A method of gear design optimization

Abstract

The application discloses a gear design optimization method, improves the calculation precision of gear transmission system meshing stiffness, and guarantees the transmission performance of gear teeth under variable load conditions. The method comprises the following steps: 1, constructing a gear comprehensive stiffness model based on gear teeth under variable load; 2, obtaining initial values of gear meshing pair tooth profile design parameters; 3, substituting the set load and the initial values of the gear meshing pair tooth profile design parameters obtained in step 2 into the gear comprehensive stiffness model constructed in step 1 to obtain the comprehensive stiffness of the gear; 4, obtaining the nominal stiffness of the gear meshing pair according to the initial values of the gear meshing pair tooth profile design parameters obtained in step 2; comparing the nominal stiffness of the gear meshing pair and the comprehensive stiffness of the gear obtained in step 3, if the comprehensive stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then the initial values of the gear meshing pair tooth profile design parameters obtained in step 2 are taken as the actual gear design parameter values.

Description

Technical Field

[0001] This invention belongs to the field of gear design, and specifically relates to a gear design optimization method. Background Technology

[0002] Gear transmission is an extremely common form of transmission in mechanical equipment, and mechanical vibration has a significant impact on the transmission accuracy and smoothness of the equipment. Changes in stiffness are a major cause of vibration in mechanical systems. Mechanical transmission systems often operate under diverse conditions and are subject to varying loads. Therefore, it is essential to conduct in-depth research on the influence of load and transmission ratio on the overall meshing stiffness of gears, and then optimize the nominal parameters of gears through stiffness verification to further enhance their transmission performance.

[0003] Existing methods for calculating gear stiffness mainly fall into three categories: analytical methods, finite element methods, and experimental methods. Existing methods all have significant drawbacks in stiffness calculation: (1) They do not consider the influence of load factors: When a gear bears different loads, the deformation at different positions of each tooth varies, leading to changes in the meshing period for different numbers of teeth, resulting in inaccurate calculation of the impact response period phase; (2) They cannot characterize the excitation form of different types of stiffness: Loads have different effects on different stiffness components such as axial compressive stiffness, Hertzian contact stiffness, and matrix stiffness, and their influence coefficients change with different meshing positions. Current analytical stiffness models cannot accurately characterize this phenomenon. Therefore, existing methods for calculating gear meshing stiffness need further improvement to accurately characterize the influence of loads on stiffness, thereby designing more precise gear parameters. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a gear design optimization method, which takes into account the influence of gear load on the impact response period phase, improves the calculation accuracy of the meshing stiffness of the gear transmission system, and optimizes the gear parameters to ensure the transmission performance of the gear teeth under variable load conditions.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A gear design optimization method, the method comprising: Step 1: Construct a gear comprehensive stiffness model based on gear teeth under variable loads; Step 2: Obtain the initial values ​​of the gear meshing tooth profile design parameters, including module, pressure angle, tooth width, number of teeth, center distance, and transmission ratio; Step 3: Substitute the set load and the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2 into the gear comprehensive stiffness model constructed in Step 1 to obtain the comprehensive stiffness of the gear. Step 4: Based on the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2, obtain the nominal stiffness of the gear meshing pair; compare the nominal stiffness of the gear meshing pair with the comprehensive stiffness of the gear obtained in Step 3. If the comprehensive stiffness of the gear obtained in Step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2 are used as the actual gear design parameter values. If the overall stiffness of the gear obtained in step 3 is less than the nominal stiffness of the gear meshing pair, then return to step 3, change the gear meshing pair tooth profile design parameter value obtained in step 2, and substitute the set load and the changed gear meshing pair tooth profile design parameter value back into the gear overall stiffness model constructed in step 1 to obtain the gear overall stiffness, until the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair; the gear meshing pair tooth profile design parameter value that satisfies the condition that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear meshing pair is used as the actual gear design parameter value.

[0006] As a preferred example, step 4 further includes: if the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then compare whether the gear meshing sub-stiffness meets the sub-stiffness preset condition. If the sub-stiffness preset condition is met, then the gear meshing pair tooth profile design parameter value that satisfies the requirement that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear pair is used as the actual gear design parameter value. If the sub-stiffness preset condition is not met, return to step 3, change the initial value of the gear meshing pair tooth profile design parameter obtained in step 2, and resubstitute the set load and the changed gear meshing pair tooth profile design parameter value into the gear comprehensive stiffness model constructed in step 1 to obtain the comprehensive stiffness of the gear, until the comprehensive stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair and meets the sub-stiffness preset condition; the gear meshing pair tooth profile design parameter value that meets the sub-stiffness preset condition and satisfies the requirement that the comprehensive stiffness of the gear is greater than or equal to the nominal stiffness of the gear pair is used as the actual gear design parameter value.

[0007] As a preferred example, the gear meshing sub-stiffness includes gear meshing bending stiffness, gear meshing shear stiffness, gear meshing axial compressive stiffness, gear meshing base stiffness, and gear meshing Hertzian contact stiffness; the preset condition for the sub-stiffness is that the calculated sub-stiffness value is greater than or equal to the sub-stiffness threshold.

[0008] As a preferred example, the method further includes: step 5, returning to step 3, changing the set load, and obtaining the actual gear design parameter value after changing the set load.

[0009] As a preferred example, step 1 includes: Step 101: Calculate the load on the gear teeth using formula (1). Below, the meshing stiffness of single and double teeth : Equation (1) in, A value of 1 indicates single-gear meshing; A value of 2 indicates double gear meshing; Indicates under load Below is the influence coefficient of gear speed during single-gear meshing or double-gear meshing, which is dimensionless; Indicates under load Below, the influence coefficient of tooth profile for single-tooth meshing or double-tooth meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Axial compressive stiffness under action, unit: N / m; The transfer function representing the load influence coefficient of axial compressive stiffness under single-gear meshing or double-gear meshing is dimensionless; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Bending stiffness under load, unit: N / m; The transfer function representing the load influence coefficient of bending stiffness under single-gear meshing or double-gear meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Shear stiffness under action, unit: N / m; The transfer function representing the load influence coefficient of shear stiffness under single-gear or double-gear meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Matrix stiffness under action, unit: N / m; The dimensionless coefficient represents the influence coefficient on the stiffness of the tooth matrix under different loads for single-tooth meshing or double-tooth meshing. This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Hertzian contact stiffness under action, unit: N / m; The dimensionless coefficient represents the influence coefficient of the Hertzian contact stiffness of teeth in single-tooth meshing or double-tooth meshing under different loads. Step 102: Calculate the elastic deformation and phase length of the gear teeth in the single-tooth meshing zone and the double-tooth meshing zone; Step 103: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under single-tooth meshing and double-tooth meshing conditions; Step 104: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under three-tooth meshing conditions; Step 105: Combine the comprehensive meshing stiffness of the same cycle to synthesize the comprehensive meshing stiffness of multiple cycles, which serves as the gear comprehensive stiffness model.

[0010] As a preferred example, in step 101, Equation (2) Equation (3) Equation (4) Equation (5) Equation (6) In the formula, Indicates the gear teeth under load Bending stiffness under load, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth bending stiffness; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; The angle between the direction of the force at the meshing point of the gear teeth and the vertical direction, expressed in radians; The angle between the center of the tooth and the root point of the tooth, in radians; The elastic modulus of the gear tooth material, expressed in Pa. Indicates the tooth width, unit: meter; Indicates the gear teeth under load Shear stiffness under action, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth shear stiffness; Poisson's ratio, representing the material of the gear teeth, is dimensionless. Indicates the gear teeth under load Axial compressive stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the axial compressive stiffness of the gear teeth; Indicates the gear teeth under load Matrix stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the gear tooth matrix stiffness; Indicates the tooth thickness, unit: meter; This represents the distance from the point where the force acting on the tooth intersects with the centerline of the tooth to the tooth root, expressed in meters. Indicates the gear teeth under load Hertzian contact stiffness under action, unit: N / m; This represents the influence coefficient of the Hertzian contact stiffness of the gear teeth, and is dimensionless.

[0011] As a preferred example, step 102 includes: Calculate the elastic deformation and phase length of a single tooth in the meshing zone, specifically including: Under an external load, the elastic deformation of a single pair of gear teeth is calculated according to equation (7). for: Equation (7) in, This indicates that the gear is subjected to an external load, measured in Newton-meters (N·m). This represents the combined meshing stiffness of a single tooth pair, in Newtons per meter (N / m). This indicates the gear radius corresponding to the current meshing position, in meters. The load is obtained according to equation (8). Single tooth meshing phase length : Equation (8) in, Calculate according to the following formula: ; In the formula, Indicates the number of teeth on the driving wheel. Indicates the number of teeth on the driven gear; The angle between the line connecting the center and the point of contact of the meshing gear and the point of tangency between the center and the base circle, in radians; This indicates the gear radius corresponding to the current meshing position, in meters. Calculate the elastic deformation and phase length of the teeth in the double-tooth meshing zone, specifically including: When the gears enter the double-tooth meshing zone, the load on the gear pair... The meshing is borne by two pairs of gear teeth. According to equation (9), the elastic deformation of the gear teeth involved in the meshing is calculated as follows: Equation (9) in, The elastic deformation of the first pair of teeth involved in meshing, expressed in meters; This indicates the combined meshing stiffness of a double tooth pair, in Newtons per meter (N / m). This indicates the gear radius corresponding to the current meshing position of the first pair of teeth involved in meshing, in meters; The elastic deformation of the second pair of teeth involved in meshing, expressed in meters; This indicates the gear radius corresponding to the current meshing position of the second pair of teeth involved in meshing, in meters; The load is obtained according to equation (10). Lower double-tooth meshing phase length : Equation (10).

[0012] As a preferred example, step 103 includes: Step 1031: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under single-tooth meshing conditions, specifically including: If the elastic deformation of a single pair of gear teeth Larger than tooth gap If the gear engages in double-tooth meshing prematurely, the combined meshing stiffness of a single pair of gear teeth should be recalculated according to equation (11). Then proceed to step 104; Equation (11) In the formula, This represents the overall meshing stiffness of a single gear pair, in Newtons per meter (N / m). The gear rotation angle corresponding to the final meshing position in the single-tooth meshing zone, in radians; The gear radius corresponding to the final meshing position in the single-tooth meshing zone, in meters; and These represent the gear radii corresponding to the current meshing positions of the two pairs of teeth, in meters; If the elastic deformation of a single pair of gear teeth Smaller than tooth gap Then proceed to step 1032; Step 1032: Calculate the overall meshing stiffness of the teeth in the meshing phase interval under double-tooth meshing conditions, specifically including: When two teeth are meshing, the elastic deformation of the two pairs of teeth is compared according to the current meshing position. If... Then, the combined stiffness of the meshing of the two pairs of gear teeth is calculated according to equation (12). : Equation (12) In the formula, This represents the overall meshing stiffness of a single gear pair, in Newtons per meter (N / m). Indicates the meshing radius corresponding to the meshing position of the first pair of gear teeth, in meters; This represents the change in the rotation angle of the first pair of meshing gear teeth during the meshing process, in radians. Indicates the meshing radius corresponding to the meshing position of the third pair of gear teeth, in meters; like Then, the combined stiffness of the meshing of the two pairs of gear teeth is calculated according to equation (13). : Equation (13) In the formula, and These represent the gear radii corresponding to the current meshing positions of the two pairs of teeth, in meters; This indicates the change in the rotation angle of the second pair of meshing gear teeth during the meshing process, in radians.

[0013] As a preferred example, step 104 includes: Under load Under the action of the action, the elastic deformation of the three teeth is calculated using equation (14): Equation (14) In the formula, This represents the elastic deformation of the first pair of teeth during three-tooth meshing, in meters. This indicates the elastic deformation of the second pair of teeth during three-tooth meshing, in meters. This indicates the elastic deformation of the third pair of teeth during three-tooth meshing, in meters. The combined stiffness of the meshing teeth when three teeth are engaged, expressed in Newtons per meter (N / m). Indicates the meshing radius corresponding to the meshing position of the first pair of gear teeth, in meters; Indicates the meshing radius corresponding to the meshing position of the second pair of gear teeth, in meters; Indicates the meshing radius corresponding to the meshing position of the third pair of gear teeth, in meters; Determine the elastic deformation of the gear teeth and the clearance between the three pairs of teeth. If the elastic deformation of the gear teeth is greater than the clearance between the three pairs of teeth, then the gear enters the three-tooth meshing zone, and the gear load... It is supported by three pairs of gear teeth; the meshing phase length of the three teeth is calculated using equation (15). for: Equation (15) The overall stiffness of the meshing teeth during three-tooth meshing is calculated using equation (16). Then proceed to step 105; Equation (16) In the formula, Indicates the total number of teeth pairs involved in meshing; Indicates the first The gear radius corresponding to the current meshing position of the gear teeth, in meters; Indicates the angle as The radius of the time, in meters; Expresses the amount of elastic deformation of the gear teeth, in meters; The clearance between meshing gear teeth, expressed in meters. Indicates the first The gear radius corresponding to the current meshing position of the gear teeth, in meters; If the elastic deformation of the gear teeth is less than the clearance between the three pairs of gear teeth, proceed to step 105.

[0014] Compared with existing technologies, the gear design optimization method of this invention considers the influence of gear load on the phase of the impact response period, improves the calculation accuracy of the meshing stiffness of the gear transmission system, and optimizes gear parameters to ensure the transmission performance of the gear pair under variable load conditions. This method first constructs a gear comprehensive stiffness model; then obtains the initial values ​​of the gear meshing pair tooth profile design parameters; next, it substitutes the set load and the obtained initial values ​​of the gear meshing pair tooth profile design parameters into the constructed gear comprehensive stiffness model to obtain the comprehensive stiffness of the gear; finally, it compares the nominal stiffness of the gear meshing pair with the comprehensive stiffness of the gear obtained in step 3. This method considers the influence of load on the meshing stiffness of the transmission gear teeth under different working conditions, making the calculated meshing stiffness more closely match the actual load conditions and resulting in more accurate meshing stiffness. Attached Figure Description

[0015] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a flowchart of step 1 in an embodiment of the present invention; Figure 3 The diagram shows the performance of the gear in test scheme 1 of the present invention; wherein, (a) is the comprehensive meshing stiffness diagram of the gear in test scheme 1, and (b) is the influence diagram of the load torque on the comprehensive meshing stiffness of the gear in test scheme 1. Figure 4 The diagram shows the performance of the gear in test scheme 2 of the present invention; wherein, (a) is the comprehensive meshing stiffness diagram of the gear in test scheme 2, and (b) is the influence diagram of the load torque on the comprehensive meshing stiffness of the gear in test scheme 2. Figure 5 The diagram shows the bending stiffness of the meshing gear teeth in an embodiment of the present invention; wherein (a) is the bending stiffness diagram of the meshing gear teeth obtained in test scheme 1, and (b) is the bending stiffness diagram of the meshing gear teeth obtained in test scheme 2. Figure 6 The diagrams are of the shear stiffness of meshing gear teeth in the embodiments of the present invention, wherein (a) is the shear stiffness diagram of meshing gear teeth obtained in test scheme 1, and (b) is the shear stiffness diagram of meshing gear teeth obtained in test scheme 2. Detailed Implementation

[0016] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0017] like Figure 1 As shown, a gear design optimization method of the present invention includes: Step 1: Construct a gear comprehensive stiffness model based on gear teeth under variable loads; Step 2: Obtain the initial values ​​of the gear meshing tooth profile design parameters, including module, pressure angle, tooth width, number of teeth, center distance, and transmission ratio; Step 3: Substitute the set load and the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2 into the gear comprehensive stiffness model constructed in Step 1 to obtain the comprehensive stiffness of the gear. Step 4: Based on the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2, obtain the nominal stiffness of the gear meshing pair; compare the nominal stiffness of the gear meshing pair with the comprehensive stiffness of the gear obtained in Step 3. If the comprehensive stiffness of the gear obtained in Step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2 are used as the actual gear design parameter values. If the overall stiffness of the gear obtained in step 3 is less than the nominal stiffness of the gear meshing pair, then return to step 3, change the gear meshing pair tooth profile design parameter value obtained in step 2, and substitute the set load and the changed gear meshing pair tooth profile design parameter value back into the gear overall stiffness model constructed in step 1 to obtain the gear overall stiffness, until the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair; the gear meshing pair tooth profile design parameter value that satisfies the condition that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear meshing pair is used as the actual gear design parameter value.

[0018] In the above method, the nominal stiffness of the gear meshing pair is obtained based on the initial values ​​of the gear meshing pair tooth profile design parameters obtained in step 2. The nominal stiffness of the gear meshing pair is the gear meshing pair stiffness obtained under no load, and is specifically calculated according to equations (1) to (6).

[0019] In the above method, firstly, a gear comprehensive stiffness model is constructed; then, the initial values ​​of the gear meshing pair tooth profile design parameters are obtained; next, the set load and the obtained initial values ​​of the gear meshing pair tooth profile design parameters are substituted into the constructed gear comprehensive stiffness model to obtain the gear comprehensive stiffness; finally, the nominal stiffness of the gear meshing pair is compared with the gear comprehensive stiffness obtained in step 3. If the gear comprehensive stiffness obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, it proves that the gear teeth meet the strength requirements under load, and the initial values ​​of the gear meshing pair tooth profile design parameters obtained in step 2 are used as the actual gear design parameter values. If the overall stiffness of the gear obtained in step 3 is less than the nominal stiffness of the gear meshing pair, it proves that the gear teeth do not meet the strength requirements under load, i.e., the gear teeth are not strong enough. Then return to step 3, change the gear meshing pair tooth profile design parameter value obtained in step 2, and resubmit the set load and the changed gear meshing pair tooth profile design parameter value into the gear overall stiffness model constructed in step 1 to obtain the gear overall stiffness until the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair. The gear meshing pair tooth profile design parameter value that satisfies the condition that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear meshing pair is taken as the actual gear design parameter value.

[0020] The method described in the above embodiments considers the influence of load on the meshing stiffness of transmission gear teeth under different working conditions, making the calculated meshing stiffness more consistent with actual load conditions and thus more accurate. This method can be used to verify the strength of gears under load during the design and manufacturing stage, transforming gear production inspection from traditional experience-based testing to precise verification. It has particularly significant application value for the design optimization and inspection of non-standard gears.

[0021] Preferably, step 4 further includes: if the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then compare whether the gear meshing sub-stiffness meets the sub-stiffness preset condition. If the sub-stiffness preset condition is met, then the gear meshing pair tooth profile design parameter value that satisfies the requirement that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear pair is used as the actual gear design parameter value; if the sub-stiffness preset condition is not met, then return to step 3, change the initial value of the gear meshing pair tooth profile design parameter obtained in step 2, and re-substitute the set load and the changed gear meshing pair tooth profile design parameter value into the gear overall stiffness model constructed in step 1 to obtain the overall stiffness of the gear, until step 3 obtains that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear meshing pair and satisfies the sub-stiffness preset condition; then the gear meshing pair tooth profile design parameter value that satisfies the sub-stiffness preset condition and satisfies the requirement that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear pair is used as the actual gear design parameter value.

[0022] In the above method, if the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then the gear meshing sub-stiffness is compared to see if it meets the preset sub-stiffness conditions. This allows the solution to cover gears for different applications. For example, depending on the actual working conditions, some gear teeth are mainly subjected to bending stress, meaning that the bending stiffness accounts for a large proportion of the load during operation, requiring higher bending stiffness.

[0023] Preferably, the gear meshing stiffness includes gear meshing bending stiffness. Gear meshing shear stiffness Axial compressive stiffness of gear meshing Gear meshing base stiffness Hertz contact stiffness of gear meshing The sub-stiffness preset condition is that the calculated sub-stiffness value is greater than or equal to the sub-stiffness threshold. The sub-stiffness of each gear mesh is calculated according to equations (2) to (6), and then compared with the sub-stiffness threshold of each gear mesh. If the calculated sub-stiffness value is greater than or equal to the sub-stiffness threshold, the design requirements are met.

[0024] Equation (2) Equation (3) Equation (4) Equation (5) Equation (6) In the formula, Indicates the gear teeth under load Bending stiffness under load, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth bending stiffness; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; The angle between the direction of the force at the meshing point of the gear teeth and the vertical direction, expressed in radians; The angle between the center of the tooth and the root point of the tooth, in radians; The elastic modulus of the gear tooth material, expressed in Pa. Indicates the tooth width, unit: meter; Indicates the gear teeth under load Shear stiffness under action, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth shear stiffness; Poisson's ratio, representing the material of the gear teeth, is dimensionless. Indicates the gear teeth under load Axial compressive stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the axial compressive stiffness of the gear teeth; Indicates the gear teeth under load Matrix stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the gear tooth matrix stiffness; Indicates the tooth thickness, unit: meter; This represents the distance from the point where the force acting on the tooth intersects with the centerline of the tooth to the tooth root, expressed in meters. Indicates the gear teeth under load Hertzian contact stiffness under action, unit: N / m; This represents the influence coefficient of the Hertzian contact stiffness of the gear teeth, and is dimensionless.

[0025] Preferably, the method further includes: step 5, returning to step 3, changing the set load, and obtaining the actual gear design parameter values ​​after changing the set load. Since gears will bear different loads, in this preferred embodiment, the actual gear design parameter values ​​under different loads are obtained by changing the set load. This is more conducive to accurately obtaining gear design parameter values ​​that meet the design requirements.

[0026] Preferred, such as Figure 2 As shown, step 1 includes: Step 101: Calculate the load on the gear teeth using formula (1). Below, the meshing stiffness of single and double teeth : Equation (1) in, A value of 1 indicates single-gear meshing; A value of 2 indicates double gear meshing; Indicates under load Below is the influence coefficient of gear speed during single-gear meshing or double-gear meshing, which is dimensionless; Indicates under load Below, the influence coefficient of tooth profile for single-tooth meshing or double-tooth meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Axial compressive stiffness under action, unit: N / m; The transfer function representing the load influence coefficient of axial compressive stiffness under single-gear meshing or double-gear meshing is dimensionless; , ,in, Indicates under load Below, the influence coefficient of gear speed during gear meshing is dimensionless; Indicates under load Below, the influence coefficient of tooth profile during gear meshing is dimensionless; The distance between the initial meshing point in the direction of gear shaft compression and the center of gear rotation, in meters; This indicates the angular velocity of the gear teeth, measured in radians per second. Indicates the rotation time of the gear teeth, in seconds; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Bending stiffness under load, unit: N / m; The transfer function representing the load influence coefficient of bending stiffness under single-gear meshing or double-gear meshing is dimensionless; , ,in, The distance between the starting point of meshing in the direction of gear bending and the center of gear rotation, in meters; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Shear stiffness under action, unit: N / m; The transfer function representing the load influence coefficient of shear stiffness under single-gear or double-gear meshing is dimensionless; , ,in, The distance between the starting point of engagement in the shearing direction of the gear and the center of rotation of the gear, in meters; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Matrix stiffness under action, unit: N / m; The dimensionless coefficient represents the influence coefficient on the stiffness of the tooth matrix under different loads for single-tooth meshing or double-tooth meshing. This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Hertzian contact stiffness under action, unit: N / m; The dimensionless coefficient represents the influence coefficient of the Hertzian contact stiffness of teeth in single-tooth meshing or double-tooth meshing under different loads. Step 102: Calculate the elastic deformation and phase length of the gear teeth in the single-tooth meshing zone and the double-tooth meshing zone; Step 103: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under single-tooth meshing and double-tooth meshing conditions; Step 104: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under three-tooth meshing conditions; Step 105: Combine the comprehensive meshing stiffness of the same cycle to synthesize the comprehensive meshing stiffness of multiple cycles, which serves as the gear comprehensive stiffness model.

[0027] This invention constructs a gear comprehensive stiffness model based on variable loads on gear teeth. This model fully considers the actual working conditions of gear transmission systems under varying loads in applications. It establishes a mapping relationship between external loads and gear tooth meshing positions, builds meshing periodic stiffness models with different tooth numbers considering load influence, obtains a load-adaptive gear meshing period variation model, and derives the transfer function of the load's influence coefficient on different types of sub-stiffness. These are then introduced into the overall stiffness model, completing the construction of an improved gear comprehensive stiffness model considering load influence. Compared with existing stiffness calculation models, this invention overcomes the problems of inaccurate calculation of the impact response period phase due to load variations and the inability to accurately represent the excitation forms of different types of stiffness. The stiffness values ​​of the gear transmission system obtained through the gear comprehensive stiffness model proposed in this invention are closer to actual engineering conditions. The technical solution proposed in this invention has good practical engineering application value for gear design optimization and verification.

[0028] Preferably, in step 101, Equation (2) Equation (3) Equation (4) Equation (5) Equation (6) In the formula, Indicates the gear teeth under load Bending stiffness under load, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth bending stiffness; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; The angle between the direction of the force at the meshing point of the gear teeth and the vertical direction, expressed in radians; The angle between the center of the tooth and the root point of the tooth, in radians; The elastic modulus of the gear tooth material is expressed in Pa, which is equivalent to Newtons per square meter. Indicates the tooth width, unit: meter; Indicates the gear teeth under load Shear stiffness under action, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth shear stiffness; Poisson's ratio, representing the material of the gear teeth, is dimensionless. Indicates the gear teeth under load Axial compressive stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the axial compressive stiffness of the gear teeth; Indicates the gear teeth under load Matrix stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the gear tooth matrix stiffness; Indicates the tooth thickness, unit: meter; This represents the distance from the point where the force acting on the tooth intersects with the centerline of the tooth to the tooth root, expressed in meters. Indicates the gear teeth under load Hertzian contact stiffness under action, unit: N / m; This represents the influence coefficient of the Hertzian contact stiffness of the gear teeth, and is dimensionless.

[0029] Preferably, step 102 includes: A pair of gears are subjected to external loads In the single-tooth meshing zone, all loads on this gear are borne by a single pair of meshing teeth. The elastic deformation and phase length of the teeth in the single-tooth meshing zone are calculated, specifically including: When a pair of gears are subjected to an external load Under the action, the elastic deformation of a single pair of gear teeth is calculated according to equation (7). for: Equation (7) in, This indicates that the gear is subjected to an external load, measured in Newton-meters (N·m). This represents the combined meshing stiffness of a single tooth pair, in Newtons per meter (N / m); according to formula (1) When equal to 1, the calculated result is for ; This indicates the gear radius corresponding to the current meshing position, in meters. The load is obtained according to equation (8). Single tooth meshing phase length : Equation (8) in, Calculate according to the following formula: ; In the formula, Indicates the number of teeth on the driving wheel. Indicates the number of teeth on the driven gear; The angle between the line connecting the center and the point of contact of the meshing gear and the point of tangency between the center and the base circle, in radians; This indicates the gear radius corresponding to the current meshing position, in meters.

[0030] Calculate the elastic deformation and phase length of the teeth in the double-tooth meshing zone, specifically including: When the gears enter the double-tooth meshing zone, the load on the gear pair... The meshing is borne by two pairs of gear teeth. According to equation (9), the elastic deformation of the gear teeth involved in the meshing is calculated as follows: Equation (9) in, The elastic deformation of the first pair of teeth involved in meshing, expressed in meters; This represents the combined meshing stiffness of the double-tooth pair, in Newtons per meter (N / m); according to equation (1) When equal to 2, the calculated result is for ; This indicates the gear radius corresponding to the current meshing position of the first pair of teeth involved in meshing, in meters; The elastic deformation of the second pair of teeth involved in meshing, expressed in meters; This indicates the gear radius corresponding to the current meshing position of the second pair of gear teeth involved in the meshing, in meters.

[0031] The load is obtained according to equation (10). Lower double-tooth meshing phase length : Equation (10).

[0032] The presence of load causes changes in some meshing parameters, resulting in a change in the meshing phase. More accurate phase information can be obtained through equation (10).

[0033] Preferably, step 103 includes: Step 1031: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under single-tooth meshing conditions, specifically including: Calculating the overall meshing stiffness of a single pair of teeth reveals that changes in elastic deformation during single-pair meshing may lead to premature engagement with double teeth. If the elastic deformation of a single pair of teeth... Larger than tooth gap If the gear engages in double-tooth meshing prematurely, the combined meshing stiffness of a single pair of gear teeth should be recalculated according to equation (11). Then proceed to step 104; Equation (11) In the formula, This represents the overall meshing stiffness of a single gear pair, in Newtons per meter (N / m). The gear rotation angle corresponding to the final meshing position in the single-tooth meshing zone, in radians; The gear radius corresponding to the final meshing position in the single-tooth meshing zone, in meters; and These represent the gear radii corresponding to the current meshing positions of the two pairs of teeth, in meters; If the elastic deformation of a single pair of gear teeth Smaller than tooth gap Then proceed to step 1032.

[0034] Step 1032: Calculate the overall meshing stiffness of the teeth in the meshing phase interval under double-tooth meshing conditions, specifically including: When two teeth are meshing, the elastic deformation of the two pairs of teeth is compared according to the current meshing position. If... Then, the combined stiffness of the meshing of the two pairs of gear teeth is calculated according to equation (12). : Equation (12) In the formula, This represents the overall meshing stiffness of a single gear pair, in Newtons per meter (N / m). Indicates the meshing radius corresponding to the meshing position of the first pair of gear teeth, in meters; This represents the change in the rotation angle of the first pair of meshing gear teeth during the meshing process, in radians. Indicates the meshing radius corresponding to the meshing position of the third pair of gear teeth, in meters; like Then, the combined stiffness of the meshing of the two pairs of gear teeth is calculated according to equation (13). : Equation (13) In the formula, and These represent the gear radii corresponding to the current meshing positions of the two pairs of teeth, in meters; This indicates the change in the rotation angle of the second pair of meshing gear teeth during the meshing process, in radians.

[0035] In typical gear transmission systems, single-to-double tooth meshing occurs alternately during meshing. The technical method proposed in this invention fully considers the influence of load on the elastic deformation of teeth at different meshing positions during meshing, as well as the influence of load on the meshing cycle for different numbers of teeth. This results in a load-adaptive gear meshing cycle variation model. By comparing the influence of load on the phase of the single-to-double tooth region in real time based on the meshing position, the meshing cycle is updated in real time. This makes the stiffness calculation closer to the engineering reality of gear transmission, and the calculated stiffness value is more accurate, providing more reliable support for gear optimization and verification.

[0036] Furthermore, excessive loads may cause a continuous increase in tooth deformation, leading to multi-tooth meshing. When a gear enters the multi-tooth meshing zone, the gear load is typically borne by three pairs of teeth. Preferably, step 104 includes: Under load Under the action of the action, the elastic deformation of the three teeth is calculated using equation (14): Equation (14) In the formula, This represents the elastic deformation of the first pair of teeth during three-tooth meshing, in meters. This represents the elastic deformation of the second pair of teeth during three-tooth meshing, in meters. This indicates the elastic deformation of the third pair of teeth during three-tooth meshing, in meters. The combined stiffness of the meshing teeth when three teeth are engaged, expressed in Newtons per meter (N / m). Indicates the meshing radius corresponding to the meshing position of the first pair of gear teeth, in meters; Indicates the meshing radius corresponding to the meshing position of the second pair of gear teeth, in meters; Indicates the meshing radius corresponding to the meshing position of the third pair of gear teeth, in meters; Determine the elastic deformation of the gear teeth and the clearance between the three pairs of teeth. If the elastic deformation of the gear teeth is greater than the clearance between the three pairs of teeth, then the gear enters the three-tooth meshing zone, and the gear load... It is supported by three pairs of gear teeth; the meshing phase length of the three teeth is calculated using equation (15). for: Equation (15) The overall stiffness of the meshing teeth during three-tooth meshing is calculated using equation (16). Then proceed to step 105; Equation (16) In the formula, Indicates the total number of teeth pairs involved in meshing; Indicates the first The gear radius corresponding to the current meshing position of the gear teeth, in meters; Indicates the angle as The radius of the time, in meters; Expresses the amount of elastic deformation of the gear teeth, in meters; The clearance between meshing gear teeth, expressed in meters. Indicates the first The gear radius corresponding to the current meshing position of the gear teeth, in meters; If the elastic deformation of the gear teeth is less than the clearance between the three pairs of gear teeth, proceed to step 105.

[0037] The gear design optimization method of this invention, based on the influence of different loads on the deformation of meshing teeth at different positions and the influence of load on the phase of the impact response period, establishes a transfer function of the influence coefficient of load on different types of sub-stiffness, and introduces it into the overall stiffness model, thereby constructing an improved gear stiffness calculation method that considers the influence of load. Simultaneously, this method further considers the sensitivity of meshing sub-stiffness (bending stiffness, shear stiffness, axial compressive stiffness, base stiffness, and Hertzian contact stiffness) to load changes. This invention overcomes the problem of existing methods being unable to accurately characterize the time-varying meshing stiffness of gear teeth under load changes, improves the calculation accuracy of meshing stiffness under actual operating conditions of the transmission system, and has practical application value for the optimization design of transmission systems and the improvement of transmission smoothness.

[0038] The method in this embodiment constructs a gear comprehensive stiffness model considering the load effect based on the method described in step 1, and explores the influence of load on the deformation of meshing teeth at different meshing positions and on the phase of the impact response period, thereby obtaining more accurate meshing stiffness values ​​of the teeth under different load conditions. This method makes the calculated stiffness values ​​of meshing teeth under different load conditions closer to reality. The method in this embodiment has practical application value for verifying the tooth strength and optimizing the tooth profile of gears under varying load conditions and non-standard gears.

[0039] Example: Two verification methods were used to verify the technical solution of the present invention. Verification method 1: Verifying the effect of setting different loads on the meshing stiffness of the gear transmission in the method of the present invention; Verification method 2: Verifying the effect of testing the transmission ratio and load on the meshing stiffness of the gear transmission in the method of the present invention. Three load torques were set for each verification method: 5 N•m, 25 N•m, and 125 N•m. The transmission ratio of verification method 1 was 1:1, and the transmission ratio of verification method 2 was 1:1.5. The gear parameters and load settings are shown in Table 1.

[0040] Table 1 Basic Parameters of Gears

[0041] (1) The gear comprehensive meshing stiffness calculated using the gear comprehensive stiffness model constructed by the method of this invention is compared with the gear comprehensive meshing stiffness calculated using the existing stiffness model (reference: Peng D., Smith W A., Borghesani P., et al. Comprehensive planet gear diagnostics: Use of transmission error and meshphasing to distinguish localised fault types and identify faulty gears. Mechanical Systems and Signal Processing, 2019, 127: 531-550.) to obtain Figure 3 (a) and Figure 4 (a). Comparative analysis of the effects of load and transmission ratio on the overall meshing stiffness of gears. Figure 3 To verify the performance of the gear in Scheme 1, (a) is the comprehensive meshing stiffness of the gear in Scheme 1, and (b) is the influence of the load on the comprehensive meshing stiffness of the gear in Scheme 1. Figure 3 (b) is based on Figure 3 (a) is a line graph obtained from the comprehensive meshing stiffness difference corresponding to different loads, where K 25 -K5 represents the line obtained by subtracting the comprehensive meshing stiffness value at a load of 5 N·m from the comprehensive meshing stiffness value at a load of 25 N·m; K 125 -K 25 The line represents the combined meshing stiffness value obtained by subtracting the combined meshing stiffness value at a load of 25 N·m from the combined meshing stiffness value at a load of 125 N·m.

[0042] Figure 4 The diagram shows the performance of the gears in test scheme 2. Among them, (a) is the diagram of the overall meshing stiffness of the gears in test scheme 2, and (b) is the diagram of the effect of load torque on the overall meshing stiffness of the gears in test scheme 2. Figure 4 (b) is based on Figure 4 (a) is a line graph showing the difference in comprehensive meshing stiffness under different loads and transmission ratios, where K 25 -K5 represents the line obtained by subtracting the combined meshing stiffness value of 5 N·m from the combined meshing stiffness value under a load of 25 N·m; K 125 -K 25 The line represents the combined meshing stiffness value obtained by subtracting the combined meshing stiffness value of 25 N·m from the combined meshing stiffness value of 125 N·m.

[0043] from Figure 3and Figure 4 As can be seen from this, the gear composite meshing stiffness calculated by the method of this invention not only includes the single meshing region and the double meshing region, but also includes the transition region closely related to the load magnitude (such as...). Figure 3 (a) and Figure 4 (as shown in (a)), where the larger the load, the wider the transition zone, and the smoother the stiffness switching between the single and double meshing zones. The transmission ratio also has a significant impact on the transition zone; the larger the transmission ratio, the smaller the stiffness difference between the single and double meshing zones, and this phenomenon is more pronounced under heavy load conditions.

[0044] The amplitude of the increase in the overall gear meshing stiffness caused by the increase in load torque fluctuates most dramatically in the transition zone; the amplitude of the increase in the overall gear meshing stiffness caused by the increase in load torque is relatively small in the double meshing zone, while its amplitude in the single meshing zone depends on the transmission ratio, where the larger the transmission ratio, the smaller the fluctuation of the increase in the overall gear meshing stiffness.

[0045] The above results confirm the necessity of considering factors such as load, meshing position and transmission ratio in the gear composite meshing stiffness, and verify the rationality and accuracy of the gear composite stiffness model constructed by the method of the present invention compared with existing stiffness models.

[0046] (2) Taking bending stiffness and shear stiffness as examples, the influence of load on bending stiffness and shear stiffness is analyzed, and the influence of factors such as load and meshing position on the overall meshing stiffness of the gear is further explained. The bending stiffness and shear stiffness values ​​of the meshing teeth are calculated using the existing stiffness model and the gear overall stiffness model constructed in this invention, respectively. For the gear in test scheme 1, the bending stiffness value of the meshing teeth is calculated using the existing stiffness model and the gear overall stiffness model constructed in this invention, and the results are obtained. Figure 5 (a) For the gear in test scheme 2, the bending stiffness value of the meshing teeth is calculated using the existing stiffness model and the gear integrated stiffness model constructed in this invention, and the results are obtained. Figure 5 (b) For the gear in test scheme 1, the shear stiffness value of the meshing teeth is calculated using the existing stiffness model and the gear integrated stiffness model constructed in this invention, and the results are obtained. Figure 6 (a) For the gear in test scheme 2, the shear stiffness value of the meshing teeth is calculated using the existing stiffness model and the gear integrated stiffness model constructed in this invention, and the results are obtained. Figure 6 (b).

[0047] from Figure 5 It can be seen that when the load on the meshing gear teeth changes, the bending stiffness of the meshing gear teeth increases with the increase of the load. When the load increases from 5 N·m to 25 N·m, the meshing stiffness of the gear teeth increases from 1.83 × 10⁻⁶. 9 N·m -1 Increased to 4.31×10 9 N·m-1 When the load increases from 25 N·m to 125 N·m, the gear meshing stiffness increases from 4.31 × 10⁻⁶. 9 N·m -1 Increased to 4.82×10 9 N·m -1 As the load continues to increase, the upward trend of bending stiffness gradually slows down. The meshing stiffness of the gear teeth does not change significantly in amplitude at different meshing positions during meshing because the torsional torque of the gear teeth remains constant during meshing. Furthermore, changes in the gear ratio have little effect on the meshing bending stiffness of the meshing gear teeth.

[0048] from Figure 6 It can be seen that when gears mesh, the stiffness of the meshing gears first increases and then decreases as the meshing point changes from the tooth root to the tooth tip. When the load on the meshing gears changes, the shear stiffness of the meshing gears increases with the increase of the load. When the load increases from 5 N·m to 25 N·m, the meshing stiffness increases from 2.11 × 10⁻⁶ N·m to 25 N·m. 10 N·m -1 Increased to 2.62 × 10 10 N·m -1 When the load increases from 25 N·m to 125 N·m, the gear tooth meshing stiffness increases from 2.62 × 10⁻⁶. 10 N·m -1 Increased to 5.18×10 10 N·m -1 As can be seen, the shear stiffness increases slowly with the continuous increase of load. Furthermore, the meshing stiffness value is symmetrical about the maximum stiffness value within the meshing range because when the transmission ratio is 1:1, the line connecting the centers of the driven and driving gears passes through the midpoint of the meshing line. When the gear transmission ratio changes, the position of the maximum value of the meshing stiffness curve is no longer symmetrical about the entire meshing range, but shifts to the right. This is because when the gear transmission ratio changes from 1:1 to 1:1.5, the driving and driven gears no longer rotate at the same angular velocity, causing the intersection of the line connecting the centers of the driving and driven gears with the meshing line to no longer coincide with the midpoint of the meshing line. This results in the maximum meshing stiffness no longer exhibiting symmetry.

[0049] The gear integrated stiffness model constructed by the method of the present invention can fully consider the influence of load and transmission ratio on the meshing stiffness of meshing gear teeth, and also fully consider the influence of load changes and transmission ratio on the stiffness of each meshing element (bending stiffness, shear stiffness, axial compression stiffness, base stiffness and Hertzian contact stiffness), thereby enabling the constructed gear integrated stiffness model to calculate stiffness values ​​more accurately, making gear parameter design more precise.

[0050] In the method of this invention, step 1 constructs the mapping relationship between external load and gear tooth meshing position, establishes a meshing period stiffness model with different number of teeth considering the influence of load, and obtains a gear meshing period variation model that is load-adaptive.

[0051] This invention considers the transfer function of the influence coefficient of load on different types of sub-stiffness and introduces it into the overall comprehensive stiffness model to complete the construction of an improved gear stiffness calculation model that takes into account the influence of load. This invention considers load influencing factors and introduces influence coefficients to characterize the impact of different meshing positions on meshing stiffness, overcoming the problem of inaccurate calculation of the impact response period phase in existing methods, and improving the calculation method of time-varying gear meshing stiffness. This invention has good engineering application value for gear tooth design optimization and ensuring the operational stability of mechanical equipment.

Claims

1. A gear design optimization method, characterized in that, The method includes: Step 1: Construct a gear comprehensive stiffness model based on gear teeth under variable loads; Step 2: Obtain the initial values ​​of the gear meshing tooth profile design parameters, including module, pressure angle, tooth width, number of teeth, center distance, and transmission ratio; Step 3: Substitute the set load and the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2 into the gear comprehensive stiffness model constructed in Step 1 to obtain the comprehensive stiffness of the gear. Step 4: Based on the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2, obtain the nominal stiffness of the gear meshing pair; compare the nominal stiffness of the gear meshing pair with the comprehensive stiffness of the gear obtained in Step 3. If the comprehensive stiffness of the gear obtained in Step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then the initial values ​​of the gear meshing pair tooth profile design parameters obtained in Step 2 are used as the actual gear design parameter values. If the overall stiffness of the gear obtained in step 3 is less than the nominal stiffness of the gear meshing pair, then return to step 3, change the gear meshing pair tooth profile design parameter value obtained in step 2, and substitute the set load and the changed gear meshing pair tooth profile design parameter value back into the gear overall stiffness model constructed in step 1 to obtain the gear overall stiffness, until the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair; the gear meshing pair tooth profile design parameter value that satisfies the condition that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear meshing pair is used as the actual gear design parameter value.

2. The gear design optimization method according to claim 1, characterized in that, Step 4 further includes: if the overall stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair, then compare whether the gear meshing sub-stiffness meets the sub-stiffness preset condition. If the sub-stiffness preset condition is met, then the gear meshing pair tooth profile design parameter value that satisfies the requirement that the overall stiffness of the gear is greater than or equal to the nominal stiffness of the gear pair is used as the actual gear design parameter value. If the sub-stiffness preset condition is not met, return to step 3, change the initial value of the gear meshing pair tooth profile design parameter obtained in step 2, and resubstitute the set load and the changed gear meshing pair tooth profile design parameter value into the gear comprehensive stiffness model constructed in step 1 to obtain the comprehensive stiffness of the gear, until the comprehensive stiffness of the gear obtained in step 3 is greater than or equal to the nominal stiffness of the gear meshing pair and meets the sub-stiffness preset condition; the gear meshing pair tooth profile design parameter value that meets the sub-stiffness preset condition and satisfies the requirement that the comprehensive stiffness of the gear is greater than or equal to the nominal stiffness of the gear pair is used as the actual gear design parameter value.

3. The gear design optimization method according to claim 2, characterized in that, The gear mesh stiffness includes gear mesh bending stiffness, gear mesh shear stiffness, gear mesh axial compressive stiffness, gear mesh base stiffness, and gear mesh Hertz contact stiffness. The sub-stiffness preset condition is that the calculated sub-stiffness value is greater than or equal to the sub-stiffness threshold.

4. The gear design optimization method according to claim 1, characterized in that, The method further includes: Step 5: Return to step 3, change the set load, and obtain the actual gear design parameter values ​​after changing the set load.

5. The gear design optimization method according to claim 1, characterized in that, Step 1 includes: Step 101: Calculate the gear tooth load using formula (1). Below, the meshing stiffness of single and double teeth : Equation (1) in, A value of 1 indicates single-gear meshing; A value of 2 indicates double gear meshing; Indicates under load Below is the influence coefficient of gear speed during single-gear meshing or double-gear meshing, which is dimensionless; Indicates under load Below, the influence coefficient of tooth profile for single-tooth meshing or double-tooth meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Axial compressive stiffness under action, unit: N / m; The transfer function representing the load influence coefficient of axial compressive stiffness under single-gear meshing or double-gear meshing is dimensionless; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Bending stiffness under load, unit: N / m; The transfer function representing the load influence coefficient of bending stiffness under single-gear meshing or double-gear meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Shear stiffness under action, unit: N / m; The transfer function representing the load influence coefficient of shear stiffness under single-gear or double-gear meshing is dimensionless; This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Matrix stiffness under action, unit: N / m; The dimensionless coefficient represents the influence coefficient on the stiffness of the tooth matrix under different loads for single-tooth meshing or double-tooth meshing. This indicates whether the teeth in single-tooth or double-tooth meshing are under load. Hertzian contact stiffness under action, unit: N / m; The dimensionless coefficient represents the influence coefficient of the Hertzian contact stiffness of teeth in single-tooth meshing or double-tooth meshing under different loads. Step 102: Calculate the elastic deformation and phase length of the gear teeth in the single-tooth meshing zone and the double-tooth meshing zone; Step 103: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under single-tooth meshing and double-tooth meshing conditions; Step 104: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under three-tooth meshing conditions; Step 105: Combine the comprehensive meshing stiffness of the same cycle to synthesize the comprehensive meshing stiffness of multiple cycles, which serves as the gear comprehensive stiffness model.

6. The gear design optimization method according to claim 5, characterized in that, In step 101, Equation (2) Equation (3) Equation (4) Equation (5) Equation (6) In the formula, represents the gear teeth under load. Bending stiffness under load, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth bending stiffness; The angle between the centerline of the gear tooth and the point of contact with the tangent point of the pitch circle, in radians; The angle between the direction of the force at the meshing point of the gear teeth and the vertical direction, expressed in radians; The angle between the center of the tooth and the root point of the tooth, in radians; The elastic modulus of the gear tooth material, expressed in Pa. Indicates the tooth width, unit: meter; Indicates the gear teeth under load Shear stiffness under action, unit: N / m; The dimensionless coefficient representing the influence coefficient of gear tooth shear stiffness; Poisson's ratio, representing the material of the gear teeth, is dimensionless. Indicates the gear teeth under load Axial compressive stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the axial compressive stiffness of the gear teeth; Indicates the gear teeth under load Matrix stiffness under action, unit: N / m; The dimensionless coefficient representing the influence of the gear tooth matrix stiffness; Indicates the tooth thickness, unit: meter; This represents the distance from the point where the force acting on the tooth intersects with the centerline of the tooth to the tooth root, expressed in meters. Indicates the gear teeth under load Hertzian contact stiffness under action, unit: N / m; This represents the influence coefficient of the Hertzian contact stiffness of the gear teeth, and is dimensionless.

7. The gear design optimization method according to claim 5, characterized in that, Step 102 includes: Calculate the elastic deformation and phase length of a single tooth in the meshing zone, specifically including: Under an external load, the elastic deformation of a single pair of gear teeth is calculated according to equation (7). for: Equation (7) in, This indicates that the gear is subjected to an external load, measured in Newton-meters (N·m). This represents the combined meshing stiffness of a single tooth pair, in Newtons per meter (N / m). This indicates the gear radius corresponding to the current meshing position, in meters. The load is obtained according to equation (8). Single tooth meshing phase length : Equation (8) in, Calculate according to the following formula: ； In the formula, Indicates the number of teeth on the driving wheel. Indicates the number of teeth on the driven gear; The angle between the line connecting the center and the point of contact of the meshing gear and the point of tangency between the center and the base circle, in radians; This indicates the gear radius corresponding to the current meshing position, in meters. Calculate the elastic deformation and phase length of the teeth in the double-tooth meshing zone, specifically including: When the gears enter the double-tooth meshing zone, the load on the gear pair... The meshing is borne by two pairs of gear teeth. According to equation (9), the elastic deformation of the gear teeth involved in the meshing is calculated as follows: Equation (9) in, The elastic deformation of the first pair of teeth involved in meshing, expressed in meters; This indicates the combined meshing stiffness of a double tooth pair, in Newtons per meter (N / m). This indicates the gear radius corresponding to the current meshing position of the first pair of teeth involved in meshing, in meters; The elastic deformation of the second pair of teeth involved in meshing, expressed in meters; This indicates the gear radius corresponding to the current meshing position of the second pair of teeth involved in meshing, in meters; The load is obtained according to equation (10). Lower double-tooth meshing phase length : Equation (10).

8. The gear design optimization method according to claim 5, characterized in that, Step 103 includes: Step 1031: Calculate the overall meshing stiffness of the gear teeth in the meshing phase interval under single-tooth meshing conditions, specifically including: If the elastic deformation of a single pair of gear teeth Larger than tooth gap If the gear engages in double-tooth meshing prematurely, the combined meshing stiffness of a single pair of gear teeth should be recalculated according to equation (11). Then proceed to step 104; Equation (11) In the formula, This represents the overall meshing stiffness of a single gear pair, in Newtons per meter (N / m). The gear rotation angle corresponding to the final meshing position in the single-tooth meshing zone, in radians; The gear radius corresponding to the final meshing position in the single-tooth meshing zone, in meters; and These represent the gear radii corresponding to the current meshing positions of the two pairs of teeth, in meters; If the elastic deformation of a single pair of gear teeth Smaller than tooth gap Then proceed to step 1032; Step 1032: Calculate the overall meshing stiffness of the teeth in the meshing phase interval under double-tooth meshing conditions, specifically including: When two teeth are meshing, the elastic deformation of the two pairs of teeth is compared according to the current meshing position. If... Then, the combined stiffness of the meshing of the two pairs of gear teeth is calculated according to equation (12). : Equation (12) In the formula, This represents the overall meshing stiffness of a single gear pair, in Newtons per meter (N / m). Indicates the meshing radius corresponding to the meshing position of the first pair of gear teeth, in meters; This represents the change in the rotation angle of the first pair of meshing gear teeth during the meshing process, in radians. Indicates the meshing radius corresponding to the meshing position of the third pair of gear teeth, in meters; like Then, the combined stiffness of the meshing of the two pairs of gear teeth is calculated according to equation (13). : Equation (13) In the formula, and These represent the gear radii corresponding to the current meshing positions of the two pairs of teeth, in meters; This indicates the change in the rotation angle of the second pair of meshing gear teeth during the meshing process, in radians.

9. The gear design optimization method according to claim 5, characterized in that, Step 104 includes: Under load Under the action of the action, the elastic deformation of the three teeth is calculated using equation (14): Equation (14) In the formula, This represents the elastic deformation of the first pair of teeth during three-tooth meshing, in meters. This indicates the elastic deformation of the second pair of teeth during three-tooth meshing, in meters. This indicates the elastic deformation of the third pair of teeth during three-tooth meshing, in meters. The combined stiffness of the meshing teeth when three teeth are engaged, expressed in Newtons per meter (N / m). Indicates the meshing radius corresponding to the meshing position of the first pair of gear teeth, in meters; Indicates the meshing radius corresponding to the meshing position of the second pair of gear teeth, in meters; Indicates the meshing radius corresponding to the meshing position of the third pair of gear teeth, in meters; Determine the elastic deformation of the gear teeth and the clearance between the three pairs of teeth. If the elastic deformation of the gear teeth is greater than the clearance between the three pairs of teeth, then the gear enters the three-tooth meshing zone, and the gear load... It is supported by three pairs of gear teeth; the meshing phase length of the three teeth is calculated using equation (15). for: Equation (15) The overall stiffness of the meshing teeth during three-tooth meshing is calculated using equation (16). Then proceed to step 105; Equation (16) In the formula, Indicates the total number of teeth pairs involved in meshing; Indicates the first The gear radius corresponding to the current meshing position of the gear teeth, in meters; Indicates the angle as The radius of the time, in meters; Expresses the amount of elastic deformation of the gear teeth, in meters; The clearance between meshing gear teeth, expressed in meters. Indicates the first The gear radius corresponding to the current meshing position of the gear teeth, in meters; If the elastic deformation of the gear teeth is less than the clearance between the three pairs of gear teeth, proceed to step 105.

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