A method and apparatus for calculating the coupling effect of adjacent meshing points on a gear meshing line

Abstract

The application discloses a kind of calculation method and device of coupling action of adjacent engagement point on gear meshing line, including the non-uniform load difference generated by non-equilibrium bending moment of adjacent engagement point, according to the basic parameters of helical gear and the non-equilibrium bending moment, the coupling action stiffness between adjacent coupling points on contact line is calculated;According to the coupling action stiffness between adjacent coupling points on contact line, based on the static equilibrium principle, the solving model of helical gear load distribution is constructed, the solving model is repeatedly updated and calculated, and the load distribution of each engagement point along the contact line of helical gear is obtained, according to the load distribution of each engagement point, the single-tooth comprehensive engagement stiffness of helical gear pair is calculated.The application does not need to preset the load distribution of different engagement points on meshing line in the process of engagement, does not need to determine the value of relevant influencing factors by finite element model calculation, has accuracy and high efficiency when calculating the comprehensive engagement stiffness of gear pair.

Description

Technical Field

[0001] This invention relates to the field of gear meshing technology, specifically a method and apparatus for calculating the coupling effect of adjacent meshing points on a gear meshing line. Background Technology

[0002] The main function of gear transmission systems is to transmit power and motion. Due to their advantages such as stable transmission ratio, large power transmission, stable transmission, high load-bearing capacity, and long service life, they are widely used in complex mechanical equipment in various fields such as rail transportation, ships, and aerospace. They are the most common type of mechanical transmission.

[0003] During gear meshing, the number of meshing tooth pairs exhibits a periodic alternation, resulting in a time-varying periodicity in the overall meshing stiffness of the gear transmission. Transmission errors mainly include manufacturing errors, assembly errors, gear geometric parameters such as tooth profile modifications, and elastic deformation of the gear under load. The time-varying meshing stiffness of the gear is the primary excitation of the gear transmission system, and accurately obtaining the time-varying meshing stiffness of the gear pair is a prerequisite for dynamic analysis of the gear system. Errors inevitably occur during the machining, manufacturing, and installation of gear pairs, affecting their axial meshing characteristics. To improve the meshing state and reduce vibration and noise in the gear system, tooth profile and tooth direction modifications are necessary. After modification, the coupling effect between different meshing points along the meshing line is intensified during meshing, and the load distribution differences between different meshing points increase.

[0004] Currently, most studies on calculating the meshing stiffness of gear pairs with modified tooth profiles neglect the coupling interaction between adjacent meshing points. Although a few studies have addressed this issue, existing research on the coupling effect between adjacent meshing points requires pre-determining the influencing factors and pre-setting the loads acting on each meshing point, then using the deformation difference between adjacent meshing points to calculate the overall meshing stiffness. However, when applied to helical gears, when the basic design parameters of the helical gear change, the initial values ​​of these influencing factors may no longer be applicable, requiring iterative updates. This iterative update process is complex and time-consuming, leading to low computational efficiency. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies when applied to helical gears. When the basic design parameters of helical gears change, the initial values ​​of these influencing factors may no longer be applicable, requiring iterative updates. However, the iterative update process is complex and time-consuming, leading to low computational efficiency. This invention provides a method and apparatus for calculating the coupling effect of adjacent meshing points on the gear meshing line. This method achieves the effect of not requiring prior assumptions about the load distribution of different meshing points on the meshing line during the meshing process, not requiring the determination of relevant influencing factors through finite element model calculations, and not requiring iterative update calculations. It is accurate and efficient in calculating the comprehensive meshing stiffness of gear pairs.

[0006] The objective of this invention is achieved through the following technical solution: One aspect provides a method for calculating the coupling effect between adjacent meshing points on the gear meshing line, including: Based on the difference in meshing force between different meshing points along the contact line of the helical gear, the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points is calculated, and the coupling stiffness between adjacent coupling points on the contact line is calculated based on the basic parameters of the helical gear and the unbalanced bending moment; wherein, the basic parameters of the helical gear include at least the elastic modulus, shear modulus and moment of inertia. Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of helical gears is constructed based on the static balance principle. The solution model is repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear. Based on the load distribution at each meshing point, the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated.

[0007] In one possible design, the calculation of the unbalanced bending moment generated by the non-uniform load difference at adjacent meshing points includes: The unbalanced bending moment generated by the non-uniform load difference on the meshing force components at the end faces of adjacent meshing points is calculated using the following formula: ; in, Indicates the y-axis component of the meshing force. Bending moment generated by the plane Indicates the y-axis component of the meshing force. The torque generated by the plane This represents the bending torque generated by the x-axis component of the meshing force. Indicates the first One helical gear meshing point, Indicates the first One helical gear meshing point, Indicates the base circle helix angle. Indicates the engagement angle. This represents the distance along the tooth profile between the meshing points of adjacent tooth slices. This indicates the tooth width of the helical gear slice. .

[0008] In one possible design, based on the basic parameters of the helical gear and the unbalanced bending moment, the coupling stiffness between adjacent coupling points on the contact line is calculated, including: Based on the elastic modulus, shear modulus, and moment of inertia, an equation is constructed based on the potential energy principle to express the energy stored in the helical gear slices by the unbalanced bending moment of the variable cross-section cantilever beam. The equation is as follows: ; in, express Planar energy components, express Planar energy components, express Planar energy components, Indicates the elastic modulus. Indicates shear modulus, express The rotational inertia components of the plane, express The rotational inertia components of the plane, express The rotational inertia components of the plane, express Planar energy components, express Planar energy components, express Planar energy components; Based on the energy equation, the stiffness component of the coupling effect between adjacent coupling points on the contact line is calculated using the following formula: ; in, Indicates the cantilever beam model along x Effective length of the shaft; The coupling stiffness between adjacent meshing points on the contact line is calculated based on the coupling stiffness component between adjacent coupling points on the contact line. The calculation formula is as follows: ; in, It represents the coupling stiffness between adjacent meshing points on the contact line.

[0009] In one possible design, the rotational inertia component Component of rotational inertia and the component of rotational inertia The calculation formulas are as follows: ; in, This represents 1 / 2 tooth thickness of the micro-section.

[0010] In one possible design, based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gear is constructed based on the principle of static equilibrium. This solution model is then repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear, including: Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gear is constructed based on the principle of static equilibrium. The model expression is as follows: ; in, These represent the meshing forces at different meshing points along the contact line. These represent the tooth stiffness of each gear slice. This indicates the coupling stiffness between the first and second engagement points. This indicates the coupling stiffness between the second and third engagement points, and so on. This represents the coupling stiffness between the (n-1)th meshing point and the nth meshing point. These represent the tooth profile error of each gear slice. This indicates the static transmission error during gear meshing. This represents the driving torque applied to the gear. Indicates the base circle radius; The solution model is repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear; if the calculated meshing force is negative, it means that there is no meshing at the corresponding meshing point, and the meshing force is zero.

[0011] In one possible design, the combined meshing stiffness of a single tooth of the helical gear pair is calculated based on the load distribution at each meshing point, using the following formula: ; in, This represents the combined meshing stiffness of a single tooth in a helical gear pair. Represents the nth gear slice in the nth gear slice. The profile error of a gear slice.

[0012] The second aspect provides a calculation device for the coupling effect of adjacent meshing points on a gear meshing line, comprising: The coupling effect calculation module is used to calculate the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points based on the difference in meshing force between different meshing points of the helical gear along the contact line, and to calculate the coupling effect stiffness between adjacent coupling points on the contact line based on the basic parameters of the helical gear and the unbalanced bending moment; wherein, the basic parameters of the helical gear include at least the elastic modulus, shear modulus and moment of inertia. The meshing stiffness calculation module is used to construct a solution model of the load distribution of helical gears based on the static balance principle, according to the coupling stiffness between adjacent coupling points on the contact line. The solution model is repeatedly updated and calculated to obtain the load distribution of each meshing point of the helical gears. Based on the load distribution of each meshing point, the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated.

[0013] A third aspect provides a computer device comprising a memory, a processor, and a transceiver connected in sequence, wherein the memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute a method for calculating the coupling effect of adjacent meshing points on a gear meshing line as described in any possible design of the first aspect.

[0014] The fourth aspect provides a computer-readable storage medium storing instructions that, when executed on a computer, perform a method for calculating the coupling effect of adjacent meshing points on a gear meshing line as described in any possible design of the first aspect.

[0015] The advantages of this invention compared to the prior art are: This invention calculates the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points based on the distribution difference of the meshing force of helical gears along the contact line. Then, based on the basic parameters of the helical gears and the unbalanced bending moment, it calculates the coupling stiffness between adjacent coupling points on the contact line. Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gears is constructed based on the static balance principle. The solution model is repeatedly updated to obtain the load distribution at each meshing point of the helical gears. Based on the load distribution at each meshing point, the comprehensive meshing stiffness of a single tooth of the helical gear pair is calculated. Therefore, it eliminates the need to pre-assume the load distribution at different meshing points on the meshing line during the meshing process, and eliminates the need to obtain definite values ​​of relevant influencing factors through finite element model calculations. This method is accurate and efficient in calculating the comprehensive meshing stiffness of the gear pair, and can more accurately reflect the dynamic characteristics of the gear transmission system under modified state conditions. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the calculation method for the coupling effect between adjacent meshing points on the gear meshing line according to an embodiment of this application. Figure 2 This is a schematic diagram of the helical gear meshing force in an embodiment of this application; Figure 3 This is a diagram showing the distribution of meshing force along the contact line in the embodiments of this application; Figure 4(a) is a schematic diagram of the bending moment generated by the meshing force y-axis component in the xoz plane and the torque generated in the yoz plane in the embodiment of this application; Figure 4(b) is a schematic diagram of the bending torque generated by the x-axis component of the meshing force in the embodiment of this application; Figure 5 This is a schematic diagram illustrating the effect of coupling stiffness on overall meshing stiffness in the embodiments of this application; Figures 6(a), 6(b), and 6(c) are comparison diagrams of the comprehensive stiffness of helical gears with different helix angles according to embodiments of this application, wherein (a) 10°; (b) 15°; and (c) 20°. Figures 7(a), 7(b), and 7(c) show the meshing characteristic curves of gears with different modified lengths according to embodiments of this application, where (a) is the meshing stiffness; (b) is the load transmission error; and (c) is the load distribution coefficient. Figures 8(a), 8(b), and 8(c) are schematic diagrams of the load distribution on the helical gear teeth of different modified lengths in embodiments of this application, wherein (a) L n =0.4, C n =0.8; (b) L n =0.8, C n =0.8; (c) L n =1.2, C n =0.8. Detailed Implementation

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, and not all of them. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention. It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0020] Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0021] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0022] Example like Figures 2-3 As shown, when the gear is a helical gear, the stiffness components differ between different meshing points on the helical gear line, especially when there are modification and assembly errors along the axial direction, the differences are more pronounced. Figure 2 The diagram shows the distribution of meshing force along the contact line. It can be seen that different meshing points on the involute tooth profile are located at different positions. To ensure consistent deformation along the contact line under load, different meshing forces will be generated at each meshing point. Figure 3 The diagram shows the distribution of meshing force along the contact line. The first and last gear slices are coupled with only one adjacent meshing point. When the j-th random helical gear meshing point is taken as a reference, both helical gear meshing points on either side will affect it. As can be seen from the diagram, the load at different meshing points is uneven, with a load gradient along the contact line, causing unbalanced bending moments relative to the centroid of adjacent meshing points. Based on this, this application proposes the following calculation method for the coupling effect of adjacent meshing points on the gear meshing line to achieve accurate and efficient calculation of the overall meshing stiffness of the gear pair.

[0023] like Figure 1 As shown, one embodiment of this application provides a method for calculating the coupling effect of adjacent meshing points on the gear meshing line, including but not limited to steps S1-S2: Step S1. Based on the difference in meshing force between different meshing points along the contact line of the helical gear, calculate the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points, and calculate the coupling stiffness between adjacent coupling points on the contact line based on the basic parameters of the helical gear and the unbalanced bending moment; wherein, the basic parameters of the helical gear include at least the elastic modulus, shear modulus and moment of inertia; It should be noted that, since the axial component of the meshing force at each meshing point is distributed along the contact line and there is no unbalanced moment, preferably, this embodiment only considers the unbalanced bending moment caused by the end face meshing force component. The schematic diagrams of the unbalanced bending moment effect of the load difference on adjacent meshing points are shown in Figures 4(a) and 4(b). Specifically, in one possible design, calculating the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points includes: The unbalanced bending moment generated by the non-uniform load difference on the meshing force components at the end faces of adjacent meshing points is calculated using the following formula: ; in, Indicates the y-axis component of the meshing force. Bending moment generated by the plane Indicates the y-axis component of the meshing force. The torque generated by the plane This represents the bending torque generated by the x-axis component of the meshing force. Indicates the first One helical gear meshing point, Indicates the first One helical gear meshing point, Indicates the base circle helix angle. Indicates the engagement angle. This represents the distance along the tooth profile between the meshing points of adjacent tooth slices. This indicates the tooth width of the helical gear slice. .

[0024] Step S2. Based on the coupling stiffness between adjacent coupling points on the contact line, construct a solution model for the load distribution of the helical gear based on the static balance principle. Repeatedly update the solution model to obtain the load distribution of each meshing point of the helical gear. Based on the load distribution of each meshing point, calculate the single-tooth comprehensive meshing stiffness of the helical gear pair.

[0025] In one specific embodiment of step S2, based on the basic parameters of the helical gear and the unbalanced bending moment, the coupling stiffness between adjacent coupling points on the contact line is calculated, including: Based on the elastic modulus, shear modulus, and moment of inertia, an equation is constructed based on the potential energy principle to express the energy stored in the helical gear slices by the unbalanced bending moment of the variable cross-section cantilever beam. The equation is as follows: ; in, express Planar energy components, express Planar energy components, express Planar energy components, Indicates the elastic modulus. Indicates shear modulus, express The rotational inertia components of the plane, express The rotational inertia components of the plane, express The rotational inertia components of the plane, express Planar energy components, express Planar energy components, express Planar energy components; Based on the energy equation, the stiffness component of the coupling effect between adjacent coupling points on the contact line is calculated using the following formula: ; in, Indicates the cantilever beam model along x Effective length of the shaft; The coupling stiffness between adjacent meshing points on the contact line is calculated based on the coupling stiffness component between adjacent coupling points on the contact line. The calculation formula is as follows: ; in, It represents the coupling stiffness between adjacent meshing points on the contact line.

[0026] In one specific embodiment of step S2, the rotational inertia component Component of rotational inertia and the component of rotational inertia The calculation formulas are as follows: ; in, This represents 1 / 2 tooth thickness of the micro-section.

[0027] like Figure 5As shown, the effect of coupling stiffness on the overall meshing stiffness is illustrated. The coupling interaction between adjacent meshing points is reflected in the total deformation under load difference. Based on this, in a specific embodiment of step S2, a solution model for the load distribution of the helical gear is constructed based on the static equilibrium principle according to the coupling stiffness between adjacent coupling points on the contact line. The solution model is repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear, including: (1) Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gear is constructed based on the static equilibrium principle. The model expression is as follows: ; in, These represent the meshing forces at different meshing points along the contact line. These represent the tooth stiffness of each gear slice. This indicates the coupling stiffness between the first and second engagement points. This indicates the coupling stiffness between the second and third engagement points, and so on. This represents the coupling stiffness between the (n-1)th meshing point and the nth meshing point. These represent the tooth profile error of each gear slice. This indicates the static transmission error during gear meshing. This represents the driving torque applied to the gear. Indicates the base circle radius; As can be seen from the above model, the formula contains... n +1 deformation-coordination equilibrium equation equals the unknown variable ( F 1, F 2, …, F n , δ L The number of meshing points can be determined by repeatedly updating the calculations, thus enabling a unique solution to the above model, obtaining the meshing force at each meshing point, and subsequently the load distribution at each meshing point and the static transmission error after loading.

[0028] (2) The solution model is repeatedly updated and calculated to obtain the load distribution of each meshing point of the helical gear; if the calculated meshing force is negative, it means that there is no meshing at the corresponding meshing point, and the meshing force is zero at this time.

[0029] In one specific embodiment of step S2, the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated based on the load distribution at each meshing point, using the following formula: ; in, This represents the combined meshing stiffness of a single tooth in a helical gear pair. Represents the nth gear slice in the nth gear slice. The tooth profile error of a single gear slice; wherein, the comprehensive meshing stiffness of a single tooth includes tooth stiffness, gear body stiffness, contact stiffness and coupling stiffness of adjacent meshing points.

[0030] Based on the above disclosure, this application embodiment calculates the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points according to the difference in meshing force between different meshing points of the helical gear along the contact line, and calculates the coupling stiffness between adjacent coupling points on the contact line according to the basic parameters of the helical gear and the unbalanced bending moment; based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gear is constructed based on the static balance principle, and the solution model is repeatedly updated to obtain the load distribution of each meshing point of the helical gear, and the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated according to the load distribution of each meshing point; thus, it is not necessary to pre-assume the load distribution of different meshing points on the meshing line during the meshing process, and it is not necessary to obtain the definite values ​​of relevant influencing factors through finite element model calculation, which has accuracy and efficiency in calculating the comprehensive meshing stiffness of the gear pair, and can more accurately reflect the dynamic characteristics of the gear transmission system in the modified state.

[0031] The second aspect provides a calculation device for the coupling effect of adjacent meshing points on a gear meshing line, comprising: The coupling effect calculation module is used to calculate the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points based on the difference in meshing force between different meshing points of the helical gear along the contact line, and to calculate the coupling effect stiffness between adjacent coupling points on the contact line based on the basic parameters of the helical gear and the unbalanced bending moment; wherein, the basic parameters of the helical gear include at least the elastic modulus, shear modulus and moment of inertia. The meshing stiffness calculation module is used to construct a solution model of the load distribution of helical gears based on the static balance principle, according to the coupling stiffness between adjacent coupling points on the contact line. The solution model is repeatedly updated and calculated to obtain the load distribution of each meshing point of the helical gears. Based on the load distribution of each meshing point, the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated.

[0032] The working process, working details and technical effects of the aforementioned computer-readable storage medium provided in the second aspect of this embodiment can be found in the method described in the first aspect or any possible design of the first aspect, and will not be repeated here.

[0033] A third aspect provides a computer device comprising a memory, a processor, and a transceiver connected in sequence, wherein the memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute a method for calculating the coupling effect of adjacent meshing points on a gear meshing line as described in any possible design of the first aspect.

[0034] Specifically, the memory may include, but is not limited to, Random-Access Memory (RAM), Read-Only Memory (ROM), Flash Memory, First-In-First-Out (FIFO) Memory, and / or First-In-Last-Out (FILO) Memory, etc.; the processor may not be limited to the STM32F105 series microprocessor; the transceiver may be, but is not limited to, a WiFi (Wireless Fidelity) wireless transceiver, a Bluetooth wireless transceiver, a GPRS (General Packet Radio Service) wireless transceiver, and / or a ZigBee (a low-power LAN protocol based on the IEEE 802.15.4 standard) wireless transceiver, etc. Furthermore, the computer device may also include, but is not limited to, a power module, a display screen, and other necessary components.

[0035] The working process, working details and technical effects of the aforementioned computer device provided in the third aspect of this embodiment can be found in the method described in the first aspect or any possible design of the first aspect, and will not be repeated here.

[0036] Fourthly, the present invention provides a computer-readable storage medium storing instructions that, when executed on a computer, perform a method for calculating the coupling effect of adjacent meshing points on a gear meshing line as described in any possible design of the first aspect.

[0037] The computer-readable storage medium refers to a carrier for storing data, which may include, but is not limited to, floppy disks, optical disks, hard disks, flash memory, USB flash drives and / or memory sticks, etc. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices.

[0038] The working process, working details and technical effects of the aforementioned computer-readable storage medium provided in the fourth aspect of this embodiment can be found in the method described in the first aspect or any possible design of the first aspect, and will not be repeated here.

[0039] Application examples Figures 6-8 show the calculation results of the single-tooth comprehensive meshing stiffness using the above-mentioned calculation method of coupling effect between adjacent meshing points on the gear meshing line, and the comparison with existing single-tooth comprehensive meshing stiffness calculation methods, as follows: The basic parameters of the helical gear used in this application example are shown in Table 1 below: Table 1 Basic Design Parameters of Helical Gears Figures 6(a), 6(b), and 6(c) show a comparison of the combined meshing stiffness of helical gears with different helix angles obtained by the method of this application and existing calculation methods. As can be seen from the figures, the meshing stiffness calculated by the existing model 1, which does not consider the coupling effect between adjacent loaded teeth, deviates significantly from the finite element results. For the meshing stiffness results obtained by the existing model 2, there are certain deviations for both three-tooth and two-tooth meshing, which may be due to the poor universality of the influencing factor values ​​extracted from the finite element results. Because the structural coupling effect is considered, the finite element results for the three different helix angles of 10°, 15°, and 20° all agree well with those of model 3 (the model using the method of this application). The maximum relative errors of the meshing stiffness calculated by Model 2 and the finite element model were 16.37%, 12.70%, and 5.91%, respectively; while the maximum relative errors of the meshing stiffness of helical gears for the three helix angles by Model 3 and the finite element model were 5.15%, 5.31%, and 3.53%, respectively. The difference in meshing stiffness calculated by Model 2 and Model 3 was smallest when the helix angle was 20°. As the helix angle decreased, the difference in the calculated results between the two models became increasingly apparent when the helix angle was 20°. On helical gear pairs with large helix angles, the load differences between adjacent meshing points were more significant.

[0040] Figures 7(a), 7(b), and 7(c) show the effects of different modification lengths on the meshing characteristics of helical gears. The helix angle of the helical gears used was 15°, and the tooth width and hub bore radius were both 30 mm. The calculated contact ratio of the helical gears used was 2.249. It can be seen that, regardless of whether it is three-tooth meshing or two-tooth meshing, the minimum meshing stiffness amplitude increases with the increase of modification length. When the modification amount is Cn=0.8, the three-tooth meshing decreases by approximately 10.59%, 14.04%, and 14.04%, while the two-tooth meshing decreases by approximately 7.79%, 12.32%, and 14.67%. The load transfer error curve shows the opposite trend to the meshing stiffness results. It is worth mentioning that even a small modification can lead to a considerable change in the load distribution coefficient, as shown in Figure 7(c). With the increase of modification length, the range and amplitude of the load distribution coefficient first increase, and when the load distribution coefficient reaches its maximum value of 1, the range of the load distribution coefficient increases further.

[0041] Figures 8(a), 8(b), and 8(c) show the load distribution of helical gear teeth with different modification lengths. As can be seen from the figures, with the increase of the modification length, sharp-angle contact between the tooth tip and root is avoided, thus increasing the load distribution coefficient in the middle region and consequently increasing the load distribution. For a large constant modification length of Cn=0.8, when the modification length reaches Ln=1.2, the load distribution in the tooth first increases and then decreases, indicating that there is a potential optimal value for the modification length. A modification length that is too long or too short will adversely affect the dynamic performance of the gear.

[0042] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for calculating the coupling effect between adjacent meshing points on a gear meshing line, characterized in that, include: Based on the difference in meshing force between different meshing points along the contact line of the helical gear, the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points is calculated, and the coupling stiffness between adjacent coupling points on the contact line is calculated based on the basic parameters of the helical gear and the unbalanced bending moment; wherein, the basic parameters of the helical gear include at least the elastic modulus, shear modulus and moment of inertia. Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of helical gears is constructed based on the static balance principle. The solution model is repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear. Based on the load distribution at each meshing point, the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated. Calculate the unbalanced bending moment generated by the non-uniform load difference at adjacent meshing points, including: The unbalanced bending moment generated by the non-uniform load difference on the meshing force components at the end faces of adjacent meshing points is calculated using the following formula: ; in, Indicates the y-axis component of the meshing force. Bending moment generated by the plane Indicates the y-axis component of the meshing force. The torque generated by the plane This represents the bending torque generated by the x-axis component of the meshing force. Indicates the first One helical gear meshing point, Indicates the first One helical gear meshing point, Indicates the base circle helix angle. Indicates the engagement angle. This represents the distance along the tooth profile between the meshing points of adjacent tooth slices. This indicates the tooth width of the helical gear slice. ; Based on the basic parameters of the helical gear and the unbalanced bending moment, calculate the coupling stiffness between adjacent coupling points on the contact line, including: Based on the elastic modulus, shear modulus, and moment of inertia, an equation is constructed based on the potential energy principle to express the energy stored in the helical gear slices by the unbalanced bending moment of the variable cross-section cantilever beam. The equation is as follows: ； in, express Planar energy components, express Planar energy components, express Planar energy components, Indicates the elastic modulus. Indicates shear modulus, express The rotational inertia components of the plane, express The rotational inertia components of the plane, express The rotational inertia components of the plane, express Planar energy components, express Planar energy components, express Planar energy components; Based on the energy equation, the stiffness component of the coupling effect between adjacent coupling points on the contact line is calculated using the following formula: ； in, Indicates the cantilever beam model along x Effective length of the shaft; The coupling stiffness between adjacent meshing points on the contact line is calculated based on the coupling stiffness component between adjacent coupling points on the contact line. The calculation formula is as follows: ； in, This indicates the coupling stiffness between adjacent meshing points on the contact line; Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gear is constructed based on the static equilibrium principle. The solution model is repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear, including: Based on the coupling stiffness between adjacent coupling points on the contact line, a solution model for the load distribution of the helical gear is constructed based on the principle of static equilibrium. The model expression is as follows: ； in, These represent the meshing forces at different meshing points along the contact line. These represent the tooth stiffness of each gear slice. This indicates the coupling stiffness between the first and second engagement points. This indicates the coupling stiffness between the second and third engagement points, and so on. This represents the coupling stiffness between the (n-1)th meshing point and the nth meshing point. These represent the tooth profile error of each gear slice. This indicates the static transmission error during gear meshing. This represents the driving torque applied to the gear. Indicates the base circle radius; The solution model is repeatedly updated and calculated to obtain the load distribution at each meshing point of the helical gear; if the calculated meshing force is negative, it means that there is no meshing at the corresponding meshing point, and the meshing force is zero.

2. The method for calculating the coupling effect of adjacent meshing points on the gear meshing line according to claim 1, characterized in that, Components of rotational inertia Component of rotational inertia and the component of rotational inertia The calculation formulas are as follows: ； in, This represents 1 / 2 tooth thickness of the micro-section.

3. The method for calculating the coupling effect of adjacent meshing points on the gear meshing line according to claim 1, characterized in that, Based on the load distribution at each meshing point, the single-tooth combined meshing stiffness of the helical gear pair is calculated using the following formula: ； in, This represents the combined meshing stiffness of a single tooth in a helical gear pair. Represents the nth gear slice in the nth gear slice. The profile error of a gear slice.

4. A calculation device for the coupling effect of adjacent meshing points on a gear meshing line, used to implement the calculation method for the coupling effect of adjacent meshing points on a gear meshing line as described in any one of claims 1-3, characterized in that, include: The coupling effect calculation module is used to calculate the unbalanced bending moment generated by the non-uniform load difference on adjacent meshing points based on the distribution difference of the helical gear meshing force along the contact line, and to calculate the coupling effect stiffness between adjacent coupling points on the contact line based on the basic parameters of the helical gear and the unbalanced bending moment; wherein, the basic parameters of the helical gear include at least the elastic modulus, shear modulus and moment of inertia; The meshing stiffness calculation module is used to construct a solution model of the load distribution of helical gears based on the static balance principle, according to the coupling stiffness between adjacent coupling points on the contact line. The solution model is repeatedly updated and calculated to obtain the load distribution of each meshing point of the helical gears. Based on the load distribution of each meshing point, the single-tooth comprehensive meshing stiffness of the helical gear pair is calculated.

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