A method for measuring time-varying mesh stiffness of a gear

Abstract

The application discloses a gear time-varying meshing stiffness measurement method, which comprises the following steps: S1, a measurement model between current and time-varying meshing stiffness is established based on Hertz contact theory and Ishikawa formula; S2, a closed circuit is formed by connecting a driving gear, a driven gear and a power supply in series, and time-varying current of the circuit is measured; and S3, the time-varying current measured in S2 is substituted into the measurement model to obtain time-varying meshing stiffness of the gear. The application improves the measurement precision and efficiency of the gear time-varying meshing stiffness.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear mesh stiffness measurement, in particular to a kind of gear time-varying mesh stiffness measurement method. BACKGROUND

[0002] Gear transmission has become the most widely used transmission form in modern machinery, and very high requirements are put forward for gear transmission in all aspects, mainly to ensure low vibration and low noise of gear transmission under the premise of meeting high bearing capacity and high reliability. Mesh stiffness is the inherent characteristic of gear, and is periodic change, with strong time-varying characteristics, the time-varying characteristics of mesh stiffness will cause stiffness excitation in the transmission process of gear, and then make dynamic excitation force of gear system, that is, mesh stiffness is one of the important excitation sources of gear vibration and noise, therefore, the research on time-varying mesh stiffness in gear transmission has important significance.

[0003] At present, the main methods for obtaining gear time-varying mesh stiffness are finite element method, analytical method and direct measurement method. Among them, the finite element method is to discretize the finite element model of gear meshing by establishing the finite element model of gear meshing, and the mesh stiffness is obtained by solving the model with reasonable boundary conditions; the analytical method is to establish a mathematical model based on material mechanics and elasticity to solve the gear time-varying mesh stiffness, but the simplification in the process of establishing the theoretical model brings certain error to the calculation result, among them, Ishikawa formula is widely used, but it does not consider the deformation of gear teeth, which leads to larger error in calculation result; the direct measurement method is to bury piezoelectric material in the gear to measure the normal pressure of gear meshing and the deformation of gear, and then calculate the time-varying mesh stiffness of gear, but the buried piezoelectric material will damage the overall structure of the gear, resulting in larger error in the measurement result of time-varying mesh stiffness. SUMMARY

[0004] In order to solve the problem of large measurement error of gear time-varying mesh stiffness in the prior art, the present application provides a kind of gear time-varying mesh stiffness measurement method, which improves the measurement accuracy and efficiency of gear time-varying mesh stiffness.

[0005] In order to achieve the above purpose, the specific scheme adopted by the present application is as follows: a kind of gear time-varying mesh stiffness measurement method, comprising the following steps:

[0006] S1, a measurement model between current and time-varying mesh stiffness is established based on Hertz contact theory and Ishikawa formula;

[0007] S2, the driving gear, driven gear and power supply are connected in series to form a closed circuit, and the time-varying current of the circuit is measured;

[0008] S3, the time-varying current measured in S2 is substituted into the measurement model to obtain the time-varying mesh stiffness of the gear.

[0009] As an optimization scheme of the above-mentioned gear time-varying meshing stiffness measurement method, S1 comprises the following steps:

[0010] S11, establishing the relationship between the curvature and the contact deformation at the meshing position of the driving gear and the driven gear based on the Hertz contact theory;

[0011] S12, obtaining the bending deformation of the trapezoid, the bending deformation of the rectangle, the shear deformation and the basic deformation of the driving gear and the driven gear respectively based on the Ishikawa formula, and obtaining the deformation of a gear tooth at the normal load action point along the meshing line direction;

[0012] S13, obtaining the total deformation at the meshing position by combining S11 and S12, and obtaining the time-varying meshing stiffness according to the total deformation, and establishing the relationship between the curvature and the time-varying meshing stiffness at the meshing position of the driving gear and the driven gear;

[0013] S14, establishing the relationship between the time-varying current and the curvature at the meshing position of the driving gear and the driven gear;

[0014] S15, combining the relationship between the curvature and the time-varying meshing stiffness in S13 and the relationship between the curvature and the time-varying current to establish a measurement model of the time-varying meshing stiffness and the time-varying current.

[0015] As another optimization scheme of the above-mentioned gear time-varying meshing stiffness measurement method, S11 comprises:

[0016] S111, forming a normal contact load at the meshing position of the driving gear and the driven gear, and under the action of the normal contact load, the meshing position of the driving gear and the driven gear produces elastic deformation to form a contact ellipse, and the ellipticity parameter c of the contact ellipse is:

[0017]

[0018] Wherein, Σρ1 is the curvature of the driving gear at the meshing position, and Σρ2 is the curvature of the driven gear at the meshing position;

[0019] S112, calculating the first type of elliptic integral and the second type of elliptic integral:

[0020]

[0021] S113, calculating the major axis a and the minor axis b of the contact ellipse according to the ellipticity parameter, the first type of elliptic integral and the second type of elliptic integral:

[0022]

[0023] Wherein, E is the elastic modulus, F NF is the load force, Σρ is the curvature of the driving gear and the driven gear at the meshing position, and Σρ = Σρ1 + Σρ2;

[0024] The contact deformation amount is δ

[0025]

[0026] The bending deformation amount of the trapezoid is δ

[0027]

[0028] The bending deformation amount of the rectangle is δ

[0029]

[0030] The shear deformation amount is δ

[0031]

[0032] The base deformation amount is δ

[0033]

[0034] The deformation amount of one tooth at the normal load action point along the meshing line direction is δ

[0035] δ = δ Bt + δ Br + δ s + δ G

[0036] Wherein, F N is the load force, E is the elastic modulus, S F is the dedendum circle tooth thickness, x is the deflection coefficient, h x is the position height of the force point, h i is the parameter related to the trapezoidal shape, h r is the approximate tooth rectangle height, B is the tooth width, ω x is the angle between the force direction and the horizontal direction, and v is the Poisson's ratio.

[0037] As another optimization scheme of the above-mentioned gear time-varying meshing stiffness measurement method: S131, the total deformation amount of the gear meshing position is calculated to obtain δ

[0038] δ 总 = δ pV + δ1+ δ2

[0039] Wherein, δ pVδ1 is the deformation of the tooth of the driving gear in the direction of the engagement line at the point of action of the normal load, δ2 is the deformation of the tooth of the driven gear in the direction of the engagement line at the point of action of the normal load;

[0040] S132, the time-varying engagement stiffness is obtained according to the total deformation at the engagement of the gear:

[0041] k = F N / (δ 总 ·B)

[0042] wherein F N is the load force, and B is the tooth width;

[0043] The relationship between the curvature sum and the time-varying engagement stiffness is obtained as:

[0044]

[0045] wherein E is the elastic modulus, B is the tooth width, δ1 is the deformation of the tooth of the driving gear in the direction of the engagement line at the point of action of the normal load, δ2 is the deformation of the tooth of the driven gear in the direction of the engagement line at the point of action of the normal load, Σρ is the curvature sum of the driving gear and the driven gear at the engagement, c is the ellipticity parameter, Π is the first kind of elliptic integral, and Γ is the second kind of elliptic integral.

[0046] As another optimization scheme of the above-mentioned gear time-varying engagement stiffness measurement method: in S14, the relationship between the current and the curvature sum is established:

[0047]

[0048] wherein U is the voltage, B is the tooth width, Σρ is the curvature sum of the driving gear and the driven gear at the engagement, Π is the first kind of elliptic integral, E is the elastic modulus, λ is the resistivity, L is the theoretical length of the gear conductor, F N is the load force, and c is the ellipticity parameter.

[0049] As another optimization scheme of the above-mentioned gear time-varying engagement stiffness measurement method: in S15, the relationship between the current and the engagement stiffness is:

[0050]

[0051] wherein U is the input voltage, B is the tooth width, Σρ is the curvature sum of the driving gear and the driven gear at the engagement, Γ is the second kind of elliptic integral, E is the elastic modulus, λ is the resistivity, L is the theoretical length of the gear conductor, I is the time-varying current of the gear, FN is the load force, c is the ellipticity parameter, W1 = δ Bt1 / F N , and X1 = δ Br1 / FN Y1 = δ s1 F N Z1 = δ G1 F N W2 = δ Bt2 F N X2 = δ Br2 F N Y2 = δ s2 F N Z2 = δ G2 F N δ Bt1 is the bending deformation of the trapezoidal shape of the driving gear, δ Br1 is the bending deformation of the rectangular shape of the driving gear, δ s1 is the shear deformation of the driving gear, δ G1 is the base deformation of the driving gear, δ Bt2 is the bending deformation of the trapezoidal shape of the driven gear, δ Br2 is the bending deformation of the rectangular shape of the driven gear, δ s2 is the shear deformation of the driven gear, δ G2 is the base deformation of the driven gear.

[0052] Another optimization scheme of the above-mentioned measurement method of time-varying meshing stiffness of a gear: in the S3, the measured time-varying current is brought into the measurement model after amplification and filtering processing.

[0053] Compared with the prior art, the present application has the following beneficial effects:

[0054] The present application provides a measurement method of time-varying meshing stiffness of a gear, a measurement model between current and time-varying meshing stiffness is established based on Hertz contact theory and Ishikawa formula, when measuring the time-varying meshing stiffness, only the current needs to be measured and substituted into the measurement model, thereby improving the measurement accuracy and efficiency of the time-varying meshing stiffness of the gear. DETAILED DESCRIPTION

[0055] The technical solutions of the present application will be further described in detail below in combination with specific embodiments, and the parts not described and disclosed in the following embodiments of the present application should be understood as the prior art known or should be known by those skilled in the art, such as acquisition of time-varying current, linear regression method, etc.

[0056] A measurement method of time-varying meshing stiffness of a gear, comprising the following steps:

[0057] S1, a measurement model between current and time-varying meshing stiffness is established based on Hertz contact theory and Ishikawa formula, according to the Hertz contact theory, elastic deformation is generated at the contact site of two contact objects, therefore, the shape of the contact surface at the contact site is elliptical.

[0058] Specifically, S1 comprises:

[0059] S11, establishing a relationship between the curvature and the contact deformation at the meshing position of the driving gear and the driven gear based on the Hertz contact theory.

[0060] Specifically, S11 comprises:

[0061] S111, a normal contact load is formed at the meshing position of the driving gear and the driven gear, and under the action of the normal contact load, the meshing position of the driving gear and the driven gear produces elastic deformation to form a contact ellipse on the contact surface, and an ellipticity parameter c of the contact ellipse is:

[0062]

[0063] Wherein, Σρ1 is the curvature of the driving gear at the meshing position, and Σρ2 is the curvature of the driven gear at the meshing position. The contact ellipse parameter is related to the curvature at the meshing position.

[0064] S112, the first type of elliptic integral and the second type of elliptic integral are calculated by using a linear regression method:

[0065]

[0066] S113, the major axis a and the minor axis b of the contact ellipse are calculated according to the ellipticity parameter, the first type of elliptic integral and the second type of elliptic integral:

[0067]

[0068] Wherein, E is the elastic modulus, F N is the load force, and Σρ is the curvature of the driving gear and the driving gear at the meshing position, and Σρ = Σρ1 + Σρ2.

[0069] S114, the contact deformation is:

[0070]

[0071] The relationship between the curvature Σρ and the contact deformation is obtained.

[0072] S12, the bending deformation of the trapezoid, the bending deformation of the rectangle, the shear deformation and the basic deformation of the driving gear and the driven gear are obtained based on the Ishikawa formula, and the deformation of a tooth at the normal load action point along the meshing line is obtained.

[0073] Specifically, the bending deformation of the trapezoid is:

[0074]

[0075] Wherein, F NF is the load force, E is the elastic modulus, S is the tooth thickness, x is the displacement coefficient, h is the tooth height F F is the load force, E is the elastic modulus, S is the tooth thickness, x is the displacement coefficient, h is the tooth height x F is the load force, E is the elastic modulus, S is the tooth thickness, x is the displacement coefficient, h is the tooth height i F is the load force, E is the elastic modulus, S is the tooth thickness, x is the displacement coefficient, h is the tooth height r F is the load force, E is the elastic modulus, S is the tooth thickness, x is the displacement coefficient, h is the tooth height x F is the load force, E is the elastic modulus, S is the tooth thickness, x is the displacement coefficient, h is the tooth height

[0076] The bending deformation of the rectangle is:

[0077]

[0078] The shear deformation is:

[0079]

[0080] The base deformation is:

[0081]

[0082] The deformation of a tooth at the normal load point along the meshing line direction is:

[0083] δ = δ Bt + δ Br + δ s + δ G .

[0084] S13, in combination with S11 and S12, obtains the total deformation at the meshing position, and obtains the time-varying meshing stiffness according to the total deformation, and establishes the relationship between the curvature of the meshing position of the driving gear and the driven gear and the time-varying meshing stiffness.

[0085] Specifically, S13 includes:

[0086] S131, the total deformation at the meshing position of the gear is calculated:

[0087] δ 总 = δ pV + δ1+ δ2

[0088] Wherein, δ pV is the contact deformation of the driving gear and the driven gear at the meshing position, δ1 is the deformation of the tooth of the driving gear at the normal load point along the meshing line direction, and δ2 is the deformation of the tooth of the driven gear at the normal load point along the meshing line direction;

[0089] S132, the time-varying meshing stiffness is obtained according to the total deformation at the meshing position of the gear

[0090] k = F N / (δ 总 ·B)

[0091] Among them, F N B is the load force, and B is the tooth width;

[0092]

[0093] The above δ pV Substituting into the above equation, the relationship between curvature and time-varying meshing stiffness is obtained as follows:

[0094]

[0095] Where E is the elastic modulus, B is the tooth width, δ1 is the deformation of the teeth of the driving gear along the meshing line at the point of application of the normal load, δ2 is the deformation of the teeth of the driven gear along the meshing line at the point of application of the normal load, Σρ is the sum of the curvatures of the driving gear and the driving gear at the meshing point, c is the ellipticity parameter, Π is the elliptic integral of the first kind, and Γ is the elliptic integral of the second kind.

[0096] S14, establish the relationship between the time-varying current and the curvature at the meshing point of the driving and driven gears.

[0097] Specifically, the time-varying current of the gear is:

[0098]

[0099] Where a is the major axis of the contact ellipse, L is the theoretical length of the gear conductor, B is the tooth width, U is the voltage, and λ is the resistivity.

[0100] Substituting 'a' into the above equation, we get:

[0101]

[0102] Transforming the above equation yields the curvature sum:

[0103]

[0104] S15, combining the relationship between curvature and time-varying meshing stiffness in S13 and S14, and the relationship between curvature and time-varying current, establish a measurement model for time-varying meshing stiffness and time-varying current.

[0105] Substituting the expression for the sum of curvatures into the relationship between the sum of curvatures and the time-varying meshing stiffness, we obtain the relationship between the time-varying current and the time-varying meshing stiffness:

[0106]

[0107] Where U is the voltage, B is the tooth width, Σρ is the sum of the curvatures of the driving gear and the driving gear at the meshing point, Γ is the elliptic integral of the second kind, E is the elastic modulus, λ is the resistivity, L is the theoretical length of the gear conductor, I is the time-varying current of the gear, and F...N Where c is the load force, and c is the ellipticity parameter, W1 = δ Bt1 / F N X1 = δ Br1 / F N Y1=δ s1 / F N Z1 = δ G1 / F N W2 = δ Bt2 / F N X2 = δ Br2 / F N Y2=δ s2 / FN, Z2=δ G2 / F N δ Bt1 For the trapezoidal bending deformation of the driving gear, δ Br1 For the rectangular bending deformation of the driving gear, δ s1 For the shear deformation of the driving gear, δ G1 For the deformation of the base of the driving gear, δ Bt2 For the trapezoidal bending deformation of the driven gear, δ Br2 Let δs2 be the rectangular bending deformation of the driven gear, and δs2 be the shear deformation of the driven gear. G2 The deformation of the driven gear's base material.

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] Among them, F N Where E1 is the elastic modulus of the driving gear, E2 is the elastic modulus of the driven gear, and S is the load force. F1 For the root circle thickness of the driving gear, S F2 Let x1 be the tooth root circle thickness of the driven gear, x2 be the modification coefficient of the driving gear, and h be the modification coefficient of the driven gear. x1 h represents the height of the point where the driving gear is subjected to force. x2 h is the height of the point where the driven gear is subjected to force.i1 h is a parameter related to the trapezoidal shape of the driving gear. i2 h is a parameter related to the trapezoidal shape of the driven gear. r1 h is the approximate tooth rectangle height of the driving gear. r2 Let B1 be the approximate tooth rectangle height of the driven gear, B2 be the tooth width of the driving gear, and ω be the tooth width of the driven gear. x1 ω is the angle between the direction of the force on the driving gear and the horizontal direction. x2 The angle between the direction of the force on the driven gear and the horizontal direction.

[0117] By determining the degree of overlap, the rotation angle and time corresponding to the meshing zone are obtained, thus yielding ω. x .

[0118] S2, the driving gear, driven gear and power supply are connected in series to form a closed circuit, and the time-varying current of the circuit is measured.

[0119] S3, substitute the time-varying current measured in S2 into the measurement model to obtain the time-varying meshing stiffness of the gear.

[0120] This invention, when measuring time-varying meshing stiffness, only requires measuring the time-varying current of the gear. Substituting this time-varying current into the measurement model yields the gear meshing stiffness. Measuring the gear current does not require embedding piezoelectric material within the gear, thus preserving the gear's structure. The remaining parameters within the measurement model are the gear's design parameters. This method is simpler and simultaneously improves the accuracy and efficiency of measuring time-varying gear meshing stiffness.

[0121] In this embodiment, the measured time-varying current is amplified and filtered before being incorporated into the measurement model.

[0122] The time-varying meshing stiffness of a single tooth is:

[0123]

[0124] The time-varying meshing stiffness of the two-tooth teeth is:

[0125]

[0126] Where k is the time-varying meshing stiffness.

[0127] The measuring device used in this embodiment includes an input control module, a gear working module, and a post-processing module. The input control module includes a data fusion unit, mainly used to calculate the real-time torque, force, and moment of contact between the driving gear and the driven gear. The gear working module mainly includes an input shaft, a driving gear, a driven gear, and an output shaft. The data post-processing module determines the proportional coefficient between the time-varying meshing stiffness and the time-varying current by identifying the gear rotation angle and time, and amplifies, filters, and visualizes the output signal.

[0128] The foregoing description of the disclosed embodiments enables one skilled in the art to make or use the application. Numerous modifications of those embodiments can be apparent to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without the use of the innovation falling outside the spirit and scope of the application. Therefore, the application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for measuring the time-varying meshing stiffness of gears, characterized in that: Includes the following steps: S1, a measurement model between current and time-varying meshing stiffness is established based on Hertzian contact theory and Ishikawa formula; S11, based on Hertzian contact theory, establishes the relationship between the curvature at the meshing point of the driving gear and the amount of contact deformation; S11 includes: S111, a normal contact load is formed at the meshing point of the driving gear and the driven gear. Under the action of the normal contact load, elastic deformation occurs at the meshing point of the driving gear and the driven gear, causing the contact surface to form a contact ellipse. The ellipticity parameter c of the contact ellipse is: Wherein, Σρ1 is the curvature of the driving gear at the meshing point, and Σρ2 is the curvature of the driven gear at the meshing point; S112, calculate the elliptic integral of the first and second kind: S113, based on the ellipticity parameter, the first kind of elliptic integral, and the second kind of elliptic integral, the major semi-axis a and minor semi-axis b of the contact ellipse are calculated as follows: Where E is the elastic modulus, F N The load force is Σρ, which is the curvature of the driving gear and the driving gear at the meshing point, and Σρ = Σρ1 + Σρ2. S114, the contact deformation is: S12, based on the Ishikawa formula, the bending deformation of the trapezoid, the bending deformation of the rectangle, the shear deformation and the basic deformation of the driving gear and the driven gear are obtained respectively, and the deformation of a tooth along the meshing line at the point of application of the normal load is obtained. S13, combined with S11 and S12 above, the total deformation at the meshing point is obtained, and the time-varying meshing stiffness is obtained based on the total deformation. The relationship between the curvature at the meshing point of the driving gear and the driven gear and the time-varying meshing stiffness is established. S14, establish the relationship between the time-varying current and the curvature at the meshing point of the driving gear and the driven gear; The time-varying current of the gear is: Where a is the major axis of the contact ellipse, L is the theoretical length of the gear conductor, B is the tooth width, U is the voltage, and λ is the resistivity; Substituting 'a' into the above equation, we get: Where U is the voltage, B is the tooth width, Σρ is the sum of the curvatures of the driving gear and the driving gear at the meshing point, Π is the elliptic integral of the first kind, E is the elastic modulus, λ is the resistivity, L is the theoretical length of the gear conductor, and F... N For load force, c is the ellipticity parameter; S15, combining the curvature in S13 and S14 with the relationship between curvature and time-varying meshing stiffness and the relationship between curvature and time-varying current, establish a measurement model for time-varying meshing stiffness and time-varying current. S2, the driving gear, driven gear and power supply are connected in series to form a closed circuit, and the time-varying current of the circuit is measured; S3, substitute the time-varying current measured in S2 into the measurement model to obtain the time-varying meshing stiffness of the gear.

2. The method for measuring the time-varying meshing stiffness of gears as described in claim 1, characterized in that: In S12, the bending deformation of the trapezoid is: The bending deformation of the rectangle is: The amount of shear deformation is: The amount of matrix deformation is: The deformation of a gear tooth along the meshing line at the point of application of the normal load is: d=d Bt +d Br +d s +d G Among them, F N Where E is the load force, E is the elastic modulus, and S is the elastic modulus. F Where x is the tooth root circle thickness, h is the displacement coefficient, and y is the tooth root circle thickness. x h is the height of the point where the force is applied. i h is a parameter related to the shape of the trapezoid. r The height of the approximate tooth rectangle is given by ω, where B is the tooth width. x Let ν be the angle between the direction of the force and the horizontal direction, and ν be Poisson's ratio.

3. The method for measuring the time-varying meshing stiffness of gears as described in claim 1, characterized in that: S3 includes: S131, the total deformation at the gear meshing point is calculated: δ 总 =δ pV +δ1+δ2 where, δ pV δ1 represents the contact deformation of the driving gear and driven gear at the meshing point, δ2 represents the deformation of the teeth of the driving gear along the meshing line at the point of application of the normal load, and δ2 represents the deformation of the teeth of the driven gear along the meshing line at the point of application of the normal load. S132, the time-varying meshing stiffness is obtained from the total deformation at the gear meshing point as follows: k=F N / (d 总 ·B) Among them, F N B is the load force, and B is the tooth width; The relationship between curvature and time-varying meshing stiffness is obtained as follows: Where E is the elastic modulus, B is the tooth width, δ1 is the deformation of the teeth of the driving gear along the meshing line at the point of application of the normal load, δ2 is the deformation of the teeth of the driven gear along the meshing line at the point of application of the normal load, Σρ is the sum of the curvatures of the driving gear and the driving gear at the meshing point, c is the ellipticity parameter, Π is the elliptic integral of the first kind, and Γ is the elliptic integral of the second kind.

4. The method for measuring the time-varying meshing stiffness of gears as described in claim 1, characterized in that: In S15, the relationship between current and meshing stiffness is as follows: Where U is the input voltage, B is the tooth width, Σρ is the sum of the curvatures of the driving gear and the driving gear at the meshing point, Γ is the elliptic integral of the second kind, E is the elastic modulus, λ is the resistivity, L is the theoretical length of the gear conductor, I is the time-varying current of the gear, and F... N Where c is the load force, and c is the ellipticity parameter, W1 = δ Bt1 / F N X1 = δ Br1 / F N Y1=δ s1 / F N Z1 = δ G1 / F N W2 = δ Bt2 / F N X2 = δ Br2 / F N Y2=δ s2 / F N Z2=δ G2 / F N δ Bt1 For the trapezoidal bending deformation of the driving gear, δ Br1 For the rectangular bending deformation of the driving gear, δ s1 For the shear deformation of the driving gear, δ G1 For the deformation of the base of the driving gear, δ Bt2 For the trapezoidal bending deformation of the driven gear, δ Br2 For the rectangular bending deformation of the driven gear, δ s2 For the shear deformation of the driven gear, δ G2 The deformation of the driven gear's base material.

5. The method for measuring the time-varying meshing stiffness of gears as described in claim 1, characterized in that: In step S3, the measured time-varying current is amplified and filtered before being incorporated into the measurement model.

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