the single-tooth meshing area. Therefore, the meshing cycle of the gear pair 2 is T, and the meshing rules of the gear pairs 3 and 4 are the same as those of the gear pair 2, and so on.

[0052] In the double-tooth meshing area, the pressure angles at the two meshing points are different and need to be synthesized for subsequent calculations. Take the average value of the pressure angles at points B1 and C1 at the beginning and end of double-tooth meshing as the pressure angle in the double-tooth meshing area, from which the periodic change law of the single-tooth and double-tooth alternating pressure angles in the entire meshing process can be obtained.

[0053] Step 2: Establish the model of the S-shaped helical planetary gear train

[0054] Adopt the lumped parameter method to establish the nonlinear dynamic model of the helical planetary gear train. For the convenience of model establishment and analysis, the following assumptions are made: each gear is simplified as a cylinder with the flexibility of the wheel body ignored and the mass concentrated; each meshing pair is represented by a spring-damper element, and the elastic coefficient and damping coefficient are the tooth meshing stiffness and meshing damping respectively; each planetary gear is equally angularly distributed on the planet carrier; the friction effect between gears is ignored.

[0055] Based on the above model assumptions, establish the dynamic model of the planetary gear system. In the planetary gear train, the sun gear is used as the input, the planet carrier is used as the output, and the internal gear ring is fixed to the housing, as Figure 2 shown.

[0056] r, s, c, p n (n = 1, 2, 3) respectively represent the internal gear ring, the planet carrier, the sun gear and the planet gear in the gear train. x i , y i , z i and u ix , u iy , u iz (i = r, c, s, n) respectively represent the linear displacement of elastic deformation of each component along the x, y, z directions and the torsional deformation linear displacement around the x, y, z axes; k ix , k iy and c ix , c iy respectively represent the support stiffness and support damping of each component along the x, y directions; k ju and c ju (j = c, s, r) respectively represent the torsional stiffness and damping of each component around its axis; k jz , C jz respectively represent the radial (including x-direction and y-direction) support stiffness and damping of the support bearing of the component; k jb , C jb respectively represent the axial support stiffness and damping of the support bearing of the component; k cn , C cn respectively represent the radial support stiffness and damping of the planet gear shaft bearing to the planet gear; k cnz , C cnz respectively represent the axial support stiffness and damping of the planet gear shaft bearing to the planet gear; k cnb , C cnb respectively represent the torsional vibration stiffness and damping when the planet gear rotates around the x-axis or y-axis; k rn , k sn and c rn , c sn respectively represent the meshing stiffness and meshing damping of the internal / external meshing pair; α r , α s respectively are the pressure angles corresponding to the tooth profiles of the internal and external meshing pairs at the pitch circle meshing; e rn , e sn respectively are the equivalent meshing errors of the internal and external meshing gear pairs; b rn , b sn respectively are the backlash of the internal and external meshing gear pairs; Ψ n = 2π(n - 1) / N is the position angle of the nth planet gear.

[0057] Step 3: Derive the nonlinear dynamic equation of the helical planetary gear train

[0058] From Figure 2It can be seen that there are relative deformations and meshing errors between the gear pairs. Therefore, the elastic deformation coordination conditions of the gear pairs must be considered when deriving the dynamic equations of the planetary gear train. According to Figure 2 the dynamic model of the planetary gear train, the relative displacements between the components can be obtained through coordinate transformation, and the results are as follows.

[0059] The relative displacement of the external meshing gear pair along the meshing line direction can be expressed as:

[0060] δ sn =x s sinψ sn cosβ - y s cosψ sn cosβ - z s sinβ - u sz cosβ - x n sinα s cosβ + y n cosα s cosβ

[0061] +z n sinβ - u nz cosβ - u sx sinψ n sinβ + u sy cosψ n sinβ + u ny sinβ / cosα s +e sn

[0062] The relative displacement of the internal meshing gear pair along the meshing line direction can be expressed as:

[0063] δ rn = - x r sinψ rn cosβ - y r cosψ rn cosβ + z r sinβ - u rz cosβ + x n sinα r cosβ + y n cosα r cosβ

[0064] - z n sinβ + u nz cosβ + u rx sinψ n sinβ - u ry cosψ n sinβ + uny sinβ / cosα r +e rn

[0065] δ hn (h = s, r) is the relative displacement of the meshing pair;

[0066] During the gear meshing process, factors such as manufacturing and installation errors will cause a clearance to exist before the gear pair comes into contact, which has an important impact on the dynamic response of the gear pair. The nonlinear function of the backlash of the meshing pair can be expressed as:

[0067]

[0068] b hn is the backlash of the gear pair. Based on Figure 2 the established dynamic model of the helical planetary gear train, the nonlinear dynamic differential equation of the planetary gear train is derived.

[0069] Differential equation of the motion of the planet carrier:

[0070]

[0071] Differential equation of the motion of the sun gear:

[0072]

[0073] Differential equation of the motion of the internal gear ring:

[0074]

[0075] Differential equation of the motion of the nth planet gear:

[0076]

[0077] In the formula, N is the number of planet gears; m i is the mass of each component; r i is the base circle radius of each component; I ix , I iy , I iz are the moments of inertia of each component about the x, y, and z axes respectively; r ms , r mr are the pitch circle radii of the sun gear and the planet gear respectively; T s , T c are the torques of the sun gear and the planet carrier respectively. ω c is the rotational speed of the planet carrier.

[0078] For ease of programming calculation, the scalar scale b a = b s1 / 2 and the time scale The above kinematic differential equations are made dimensionless, and the relevant dimensionless process is as follows.

[0079] Scalar term:

[0080] First derivative term:

[0081] Second derivative term:

[0082] After dimensionless treatment, substituting the dimensionless parameters into the differential equations, the dimensionless kinematic differential equations of the helical planetary gear train are derived as follows:

[0083]

[0084] In the formula, are the dimensionless mass matrix, dimensionless damping matrix, dimensionless gyroscopic matrix, dimensionless support stiffness matrix, dimensionless centripetal stiffness matrix, dimensionless meshing stiffness matrix, dimensionless external excitation array, and dimensionless internal excitation array respectively. Among them, the dimensionless damping matrix Adopts the Rayleigh damping formula:

[0085]

[0086] ε and ζ are the mass proportionality coefficient and the stiffness proportionality coefficient respectively.

[0087] Step 4: Fitting of internal excitation of the dynamic model

[0088] The gear system generates a dynamic response under the action of dynamic excitation. The dynamic excitation of the system is divided into two parts: external excitation and internal excitation. External excitation is the excitation of the system from outside the system, mainly referring to the driving torque of the prime mover and the resistance torque of the load. Internal excitation refers to the dynamic excitation generated during the meshing process of the gear pair teeth. During the meshing process of the S-shaped helical planetary gear, the internal excitation includes stiffness excitation, error excitation, and excitation caused by the change of the pressure angle. They are all important influencing factors of the system's nonlinear dynamic characteristics and the main sources of system vibration and noise. Correctly describing the internal excitation is the premise for dynamic analysis.

[0089] The magnitude of the meshing stiffness directly affects the ability of the gear teeth to resist deformation and is an important factor affecting the nonlinear dynamic behavior of the system. During the gear meshing process, the meshing stiffness shows periodic fluctuations with the single and double tooth alternate meshing of the gear pair. Based on the finite element method, a corresponding finite element model is established using the simulation software Abaqus for contact bearing analysis to calculate the time-varying meshing stiffness of the internal and external meshing pairs of the S-shaped helical planetary gear train, and the Fourier function is used to perform curve fitting on the obtained time-varying meshing stiffness. The formula is as follows:

[0090]

[0091] where k pr (t) and k sp (t) are the time-varying mesh stiffnesses of the internal and external meshing pairs respectively; k rm and k sm are the average values of the time-varying mesh stiffnesses of the internal and external meshing pairs respectively; is the coefficient of the λ-th harmonic term of the Fourier series. The coefficients are shown in Table 2. l is the order of the harmonic terms of the Fourier fitting, taking the 4th harmonic; ω m is the meshing frequency of the planetary gear train; γ ri and γ si are the phase differences of the i-th internal and external meshing pairs.

[0092] Since the actual machining accuracy of gears generally cannot meet the ideal requirements, errors will inevitably occur during manufacturing and assembly. These errors generate periodic excitation to the system as the gears rotate, which will not only cause vibration and noise in the transmission system, but also reduce the load-carrying capacity of the system due to the load sharing problem, seriously restricting the exertion of the advantages of the planetary gear train. The manufacturing errors of the gear transmission system and the motion errors caused by the elastic deformation of the gear teeth are called static transmission errors. As one of the main internal excitations of the planetary gear train, the static transmission errors directly affect the vibration characteristics of the gear system. Similarly, using the finite element method and combining the simulation results, the static transmission errors of the internal and external meshing pairs can be obtained and Fourier fitting can be performed on them. The fitting formula is:

[0093]

[0094] where e ri (t) and e si (t) are the static transmission errors of the internal and external meshing pairs respectively; e rm and e sm are the average values of the static transmission errors of the internal and external meshing pairs respectively; is the coefficient of the λ-th harmonic term of the Fourier series. The coefficients are shown in Table 3.

[0095] Similar to the mesh stiffness, for a planetary gear train with a curved meshing line, the pressure angle will also change periodically with the alternate meshing of single and double teeth of the gear teeth during the meshing process, thus forming an internal excitation source, causing vibration of the system and affecting the dynamic response of the system. Therefore, the time-varying pressure angle can be regarded as an important factor affecting the nonlinear dynamic behavior of the system. Similarly, according to the periodic change law of the pressure angle, after converting it to radian system, Fourier fitting is performed on it, and the formula is as follows:

[0096]

[0097] where α r (t) and α s (t) are the time-varying pressure angle functions of the internal and external meshing pairs respectively; α rm and α sm are the average values of the pressure angles of the internal and external meshing pairs respectively; is the coefficient of the λ-th harmonic term of the Fourier series, and the coefficients are shown in Table 4.

[0098] Step 5: Analyze the dynamic performance of the helical planetary gear train

[0099] Under the conditions of considering the time-varying meshing stiffness, static transmission error, time-varying pressure angle, backlash and damping, etc., the meshing forces between the planet gear and the sun gear, and between the planet gear and the internal gear ring can be expressed as:

[0100]

[0101] f(δ sn ) and f(δ rn ) are the backlash nonlinear functions of the meshing pairs between the planet gear and the sun gear, and between the planet gear and the internal gear ring respectively. To obtain the dynamic meshing force, it is necessary to solve the established gear dynamics model, that is, use the 4th-order variable-step Runge-Kutta method in MATLAB to solve the dimensionless nonlinear equations, reduce the second-order differential equations to first-order differential equations, and finally give the dynamic response results. MATLAB solution requires calling the ode45 function, that is

[0102] [t,x]=ode45(odefun,span,x0,options)

[0103] odefun - Function handle, which can be a function file name, anonymous function handle or inline function name;

[0104] tspan - Interval [t0,t f or a series of scattered points [t0,t1,...,t f ;

[0105] x0 - Initial value vector;

[0106] t - Time points returned as a column vector;

[0107] x - Solution column vector corresponding to t.

[0108] To verify the proposed dynamic modeling and dynamic performance analysis method for a curve-type meshing line gear planetary gear train, the following takes the S-type helical planetary gear train as an example to illustrate the proposed analysis method. The lumped parameter method is used to establish the model, taking into account the time-varying meshing stiffness, static transmission error, and time-varying pressure angle excitation, and the dynamic response is solved by MATLAB programming to analyze the dynamic response results of the planetary gear train.

[0109] Taking the helical planetary gear train in the NGW11.2 type reducer as an example for research, this gear train takes the sun gear as the input and the planet carrier as the output, with 3 planet gears, an input speed of 300 r / min, an input torque of 100 N·m, and the main parameters of the planetary gear train are shown in Table 1.

[0110] Table 1. Design parameters of the planetary gear train

[0111]

[0112]

[0113] Step 1: Fitting of internal excitations in the dynamic model

[0114] To balance the calculation time and calculation accuracy, a five-tooth model of internal and external meshing is established in the finite element software ABAQUS, as shown in Figure 3 、 4 .

[0115] Based on the calculation data of ABAQUS, the finite element method is used to calculate the time-varying meshing stiffness and static transmission error of the internal and external meshing pairs of the S-type gear planetary gear train, as shown in Figure 5 、 Figure 6 .

[0116] According to the meshing line equation of the S-type gear, the periodic change law of the pressure angle is deduced as shown in Figure 1 , and then Fourier function fitting is carried out. The time-varying pressure angles of the internal and external meshing pairs of the S-type gear planetary gear train after fitting are shown in Figure 7 、 8 .

[0117] To facilitate the subsequent solution of the dynamic equation of the planetary gear train, Fourier functions are used to perform curve fitting on the obtained time-varying meshing stiffness, static transmission error, and time-varying pressure angle. Table 2 shows the Fourier harmonic term coefficients for fitting the time-varying meshing stiffness of the internal and external meshing pairs; Table 3 shows the Fourier harmonic term coefficients for fitting the static transmission error of the internal and external meshing pairs; Table 4 shows the Fourier harmonic term coefficients for fitting the time-varying pressure angle of the internal and external meshing pairs.

[0118] Table 2 Fourier harmonic term coefficients of the time-varying meshing stiffness of the internal and external meshing pairs

[0119]

[0120] Table 3 Fourier harmonic term coefficients of the static transmission error of the internal and external meshing pairs

[0121]

[0122] Table 4 Fourier harmonic term coefficients of the time-varying pressure angle of the internal and external meshing pairs

[0123]

[0124] Step 2: Analyze the dynamic response

[0125] Combined with the established nonlinear dynamic model of the S-type gear helical planetary gear train, the 4th-order variable-step Runge-Kutta method is used to solve the dimensionless nonlinear equations. According to the solution results of the dynamic equations, the dynamic meshing forces of the internal and external meshing pairs of the S-type helical planetary gear train are obtained. Since each phase power flow branch has the same nature, only the dynamic response results of the 1st-phase power flow branch, that is, the sun gear - planet gear 1 and planet gear 1 - internal gear ring, are given Figure 9 and Figure 10 are the results of the dynamic meshing forces of the internal and external meshes of the S-type gear planetary gear train Figure 11 and Figure 12 are the results of the dynamic transmission errors of the internal and external meshing pairs of the S-type gear planetary gear train

[0126] It can be seen from the result diagrams that: when taking into account the time-varying mesh stiffness, static transmission error, and time-varying pressure angle of the internal time-varying excitation, under the working conditions of an input torque of 100 N·m and a rotational speed of 300 r / min, the fluctuation ranges of the dynamic meshing forces of the internal and external meshing pairs of the S-type gear planetary gear train are [1818.06 N, 1889.30 N] and [1805.40 N, 1891.75 N] respectively, and the fluctuation ranges of the dynamic transmission errors are [47.54 μm, 48.96 μm] and [43.13 μm, 46.43 μm]. This example comprehensively considers the influence of multiple excitations and establishes a more refined dynamic model. The research results provide important reference value for the dynamic design and vibration control of the curve-type meshing line gear planetary gear train

[0127] The design advantages of the present invention are reflected in this example

[0128] Based on the same inventive concept, the present invention further provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is configured to execute the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is used to implement one or more instructions. Specifically, it is used to load and execute one or more instructions in the computer storage medium to implement the above method.

[0129] It should be further noted that, based on the same inventive concept, the present invention further provides a computer storage medium, on which a computer program is stored, and the computer program, when run by a processor, executes the above method. The storage medium may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may, for example, but not be limited to, an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a Random Access Memory (RAM), a Read-Only Memory (ROM), an Erasable Programmable Read-Only Memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, the computer-readable storage medium may be any tangible medium that contains or stores a program, and the program may be used by or combined with an instruction execution system, apparatus, or device.

[0130] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. The terms such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left" and "right" are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationships may also change accordingly.

[0131] As described above, the above are only the preferred embodiments of the present invention, and are not intended to limit the present invention in any other form. Any person skilled in the art may use the technical content disclosed above to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

[0132] This patent is not limited to the above best mode. Anyone inspired by this patent can derive various other forms of a method for dynamic modeling and dynamic performance analysis of a face curve meshing line gear planetary gear train. All equal changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope covered by this patent.

Claims

1. A dynamic pressure angle modeling method for a curve-type meshing line gear planetary gear train, characterized in that: Derive the slope change law by differentiating the meshing line equation based on the S-shaped gear meshing line equation, and deduce the U-shaped periodic change function of the pressure angle in the single and double tooth alternate meshing area. a n (t). In the double tooth meshing area, take the average value of the pressure angles at the starting and ending points of meshing, and synthesize the periodic change law of the pressure angle in the single and double tooth alternate meshing area; Fit the time-varying pressure angle function through the fourth-order Fourier series. a r (t).

2. The pressure angle dynamic modeling method for a curve-type meshing line gear planetary gear train according to claim 1, wherein: Pressure angle function a n (t) derivation includes: Through the inverse trigonometric function α n = arctan(y a ' ), calculate the U-shaped periodic variation law of the pressure angle with the meshing position, where y a ' is the first derivative of the meshing position variable; The equation of the contact line is a p =tan(90° - α n ) / n c , where n c is a parameter for controlling the shape of the curve, α n is the pitch circle pressure angle.

3. A dynamic pressure angle modeling method for a gear planetary gear train with a curved meshing line according to claim 2, characterized in that: The pressure angle function a n (t) is derived by combining the helix angle β to correct the direction of the contact line and the contact area.

4. A pressure angle dynamic modeling method for a curve meshing line gear planetary gear train according to claim 1, characterized in that: The harmonic coefficients of the Fourier series fitting are obtained based on the Abaqus finite element simulation data by establishing a five-tooth finite element model for internal and external meshing, extracting the time-varying meshing stiffness and static transmission error data.

5. A dynamic modeling method for a curve-type meshing line gear planetary gear train, based on the pressure angle dynamic modeling method described in any one of claims 1-4, characterized in that Couple the time-varying pressure angle function a r (t) with the time-varying mesh stiffness, static transmission error, and backlash nonlinear function of the helical planetary gear train to establish a multi-degree-of-freedom bending-torsion-axial-pendulum dynamic model; simplify the dynamic equation into a matrix form through dimensionless treatment.

6. The dynamic modeling method for a curve-type meshing line gear planetary gear train according to claim 5, wherein: The multi-degree-of-freedom bending-torsion-shaft-pendulum dynamic model is constructed in the following manner: Define the relative displacement equation of the external and internal meshing gear pairs along the meshing line direction, and the equation includes the coordinate transformation relationship between the linear displacement and angular displacement of the sun gear, planet carrier, internal gear ring and planet gear; Introduce a nonlinear function of the backlash. The function defines the contact state in segments according to the relationship between the relative displacement of the meshing pair δ hn and the backlash b hn .

7. A dynamic modeling method for a curve meshing line gear planetary gear train according to claim 6, characterized in that: The coordinate transformation relationship converts the linear displacement and angular displacement of each component into the relative displacement along the meshing line based on the position angle of the planet gear; the dimensionless processing introduces b a = b s1 / 2 and the time scale , where b s1 is the backlash of the external meshing pair of the planetary gear train; is the average meshing stiffness of the external meshing pair of the planetary gear train; m s and m 1 are the masses of the sun gear and the planet gear respectively; the damping matrix adopts the Rayleigh formula; the time-varying meshing stiffness and the static transmission error are fitted by the fourth-order Fourier series.

8. A dynamic performance analysis method for a curve-type meshing line gear planetary gear train, based on the dynamic modeling method as described in claim 5, characterized in that: Use the ode45 solver of MATLAB to perform dynamic response analysis on the dimensionless nonlinear motion differential equation, and verify the engineering applicability of the model according to the dynamic response results.

9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the steps of the method according to claim 8 are implemented.

10. A non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method according to claim 8 are implemented.

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