A method for calculating time-varying meshing stiffness of spur gears based on thermal deformation of crack-wear coupling

Abstract

This invention discloses a method for calculating the time-varying meshing stiffness of crack-wear coupled spur gears based on thermal deformation. The method includes: establishing a meshing coordinate system for the spur gear pair and inputting parameters; calculating the transient temperature field and thermoelastic displacement field during meshing; projecting the thermoelastic displacement along the meshing line direction to correct the contact point position, contact path length, base circle tooth pitch, actual overlap, and single / double tooth meshing interval; updating the tooth surface wear depth based on the contact pressure and relative sliding velocity corrected by thermal deformation; updating the tooth root crack length based on the stress intensity factor under the influence of temperature, thermal stress, and wear; constructing a unified damage section of crack-wear-thermal deformation; and obtaining the time-varying meshing stiffness of the spur gear pair through thermal deformation equivalent compliance and load distribution feedback iteration. This invention can improve the accuracy of calculating the time-varying meshing stiffness of spur gears under high load, high speed, temperature rise, and fault degradation conditions.

Description

Technical Field

[0001] This invention belongs to the technical fields of gear dynamics, thermoelastic contact analysis, fault degradation modeling and transmission system health monitoring, specifically involving a method for calculating the time-varying meshing stiffness of crack-wear coupled spur gears based on thermal deformation. Background Technology

[0002] Spur gears are widely used in aerospace, vehicle transmissions, construction machinery, wind power equipment, robot joints, and precision transmission systems. Time-varying meshing stiffness is a key parameter in gear dynamics modeling, vibration response analysis, fault diagnosis, and remaining life prediction; its calculation accuracy directly affects the accuracy of predicting the dynamic response of gear systems.

[0003] Existing methods typically calculate meshing stiffness based on potential energy methods, finite element methods, or analytical-numerical hybrid methods, mainly considering conventional stiffness components such as tooth bending, shearing, radial compression, Hertzian contact, matrix flexible deformation, and inter-tooth structural coupling. In the study of faulty gears, some methods further consider the influence of tooth root cracks or tooth surface wear on meshing stiffness.

[0004] However, under high load, high speed, or long-term operating conditions, the frictional temperature rise of the tooth surface will cause thermal deformation, which in turn changes the contact point position, contact path, base circle tooth pitch, actual overlap, and single / double tooth meshing range. At the same time, thermal deformation will also change the contact pressure and relative sliding speed, causing wear evolution, crack propagation, effective cross-section degradation, meshing stiffness, and load distribution to interact. If only a cold tooth profile model, a single crack model, a single wear model, or only material parameters are modified, it is difficult to accurately characterize the above closed-loop coupling effect. Summary of the Invention

[0005] The present invention provides a method for calculating the time-varying meshing stiffness of crack-wear coupled spur gears based on thermal deformation, which includes the following steps.

[0006] 1) Establish a spur gear pair meshing model and input parameters. Input gear geometric parameters, material thermodynamic parameters, operating condition parameters, crack parameters, and wear parameters.

[0007] 2) Calculate the transient temperature field and thermoelastic displacement field. The transient temperature field is obtained based on frictional heat generation, tooth body heat conduction, and boundary heat transfer, and the thermoelastic displacement field is solved.

[0008] 3) Correct the meshing state. Project the thermoelastic displacement along the meshing line direction to correct the contact point position, contact path length, base circle tooth pitch and actual overlap, and re-determine the single-tooth / double-tooth meshing interval.

[0009] 4) Calculate the tooth surface wear depth. Update the tooth surface wear depth based on the contact pressure and relative sliding velocity after thermal deformation correction.

[0010] 5) Calculate the tooth root crack propagation. Update the tooth root crack length based on the stress intensity factor under the influence of temperature, thermal stress, and wear.

[0011] 6) Construct a unified damage section. Subtract the wear removal area and the crack damage area from the thermally deformed tooth cross-section area to obtain a unified damage section under the coupled action of crack-wear-thermal deformation.

[0012] 7) Calculate the equivalent meshing stiffness. Based on the uniform damage section, temperature-corrected material parameters, meshing state after thermal deformation correction, and inter-tooth structural coupling relationship, calculate the equivalent meshing stiffness of each tooth pair.

[0013] 8) Calculate the equivalent compliance of thermal deformation. Obtain the load sensitivity of thermoelastic displacement along the meshing line using the load perturbation method, and introduce it as a compliance term into the total compliance.

[0014] 9) Solve the time-varying meshing stiffness using closed-loop iterative methods. Redistribute the meshing force according to the stiffness of each tooth pair, and feed the updated meshing force back to the temperature field, wear model, and crack propagation model until the meshing stiffness and meshing force converge.

[0015] A further aspect of the present invention is to project the thermoelastic displacement caused by the temperature field onto the meshing line direction, and use this projection amount to correct the contact point position, specifically as follows:

[0016]

[0017]

[0018] In the formula, For the first The amount of thermal deformation of the teeth along the meshing line; This is the unit normal vector of the meshing line after thermal deformation correction; , The driving wheel and the driven wheel are respectively at the contact point Thermoelastic displacement at the location; This refers to the location of the contact point in a cold, undeformed state. The contact point position is corrected for thermal deformation. Equations (1) and (2) can be used to convert the local thermal expansion caused by the temperature field into a correction amount for the meshing state.

[0019] Furthermore, the method recalculates the actual overlap ratio based on the contact path length and base circle tooth pitch corrected for thermal deformation, and determines the number of meshing tooth pairs accordingly, specifically as follows:

[0020]

[0021]

[0022] In the formula, This represents the actual overlap after thermal deformation correction; This is the actual contact path length after thermal deformation correction; The base circle tooth pitch is corrected for thermal deformation. This represents the number of meshing tooth pairs at the current moment. When the contact point falls into the single-tooth meshing zone... Take 1, when the contact point falls into the double-tooth meshing area. Take 2.

[0023] Furthermore, the method incorporates the thermally deformed corrected contact pressure and sliding distance into the wear depth update, and incorporates temperature, thermal stress, and wear state into the crack propagation calculation, specifically:

[0024]

[0025]

[0026]

[0027] In the formula, For gears At the tooth surface position and number of loops The cumulative wear depth below; For cyclic increments; This is the temperature-dependent wear coefficient; The contact pressure after thermal deformation correction; This is the sliding distance after thermal deformation correction; Temperature-corrected hardness; The length of the tooth root crack; This is the temperature-dependent crack propagation coefficient; The crack propagation index; The amplitude of the Type I stress intensity factor is calculated to account for the effects of wear and temperature. This is the geometric correction factor; The crack angle; The stress amplitude at the critical section of the tooth root, taking into account the effects of wear and thermal stress.

[0028] Furthermore, the method uses the thermally deformed tooth cross-sectional area as a basis, and simultaneously subtracts the wear removal area and the crack damage area within the same cross-sectional area to construct a unified damage cross-section of crack-wear-thermal deformation, specifically as follows:

[0029]

[0030]

[0031]

[0032] In the formula, This refers to the cross-sectional area of ​​the gear teeth after thermal deformation. This is the area to be removed due to wear. This is the area of ​​crack damage; The effective load-bearing section region after the coupled effects of cracking, wear, and thermal deformation; Effective cross-sectional area; For effective centroid; Effective moment of inertia; Let be a cross-sectional area micro-element. Equations (8) to (10) can avoid repeated deductions or insufficient coupling when correcting cracks and wear separately.

[0033] Furthermore, the method calculates the equivalent compliance of thermal deformation using the load perturbation method and incorporates it, along with the conventional tooth compliance, into the total compliance. Specifically:

[0034]

[0035]

[0036] In the formula, For gears The Middle Equivalent compliance to thermal deformation of teeth; This is the thermoelastic displacement along the meshing line direction; For the first For tooth meshing force; This represents the change in load. For the first Equivalent meshing stiffness of teeth; Hertzian contact stiffness; For the overall stiffness of the gear teeth; For the flexible deformation stiffness of the matrix; This is the inter-tooth structure coupling compliance term.

[0037] Furthermore, the method redistributes the meshing force according to the stiffness of each meshing tooth pair, and feeds back the updated meshing force to the frictional heat flux density, contact pressure, wear model, and crack propagation model, specifically as follows:

[0038]

[0039]

[0040] In the formula, For the first In the nth iteration The meshing force on the teeth; Total meshing force; For the first In the nth iteration Equivalent meshing stiffness of the teeth; For the first Total time-varying meshing stiffness obtained from the next iteration; This is the stiffness convergence threshold; The meshing force convergence threshold is defined by equations (13) and (14). A closed-loop feedback iteration mechanism is formed between thermal deformation, wear, cracks, uniform damage section, meshing stiffness, and load distribution.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] First, the present invention not only considers the influence of temperature on material parameters, but also the influence of thermal deformation on contact points, contact paths, actual overlap, and single / double tooth meshing intervals, and can simultaneously correct the amplitude and phase of time-varying meshing stiffness.

[0043] Second, this invention proposes thermal deformation equivalent compliance, which allows the load sensitivity of thermoelastic displacement along the meshing line direction to directly participate in the total compliance calculation.

[0044] Third, this invention constructs a unified damage section, simultaneously describing thermal deformation, wear removal, and crack damage within the same cross-sectional area, avoiding insufficient coupling caused by separate corrections. Fourth, this invention establishes a load distribution feedback iteration mechanism, which can more accurately characterize the variation law of time-varying meshing stiffness of spur gear pairs under high load, high speed, temperature rise, and fault degradation conditions. Attached Figure Description

[0045] Figure 1 This is a flowchart of the calculation process of the present invention.

[0046] Figure 2 This is a model of tooth root crack.

[0047] Figure 3 This is a schematic diagram of a worn gear.

[0048] Figure 4 This is a comparison of the time-varying meshing stiffness of the coupled faulty gear and the normal gear calculated by the calculation method provided in the embodiments of the present invention.

[0049] Figure 5 This is to compare the calculation method provided by the embodiments of the present invention with the time-varying meshing stiffness without considering the elastic modulus correction.

[0050] Figure 6 The calculation method provided in the embodiments of the present invention is compared with the closure stiffness of cracks that do not consider thermal expansion-induced cracks.

[0051] Figure 7 The comprehensive deformation of the tooth surface is calculated using the method provided in the embodiments of the present invention. Detailed Implementation

[0052] The present invention will be further described below with reference to specific embodiments. These embodiments are for illustrative purposes only and do not constitute a limitation on the scope of protection of the present invention.

[0053] Example

[0054] This embodiment provides a method for calculating the time-varying meshing stiffness of crack-wear coupled spur gears based on thermal deformation. A set of modified spur gear pairs is selected as the calculation object, and the method includes the following steps:

[0055] 1) Establish a spur gear pair meshing model and input parameters.

[0056] Based on the input parameters, the pitch circle, base circle, addendum circle, dedendum circle, actual meshing angle, cold contact path, and initial single-tooth / double-tooth meshing interval are obtained using gear geometry relationships commonly used in this field. The above basic geometric calculations are only used to determine the initial quantities required for subsequent thermal deformation correction, wear evolution, and uniform damage section calculations; the basic formulas are not listed here.

[0057] Simultaneously input material thermodynamic parameters, operating condition parameters, and damage parameters, including elastic modulus, shear modulus, Poisson's ratio, density, specific heat capacity, thermal conductivity, coefficient of linear expansion, hardness, coefficient of friction, ambient temperature, reference temperature, heat transfer coefficient, initial crack length, crack angle, initial wear depth, wear coefficient at reference temperature, and crack propagation parameters.

[0058] 2) Calculate the transient temperature field and thermoelastic displacement field.

[0059] At each discrete engagement moment, the transient temperature fields of the driving and driven wheels are solved based on the current meshing force, contact pressure, relative sliding velocity, tooth heat conduction, and boundary heat transfer, and the thermoelastic displacement field is further obtained. In the first iteration, the contact pressure and relative sliding velocity can use initial cold values; in subsequent iterations, the contact state corrected by the thermal deformation of the previous iteration is used. The transient temperature fields of the driving and driven wheels can be simplified as follows:

[0060]

[0061] In the formula, These represent the driving wheel and the driven wheel, respectively. This refers to the transient temperature of the tooth body. , , These are density, specific heat capacity, and thermal conductivity, respectively. To be allocated to gears Frictional heat input; For boundary heat transfer terms; This is the frictional heat distribution coefficient; The coefficient of friction; The contact pressure after thermal deformation correction; The relative sliding velocity after thermal deformation correction; The heat transfer coefficient; The ambient temperature.

[0062] After obtaining the temperature field, the thermoelastic displacement field can be obtained from the following simplified thermoelastic equilibrium relationship:

[0063]

[0064] In the formula, For gears Thermoelastic displacement vector; This is the temperature-dependent elasticity matrix; For small deformation strain tensors; The coefficient of linear expansion; For reference temperature; Unit tensor; This is a volumetric force term. This formula incorporates the thermal strain caused by temperature rise into the elastic equilibrium solution, which is used to obtain the thermoelastic displacement required for subsequent meshing state correction.

[0065] The temperature field and thermoelastic displacement field obtained in this step serve as inputs for 3) contact point position correction, 4) wear depth update, 5) crack propagation calculation, and 8) thermal deformation equivalent compliance calculation. The temperature field governing equation and thermoelastic equilibrium equation belong to general thermoelastic solution methods and are not presented as innovative formulas in this invention; therefore, they will not be repeated in this embodiment.

[0066] 3) Correct the meshing state.

[0067] Projecting the thermoelastic displacements of the driving and driven gears at the contact point along the meshing line, we obtain the thermal deformation of the i-th pair of teeth along the meshing line:

[0068]

[0069] The contact point locations after thermal deformation correction are:

[0070]

[0071] In the formula, For the first The amount of thermal deformation of the teeth along the meshing line; This is the unit normal vector of the meshing line after thermal deformation correction; and The driving wheel and the driven wheel are respectively at the contact point Thermoelastic displacement at the location; This refers to the location of the contact point in a cold, undeformed state. The contact point position is corrected for thermal deformation. Equations (1) and (2) are used to convert the thermoelastic displacement caused by the temperature field into a correction amount for the meshing state.

[0072] Based on the contact path length and base circle tooth pitch corrected for thermal deformation, the actual overlap ratio is recalculated:

[0073]

[0074] The number of meshing tooth pairs at the current moment is determined based on the contact point position after thermal deformation correction:

[0075]

[0076] In the formula ， This represents the actual overlap after thermal deformation correction; This is the actual contact path length after thermal deformation correction; The base circle tooth pitch is corrected for thermal deformation. This represents the number of meshing tooth pairs after thermal deformation correction. This is the single-tooth meshing zone after thermal deformation correction; This represents the double-tooth meshing region after thermal deformation correction. Therefore, the time-varying meshing stiffness calculation can reflect the changes in meshing phase and single / double-tooth switching point caused by temperature rise.

[0077] 4) Calculate the wear depth of the tooth surface.

[0078] After completing the thermal deformation contact state correction, the corrected contact pressure and sliding distance are incorporated into the wear depth update:

[0079]

[0080] In the formula, For gears At the tooth surface position and number of loops The cumulative wear depth below; For cyclic increments; This is the temperature-dependent wear coefficient; The contact pressure after thermal deformation correction; This is the sliding distance after thermal deformation correction; Temperature-corrected hardness. This formula reflects the influence of thermal deformation contact state on wear evolution.

[0081] 5) Calculate the amount of tooth root crack propagation.

[0082] The tooth root crack length is updated based on the temperature-dependent crack propagation model:

[0083]

[0084] The stress intensity factor amplitude is:

[0085]

[0086] The stress amplitude at the critical section of the tooth root can be expressed as:

[0087]

[0088] In the formula, For gears The length of the tooth root crack; This is the temperature-dependent crack propagation coefficient; The amplitude of the Type I stress intensity factor, taking into account the effects of wear and temperature; The crack propagation index; This is a geometric correction factor related to crack length, crack angle, wear depth, and temperature field; The crack angle; The stress amplitude at the critical section of the tooth root, taking into account the effects of wear and thermal stress; This represents the amplitude of the tooth root bending stress after wear correction. This represents the radial compressive stress amplitude after wear correction. This represents the amplitude of thermal stress.

[0089] 6) Construct a uniform damage cross section.

[0090] Based on the cross-sectional area of ​​the tooth after thermal deformation, both the tooth surface wear removal area and the tooth root crack damage area are simultaneously subtracted within the same cross-sectional area to obtain a unified damage cross-section:

[0091]

[0092] Calculate the effective cross-sectional area, effective centroid, and effective moment of inertia on the uniformly damaged section:

[0093]

[0094]

[0095]

[0096] In the formula, This refers to the cross-sectional area of ​​the gear teeth after thermal deformation. This is the area to be removed due to wear. This is the area of ​​crack damage; The effective load-bearing section region after the coupled effects of cracking, wear, and thermal deformation; Effective cross-sectional area; Effective centroid coordinates; The effective moment of inertia relative to the neutral axis of the cross section; Let be a cross-sectional area micro-element. By using equations (11) to (14), the repeated deduction or insufficient coupling caused by separately correcting crack damage and wear damage can be avoided.

[0097] 7) Calculate the equivalent meshing stiffness.

[0098] Based on the effective cross-sectional area, effective centroid, and effective moment of inertia obtained in step 6), and combined with temperature-corrected material parameters, the meshing state after thermal deformation correction, and the inter-tooth structural coupling relationship, the bending stiffness, shear stiffness, radial compressive stiffness, Hertzian contact stiffness, matrix flexible deformation stiffness, and inter-tooth structural coupling compliance of each tooth pair are obtained. The above individual stiffnesses can be obtained using the potential energy method, finite element method, or analytical-numerical hybrid method, which are conventional stiffness component calculations; therefore, their basic formulas will not be elaborated in this embodiment.

[0099] 8) Calculate the equivalent compliance of thermal deformation.

[0100] To incorporate the effect of thermal deformation on deformation along the meshing line direction into the overall compliance, the equivalent compliance of thermal deformation is calculated using the load perturbation method:

[0101]

[0102] In the formula, For gears The Middle Equivalent compliance to thermal deformation of teeth; This is the thermoelastic displacement along the meshing line direction; For the first For tooth meshing force; This represents the load disturbance.

[0103] Substituting the equivalent compliance due to heat deformation and the conventional compliance into the compliance series relationship, the equivalent meshing stiffness of the i-th pair of teeth is:

[0104]

[0105] When NcT teeth are engaged at the current moment, the total time-varying meshing stiffness is:

[0106]

[0107] In the formula, For the first Equivalent meshing stiffness of teeth; Hertzian contact stiffness; The combined stiffness of the gear teeth is composed of bending, shearing, and radial compression. For the flexible deformation stiffness of the matrix; This is the inter-tooth structural coupling compliance term; This refers to the overall time-varying meshing stiffness of the spur gear pair.

[0108] 9) Solve the time-varying meshing stiffness using closed-loop iterative methods.

[0109] Based on the current equivalent meshing stiffness of each meshing tooth pair, the total meshing force is redistributed:

[0110]

[0111] The convergence conditions for meshing stiffness and meshing force are:

[0112]

[0113]

[0114] In the formula, For the first In the nth iteration The meshing force on the teeth; Total meshing force; For the first In the nth iteration Equivalent meshing stiffness of the teeth; and The first Second and third Total time-varying meshing stiffness obtained from the next iteration; and The first Second and third In the nth iteration For tooth meshing force; This is the stiffness convergence threshold; This is the convergence threshold of the meshing force.

[0115] The updated meshing force is fed back to the temperature field, contact pressure, wear model, and crack propagation model, and steps 2) to 8) are re-executed. When equations (19) and (20) are satisfied simultaneously, the time-varying meshing stiffness at the current meshing moment is output; otherwise, iteration continues. By repeating steps 1) to 9) for all discrete meshing moments within a meshing cycle, the time-varying meshing stiffness curve considering the closed-loop coupling effects of thermal deformation, cracks, wear, and load distribution can be obtained.

[0116] The following example further illustrates the time-varying meshing stiffness calculation method for crack-wear coupled spur gears based on thermal deformation provided in this embodiment of the invention:

[0117] Table 1 Gear Pair Parameters

[0118] Depend on Figures 4 to 7 It is evident that the time-varying meshing stiffness of the coupled faulty gear is generally lower than that of the normal gear, indicating that root cracks, tooth surface wear, and thermal deformation collectively weaken the load-bearing capacity of the gear teeth, reducing the effective cross-sectional area and effective moment of inertia, thus leading to a decrease in meshing stiffness. After considering the temperature correction for the elastic modulus, the stiffness curve further decreases, indicating that temperature rise reduces material stiffness and increases tooth compliance. Simultaneously, thermal expansion-induced crack closure weakens the stiffness-reducing effect of crack opening to some extent, causing a slight recovery in local meshing stiffness. The overall tooth surface deformation is non-uniformly distributed along the meshing path, indicating that contact position, thermoelastic deformation, wear state, and load distribution collectively affect local tooth surface deformation. These results demonstrate that the method of this invention can simultaneously reflect the coupling relationship between thermal deformation, cracks, wear, material parameter correction, and load distribution, and can more accurately describe the variation law of the time-varying meshing stiffness of spur gear pairs under fault degradation conditions.

[0119] The present invention provides a time-varying meshing stiffness calculation method for crack-wear coupled spur gears based on thermal deformation. This method can be applied to the dynamic analysis, vibration response prediction, fault feature extraction, and remaining life assessment of spur gears in aerospace, vehicle transmission, construction machinery, wind power equipment, robot joints, and precision transmission systems. The required input parameters can be obtained through design parameters, material handbooks, experimental measurements, or finite element calculations. The output time-varying meshing stiffness curve can be directly used as input to the gear system dynamics model, thus demonstrating clear engineering applications and feasibility.

Claims

1. A method for calculating the time-varying meshing stiffness of crack-wear coupled spur gears based on thermal deformation, characterized in that, Includes the following steps: 1) Establish the meshing coordinate system and the force-deformation coordinate system of the spur gear pair, and input the gear geometric parameters, material thermodynamic parameters, working condition parameters, crack parameters and wear parameters; 2) Calculate the transient temperature field based on the heat generated by friction on the tooth surface, the heat conduction of the tooth body, and the heat transfer at the boundary, and solve for the thermoelastic displacement fields of the driving wheel and the driven wheel; 3) Project the thermoelastic displacement of the driving and driven gears at the contact point along the meshing line direction to correct the contact point position, contact path length, base circle tooth pitch, actual overlap, and single / double tooth meshing range. 4) Update the tooth surface wear depth based on the contact pressure and relative sliding speed after thermal deformation correction; 5) Update the tooth root crack length based on the tooth root stress intensity factor under the influence of temperature, thermal stress, and wear; 6) By subtracting the wear removal area and crack damage area from the cross-sectional area of ​​the tooth after thermal deformation, a unified damage section is constructed, and the effective cross-sectional area, effective centroid, and effective moment of inertia are calculated; 7) Calculate the equivalent meshing stiffness of each meshing tooth pair based on the unified damage section, temperature-corrected material parameters, and thermal deformation-corrected meshing state. 8) Calculate the equivalent compliance of thermal deformation using the load perturbation method, and introduce it as a compliance term into the series-parallel relationship of meshing stiffness; 9) Redistribute the meshing force according to the stiffness of each meshing tooth pair, and feed the updated meshing force back to the temperature field, wear model and crack propagation model, iterating until the meshing stiffness and meshing force satisfy the convergence condition.

2. The method according to claim 1, characterized in that, In step 3), the amount of thermal deformation along the meshing line and the position of the contact point after thermal deformation correction satisfy the following: In the formula, For the first The amount of thermal deformation of the teeth along the meshing line. This is the unit normal vector of the meshing line after thermal deformation correction. and These represent the thermoelastic displacements of the driving and driven wheels at the contact point, respectively. This refers to the location of the cold contact point. This represents the contact point location after thermal deformation correction.

3. The method according to claim 1, characterized in that, In step 6), the unified damage cross section satisfies: In the formula, This refers to the cross-sectional area of ​​the gear teeth after thermal deformation. For the wear removal area, This is the area of ​​crack damage. To unify the damaged cross-sectional area, , and These are the effective cross-sectional area, effective centroid, and effective moment of inertia, respectively.

4. The method according to claim 1, characterized in that, In steps 4) and 5), the wear depth and crack length are updated using the following coupled relationship: In the formula, This represents the tooth surface wear depth. The length of the tooth root crack. The wear coefficient is the temperature-dependent coefficient. This is the contact pressure after thermal deformation correction. This is the sliding distance after thermal deformation correction. For temperature-corrected hardness, This represents the temperature-dependent crack propagation coefficient. The stress intensity factor amplitude takes into account the effects of wear and temperature.

5. The method according to claim 1, characterized in that, In step 8), the equivalent compliance of thermal deformation is calculated using the load perturbation method: In the formula, For gears The Middle Equivalent compliance to thermal deformation of teeth This refers to the thermoelastic displacement along the meshing line. For the first For tooth meshing force, This represents the change in load.

6. The method according to claim 1, characterized in that, In steps 7) and 9), the first The equivalent meshing stiffness and load feedback distribution of the teeth satisfy the following: In the formula, For the first For the equivalent meshing stiffness of the teeth, For Hertzian contact stiffness, The combined stiffness of the gear teeth is composed of bending, shearing, and radial compression. The stiffness of the matrix under flexible deformation. This is the inter-tooth structure coupling compliance term. For the first The iteration of the ... For tooth meshing force, This represents the total meshing force.

7. The method according to claim 6, characterized in that, Iterative convergence conditions include convergence of meshing stiffness and convergence of meshing force: In the formula, For the first The total time-varying meshing stiffness obtained from the next iteration. For the first The result of the iteration is the first For tooth meshing force, and These are the stiffness convergence threshold and the meshing force convergence threshold, respectively.

8. A system for calculating the time-varying meshing stiffness of crack-wear coupled spur gears based on thermal deformation equivalent compliance and a unified damage section, characterized in that, It includes at least one processor and a memory communicatively connected to the at least one processor; the memory stores a computer program that, when executed, implements the method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a processor, implement the method described in any one of claims 1 to 7.

Images