阅读说明：本技术 一种兆瓦级风电齿轮箱等效缩减方法 (Equivalent reduction method for megawatt wind power gear box ) 是由 朱才朝 冉峯 谭建军 宋朝省 朱永超 于 2021-08-27 设计创作，主要内容包括：本发明公开一种兆瓦级风电齿轮箱等效缩减方法,步骤为：1)计算风电齿轮箱各级齿轮的初始接触安全系数和弯曲安全系数；2)构建风电齿轮箱传动系统动力学方程,并计算风电齿轮箱传动系统固有频率；3)建立缩减后风电齿轮箱参数优化模型；建立缩减后风电齿轮箱参数优化方程；4)将缩减后的输入功率和转速输入到缩减后风电齿轮箱参数优化模型中,计算得到缩减后风电齿轮箱参数；5)将缩减后风电齿轮箱参数输入到缩减后风电齿轮箱参数优化方程中,得到轴参数缩减比和缩减后固有频率。本方法在对风电齿轮箱进行缩减的时候,考虑了缩减前后各级齿轮的强度相等以及固有特性相似,最大程度的减小的缩减前后齿轮箱之间的差异。(The invention discloses an equivalent reduction method for a megawatt wind-power gear box, which comprises the following steps: 1) calculating initial contact safety factors and bending safety factors of gears at all levels of the wind power gear box; 2) constructing a kinetic equation of the transmission system of the wind power gear box, and calculating the natural frequency of the transmission system of the wind power gear box; 3) establishing a reduced wind power gear box parameter optimization model; establishing a reduced wind power gear box parameter optimization equation; 4) inputting the reduced input power and the reduced rotating speed into a reduced wind power gear box parameter optimization model, and calculating to obtain reduced wind power gear box parameters; 5) and inputting the reduced wind power gear box parameters into a reduced wind power gear box parameter optimization equation to obtain a shaft parameter reduction ratio and a reduced natural frequency. When the wind power gear box is reduced, the method considers that the strength of gears at all stages is equal and the inherent characteristics are similar before and after reduction, and reduces the difference between the gear boxes before and after reduction to the maximum extent.)

1. A megawatt wind power gear box equivalent reduction method is characterized by comprising the following steps:

1) acquiring initial parameters of a transmission system of a wind power gear box; and acquiring and reducing the input power and the rotating speed of the transmission system of the wind power gear box.

2) Calculating initial contact safety factors and bending safety factors of gears at all levels of the wind power gear box;

3) constructing a dynamic equation of the transmission system of the wind power gear box according to the initial parameters of the transmission system of the wind power gear box, and calculating the natural frequency of the transmission system of the wind power gear box;

4) establishing a reduced wind power gear box parameter optimization model according to initial contact and bending safety coefficients of gears at all levels of the wind power gear box;

establishing a parameter optimization equation of the reduced wind power gear box according to the natural frequency of the transmission system of the wind power gear box;

5) inputting the reduced input power and the reduced rotating speed into a reduced wind power gear box parameter optimization model, and calculating to obtain reduced wind power gear box parameters;

6) and inputting the reduced wind power gear box parameters into a reduced wind power gear box parameter optimization equation to obtain a shaft parameter reduction ratio and a reduced natural frequency, and obtaining a similarity ratio of the reduced natural frequency and the natural frequency of a wind power gear box transmission system.

2. The megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: the initial parameters of the wind power gear box transmission system comprise rated power, rated output rotating speed, transmission ratio, total transmission ratio, rated input torque of the wind power gear box, the number of planet wheels, center distance, modulus, pressure angle, rotating direction, gear type, tooth number, tooth width, mass and rotational inertia.

3. The megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: initial contact safety factor S_HAnd bending safety factor S_FRespectively as follows:

in the formula, K_ATo use the coefficient, K_VIs a dynamic load coefficient, K_HβFor calculating the tooth load distribution coefficient of the contact strength, K_HαFor calculating the interdental load distribution coefficient of the contact strength, K_HPCoefficient of non-uniformity of load distribution between planet wheels, Z, for calculation of contact strength_HAs a node area coefficient, Z_EIs the coefficient of elasticity, Z_εIs the coefficient of contact ratio, Z_βIs the helix angle coefficient, F_tNominal tangential force on a circle of division in the face of the gear, d₁Is the reference circle diameter of the pinion, b is the working tooth width, u is the transmission ratio, sigma_HlimTo test the contact fatigue limit of gears, Z_NTFor calculating the life factor of the contact strength, Z_LIs the coefficient of lubricant, Z_VIs a velocity coefficient, Z_RTo roughness factor, Z_WIs the work hardening coefficient, Z_XDimensional factor, K, calculated for contact strength_FβFor calculating the tooth load distribution coefficient of the bending strength, K_FαFor calculating the interdental load distribution coefficient of the bending strength, K_FPFor calculating the load distribution non-uniformity coefficient between planet wheels of bending strength, Y_FaThe tooth form factor when a load acts on the tooth tip, Y_SaThe stress correction coefficient when a load acts on the tooth tip, Y_εFor calculating the overlap ratio of the bending strength, Y_βTo calculate the overlap ratio coefficient of the bending strength, σ_FlimFor testing the tooth root bending fatigue limit stress, Y_STCalculated life factor for bending strength, Y_NTTo calculate the bending limit stress of the gear, Y_δrelTSensitivity to root fillet, Y_RrelTRelative root surface condition coefficient, Y_XDimensional factors calculated for bending strength, "+" for external gearing and "-" for internal gearing; m is_nIs the normal modulus.

4. The megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: the dynamic equation of the transmission system of the wind power gear box is as follows:

in the formula, M is a mass matrix, and K is a rigidity matrix; x is a displacement matrix;representing an acceleration matrix;

the mass matrix M and the rigidity matrix K are respectively as follows:

in the formula, M_S1、M_R1、M_C1、M_P1、M_G1And M_G2Respectively representing the mass matrixes of the sun gear, the inner gear ring, the planet carrier, the planet gear, the big gear and the small gear; k_S1、K_C1、K_P1、K_R1、K_G1And K_G2Respectively representing bearing support rigidity matrixes of a sun gear, a planet carrier, a planet gear, an inner gear ring, a large gear and a small gear; k_C1P1Representing a coupling stiffness matrix of the planet wheel and the planet carrier; k_S1P1、K_R1P1And K_G1G2And respectively representing meshing rigidity matrixes of the sun gear and the planet gear, the inner gear ring and the planet gear, and the large gear and the small gear.

5. The megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: the natural frequency omega of the transmission system of the wind power gear box meets the following formula:

wherein M is a mass matrix; k is a stiffness matrix; a is a system vibration mode; omega_iThe natural frequencies of the system orders.

6. The megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: the objective function of the reduced gearbox parameter first optimization model is as follows:

in the formula g₁Representing the contact safety factor objective function, g₂An objective function representing the contact safety factor is shown,representing the contact safety factor of each stage of gear before reduction,the contact safety factor of each stage of gear after reduction is shown,representing gear bending at stages before reductionThe safety factor of the device is high,the bending safety factor of each stage of gear after reduction is shown,representing the normal modulus reduction factor, gamma_bRepresents the face width reduction factor, and β represents the reduced pitch angle;

the constraints of the reduced gearbox parameter first optimization model are as follows:

7. the megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: the reduced wind power gear box parameters comprise modulus reduction ratios, tooth width reduction ratios and helix angles of gears at all levels.

8. The megawatt wind turbine gearbox equivalent reduction method as claimed in claim 1, wherein: the parameter optimization equation of the reduced wind power gear box is as follows:

in the formula, h represents an optimization objective function;the reduced natural frequency is represented as a function of,representing the initial natural frequency.

Technical Field

The invention relates to the technical field of wind power generation, in particular to an equivalent reduction method for a megawatt wind power gear box.

Background

With the development of wind power generation industry of various countries in the world, wind turbine generators are widely operated in various types of wind farms. The wind power speed-up gear box is used as a core component of the wind turbine generator and mainly used for converting low rotating speed and high torque of a wind wheel into high rotating speed and low torque which can be loaded by a generator. Wind power gear boxes usually adopt a multi-stage transmission mode of low-speed planetary stage transmission and high-speed parallel stage transmission, and faults are very easy to occur due to the complexity of the structure of the wind power gear boxes.

The wind power gear box is subjected to state monitoring, fault diagnosis and residual life prediction based on a big data technology, so that a reasonable maintenance plan can be made for the wind power plant, and the maintenance cost of the wind turbine generator is reduced. The operation data of the wind power gear box mainly come from an SCADA system and a CMS system, and the data is very inconvenient to acquire after years of accumulation. With the continuous improvement of the power of the wind turbine generator, the size of the generator equipment tends to be large, and if a bench test is carried out according to a prototype of the wind turbine gearbox, the cost is high, and the wind turbine gearbox can only be used for the wind turbine gearbox with a single model.

The equivalent reduction model can replace a prototype machine to carry out related test tests and obtain related test data, and is applied to the research of a wind power complete machine at present. However, the current equivalent reduction model only equates the gearbox to a simple transmission ratio, does not consider the difference between the safety factor of each stage of gears of the gearbox before and after reduction and the inherent characteristics of the gearbox, and lacks of a widely applicable equivalent reduction method.

Disclosure of Invention

The invention aims to provide an equivalent reduction method for a megawatt wind-power gearbox, which comprises the following steps:

1) and acquiring initial parameters of a transmission system of the wind power gear box. And acquiring and reducing the input power and the rotating speed of a transmission system of the wind power gear box.

The initial parameters of the wind power gear box transmission system comprise rated power, rated output rotating speed, transmission ratio, total transmission ratio, rated input torque of the wind power gear box, the number of planet wheels, center distance, modulus, pressure angle, rotating direction, gear type, tooth number, tooth width, mass and rotational inertia.

2) And calculating the initial contact safety factor and the bending safety factor of each stage of gear of the wind power gear box.

Initial contact safety factor S_HAnd bending safety factor S_FRespectively as follows:

the bending safety coefficient calculation formula is as follows:

in the formula, K_ATo use the coefficient, K_VIs a dynamic load coefficient, K_HβFor calculating the tooth load distribution coefficient of the contact strength, K_HαFor calculating the interdental load distribution coefficient of the contact strength, K_HPCoefficient of non-uniformity of load distribution between planet wheels, Z, for calculation of contact strength_HAs a node area coefficient, Z_EIs the coefficient of elasticity, Z_εIs the coefficient of contact ratio, Z_βIs the helix angle coefficient, F_tNominal tangential force on a circle of division in the face of the gear, d₁Is the reference circle diameter of the pinion, b is the working tooth width, u is the transmission ratio, sigma_HlimTo test the contact fatigue limit of gears, Z_NTFor calculating the life factor of the contact strength, Z_LIs the coefficient of lubricant, Z_VIs a velocity coefficient, Z_RTo roughness factor, Z_WIs the work hardening coefficient, Z_XDimensional factor, K, calculated for contact strength_FβTo calculateTooth load distribution coefficient of bending strength, K_FαFor calculating the interdental load distribution coefficient of the bending strength, K_FPFor calculating the load distribution non-uniformity coefficient between planet wheels of bending strength, Y_FaThe tooth form factor when a load acts on the tooth tip, Y_SaThe stress correction coefficient when a load acts on the tooth tip, Y_εFor calculating the overlap ratio of the bending strength, Y_βTo calculate the overlap ratio coefficient of the bending strength, σ_FlimFor testing the tooth root bending fatigue limit stress, Y_STCalculated life factor for bending strength, Y_NTTo calculate the bending limit stress of the gear, Y_δrelTSensitivity to root fillet, Y_RrelTRelative root surface condition coefficient, Y_XDimensional factors calculated for bending strength, "+" for external gearing and "-" for internal gearing. m is_nIs the normal modulus.

3) And constructing a kinetic equation of the wind power gear box transmission system according to the initial parameters of the wind power gear box transmission system, and calculating the natural frequency of the wind power gear box transmission system.

The dynamic equation of the transmission system of the wind power gear box is as follows:

wherein M is a mass matrix and K is a stiffness matrix. X is a displacement matrix.Representing the acceleration matrix.

The mass matrix M and the rigidity matrix K are respectively as follows:

in the formula, M_S1、M_R1、M_C1、M_P1、M_G1And M_G2Respectively representing the mass matrixes of the sun gear, the inner gear ring, the planet carrier, the planet gear, the big gear and the small gear; k_S1、K_C1、K_P1、K_R1、K_G1And K_G2Respectively representing bearing support rigidity matrixes of a sun gear, a planet carrier, a planet gear, an inner gear ring, a large gear and a small gear; k_C1P1Representing a coupling stiffness matrix of the planet wheel and the planet carrier; k_S1P1、K_R1P1And K_G1G2And respectively representing meshing rigidity matrixes of the sun gear and the planet gear, the inner gear ring and the planet gear, and the large gear and the small gear.

The natural frequency omega of the transmission system of the wind power gear box meets the following formula:

wherein M is a mass matrix; k is a stiffness matrix; a is a system vibration mode; omega_iThe natural frequencies of the system orders.

4) And establishing a reduced wind power gear box parameter optimization model according to the initial contact and bending safety coefficients of all levels of gears of the wind power gear box.

And establishing a parameter optimization equation of the reduced wind power gear box according to the natural frequency of the transmission system of the wind power gear box.

The objective function of the reduced gearbox parameter first optimization model is as follows:

in the formula g₁Representing the contact safety factor objective function, g₂An objective function representing the contact safety factor is shown,representing the contact safety factor of each stage of gear before reduction,the contact safety factor of each stage of gear after reduction is shown,representing the bending safety factor of each stage of gear before reduction,the bending safety factor of each stage of gear after reduction is shown,representing the normal modulus reduction factor, gamma_bDenotes the face width reduction factor and beta denotes the pitch angle after reduction.

The constraints of the reduced gearbox parameter first optimization model are as follows:

the reduced wind power gear box dynamic parameter optimization equation is as follows:

in the formula, h represents an optimization objective function;the reduced natural frequency is represented as a function of,representing the initial natural frequency.

5) And inputting the reduced input power and the reduced rotating speed into the first optimization model of the parameters of the wind power gear box after reduction, and calculating to obtain the gear parameters of the wind power gear box after reduction.

The reduced wind power gear box parameters comprise modulus reduction ratios, tooth width reduction ratios and helix angles of gears at all levels.

6) And calculating a quality matrix required by the optimization of the kinetic parameters according to the reduced gear parameters of the wind power gear box, inputting the quality matrix into a kinetic parameter optimization equation of the wind power gear box to obtain a shaft parameter reduction ratio and a reduced natural frequency, and obtaining a similar ratio of the reduced natural frequency to the natural frequency of the wind power gear box transmission system.

The technical effects of the invention are undoubted, and the invention has the following beneficial effects:

1) when the wind power gear box is reduced, the method considers that the strength of gears at all stages is equal and the inherent characteristics are similar before and after reduction, and reduces the difference between the gear boxes before and after reduction to the maximum extent;

2) the method can be suitable for reducing the wind power gear boxes of various power levels, and has the characteristic of wide application range.

Drawings

FIG. 1 is a flow chart of a wind turbine gearbox reduction method;

FIG. 2 is a topological diagram of a wind power gearbox structure;

FIG. 3 is a diagram of a kinetic model;

FIG. 4 is a graph of the second stage planetary stage contact safety factor versus error;

FIG. 5 is a graph of the safety coefficient of second-stage planet-stage bending relative error;

FIG. 6(a) is a graph I comparing the natural frequencies before and after downscaling; fig. 6(b) is a natural frequency comparison graph II before and after the reduction.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

referring to fig. 1 to 6, an equivalent reduction method for a megawatt wind power gearbox includes the following steps:

1) and acquiring initial parameters of a transmission system of the wind power gear box. And acquiring and reducing the input power and the rotating speed of a transmission system of the wind power gear box.

The initial parameters of the wind power gear box transmission system comprise rated power, rated output rotating speed, transmission ratio, total transmission ratio, rated input torque of the wind power gear box, the number of planet wheels, center distance, modulus, pressure angle, rotating direction, gear type, tooth number, tooth width, mass and rotational inertia.

The wind power gear box transmission system comprises a sun gear, a planet carrier, an inner gear ring and a planet gear; the number of the planet wheels is n; x is the number of_j、y_jRespectively projecting the vibration line displacements of the centers of mass of the sun gear, the planet carrier and the inner gear ring on an inertial coordinate system; j is s, c, r; x is the number of_pi，y_piThe projection of the linear displacement representing the ith planet wheel mass center in a moving coordinate system; 1, 2, …, n; theta_s、θ_c、θ_r、θ_piRespectively representing the torsional angular displacement of the sun gear, the planet carrier, the inner gear ring and the planet gear;the theoretical position angle of the ith planet wheel is shown; alpha is the pressure angle of the gear; k is a radical of_psi、k_priRespectively representing the meshing rigidity of the ith planet wheel, the sun wheel and the inner gear ring; k is a radical of_sx、k_syRespectively representing the sun gear bearing stiffness; k is a radical of_px、k_pyRespectively representing the rigidity of the planet wheel bearing; k is a radical of_cx、k_cyRespectively representing the rigidity of the planet carrier bearing; k is a radical of_rx、k_ryRespectively representing the support rigidity of the inner gear ring; k is a radical of_ct、k_rt、k_stRespectively representing the circumferential directions of the planet carrier, the inner gear ring and the sun gearA support stiffness; u. of_s、u_c、u_r、u_pRespectively representing the linear displacement of the torsional angular displacement of the sun wheel, the planet carrier, the inner gear ring and the planet wheel converted to the circumference.

2) And calculating the initial contact safety factor and the bending safety factor of each stage of gear of the wind power gear box.

Initial contact safety factor S_HAnd bending safety factor S_FRespectively as follows:

the bending safety coefficient calculation formula is as follows:

in the formula, K_ATo use the coefficient, K_VIs a dynamic load coefficient, K_HβFor calculating the tooth load distribution coefficient of the contact strength, K_HαFor calculating the interdental load distribution coefficient of the contact strength, K_HPCoefficient of non-uniformity of load distribution between planet wheels, Z, for calculation of contact strength_HAs a node area coefficient, Z_EIs the coefficient of elasticity, Z_εIs the coefficient of contact ratio, Z_βIs the helix angle coefficient, F_tNominal tangential force on a circle of division in the face of the gear, d₁Is the reference circle diameter of the pinion, b is the working tooth width, u is the transmission ratio, sigma_HlimTo test the contact fatigue limit of gears, Z_NTFor calculating the life factor of the contact strength, Z_LIs the coefficient of lubricant, Z_VIs a velocity coefficient, Z_RTo roughness factor, Z_WIs the work hardening coefficient, Z_XDimensional factor, K, calculated for contact strength_FβFor calculating the tooth load distribution coefficient of the bending strength, K_FαFor calculating the interdental load distribution coefficient of the bending strength, K_FPFor calculating the load distribution non-uniformity coefficient between planet wheels of bending strength, Y_FaTooth form for load acting on tooth topCoefficient of Y_SaThe stress correction coefficient when a load acts on the tooth tip, Y_εFor calculating the overlap ratio of the bending strength, Y_βTo calculate the overlap ratio coefficient of the bending strength, σ_FlimFor testing the tooth root bending fatigue limit stress, Y_STCalculated life factor for bending strength, Y_NTTo calculate the bending limit stress of the gear, Y_δrelTSensitivity to root fillet, Y_RrelTRelative root surface condition coefficient, Y_XDimensional factors calculated for bending strength, "+" for external gearing and "-" for internal gearing. m is_nIs the normal modulus.

3) And constructing a kinetic equation of the wind power gear box transmission system according to the initial parameters of the wind power gear box transmission system, and calculating the natural frequency of the wind power gear box transmission system.

The dynamic equation of the transmission system of the wind power gear box is as follows:

wherein M is a mass matrix and K is a stiffness matrix. X is a displacement matrix.Representing an acceleration matrix;

the mass matrix M and the rigidity matrix K are respectively as follows:

in the formula, M_S1、M_R1、M_C1、M_P1、M_G1And M_G2Respectively showing the quality of the sun gear, the inner gear ring, the planet carrier, the planet gear, the big gear and the small gearA quantity matrix; k_S1、K_C1、K_P1、K_R1、K_G1And K_G2Respectively representing bearing support rigidity matrixes of a sun gear, a planet carrier, a planet gear, an inner gear ring, a large gear and a small gear; k_C1P1Representing a coupling stiffness matrix of the planet wheel and the planet carrier; k_S1P1、K_R1P1And K_G1G2And respectively representing meshing rigidity matrixes of the sun gear and the planet gear, the inner gear ring and the planet gear, and the large gear and the small gear.

The natural frequency omega of the transmission system of the wind power gear box meets the following formula:

wherein M is a mass matrix; k is a stiffness matrix; a is a system vibration mode; omega_iThe natural frequencies of the system orders.

4) And establishing a reduced wind power gear box parameter optimization model according to the initial contact and bending safety coefficients of all levels of gears of the wind power gear box.

And establishing a parameter optimization equation of the reduced wind power gear box according to the natural frequency of the transmission system of the wind power gear box.

The objective function of the reduced gearbox parameter first optimization model is as follows:

in the formula g₁Representing the contact safety factor objective function, g₂An objective function representing the contact safety factor is shown,representing the contact safety factor of each stage of gear before reduction,the contact safety factor of each stage of gear after reduction is shown,representing the bending safety factor of each stage of gear before reduction,the bending safety factor of each stage of gear after reduction is shown,representing the normal modulus reduction factor, gamma_bDenotes the face width reduction factor and beta denotes the pitch angle after reduction.

The constraints of the reduced gearbox parameter first optimization model are as follows:

the reduced wind power gear box dynamic parameter optimization equation is as follows:

in the formula, h represents an optimization objective function;the reduced natural frequency is represented as a function of,representing the initial natural frequency.

5) And inputting the reduced input power and the reduced rotating speed into the first optimization model of the parameters of the wind power gear box after reduction, and calculating to obtain the gear parameters of the wind power gear box after reduction.

The reduced wind power gear box parameters comprise modulus reduction ratios, tooth width reduction ratios and helix angles of gears at all levels.

6) And calculating a quality matrix required by the optimization of the kinetic parameters according to the reduced gear parameters of the wind power gear box, inputting the quality matrix into a kinetic parameter optimization equation of the wind power gear box to obtain a shaft parameter reduction ratio and a reduced natural frequency, and obtaining a similar ratio of the reduced natural frequency to the natural frequency of the wind power gear box transmission system.

Example 2:

referring to fig. 1 to 6, an equivalent reduction method for a megawatt wind power gearbox includes the following steps:

step 1) calculating initial contact and bending safety coefficients of gears at all stages of a gearbox based on GB/T3480 standard according to initial parameters of a transmission system of a wind power gearbox;

step 2) constructing a dynamic equation of the wind power gear box transmission system according to the initial parameters of the wind power gear box transmission system, and calculating the natural frequency of the gear box transmission system;

step 3) according to the contact and bending safety coefficients calculated in the step 1, constructing an optimized calculation objective function of the reduced gear box parameters, bringing the reduced input power and the reduced rotating speed into the optimized calculation objective function, and calculating to obtain the modulus reduction ratio, the tooth width reduction ratio and the spiral angle of each reduced gear;

and 4) constructing an optimized calculation objective function of the reduced gear box parameters according to the natural frequency calculated in the step 2, substituting the optimized calculation objective function into the gear parameters calculated in the step 3, and calculating to obtain a shaft parameter reduction ratio and the reduced natural frequency.

Example 3:

the equivalent reduction method for the megawatt wind power gear box is used for carrying out equivalent reduction on a certain 5MW wind power gear box and mainly comprises the following steps:

1) determining a wind power gear box which consists of two planetary stages and one parallel stage, wherein the structural topological diagram is shown in figure 1, and the main parameters are shown in table 1.

TABLE 15 MW wind power gearbox parameters

The basic parameters of the 5MW wind power gear box are as follows: rated power of 5MW, rated output rotation speed of 1212rpm, total transmission ratio of 120.7, input torque calculation formula as:

therefore, the low-speed rated input torque T of the wind power gearbox can be calculated to be 4754803N m.

According to basic parameters of gears at all stages of a wind power gear box, calculating initial contact safety factor S of transmission at all stages of the gear box based on GB/T3480 standard_HAnd bending safety factor S_F. Wherein the calculation formula of the contact safety coefficient is as follows:

the bending safety coefficient calculation formula is as follows:

in the formula, K_ATo use the coefficient, K_VIs a dynamic load coefficient, K_HβFor calculating the tooth load distribution coefficient of the contact strength, K_HαFor calculating the interdental load distribution coefficient of the contact strength, K_HPCoefficient of non-uniformity of load distribution between planet wheels, Z, for calculation of contact strength_HAs a node area coefficient, Z_EIs the coefficient of elasticity, Z_εIs the coefficient of contact ratio, Z_βIs the helix angle coefficient, F_tNominal tangential force on a circle of division in the face of the gear, d₁Is the reference circle diameter of the pinion, b is the working tooth width, u is the transmission ratio, sigma_HlimTo test the contact fatigue limit of gears, Z_NTFor calculating the life factor of the contact strength, Z_LIs the coefficient of lubricant, Z_VIs a velocity coefficient, Z_RTo roughness factor, Z_WIs the work hardening coefficient, Z_XDimensional factor, K, calculated for contact strength_FβFor calculating the tooth load distribution coefficient of the contact strength, K_FαInterdental load distribution coefficient for calculation of contact Strength, Y_FaThe tooth form factor when a load acts on the tooth tip, Y_SaThe stress correction coefficient when a load acts on the tooth tip, Y_εFor calculating the overlap ratio of the bending strength, Y_βTo calculate the overlap ratio coefficient of the bending strength, σ_FlimFor testing the tooth root bending fatigue limit stress, Y_STCalculated life factor for bending strength, Y_NTTo calculate the bending limit stress of the gear, Y_δrelTSensitivity to root fillet, Y_RrelTRelative root surface condition coefficient, Y_XDimensional factors calculated for bending strength, "+" for external gearing and "-" for internal gearing.

The contact safety factors of gears of each stage of the gearbox are calculated and shown in the table 2:

TABLE 2 contact safety factor of gears at various stages

The bending safety factors of the gears at all stages are shown in table 3:

TABLE 3 Gear bending safety factor at various levels

2) According to the initial parameters of the wind power gearbox transmission system, a bending-torsion coupling dynamic model of the wind power gearbox transmission system shown in fig. 3 is constructed by adopting a concentrated mass method, and two degrees of freedom of translation and one degree of freedom of rotation around a shaft are considered in each component. In the figure, subscripts s, c, r and p denote sun gear, carrier, internal teeth, respectivelyThe number of the planet wheels is n, and the serial number is represented by i (i is 1, 2, …, n). x is the number of_j，y_j(j is s, c, r) is the projection of the vibration line displacement of the center of mass of the sun gear, the planet carrier and the inner gear ring on an inertial coordinate system respectively; x is the number of_pi，y_pi(i ═ 1, 2, …, n) represents the projection of the linear displacement of the ith planet centroid onto the moving coordinate system; theta_s、θ_c、θ_r，θ_piRespectively representing the torsional vibration angular displacement of the sun gear, the planet carrier, the inner gear ring and the planet gear, and regulating the anticlockwise rotation to be positive;the theoretical position angle of the ith planet wheel is shown; alpha is the pressure angle of the gear. k is a radical of_psi，k_priRespectively representing the meshing rigidity of the ith planet wheel, the sun wheel and the inner gear ring; k is a radical of_sx，k_syRespectively representing the sun gear bearing stiffness; k is a radical of_px，k_pyRespectively representing the rigidity of the planet wheel bearing; k is a radical of_cx，k_cyRespectively representing the rigidity of the planet carrier bearing; k is a radical of_rx，k_ryRespectively representing the support rigidity of the inner gear ring; k is a radical of_ct，k_rt，k_stThe circumferential support stiffness of the planet carrier, the ring gear and the sun gear is respectively shown. u. of_s，u_c，u_r，u_pAnd the torsional angular displacement of the sun gear, the planet carrier, the inner gear ring and the planet gear is converted into the linear displacement on the circumference. The differential equation for the natural vibration of the gearbox drive train is given by:

the natural frequency equation for the gearbox system is then:

where M is the mass matrix, K is the stiffness matrix, ω_iThe natural frequencies of the system orders.

The natural frequency of the 5MW wind power gearbox is calculated as shown in Table 4:

natural frequency of 45 MW wind power gear box

3) And (3) according to the contact and bending safety coefficients calculated in the step (1), constructing an optimized calculation objective function of the reduced gear box parameters, bringing the reduced input power and the reduced rotating speed into the optimized calculation objective function, and calculating to obtain the modulus reduction ratio, the tooth width reduction ratio and the spiral angle of each stage of reduced gears. The reduction ratio is calculated by the following first two optimization objective functions, and the third formula is a constraint condition.

In the formula g₁Representing the contact safety factor objective function, g₂An objective function representing the contact safety factor is shown,representing the contact safety factor of each stage of gear before reduction,the contact safety factor of each stage of gear after reduction is shown,representing the bending safety factor of each stage of gear before reduction,the bending safety factor of each stage of gear after reduction is shown,representing the normal modulus reduction factor, gamma_bDenotes the face width reduction factor and beta denotes the pitch angle after reduction. And the contact safety factor of each stage of gear is more than 1.25 and the bending safety factor is more than 1.6 after the constraint condition requirement is reduced.

Gearbox parameter reductions for four power levels, 500kW, 50kW,5kW and 0.5kW, were selected as shown in Table 5, and comparative analyses for second level safety factors of 5000kW (5MW), 500kW, 50kW,5kW and 0.5kW were performed as shown in Table 6.

TABLE 5 different Power class reduction ratios

TABLE 6 safety factor for different power classes

Fig. 4 shows the contact safety factor relative error of all power grade second-stage gears after reduction, and fig. 5 shows the bending safety factor relative error of all power grade second-stage gears after reduction, wherein the relative error is within 5%.

4) And (3) according to the natural frequency obtained by calculation in the step (2), constructing an optimized calculation objective function of the reduced gear box parameters by taking the minimum difference value delta f of the natural frequency of each step before and after reduction as a target, substituting the gear parameters obtained by calculation in the step (3), and calculating to obtain a shaft parameter reduction ratio and the reduced natural frequency. The equivalent stiffness is calculated according to the following optimization objective function:

in the formula, h represents an optimization objective function,the reduced natural frequency is represented as a function of,representing the initial natural frequency.

The reduction ratios of the axis parameters for four power levels of 500kW, 50kW,5kW and 0.5kW are selected as shown in Table 7, and the natural frequencies for five power levels of 5000kW (5MW), 500kW, 50kW,5kW and 0.5kW are analyzed in comparison as shown in Table 8.

TABLE 7 shaft parameter reduction ratio

TABLE 8 Natural frequencies

As can be seen from the table, the relative errors of the first 14 natural frequencies are within 6%, and the relative errors of the first 8 natural frequencies are within 1%, so that the reliability of the method is verified.

Fig. 6 is a comparison result of the first 14 th order natural frequency of all power levels after the reduction and the natural frequency before the reduction, and it can be seen that the natural frequency after the reduction fluctuates around the initial frequency and the fluctuation amplitude is small.