Linear simplification method for finite element model of gear transmission rotor system

Abstract

The present application belongs to the field of mechanical engineering, and particularly relates to a linear simplification method of a finite element model of a gear transmission device rotor system. In order to solve the problem of low efficiency in the calculation of the existing finite element model of the gear transmission device rotor system, a linear simplification method of the finite element model of the gear transmission device rotor system is provided, which comprises the following steps: constructing a spur gear pair meshing coupling type dynamic model and a gear pair transient impact dynamic analysis model of the gear transmission device rotor system; establishing a gear tooth equivalent spring finite element simplified model according to the obtained spur gear pair meshing coupling type dynamic model and the gear pair transient impact dynamic analysis model; using the gear tooth equivalent spring finite element simplified model to perform finite element analysis on the gear transmission device rotor system to obtain an analysis result. The problem of low efficiency in the calculation of the existing finite element model of the gear transmission device rotor system is solved.

Description

Technical Field

[0001] This invention belongs to the field of mechanical engineering, and in particular relates to a linear simplification method for the finite element model of a rotor system of a gear transmission device. Background Technology

[0002] Gear transmission devices, due to their unique transmission method, can transmit motion and power between any shafts in space, possessing advantages such as a large power range, long service life, and safe and reliable operation. Besides their good performance, their strong impact resistance has garnered widespread attention from academia and industry in various fields, including machinery, electronics, marine engineering, and energy. However, when studying the impact resistance characteristics of gear transmission systems, whether investigating the strength or stiffness of the gear teeth, the tooth mesh size needs to be sufficiently small to reflect the tooth structure. This significantly increases computation time during complete impact resistance finite element analysis, resulting in low finite element computation efficiency. The literature "Yang Taiwei. Vibration Analysis and Optimization of High-Speed ​​Spur Gear Meshing. Chongqing University, 2018" established a three-dimensional finite element model of high-speed gear meshing and conducted simulation analysis and optimization of gear engagement and disengagement impacts, obtaining the optimal modification amount for the gear rotor system. However, this paper still retains the complex nonlinear model and coupling effect in the vibration analysis of traditional gear transmission devices. It establishes a traditional Tie connection finite element model with teeth, sets the contact point as Tie contact, and requires a large number of mesh refinements. This has significant limitations in terms of computational complexity, computational efficiency, and resource consumption.

[0003] Therefore, the calculation of the existing finite element model of the rotor system of the gear transmission device suffers from low efficiency. Summary of the Invention

[0004] The purpose of this invention is to address the problem of low computational efficiency in existing finite element models of gear transmission rotor systems. A linear simplification method for finite element models of gear transmission rotor systems is proposed, comprising:

[0005] Step 1: Construct a meshing coupling dynamic model of the spur gear pair and a transient impact dynamic analysis model of the gear pair in the rotor system of the gear transmission device;

[0006] Step 2: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, establish a simplified finite element model of the equivalent spring of the gear teeth;

[0007] Step 3: Use the simplified finite element model of the equivalent spring of the gear teeth to perform finite element analysis on the rotor system of the gear transmission device and obtain the analysis results.

[0008] The analysis results include: single-tooth meshing biaxial impact analysis results and double-tooth meshing biaxial impact analysis results, specifically: analysis results of gear tooth strength and stiffness changes, gear tooth stress changes during meshing, etc.

[0009] The specific process for constructing the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair in step 1 of the gear transmission device rotor system is as follows:

[0010] Step 1.1: Consider only the torsional system of the gear pair in the rotor system of the gear transmission device, and do not consider the gear pair support system, establish the dynamic model of the torsional system of the gear pair;

[0011] The rotor system of the gear transmission device includes: a gear pair torsion system and a gear pair support system;

[0012] The gear pair support system includes a drive shaft and bearings;

[0013] The gear pair torsion system includes a driving gear and a driven gear;

[0014] Step 1.2: Based on the dynamic model of the gear pair torsional system, construct a meshing coupling dynamic model of the spur gear pair.

[0015] In the dynamic model of the meshing coupling type of spur gear pair, both the driving gear and the driven gear are spur gears.

[0016] Step 1.3: Based on the meshing coupling dynamic model of the spur gear pair obtained in Step 1.2, construct the transient impact dynamic analysis model of the gear pair.

[0017] In step 2, a simplified finite element model of the equivalent spring of the gear teeth is established based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in step 1. The specific process is as follows:

[0018] Step 2.1: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, establish a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupling spur gear transmission;

[0019] Step 2.2: Based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission, construct a simplified single-tooth meshing model of the gear pair;

[0020] Step 2.3: Based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission, construct a simplified double-tooth meshing model for the gear pair;

[0021] Step 2.4: Use the simplified single-tooth meshing model and the simplified double-tooth meshing model of the gear pair as the simplified finite element model of the equivalent spring of the gear teeth.

[0022] The beneficial effects of this invention are as follows:

[0023] This invention provides a simplified method for the finite element model of a rotor system of a gear transmission device, which is used to accurately predict the impact characteristics and dynamic response of the gear transmission system, thereby reducing the computational complexity of finite element calculations and improving computational efficiency. This achieves the requirements for design optimization and performance improvement of gear transmission devices, and promotes the further application of gear transmission devices in the field of impact dynamics research on structural response and load transfer.

[0024] This invention proposes a novel linear simplification method for the finite element model of a gear transmission rotor system. This method mainly includes the derivation of the transient impact dynamics analysis model of the gear, the establishment of a simplified spring model for the bending-torsional coupling vibration analysis of meshing spur gear transmissions, simplified analysis of single-tooth and double-tooth meshing intervals, and the study of the influence of different simplification methods on the natural frequency and impact response of the rotor system. This significantly improves the computational efficiency of the finite element model of the gear transmission rotor system. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the single-tooth meshing tie connection of the present invention;

[0026] Figure 2 This is a simplified schematic diagram of the single-tooth meshing spring of the present invention;

[0027] Figure 3 This is a simplified schematic diagram of the double-tooth meshing spring of the present invention;

[0028] Figure 4 This is a schematic diagram of the direct coupling of the toothed cross section of the present invention;

[0029] Figure 5 This is a diagram illustrating the disconnected nature of the method;

[0030] Figure 6 This is a schematic diagram of the finite element model of the Tie connection for modal calculation of a single-tooth spur gear pair according to the present invention.

[0031] Figure 7 This is a simplified finite element model of the spring for modal calculation of a single-tooth spur gear pair according to the present invention;

[0032] Figure 8 This is a schematic diagram of the stress response time history curve of the unit under single-tooth meshing uniaxial impact according to the present invention;

[0033] Figure 9 This is a schematic diagram of the stress response time history curve of the unit under single-tooth meshing biaxial impact of the present invention;

[0034] Figure 10 This is the stress response time-history curve of the unit under dual-tooth meshing uniaxial impact of the present invention;

[0035] Figure 11 This is the stress response time history curve of the unit under biaxial impact with double teeth according to the present invention. Detailed Implementation

[0036] Specific implementation method one: Combining Figure 1 This invention describes the following:

[0037] Step 1: Construct a meshing coupling dynamic model of the spur gear pair and a transient impact dynamic analysis model of the gear pair in the rotor system of the gear transmission device;

[0038] Step 2: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, establish a simplified finite element model of the equivalent spring of the gear teeth;

[0039] Step 3: Use the simplified finite element model of the equivalent spring of the gear teeth to perform finite element analysis on the rotor system of the gear transmission device and obtain the analysis results.

[0040] The analysis results include: single-tooth meshing biaxial impact analysis results and double-tooth meshing biaxial impact analysis results, specifically: analysis results of gear tooth strength and stiffness changes, gear tooth stress changes during meshing, etc.

[0041] Specific Implementation Method Two: The difference between this implementation method and Specific Implementation Method One is that...

[0042] The specific process for constructing the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair in step 1 of the gear transmission device rotor system is as follows:

[0043] Step 1.1: Consider only the torsional system of the gear pair in the rotor system of the gear transmission device, and do not consider the gear pair support system, establish the dynamic model of the torsional system of the gear pair;

[0044] The rotor system of the gear transmission device includes: a gear pair torsion system and a gear pair support system;

[0045] The gear pair support system includes a drive shaft and bearings;

[0046] The gear pair torsion system includes a driving gear and a driven gear;

[0047] Step 1.2: Based on the dynamic model of the gear pair torsional system, construct a meshing coupling dynamic model of the spur gear pair.

[0048] In the dynamic model of the meshing coupling type of spur gear pair, both the driving gear and the driven gear are spur gears.

[0049] Step 1.3: Based on the meshing coupling dynamic model of the spur gear pair obtained in Step 1.2, construct the transient impact dynamic analysis model of the gear pair.

[0050] The other steps and parameters are the same as in Specific Implementation Method 1.

[0051] Specific Implementation Method Three: The difference between this implementation method and Specific Implementation Method One is that...

[0052] The dynamic model of the gear pair torsional system in step 1.1 is expressed by the following formula:

[0053]

[0054] In the formula, M represents the mass matrix of the gear pair torsional system, and x represents the dynamic displacement vector of the gear pair. The derivative of x is... express The derivative of x s P represents the relative displacement vector of the gear pair. s Indicates load;

[0055] The following variables are all functions of time t, where C represents the damping matrix of the gear pair torsional system, K represents the time-varying meshing stiffness of the gear pair torsional system, and e represents the gear comprehensive error.

[0056] The other steps and parameters are the same as in one of the specific implementation methods one or two.

[0057] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One through Four in that...

[0058] In step 1.2, based on the dynamic model of the gear pair torsional system, a meshing coupling dynamic model of the spur gear pair is constructed. The specific process is as follows:

[0059] The meshing coupling dynamic model of a spur gear pair is based on the dynamic models of the gear pair torsional system and the gear pair support system. Ignoring tooth surface friction, a meshing coupling dynamic model of the spur gear pair is constructed, expressed by the following formula:

[0060]

[0061]

[0062] In the formula, m represents the mass of the gear pair; m p I represents the mass of the driving gear. p The moment of inertia of the driving gear, mg I represents the mass of the driven gear. g This represents the moment of inertia of the driven gear. express The derivative of Let δ represent the derivative of δ, where δ represents the gear pair meshing displacement; c represents the gear pair meshing coupling damping; k represents the gear pair meshing coupling stiffness; and p represents the gear pair meshing coupling load.

[0063] k py k represents the stiffness of the drive shaft support. gy k represents the bearing support stiffness. m c represents the overall meshing stiffness of the gear pair. py Indicates the damping of the drive shaft, c gy Indicates bearing damping, c m R represents the damping of the gear pair. p Represents the base circle radius R of the driving gear teeth. g This represents the base circle radius of the driven gear teeth. T represents the derivative of e. P This indicates the torque transmitted by the driving gear.

[0064] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0065] Specific Implementation Method Five: The difference between this implementation method and Specific Implementation Methods One to Four is that...

[0066] In step 1.3, based on the meshing coupling dynamic model of the spur gear pair obtained in step 1.2, a transient impact dynamic analysis model of the gear pair is derived; the specific process is as follows:

[0067] The gear dynamics of the spur gear pair meshing coupling dynamic model are set as transient gears, and the calculation state is the ideal meshing state, without considering the gear comprehensive error; a transient impact dynamic analysis model of the gear pair is constructed, expressed by the formula:

[0068]

[0069] In the formula, M 1 Let C represent the tooth mass, P represent the tooth impact load, and C represent the tooth impact load. 1 K represents the gear meshing damping. 1 Indicates the meshing stiffness of gear teeth;

[0070]

[0071] In the formula, ξ g k represents the gear meshing damping ratio. m R represents the overall meshing stiffness of the gear pair. p Represents the base circle radius R of the driving gear teeth.g I represents the base circle radius of the driven gear teeth. p The moment of inertia of the driving gear teeth, I g The moment of inertia of the passive gear teeth is represented by the transient gear, which is the instantaneous dynamic response of the gear transmission system during the gear transmission process due to factors such as external excitation, load changes, uneven gear meshing, and elastic deformation of the system; other steps and parameters are the same as in one of the specific implementation methods one to four.

[0072] Specific Implementation Method Six: The difference between this implementation method and Specific Implementation Methods One to Five is that...

[0073] In step 2, a simplified finite element model of the equivalent spring of the gear teeth is established based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in step 1. The specific process is as follows:

[0074] Step 2.1: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, establish a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupling spur gear transmission;

[0075] Step 2.2: Based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission, construct a simplified single-tooth meshing model of the gear pair;

[0076] Step 2.3: Based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission, construct a simplified double-tooth meshing model for the gear pair;

[0077] Step 2.4: Use the simplified single-tooth meshing model and the simplified double-tooth meshing model of the gear pair as the simplified finite element model of the equivalent spring of the gear teeth; other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0078] Specific Implementation Method Seven: The difference between this implementation method and Specific Implementation Methods One through Six is ​​that...

[0079] In step 2.1, based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in step 1, a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupling spur gear transmission is established; the specific process is as follows:

[0080] Step 2.1.1: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, determine the basic structure of the rotor system of the gear transmission device.

[0081] The basic structure of the rotor system of the gear transmission device includes: a transmission shaft, bearings, a driving gear, and a driven gear;

[0082] The basic structure of the rotor system of the gear transmission device is known to those skilled in the art, as determined by the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair in step 1. This is because the basic model is very simplified and no other special parameters are set.

[0083] Step 2.1.2: Based on the basic structure of the rotor system of the gear transmission device, construct a simplified spring model for the bending-torsional coupling vibration analysis of the meshing spur gear transmission;

[0084] The other steps and parameters are the same as those in any of the specific implementation methods one to six.

[0085] Specific Implementation Method Eight: The difference between this implementation method and Specific Implementation Methods One to Seven is that...

[0086] In step 2.1.2, based on the basic structure of the rotor system of the gear transmission device, a simplified spring model for bending-torsional coupling vibration analysis of the meshing spur gear transmission is constructed; the specific process is as follows:

[0087] 2.1.2.1: Based on the basic structure of the rotor system of the gear transmission device, construct the transmission shaft, driving gear, and driven gear in the finite element software;

[0088] For example, based on the meshing radius R of the driving gear in the dynamic equation... p Driven gear meshing radius R g The mass m of the driving gear p The moment of inertia I of the driving gear p The mass m of the driven gear g The moment of inertia I of the driven gear g Set the structure of the driving gear and driven gear in the finite element model in the finite element software;

[0089] 2.1.2.2: Using the combined meshing stiffness and meshing damping as the dynamic characteristics of the meshing gear pair structure in the finite element software, a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupled spur gear transmission is obtained.

[0090] The dynamic characteristics of the meshing gear pair structure include: gear pair meshing coupling damping c and gear pair meshing coupling stiffness k.

[0091] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0092] Specific Implementation Method Nine: The difference between this implementation method and Specific Implementation Methods One through Eight is that...

[0093] In step 2.2, a simplified model of single-tooth meshing of the gear pair is constructed based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission. The specific process is as follows:

[0094] Step 2.2.1: The gear teeth are not modeled using finite element methods. Instead, mass points are used in the finite element software to represent the gear teeth of both the driving and driven gears. The specific process is as follows:

[0095] In the finite element method software, X mass points are used as the tooth parts of X driving and driven gears in the de-toothed section; each tooth corresponds to one mass point.

[0096] The tooth cross-section is the cross-section of the tooth on the root circle, representing the geometric connection between the gear teeth and the gear disk; X is the number of teeth, which is a positive integer;

[0097] Step 2.2.2: In the finite element method software, an equivalent spring is used to represent the single-tooth meshing coupling between the driving gear and the driven gear, resulting in a simplified model of the single-tooth meshing of the gear pair; the specific process is as follows:

[0098] Step 2.2.2.1: Determine the timing for single-tooth meshing coupling analysis; the timing for single-tooth meshing coupling analysis is selected from the moment of minimum stiffness in the single-tooth meshing zone, corresponding to the most dangerous situation for the gear tooth. The single-tooth meshing zone is the working area where only one pair of teeth of the driving gear and the driven gear mesh.

[0099] Step 2.2.2.2: Determine the mass points of the driving gear teeth and driven gear teeth at the moment of single-tooth meshing coupling analysis, and obtain the mass point A of the driving gear teeth and the mass point B of the driven gear teeth;

[0100] Step 2.2.2.3: Between the mass point A of the driving gear tooth and the mass point B of the driven gear tooth, a first equivalent spring is used as the driving gear and the driven gear to perform single gear tooth meshing coupling;

[0101] The first equivalent spring is defined using the Connector element in the finite element analysis software; a simplified single-tooth meshing model of the gear pair is obtained.

[0102] The stiffness and damping of the equivalent spring are set as the meshing stiffness and meshing damping of the gear teeth at the analysis moment, and are calculated based on the dynamic model.

[0103] The equivalent spring is oriented along the line of engagement. Tooth surface friction is disregarded, and it is assumed that there is no coupling in the vertical direction of the line of engagement. A schematic diagram is shown below. Figure 2 As shown.

[0104] In finite element analysis software, the Connector element is selected to define elastic behavior similar to a spring, and a connection model is established between two points to describe the relative motion between components.

[0105] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0106] Specific Implementation Method Ten: The difference between this implementation method and Specific Implementation Methods One through Nine is that...

[0107] In step 2.3, a simplified model of double-tooth meshing of the gear pair is constructed based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission. The specific process is as follows:

[0108] Step 2.3.1: The gear teeth are not modeled using finite element methods. Instead, mass points are used in the finite element software to represent the gear teeth of both the driving and driven gears. The specific process is as follows:

[0109] In the finite element method software, X mass points are used as the tooth parts of X driving and driven gears in the de-toothed section; each tooth corresponds to one mass point.

[0110] The tooth cross section is the cross section of the tooth on the root circle, which characterizes the geometric connection relationship between the gear teeth and the gear disk; X is the number of teeth, and X is a positive integer;

[0111] Step 2.3.2: In the finite element method software, two equivalent springs are used to represent the single-tooth meshing coupling between the driving gear and the driven gear, resulting in a simplified double-tooth meshing model of the gear pair; the specific process is as follows:

[0112] Step 2.3.2.1: Determine the timing of the double-tooth meshing coupling analysis; the timing of the double-tooth meshing coupling analysis is selected from the moment of maximum stiffness in the double-tooth meshing zone, corresponding to the most dangerous situation of the gear teeth. The double-tooth meshing zone is the working area where the driving gear and the driven gear have two pairs of teeth meshing;

[0113] Step 2.3.2.2: Determine the mass points of the active gear teeth and passive gear teeth at the moment of double-tooth meshing coupling analysis, and obtain the mass points A1, A2, B1, and B2 of the active gear teeth.

[0114] Step 2.3.2.3: A second equivalent spring is used between the mass point A1 of the driving gear tooth and the mass point B1 of the driven gear tooth to characterize one of the meshing couplings of the double tooth meshing coupling;

[0115] Between the mass point A2 of the driving gear tooth and the mass point B2 of the driven gear tooth, a third equivalent spring is used to characterize the other meshing coupling of the double tooth meshing coupling of the gear teeth;

[0116] The second and third equivalent springs are defined using Connector elements in finite element analysis software, resulting in a simplified model of the double-tooth meshing gear pair.

[0117] The stiffness and damping of the equivalent spring are set as the meshing stiffness and damping of the gear teeth at the moment of double-tooth meshing analysis, and are calculated based on the dynamic model.

[0118] The equivalent spring is oriented along the line of engagement. Tooth surface friction is disregarded, and it is assumed that there is no coupling in the vertical direction of the line of engagement. A schematic diagram is shown below. Figure 3 As shown.

[0119] In finite element analysis software, the Connector element is selected to define elastic behavior similar to a spring, and a connection model is established between two points to describe the relative motion between components.

[0120] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0121] Simulation analysis based on specific implementation methods one through ten

[0122] From the perspectives of frequency domain and time domain, the structural modal frequencies and impact responses of different connection methods of rotor systems are compared and analyzed to verify the rationality of spring simplification.

[0123] Step 3.1: Set the connection coupling method of the gear rotor system

[0124] The first type of connection coupling is the traditional tie connection. Finite element modeling is performed on the entire spur gear system, taking a single tooth as an example.

[0125] like Figure 6 The figure shows a finite element model with a tie connection for modal calculation of a single-tooth spur gear pair. Local mesh refinement is required in the tooth region, while rotational degrees of freedom around the drive shaft are retained at both ends.

[0126] The second type of connection coupling is a simplified spring form. It retains the overall actual model of the gear, disk, and drive shaft, but does not model the gear teeth as solid entities. Instead, it simplifies them into mass points and moments of inertia. Other boundary conditions are the same as for the Tie connection. Taking a single tooth as an example...

[0127] like Figure 7 As shown, this is a simplified finite element model of the spring for modal calculation of a single-tooth spur gear pair.

[0128] To demonstrate the influence of gear pair coupling stiffness, two control groups were added. One group involved directly coupling the gears and disks after removing the gear teeth.

[0129] like Figure 4 The diagram shows a direct coupling at the cross-section after tooth removal; another diagram shows a connection between the two shafts with no coupling after tooth removal.

[0130] like Figure 5 The diagram shown is a schematic of a non-connected structure. By comparing the structural modes and impact responses of four types of connected and coupled structures, the rationality of the spring simplification is analyzed and demonstrated from both frequency and time domain perspectives.

[0131] Step 3.2: Modal Comparison of Different Simplification Methods for Gear Rotor Systems

[0132] In the comparison of the four connection and coupling structural modes of the gear rotor system, the comparative analysis of single-tooth meshing mode and double-tooth meshing mode is carried out respectively.

[0133] (1) Comparative analysis of single-tooth meshing modes: The first six modal cloud diagrams of the four connection forms of gear rotor systems under single-tooth meshing were extracted. The first six modes of the four are shown in Table 1.

[0134] Table 1. First six modal frequencies of four connection types under single-tooth meshing.

[0135] order Spring Simplification Tie connection Cross-section coupling No connection 1 8.2E-04 18.3 89.7 6.2E-04 2 1216.5 1053.2 1038.5 8.2E-04 3 2426.7 2452.0 2462.6 2408.8 4 2476.6 2456.4 2486.1 2408.9 5 2602.0 2717.4 2726.5 2604.6 6 2851.7 2784.1 2923.2 2604.7

[0136] Furthermore, the torsional, bending, and torsional-bending combined modes of the three coupled structures were compared. In the torsional modes, in the first torsional mode of the three structures, the rotation directions of the two gears were the same as the actual rotation directions. The frequencies of the first torsional modes, from smallest to largest, were: spring simplification, tie connection, and cross-section coupling.

[0137] In the second torsional mode of all three, the driving gear rotates in the opposite direction to the actual direction, while the driven gear rotates in the same direction as the actual direction, with the teeth of the two gears moving in opposite directions.

[0138] The second-order two gears perform a separation motion, but this type of motion does not exist in reality.

[0139] In the bending mode, the simplified third-order mode of the spring bends obliquely upward along the driven shaft, which is the same as the unconnected mode. The modal frequencies of the two are basically the same, and the coupling effect of the spring is zero in this direction. This direction is close to the perpendicular of the meshing line.

[0140] The fourth mode bends vertically upwards along both axes (the line connecting the wheel centers is perpendicular); the fifth mode is similar to the third mode, with the drive shaft bending obliquely upwards along a single axis.

[0141] According to the modal frequency values ​​in Table 1, among the three, the section coupling has the greatest effect on the bending stiffness of the shaft; the spring simplification increases the vertical bending stiffness of the shaft and is stronger than the tie connection.

[0142] The tie connection, compared to the spring simplification, enhances the lateral bending stiffness of the shaft. In the torsional-bending combined mode, the spring simplification results in the sixth mode, the tie connection results in the sixth mode, and the section coupling results in the fifth mode. This mode is very similar to the spring simplification and the section coupling, differing only in frequency.

[0143] Thus, the cross-sectional coupling connection is the strongest, which increases the stiffness of the structure in all directions; the spring simplification reflects the coupling in the direction of the wheel center connection (vertical), while there is almost no coupling in the direction of the wheel center connection (lateral);

[0144] Tie coupling, while simpler than spring coupling, actually enhances the lateral coupling between the two shafts, but its vertical coupling strength along the wheel center line is not as strong as that of spring coupling.

[0145] (2) Comparative analysis of the two-tooth meshing modes. The unconnected form is the same as the simplified single-tooth meshing. The first six torsional-bending mode cloud diagrams of the other three connection forms under the two-tooth meshing are extracted respectively, as shown in Table 2 below, which are the first six mode frequencies of the four connection forms under the two-tooth meshing.

[0146] Table 2. First six modal frequencies of four connection types under bitooth meshing.

[0147] order Spring Simplification Tie connection Cross-section coupling No connection 1 4.6E-03 120.1 298.9 6.2E-04 2 1398.5 1270.0 1416.5 8.3E-04 3 2416.7 2477.0 2498.1 2418.8 4 2493.6 2487.4 2501.6 2418.9 5 2609.0 2803.4 2947.7 2614.6 6 2892.5 2922.3 2982.2 2614.7

[0148] The calculated modal results for double-tooth meshing are almost identical to those for single-tooth meshing. Except for the unconnected form, the torsional, bending, and torsional-bending combined modal frequencies for all connection forms are increased. The difference lies in the fact that the fourth mode of the Tie connection changes from bending vertically downwards to bending upwards, which is closer to the simplified spring and cross-section coupling.

[0149] It was demonstrated that when the vertical coupling is enhanced, the vertical bending mode frequency of the gear rotor system also increases, and the vertical bending mode of the gear rotor system tends to move upward. This further corroborates the conclusion that "the vertical coupling strength of the Tie connection at the wheel center line is not as simple as that of the spring" when calculating the single-tooth meshing mode.

[0150] Based on the combined calculation results of single-tooth meshing and double-tooth meshing modes, the coupling form of the spring-simplified gear rotor system is closer to the actual situation. That is, the spring simplification can better reflect the real gear meshing situation compared with the tie connection. From the frequency domain perspective, the feasibility and advantages of the spring simplification model are proved.

[0151] Step 3.3: Comparison of impact response of different simplified methods for gear rotor system

[0152] This paper compares the impact responses of gear rotor systems using different simplified methods, conducting comparative analyses of single-tooth meshing single-axis impact, single-tooth meshing biaxial impact, biaxial meshing single-axis impact, and biaxial meshing biaxial impact. Referring to relevant impact tests on marine equipment, a triangular wave load with a peak value of 40g and a pulse width of 10ms was selected.

[0153] (1) Single-tooth meshing single-shaft impact analysis: stress response cloud diagram analysis of four connection forms at the peak of impact. The analysis shows that under the action of single-shaft impact load, the driving gear shaft, as the impact force shaft, has a greater response than the driven gear shaft.

[0154] The stronger the coupling, the more severe the overall response. The response intensity, from strongest to weakest, is as follows: cross-sectional coupling, tie connection, simplified spring, and no connection. The gear's disk-to-tooth connection and gear-to-drive shaft connection exhibit the most severe responses. Typical gear disk and axle elements from these areas with strong responses are selected, and their stress-response time-history curves are output.

[0155] like Figure 8 As shown, the stress response time-history curve of a single-tooth meshing single-shaft impact element is presented. In the figure, the stress response time-history curve of the driving gear structure element is consistent with the stress cloud diagram, indicating that the greater the coupling strength, the greater the element stress response.

[0156] The stress response of the cross-section coupled structure is much greater than the other three types, while the stress response of the unconnected structure is much smaller than the other three types. These two correspond to two extreme forms of gear-tooth coupling strength. The actual gear meshing coupling strength should be between the two, and the structural stress response should also be between the two stress responses.

[0157] Both the simplified spring connection and the tie connection satisfy the response law, indirectly verifying the rationality of both the tie connection and the simplified spring connection in single-tooth meshing. The stress response law of the driven wheel structural unit is basically consistent with that of the driving gear; the greater the coupling strength, the greater the stress response of the unit. Due to the influence of boundary constraints, the response value of the driven wheel structural unit is greater than that of the driving gear. The structural stress response shows a linear change during the impact load stage.

[0158] (2) Single-tooth meshing biaxial impact analysis: Stress response contour plots of the four connection types at the peak impact time were analyzed. The local stress response of the driving gear in the Tie connection was significantly different from the other three connection types, while the overall responses of the other three were similar. This indicates that the Tie connection method is not ideal when considering gear teeth. Typical elements were selected from the driving and driven gears, and the stress response time-history curves of these elements were output.

[0159] like Figure 9 As shown.

[0160] Under biaxial impact, due to the removal of constraints, more impact energy is converted into kinetic energy, resulting in a smaller overall structural response compared to uniaxial impact. During the impact load phase, the stress response of the structure exhibits a linear change. By comparing four connection types—section coupling, tie connection, spring simplification, and no connection—it is found that they are basically consistent in terms of structural stress response. Even when subjected to the same magnitude of impact load on both axes simultaneously, the choice of connection type has little impact on the overall structural response.

[0161] Comparing the stress contour plots of the four connection methods reveals that the Tie connection causes a different response in the drive gear shaft compared to the other three. Further analysis of the stress-time curves of typical elements shows that the response of the Tie connection deviates from the reasonable range between cross-sectional coupling and no connection. This deviation instability exceeds the case of spring simplification in both frequency and amplitude. Furthermore, the Tie connection requires longer computation time and consumes more computational resources. Modal analysis also reveals that the Tie connection increases lateral coupling between the two shafts. Considering all factors, spring simplification is considered a superior solution.

[0162] (3) Uniaxial impact analysis of double-tooth meshing: The magnitude and application method of the impact load of double-tooth meshing are consistent with those of single-tooth meshing. The stress response cloud diagrams of the four connection forms at the peak of the impact are analyzed.

[0163] like Figure 10 As shown, this is the time history curve of the stress response of the unit under uniaxial impact with two teeth meshing.

[0164] The overall response trend of double-tooth meshing is consistent with that of single-tooth meshing. During the impact load stage, the structural stress response changes linearly, and the response value is greater than that of single-tooth meshing, proving that the stronger the connection, the more severe the structural response.

[0165] The stress response of the cross-section coupling is greater than the other three, while the stress response of the unconnected section is less than the other three. The stress responses of the simplified spring and the tie connection are in between, which again shows that both treatments are reasonable to a certain extent when the teeth are meshing.

[0166] (4) Biaxial impact analysis of double-tooth meshing: The biaxial impact analysis of double-tooth meshing is identical to that of double-tooth uniaxial impact, except for the connection method between the two shafts. Stress response contour plots at the peak impact time are analyzed for each of the four connection types, as follows: Figure 11 As shown, this is the stress response time history curve of the element under biaxial impact with two teeth meshing.

[0167] The structural response patterns under biaxial impact with double teeth and biaxial impact with single teeth are consistent. The stress response of the structure changes linearly during the impact load stage.

[0168] The structural response is not significantly related to the coupling strength. The overall stress response values ​​of double-tooth and single-tooth pairs are relatively small, further demonstrating that the structural stress response under biaxial impact is not affected by the biaxial connection relationship.

[0169] The simplified spring connection is closer to the reasonable range than the tie connection, further proving that the simplified spring connection has more advantages than the tie connection and more realistically reflects the transmission characteristics of impact load in the gear-rotor system. The overall structural response under biaxial impact in dual-tooth meshing is less than that under uniaxial impact, for the same reason as in single-tooth meshing: increasing boundary constraints will cause more impact energy to be converted into structural strain energy, thus increasing the structural stress response.

[0170] The above four comparative analyses show that the stress response of the four connection forms, from largest to smallest, is as follows: cross-section coupling, Tie connection, spring simplification, and no connection. Tie connection is slightly larger than spring simplification, but its calculation time is three times that of spring simplification.

[0171] Under biaxial impact, the relative connection between the two axes has little impact on the overall stress response of the structure. The stress responses of the four connection types are almost identical. Compared to the tie connection, the simplified spring model's structural response is closer to the reasonable range between the responses of unconnected and fracture-coupled structures. From a time-domain perspective, the simplified spring model is more advantageous.

[0172] In summary, from both frequency and time domain perspectives, the simplified spring method can quantitatively describe the coupling strength between gear teeth, better reflect gear meshing, and the calculation results can more realistically reflect the transmission characteristics of impact loads in the gear-rotor system. Furthermore, it is unaffected by the gear tooth mesh size, resulting in higher computational efficiency and lower computational resource consumption. This fully demonstrates the effectiveness of the method proposed in this invention. The above description is merely of a preferred embodiment of the invention. It should be understood that the invention is not limited to the specific embodiments described above. Although the invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make some modifications or alterations to the disclosed technical content to create equivalent embodiments without departing from the scope of the invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments within the spirit and principles of the invention, without departing from the scope of the invention, are still within the protection scope of the invention.

Claims

1. A method of linear reduction of a finite element model of a gear transmission rotor system, characterized in that, Includes the following steps: Step 1: Construct a meshing coupling dynamic model of the spur gear pair and a transient impact dynamic analysis model of the gear pair in the rotor system of the gear transmission device; the specific process is as follows: Step 1.1: Consider only the torsional system of the gear pair in the rotor system of the gear transmission device, and do not consider the gear pair support system, establish the dynamic model of the torsional system of the gear pair; The rotor system of the gear transmission device includes: a gear pair torsion system and a gear pair support system; The gear pair support system includes a drive shaft and bearings; The gear pair torsion system includes a driving gear and a driven gear; Step 1.2: Based on the dynamic model of the gear pair torsional system, construct a meshing coupling dynamic model of the spur gear pair. In the dynamic model of the meshing coupling type of spur gear pair, both the driving gear and the driven gear are spur gears. Step 1.3: Based on the meshing coupling dynamic model of the spur gear pair obtained in Step 1.2, construct the transient impact dynamic analysis model of the gear pair; Step 2: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, establish a simplified finite element model of the equivalent spring of the gear teeth; Step 3: Use the simplified finite element model of the equivalent spring of the gear teeth to perform finite element analysis on the rotor system of the gear transmission device and obtain the analysis results.

2. The method of claim 1, wherein, The dynamic model of the gear pair torsional system in step 1.1 is expressed by the following formula: where M represents the gear pair torsional system mass matrix, x represents the gear pair dynamic displacement vector, represents the derivative of x, represents the derivative of , x s represents the gear pair relative displacement vector, P s represents the load; C represents the damping matrix of the gear pair torsional system, K represents the time-varying meshing stiffness of the gear pair torsional system, and e represents the gear comprehensive error.

3. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 2, characterized in that, In step 1.2, based on the dynamic model of the gear pair torsional system, a meshing coupling dynamic model of the spur gear pair is constructed. The specific process is as follows: The meshing coupling dynamic model of a spur gear pair is based on the dynamic models of the gear pair torsional system and the gear pair support system. Ignoring tooth surface friction, a meshing coupling dynamic model of the spur gear pair is constructed, expressed by the following formula: In the formula, m represents the mass of the gear pair; m p I represents the mass of the driving gear. p The moment of inertia of the driving gear, m g I represents the mass of the driven gear. g This represents the moment of inertia of the driven gear. express The derivative of Let δ represent the derivative of δ, where δ represents the gear pair meshing displacement; c represents the gear pair meshing coupling damping; k represents the gear pair meshing coupling stiffness; and p represents the gear pair meshing coupling load. k py k represents the stiffness of the drive shaft support. gy k represents the bearing support stiffness. m c represents the overall meshing stiffness of the gear pair. py Indicates the damping of the drive shaft, c gy Indicates bearing damping, c m R represents the damping of the gear pair. p Represents the base circle radius R of the driving gear teeth. g This represents the base circle radius of the driven gear teeth. T represents the derivative of e. P This indicates the torque transmitted by the driving gear.

4. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 3, characterized in that, In step 1.3, based on the meshing coupling dynamic model of the spur gear pair obtained in step 1.2, a transient impact dynamic analysis model of the gear pair is derived; the specific process is as follows: The gear dynamics of the spur gear pair meshing coupling dynamic model are set as transient gears, and the calculation state is the ideal meshing state, without considering the gear comprehensive error; a transient impact dynamic analysis model of the gear pair is constructed, expressed by the formula: where M 1 represents the gear mass, P represents the gear impact load, C 1 represents the gear mesh damping, K 1 represents the gear mesh stiffness.

5. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 4, characterized in that, In step 2, a simplified finite element model of the equivalent spring of the gear teeth is established based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in step 1. The specific process is as follows: Step 2.1: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, establish a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupling spur gear transmission; Step 2.2: Based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission, construct a simplified single-tooth meshing model of the gear pair; Step 2.3: Based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission, construct a simplified double-tooth meshing model for the gear pair; Step 2.4: Use the simplified single-tooth meshing model and the simplified double-tooth meshing model of the gear pair as the simplified finite element model of the equivalent spring of the gear teeth.

6. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 5, characterized in that, In step 2.1, based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in step 1, a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupling spur gear transmission is established; the specific process is as follows: Step 2.1.1: Based on the meshing coupling dynamic model of the spur gear pair and the transient impact dynamic analysis model of the gear pair obtained in Step 1, determine the basic structure of the rotor system of the gear transmission device. The basic structure of the rotor system of the gear transmission device includes: a transmission shaft, bearings, a driving gear, and a driven gear; Step 2.1.2: Based on the basic structure of the rotor system of the gear transmission device, construct a simplified spring model for the bending-torsional coupling vibration analysis of the meshing and coupling spur gear transmission.

7. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 6, characterized in that, In step 2.1.2, based on the basic structure of the rotor system of the gear transmission device, a simplified spring model for bending-torsional coupling vibration analysis of the meshing spur gear transmission is constructed; the specific process is as follows: 2.1.2.1: Based on the basic structure of the rotor system of the gear transmission device, construct the transmission shaft, driving gear, and driven gear in the finite element software; 2.1.2.2: Using the combined meshing stiffness and meshing damping as the dynamic characteristics of the meshing gear pair structure in the finite element software, a simplified spring model for the bending-torsional coupling vibration analysis of the meshing coupled spur gear transmission is obtained. The dynamic characteristics of the meshing gear pair structure include: gear pair meshing coupling damping c and gear pair meshing coupling stiffness k.

8. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 7, characterized in that, In step 2.2, a simplified model of single-tooth meshing of the gear pair is constructed based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission. The specific process is as follows: Step 2.2.1: In the finite element method software, use mass points as the gear teeth of the driving and driven gears; the specific process is as follows: In the finite element method software, X mass points are used as the tooth parts of X driving and driven gears in the de-toothed section; each tooth corresponds to one mass point. The tooth cross-section is the cross-section of the tooth on the root circle; X is the number of teeth, which is a positive integer; Step 2.2.2: In the finite element method software, an equivalent spring is used to represent the single-tooth meshing coupling between the driving gear and the driven gear, resulting in a simplified model of the single-tooth meshing of the gear pair; the specific process is as follows: Step 2.2.2.1: Determine the timing for single-tooth meshing coupling analysis; the timing for single-tooth meshing coupling analysis is selected from the point of minimum stiffness in the single-tooth meshing zone. Step 2.2.2.2: Determine the mass points of the driving gear teeth and driven gear teeth at the moment of single-tooth meshing coupling analysis, and obtain the mass point A of the driving gear teeth and the mass point B of the driven gear teeth; Step 2.2.2.3: Between the mass point A of the driving gear tooth and the mass point B of the driven gear tooth, a first equivalent spring is used as the driving gear and the driven gear to perform single gear tooth meshing coupling; The first equivalent spring is defined using the Connector element in the finite element analysis software; a simplified model of single-tooth meshing of the gear pair is obtained.

9. The linear simplification method for the finite element model of a gear transmission device rotor system according to claim 8, characterized in that, In step 2.3, a simplified model of double-tooth meshing of the gear pair is constructed based on the simplified spring model for bending-torsional coupling vibration analysis of meshing spur gear transmission. The specific process is as follows: Step 2.3.1: In the finite element method software, use mass points as the gear teeth of the driving and driven gears; the specific process is as follows: In the finite element method software, X mass points are used as the tooth parts of X driving and driven gears in the de-toothed section; each tooth corresponds to one mass point. The tooth cross section is the cross section of the tooth on the root circle; X is the number of teeth, and X is a positive integer. Step 2.3.2: In the finite element method software, two equivalent springs are used to represent the single-tooth meshing coupling between the driving gear and the driven gear, resulting in a simplified double-tooth meshing model of the gear pair; the specific process is as follows: Step 2.3.2.1: Determine the timing for the double-tooth meshing coupling analysis; the timing for the double-tooth meshing coupling analysis is selected from the point of maximum stiffness in the double-tooth meshing region. Step 2.3.2.2: Determine the mass points of the active gear teeth and passive gear teeth at the moment of double-tooth meshing coupling analysis, and obtain the mass points A1, A2, B1, and B2 of the active gear teeth. Step 2.3.2.3: A second equivalent spring is used between the mass point A1 of the driving gear tooth and the mass point B1 of the driven gear tooth to characterize one of the meshing couplings of the double tooth meshing coupling; Between the mass point A2 of the driving gear tooth and the mass point B2 of the driven gear tooth, a third equivalent spring is used to characterize the other meshing coupling of the double tooth meshing coupling of the gear teeth; The second and third equivalent springs are defined using Connector elements in finite element analysis software; A simplified model of double-tooth meshing of the gear pair is obtained.

Images