Fatigue life model and optimization method of single-row tapered roller bearings

Abstract

The present invention discloses a fatigue life model and optimization method of a single-row tapered roller bearing, which requires the calculation of contact load, contact stress and fatigue life. Generally speaking, fatigue damage will occur at the maximum contact load when the life is reached. Theoretically, the failure of parts starts from the maximum contact load. What is calculated here is how long the rolling element or ring at the maximum contact load can cycle under the maximum stress, not the influence of the failure of a certain roller (or ring) or other parts of the bearing on the life of the bearing. The present invention simultaneously meets the following requirements: fatigue life, static strength and static load-bearing capacity meet the requirements, and the total volume and the total volume of the upwind bearing and the downwind bearing are the smallest. Under the premise of meeting the performance requirements and the 20-year service life specified in the IEC61400‑4 standard, the volume and the total volume of the two wind turbine main bearings are reduced by 13.68%, which reduces the production and transportation costs, improves the economic benefits of the enterprise, and ensures the long-term stable operation of wind power equipment.

Description

Technical Field

[0001] The invention belongs to the technical field of wind power generator sets, and in particular relates to a fatigue life model and an optimization method of a single-row tapered roller bearing. Background Art

[0002] The upwind axis refers to the rotor axis located on the upwind side of the tower. Since the rotor is located in the upwind position of the tower, the rotor is mainly subjected to the thrust of the wind. The forces on the blades of the upwind axis wind turbine generator set are mainly the thrust along the wind direction and the centrifugal force generated by the rotation. The rotor of the leeward axis is located in the leeward position of the tower, and turbulence and vortices will be generated after the airflow passes through the tower. This makes the aerodynamic force on the rotor blades complex and unstable. For the tower of the leeward axis wind turbine generator set, it not only has to bear the load transmitted by the rotor, but also the dynamic load generated by the rotor working in the uneven airflow. This dynamic load may cause the tower to vibrate, so the fatigue resistance of the tower is required to be higher.

[0003] In the design of wind power equipment, bearings are key transmission components, and their performance directly affects the operating efficiency and safety of the entire wind power equipment. Most of the current bearing optimization models only use life as the optimization target and geometric performance as a constraint to optimize the geometric parameters of bearings. It is often the case that the life of wind power main bearings is relatively conservative during design, and the general design life has far exceeded the requirement of not less than 20 years of service life stipulated in the IEC61400-4 standard. Overly conservative design will lead to excessively large bearings, high production and transportation costs, high bearing costs, and reduced economic benefits for the enterprise. On the other hand, only using fatigue life as the optimization target without considering the static load-bearing capacity of the bearing will lead to early failure of the bearing due to insufficient static load-bearing capacity before fatigue occurs. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and to provide a fatigue life model and an optimization method for a single-row tapered roller bearing taking into account elastic deformation of a ring and multiple working conditions.

[0005] The present invention is achieved through the following technical solutions:

[0006] A fatigue life model for single-row tapered roller bearings in wind turbine main shafts.

[0007]

[0008]

[0009] is the fatigue life of the main bearing under the fatigue load spectrum, The fatigue life of the main bearing under a certain load condition, is the time proportion of the corresponding load condition, The calculated life of the slice unit of the inner ring of the main bearing, The calculated life of the main bearing outer ring slice unit, is the contact fatigue life between rolling element and inner raceway, is the contact fatigue life between rolling element and outer raceway, Indicates the number of rolling elements. is the number of times the rolling element rotates, Represented as outer ring, Indicated as inner ring, Number the rolling elements;

[0010] Among them, the improved LP theory is used to divide the rolling element into Slice units, The inner and outer ring raceways The basic dynamic load rating of a slice unit is

[0011] ,

[0012] in, It is the reduction factor considering the stress concentration phenomenon on the rolling element profile; is the contact angle; is the rolling element diameter; is the roller contact length; is a dimensionless parameter; middle For the contact surface, , or They correspond to the inner and outer circles respectively;

[0013] ,

[0014] in, is the pitch diameter;

[0015] is the equivalent dynamic load of the bearing inner ring raceway slice unit when the main bearing is in working condition with only the inner ring rotating and the outer ring fixed;

[0016] ,

[0017] The equivalent dynamic load of the bearing outer ring slice unit when the outer ring is stationary relative to the external load:

[0018] ,

[0019] ,

[0020] ,

[0021] is the calculated life of a single raceway,

[0022] ,

[0023] is the basic dynamic load rating of the rolling element,

[0024] ,

[0025] When the bearing rolling elements are in contact with the inner and outer raceways, the fatigue life calculation method of the rolling element segments and raceway segments is the same as that of the bearing rings. is the contact load between the rolling element and the corresponding raceway at different positions, where The index is 4 for the rolling element numbering. When the contact between the rotating ring and the rolling element relative to the applied load is line contact, the index is 4. When the contact between the stationary ring and the rolling element relative to the applied load is line contact, the index is 4.5.

[0026] A method for optimizing a single-row tapered roller bearing comprises the following steps:

[0027] 1) Establish a contact mechanics model of a single-row tapered roller bearing considering the elastic deformation of the bearing ring;

[0028] 2) Establish an optimization objective function to minimize the volume of the upwind bearing and downwind bearing of the wind turbine main shaft;

[0029] 3) establishing performance constraints and geometric constraints, wherein the performance constraints include static strength and static load-bearing capacity and fatigue life obtained by using the fatigue life model;

[0030] 4) Determine the optimization variables to achieve the optimization goal and meet the constraints;

[0031] 5) Complete the optimization design of the fan main bearing through genetic algorithm.

[0032] As one of the preferred solutions, the calculation model in step 3) is:

[0033]

[0034] in, , , are the minimum and maximum values ​​and target value of the bearing inner diameter; are the minimum and maximum values ​​and target value of the bearing outer diameter; are the minimum and maximum values ​​and target value of the bearing width; Number of rolling elements; is the rolling element diameter; is the rolling element length; is the pitch diameter; , is the minimum and maximum value of the rolling element aspect ratio; design bearing life Not less than the prescribed service life of 20 years; Allowable contact stress; contact stress The permissible contact stress shall not exceed ;Static load capacity Not exceeding the allowable safety factor .

[0035] As one of the preferred solutions, the step 4) is to use the bearing inner diameter, outer diameter, contact angle and the size and number of rolling elements as optimization variables, combined with the attached manual Figure 2

[0036]

[0037]

[0038] , are the optimization variables of the main bearings in the upwind and downwind directions of the fan respectively; They are respectively the outer diameters of the upwind and downwind main bearings of the fan; They are the inner diameters of the upwind and downwind main bearings of the fan respectively; They are respectively the rolling element diameters of the main bearings in the upwind and downwind directions of the fan; They are respectively the length of the rolling element of the main bearing in the upwind and downwind directions of the fan; They are the number of rolling elements of the main bearings in the upwind and downwind directions of the fan respectively; They are the contact angles of the main bearings in the upwind and downwind directions of the fan respectively; They are the semi-cone angles of the main bearing rollers in the upstream and downstream directions of the fan respectively.

[0039] As one of the preferred solutions, Figure 3 , the step 5) is,

[0040] First, input loads, material properties, performance requirements, and related parameters as optimization conditions;

[0041] Then, the value range of the optimization variable is determined according to the input conditions, and key parameters such as the initial population size, number of iterations and crossover rate of the genetic algorithm are set;

[0042] Then, the genetic algorithm is used to iteratively optimize the optimization variables, and after each iteration, it is evaluated whether the termination condition is met. If not, the crossover rate is gradually increased to enhance population diversity and improve search efficiency.

[0043] Finally, the optimal solution and its fitness value under different crossover rates are recorded and output, thus completing the entire optimization process.

[0044] The advantages and beneficial effects of the present invention are:

[0045] The present invention establishes an optimization design model with the sum of the volumes of upwind and downwind main bearings as the optimization target, and with geometric constraints and performance constraints (fatigue life, static strength and static load-bearing capacity) as constraints, and with the bearing aperture, outer diameter, contact angle, and the size and number of rolling elements as optimization variables. The bearing with optimal geometric parameters that meets the performance requirements (fatigue life, static strength and static load-bearing capacity) and has a service life of 20 years and has the smallest total volume and static load-bearing capacity of the upwind and downwind bearings.

[0046] Single-row tapered roller bearings are used for both upwind and downwind directions. The volumes of upwind and downwind bearings are calculated and added independently, rather than considering the upwind and downwind bearings as a whole. The upwind bearing mainly bears the thrust and centrifugal force from the wind, while the downwind bearing bears more complex aerodynamic loads and dynamic vibrations. The integrated processing may not be able to effectively consider their respective performance requirements and force characteristics. Independent calculations are taken to help clearly reflect their respective performance and volume requirements during the optimization process.

[0047] The present invention takes "minimizing the volume of the upwind shaft and downwind bearing" as the optimization goal, combining complex geometric constraints and performance constraints (such as fatigue life, static strength and static load capacity). It is not only for simple force analysis, but also an optimization design scheme proposed for the long-term operation and complex working conditions of the main bearing of wind power generation, ensuring that the bearing can achieve volume minimization under the premise of meeting the 20-year service life. Secondly, the present invention specifically considers the elastic deformation of the bearing ring and the fatigue life of multiple working conditions, and optimizes the design for the different forces and dynamic working conditions of the upper and lower wind shafts in the wind turbine generator set. The existing conventional technology may not consider these complex factors, especially the dynamic changes under extreme working conditions such as wind power generation. The modeling and optimization of this complex working condition significantly improves the fatigue resistance and static load capacity of the bearing. Finally, the present invention introduces a genetic algorithm for multi-objective and multi-constraint optimization design. The genetic algorithm can quickly and effectively find the global optimal solution, rather than the local optimal solution, when facing high-dimensional complex variables (such as bearing aperture, outer diameter, contact angle, and rolling element size and number). BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Force and deformation diagram of the ring; radial and tangential displacements on the center line of the ring and ;

[0049] Figure 2This is the structural diagram of the main bearings in the upwind and downwind directions of the fan;

[0050] Figure 3 Design flow chart for optimization;

[0051] Figure 4 Force diagram of the inner ring of the bearing;

[0052] Figure 5 Force diagram of outer ring of bearing;

[0053] Figure 6 Schematic diagram of elastic deformation of bearing ring.

[0054] For ordinary technicians in this field, other relevant drawings can be obtained based on the above drawings without any creative work. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0056] Embodiment 1

[0057] The present invention considers the elastic deformation of the ring and the fatigue life calculation model of multiple working conditions, and the specific steps include:

[0058] The rolling element is divided into Slice units are used for life calculation.

[0059] First, the inner and outer ring raceways The basic rated dynamic load of each slice unit. The ordinary LP life calculation theory only obtains the overall life of the main bearing through the ring life, and does not consider the life of the tapered rolling element and the influence of the rolling element generatrix modification and rolling element inclination on the overall life of the bearing. The improved LP theory takes the above into account to make the calculated life result more accurate:

[0060] (1)

[0061] in, It is the reduction factor considering the stress concentration phenomenon on the rolling element profile; is the contact angle; is the rolling element diameter; is the roller contact length; is a dimensionless parameter; middle For the contact surface, , or They correspond to the inner and outer circles respectively;

[0062] (2)

[0063] in, is the pitch circle diameter.

[0064] In the main bearing working state where only the inner ring rotates and the outer ring is fixed, the equivalent dynamic load of the bearing inner ring raceway slice unit is:

[0065] (3)

[0066] When the outer ring is stationary relative to the external load, the equivalent dynamic load of the bearing outer ring slice unit is:

[0067] (4)

[0068] Calculated life of the main bearing inner ring slice unit:

[0069] (5)

[0070] Calculated life of the main bearing outer ring slice unit:

[0071] (6)

[0072] Calculated life of single raceway:

[0073] (7)

[0074] Basic dynamic load rating of rolling elements:

[0075] (8)

[0076] Combined with the previous calculation process, the fatigue life calculation of the entire bearing under a single working condition is:

[0077] (9)

[0078] Where N is the number of times the rolling element rotates.

[0079] When fatigue damage occurs to the bearing, the linear cumulative damage reaches a critical value. It is usually assumed that the critical cumulative damage value is 1. This means that when the cumulative damage of the wind turbine main bearing reaches 1 after working in harsh load conditions for 20 years, fatigue failure will occur in the main bearing of the wind turbine.

[0080] Composite multi-condition fatigue life calculation:

[0081] (10)

[0082] in, is the number of cycles under the corresponding load condition, is the fatigue life under the corresponding load condition, is the time proportion of the corresponding load condition. The time proportion can be listed in the load spectrum in Table 1 below. The total number of single fatigue load conditions for the main bearing is determined as The accumulated fatigue life is achieved to meet the fatigue life requirements of multiple working conditions.

[0083] In order to ensure that the fatigue life of the main bearing meets the 20-year service requirement, the fatigue life of the main bearing under the fatigue load spectrum is further calculated: the main bearing refers to the upwind bearing or the downwind bearing, and the same calculation formula is used to calculate the contact load, contact stress, and fatigue life. Generally speaking, fatigue damage will occur at the maximum contact load when the service life is reached. According to theory, part failure begins at the maximum contact load. What is calculated here is how long the rolling element or ring at the maximum contact load can cycle under the maximum stress, not the impact of the failure of a certain roller (or ring) of the bearing on the life of the bearing.

[0084] (11)

[0085] The rated dynamic load of the rolling element is calculated based on the load distribution of the wind turbine main bearing (8), and the fatigue life value of the entire bearing under a single working condition is calculated using formulas (1)-(7) (9). Substituting this into formula (10) ultimately yields a fatigue life value that meets multiple working conditions. To ensure that the fatigue life of the main bearing meets the 20-year service requirement, the fatigue life of the main bearing under the fatigue load spectrum is further calculated (11).

[0086] Embodiment 2

[0087] The optimization method of the single-row tapered roller bearing considering the elastic deformation of the ring and multiple working conditions of the present invention comprises the following steps:

[0088] Step 1: Establish a contact mechanics model of a single-row tapered roller bearing considering the elastic deformation of the bearing ring;

[0089] Step 2: Establish the optimization objective function: the sum of the volumes of the upwind bearing (single-row tapered roller bearing) and the downwind bearing (single-row tapered roller bearing) of the wind turbine main shaft is minimized;

[0090] Step 3: Establish performance constraints and geometric constraints; the performance constraints include fatigue life, static strength and static load capacity, and the geometric constraints include bearing aperture, outer diameter, contact angle, and the size and number of rolling elements; wherein the fatigue life is obtained by the elastic deformation of the tapered roller bearing ring and the fatigue life model of multiple working conditions in Example 1;

[0091] Step 4: Determine the optimization variables to achieve the optimization goal and meet the constraints;

[0092] Step 5: Complete the optimization design of the fan main bearing through genetic algorithm.

[0093] Specifically, the step 1 is as follows:

[0094] Establish a mechanical model of the fan main bearing considering the elastic deformation of the ring:

[0095] Assuming the outer ring of the bearing is fixed, the external force (axial force , radial force and overturning moment ) acts on the inner ring, causing the inner ring to have an axial displacement , radial displacement and angular displacement .

[0096] In the angular position The inner ring is subjected to axial load , radial load , overturning moment And the contact load of the rolling element on the inner raceway The axial, radial and moment balance equations of the inner ring are listed as follows:

[0097] (12)

[0098] in: Indicates the number of rolling elements. is the contact angle between the roller and the inner raceway, For the The position angle of the roller, The pitch diameter of the main bearing.

[0099] Without considering the elastic deformation of the ring, when Hertzian contact is assumed between the rolling element and the raceway, the total contact elastic deformation between the rolling element and the raceway is:

[0100] (13)

[0101] The main shaft bearing of a wind turbine is a thin-walled bearing. Under the action of external forces, the bearing ring will produce a large bending deformation, affecting the load distribution of the main bearing. The elastic ring will undergo significant elastic deformation under the action of load, especially during the operation of the bearing. The ring can adapt to the external load and working conditions and undergo local deformation. For example, local stress concentration in the contact area between the rolling element and the ring will cause a certain elastic deformation of the contact surface. This deformation helps to disperse the load and reduce local pressure. At the position, the bending deformation at any angle of the bearing ring is ;

[0102] According to the thin-walled ring theory, the radial deformation of the main bearing under load at any position angle is:

[0103] (14)

[0104] In the formula, is the elastic modulus; is the moment of inertia; is the radius of the midline circle; is the bending moment.

[0105] The bearing ring is affected by radial load and tangential load, which produces radial and tangential displacement on the center line of the ring. and , combined with the instructions Figure 1 shown.

[0106] The total contact elastic deformation of the rolling element and raceway of a single-row tapered roller bearing considering the elastic deformation of the ring is as follows:

[0107] (15)

[0108] Single row tapered roller bearing considering ring elastic deformation Total contact load of rolling element-raceway:

[0109] (16)

[0110] is the total load deformation constant of the rolling element and the inner and outer rings. The radial displacement at each position angle can be expressed as:

[0111] (17)

[0112] and are the major and minor axes of the deformation caused by flexural deformation, is a constant. According to the Rayleigh toroidal shell's inextensibility thesis, the elongation of the torus centerline can be ignored.

[0113] Then it can be deduced that:

[0114] (18)

[0115] Substituting formula (14) into the above formula, we can get:

[0116] (19)

[0117] The strain energy of the ring due to bending is:

[0118] (20)

[0119] Substituting equation (14) and equation (17) into the above equation, we can obtain:

[0120] (twenty one)

[0121] Then the work done by the radial and tangential loads is:

[0122] (twenty two)

[0123] is the load position angle, subscript Instructions attached Figure 1 Different positions of the medium load refer to rolling elements with different numbers. The radial and tangential loads are 、 Their effects on the ring are superimposed on each other. is the radial force at different load positions; is the tangential force at different load positions. According to the virtual displacement principle, the work done by the external load is equal to the strain energy, then:

[0124] (twenty three)

[0125] Substituting equation (21) and equation (22) into the above equation, we can get and for:

[0126] (twenty four)

[0127] Then the displacement caused by radial force and the displacement caused by tangential force can be expressed as:

[0128] (25)

[0129] Since the force acting on the wheel hub is transmitted to the inner ring of the main bearing through the main shaft, this patent takes the inner ring of the main bearing as the research object and decomposes the rolling element load into the radial load. Figure 4 , Figure 5 , the bearing ring reaches a state of equilibrium under the action of radial force and rolling element load. The black single arrow represents the decomposition of the radial force on the ring, and the black double arrow represents the force exerted by the rolling element load on the ring.

[0130] Combined with the rolling element load and radial load on the inner ring of the bearing, according to formula (25) and the external load on the bearing ring and (Combined with the instructions Figure 4 , Figure 5 , the bottom Clockwise: , Indicates different positions of the rings, that is, the positions corresponding to rolling elements with different numbers), and the radial deformation of the inner ring of the bearing can be calculated and tangential deformation for:

[0131] (26)

[0132] is the contact load of the external load on the bearing ring, is the bending moment of inertia of the inner ring, is the bending moment of inertia of the outer ring;

[0133] Similarly, the radial deformation of the bearing outer ring can be calculated and tangential deformation They are:

[0134] (27)

[0135] Combined with the instructions Figure 6 , the radial elastic deformation of the bearing ring at any angle is the radial deformation of the inner ring and radial deformation of the outer ring The sum can be expressed as:

[0136] (28)

[0137] First solve for each position angle The bending deformation of the ferrule at , and then use the Newton-Raphson method to solve equation (12) to obtain the inner circle , , , substituting into formula (16), the contact load between each roller and the elastic raceway can be obtained .

[0138] The step 2 is specifically as follows:

[0139] The fan main bearing has a high manufacturing cost due to its large aperture, large outer diameter and multi-rolling element design. At the same time, its increased weight also increases transportation costs. Therefore, the total volume of the fan main bearing is optimized.

[0140] The volume of the upper and lower wind direction bearings of the fan is:

[0141] (29)

[0142] in, , , , The volume of the windward and downwind bearings of the fan, and the volume of the rolling element, outer ring, and inner ring of the windward bearing; , , is the volume of the rolling element, outer ring and inner ring of the downwind bearing.

[0143] Objective function:

[0144] (30)

[0145] The step 3 is as follows:

[0146] Considering factors such as geometric dimensions and performance constraints (fatigue life, static strength and static load capacity) as constraints:

[0147] (31)

[0148] in, , are the minimum and maximum values ​​and target value of the bearing inner diameter; 、 are the minimum and maximum values ​​and target value of the bearing outer diameter; 、 are the minimum and maximum values ​​and target value of the bearing width; Number of rolling elements; is the rolling element diameter; is the rolling element length; is the pitch diameter; , is the minimum and maximum value of the rolling element aspect ratio; design bearing life Not less than the prescribed service life of 20 years; Allowable contact stress; contact stress The permissible contact stress shall not exceed ;Static load capacity Not exceeding the allowable safety factor .

[0149] constraint Limits the geometric dimensions of the bearing. The range of the bearing inner diameter is limited; The range of the bearing outer diameter is limited; Limits the range of bearing width. Defines the performance constraints of the bearing. Constraints The number of rolling elements is constrained. Its purpose is to prevent collisions between rolling elements. It is a constraint on the rolling element diameter, which aims to prevent the contact area from being too small, causing the contact stress to exceed the allowable stress. and The length-to-diameter ratio of the rolling element is restricted. These constraints ensure that the ratio of the length to the diameter of the rolling element is within a reasonable range, thus ensuring the rationality of the bearing design. The rolling element aspect ratio range is limited. It is the bearing life constraint. Its purpose is to design the bearing life L e Not less than the specified service life of 20 years to ensure bearing durability. The maximum contact stress of the bearing rolling element is limited. This constraint requires that the contact stress of the bearing rolling element shall not exceed the allowable contact stress under any working load to ensure the safe operation of the bearing. The static load capacity of the bearing is specified to ensure the safety of the bearing under static load.

[0150] Bearing life The calculation method of is shown in formula (11);

[0151] Contact stress The following formula can be used for calculation:

[0152] (32)

[0153] in, is the curvature of the roller and the ring, is the roller length, contact load Use the method in step 1 to obtain the maximum contact load. , the roller length is a constant. After the tapered roller is sliced, the contact state of each ellipse is different, so the curvature is also different. Through geometric relationships and formula derivation, the curvature radius of the elliptical section in the normal direction of the inner raceway contact line is obtained. The radius of curvature of the elliptical section in the normal direction of the outer raceway contact line The sum of the reciprocals of the two radii of curvature is the sum of the curvatures of the roller and the ring.

[0154] Static load capacity calculate:

[0155] The static load of a bearing refers to the load capacity of the bearing when it is stationary, which is determined by the allowable plastic deformation. The static load rating of the bearing is calculated as follows:

[0156] (33)

[0157] According to the limit load condition of the spindle bearing, the radial force of the bearing is obtained. and axial force ;

[0158] According to the calculation standard of the static load rating of rolling bearings in the national standard GB / T4662-2012 / IOS76:2006, the calculation formula for the equivalent static load of a single-row bearing under external load is:

[0159] (34)

[0160] in, and They are taken from the calculation standard of the static load rating of rolling bearings in the national standard GB / T4662-2012 / IOS76:2006;

[0161] The safety factor of the bearing under the limit load condition is calculated by the following formula to ensure that its basic static load rating is sufficient and the static safety factor is is the basic static load rating Equivalent static load Ratio.

[0162] (35)

[0163] The step 4 is specifically as follows:

[0164] A variety of bearing structural parameters are used as optimization variables to improve the performance of the bearing, including the bearing inner diameter, outer diameter, contact angle, and the size and number of rolling elements.

[0165] (36)

[0166] (37)

[0167] , are the optimization variables of the main bearings in the upwind and downwind directions of the fan respectively; They are respectively the outer diameters of the upwind and downwind main bearings of the fan; They are the inner diameters of the upwind and downwind main bearings of the fan respectively; They are respectively the rolling element diameters of the main bearings in the upwind and downwind directions of the fan; They are respectively the length of the rolling element of the main bearing in the upwind and downwind directions of the fan; They are the number of rolling elements of the main bearings in the upwind and downwind directions of the fan respectively; They are the contact angles of the main bearings in the upwind and downwind directions of the fan respectively; They are the semi-cone angles of the main bearing rollers in the upstream and downstream directions of the fan respectively.

[0168] The step 5 is specifically as follows:

[0169] The population in the genetic algorithm layer is the design variables of the tapered roller bearing of the wind turbine main bearing. . Randomly generated Group Design Variables To initialize the population; different design variables Randomly exchanging the same type of data is called crossover; judging the two design variables The probability of whether a crossover operation is needed is the crossover rate; the number of times the loop is executed is the number of iterations.

[0170] First, input the load, material properties, performance requirements and related parameters as optimization conditions. Then, determine the value range of the optimization variable according to the input conditions, and set the key parameters such as the initial population size, number of iterations and crossover rate of the genetic algorithm. Then, use the genetic algorithm to iteratively optimize the optimization variables, and evaluate whether the termination conditions are met after each iteration (such as reaching the preset number of iterations or meeting the performance requirements). If not, gradually increase the crossover rate to enhance population diversity and improve search efficiency. Finally, record and output the optimal solution and its fitness value under different crossover rates, thus completing the entire optimization process.

[0171] Compared with the existing technology, the present invention has the following advantages:

[0172] The present invention satisfies the following requirements simultaneously: fatigue life, static strength and static load-bearing capacity meet the requirements, and the total volume of the upwind bearing and the downwind bearing is minimized. The production and transportation costs are reduced, and the economic benefits of the enterprise are improved. Under the premise of meeting the performance requirements and the 20-year service life specified in the IEC61400-4 standard, the volume of the two wind turbine main bearings is reduced by 13.68%, ensuring the long-term stable operation of the wind power equipment. Specific embodiments

[0174] Taking the main bearing of a domestic 4.5 MW wind turbine as an example, the structural parameters are used as optimization variables, and the geometric dimensions and geometric constraints, performance constraints (fatigue life, static strength and static load capacity) and other factors are optimized. The process is as follows:

[0175] Step 1: Calculate the total contact load between the rolling element and the raceway of a single-row tapered roller bearing taking into account the elastic deformation of the ring

[0176] The load data of the fan main bearing are shown in Table 1. According to step 1, the position angles are first solved. The bending deformation of the ferrule at , and then use the Newton-Raphson method to solve equation (12) to obtain the inner circle , substituting into formula (16), the total contact load between the rolling element and the raceway of a single-row tapered roller bearing considering the elastic deformation of the ring can be obtained: Table 1 The load on the main shaft of a domestically produced 4.5 MW wind turbine generator set.

[0177] Table 1 Main bearing load of a domestically produced 4.5 MW wind turbine

[0178]

[0179] The axial, radial and moment balance equations of the inner ring are listed in formula (12):

[0180] Step 2: Calculate the fatigue life of single-row tapered roller bearing rings considering elastic deformation and multiple working conditions

[0181] According to the load distribution of the wind turbine main bearing and the static equilibrium equation, the rated dynamic load of the rolling element is calculated (8), and the fatigue life value of the entire bearing under a single working condition is calculated by the formula (9). Substituting it into formula (10) finally obtains the fatigue life value that meets multiple working conditions. In order to ensure that the fatigue life of the main bearing meets the 20-year service requirement, the fatigue life of the main bearing under the fatigue load spectrum is further calculated (11).

[0182] Step 3: Calculate the volume of the wind turbine's upwind and downwind bearings and determine the optimization objective function

[0183] The volume of the wind turbine's upper and lower wind direction bearings can be found in formula (29):

[0184] The objective function is shown in formula (30):

[0185] Step 4: Establish performance constraints and geometric constraints

[0186] Taking geometric dimensions and performance constraints (fatigue life, static strength and static load capacity) as constraints, see formula (31):

[0187] Bearing life The calculation method of is shown in formula (11);

[0188] Contact stress The total contact load between the rolling element and the raceway of a single-row tapered roller bearing can be considered in combination with the elastic deformation of the ring in step 1. Substitute into the formula in step 3 to obtain;

[0189] Static load capacity The calculation method of is shown in the formula in step 3;

[0190] Step 5: Determine the optimization variables to achieve the optimization goal and meet the constraints

[0191] A variety of bearing structural parameters are used as optimization variables to improve the performance of the bearing, including the bearing inner diameter, outer diameter, contact angle, and the size and number of rolling elements, see formulas (36), (37);

[0192] Step 6: Complete the optimization design of the fan main bearing through genetic algorithm

[0193] The population in the genetic algorithm layer is the design variables of the tapered roller bearing of the wind turbine main bearing. . Randomly generated Group Design Variables To initialize the population; different design variables Randomly exchanging the same type of data is called crossover; judging the two design variables The probability of whether a crossover operation is needed is the crossover rate; the number of times the loop is executed is the number of iterations.

[0194] First, input the load, material properties, performance requirements and related parameters as optimization conditions. Subsequently, determine the value range of the optimization variables based on the input conditions, and set key parameters such as the initial population size, number of iterations and crossover rate of the genetic algorithm. Next, use the genetic algorithm to iteratively optimize the optimization variables, and evaluate whether the termination conditions are met after each iteration (such as reaching the preset number of iterations or meeting the performance requirements). If not, gradually increase the crossover rate to enhance population diversity and improve search efficiency. Finally, record and output the optimal solution and its fitness value under different crossover rates to complete the entire optimization process. Table 2 Comparison of optimization results of the upwind main bearing of a domestic 4.5 MW wind turbine. Table 3 Comparison of optimization results of the downwind main bearing of a domestic 4.5 MW wind turbine;

[0195] Table 2 Comparison of optimization results of the upwind main bearing of a domestic 4.5 MW wind turbine

[0196]

[0197] As shown in Table 2, by adopting the design of the present invention, for the windward main shaft bearing of the wind turbine, under the premise of meeting the fatigue load life of 20 years, the geometric dimensions are reduced in all aspects, and the overall volume of the bearing is reduced by 10.2%; and the number of rolling elements is reduced by 2. At the same time, the maximum contact stress under fatigue load is increased by 7.4%, and the static load capacity is also increased by 1.2%.

[0198] Table 3 Comparison of optimization results of downwind main bearing of a domestic 4.5 MW wind turbine

[0199]

[0200] As shown in Table 3, with the design of the present invention, for the main shaft bearing in the downwind direction of the wind turbine, under the premise of meeting the fatigue load life of 20 years, except for the slightly increased bearing width and rolling element taper angle, the other geometric dimensions are reduced in all aspects, and the overall volume of the bearing is reduced by 20.4%; and the number of rolling elements is reduced by 2. At the same time, the maximum contact stress under fatigue load is guaranteed to be increased by 4.6%, and the static load capacity is also increased by 1.2%.

[0201] In summary, for the upwind and downwind main bearings of the wind turbine, the design of the present invention can simultaneously meet the following requirements: fatigue life, static strength and static load-bearing capacity meet the requirements, and the total volume of the upwind bearing and the downwind bearing is minimal. Under the premise of meeting the performance requirements and the 20-year service life specified in the IEC61400-4 standard, the volume of the two wind turbine main bearings is reduced by 13.68%, which reduces the production and transportation costs, improves the economic benefits of the enterprise, and ensures the long-term stable operation of the wind power equipment.

[0202] The present invention is described above by way of example. It should be noted that, without departing from the core of the present invention, any simple deformation, modification or other equivalent replacement that can be made by those skilled in the art without inventive effort falls within the protection scope of the present invention.

Claims

1. A method for optimizing a single-row tapered roller bearing, characterized in that: The following steps are included: 1) Establish a contact mechanics model of a single-row tapered roller bearing considering the elastic deformation of the bearing ring; 2) Establish an optimization objective function to minimize the volume of the upwind bearing and downwind bearing of the wind turbine main shaft; 3) Establishing performance constraints and geometric constraints, wherein the performance constraints include static strength and static load capacity and fatigue life obtained by using a fatigue life model of a single-row tapered roller bearing; 4) Determine the optimization variables to achieve the optimization goal and meet the constraints; 5) Complete the optimization design of the fan main bearing through genetic algorithm, Wherein, in step 2), the volume of the upper and lower wind direction bearings of the fan and, ， in, , , , The volume of the windward and downwind bearings of the fan, and the volume of the rolling element, outer ring, and inner ring of the windward bearing; , , The volume of the rolling element, outer ring and inner ring of the downwind bearing; The objective function is ， The performance constraints are: ， in, , are the minimum and maximum values ​​and target value of the bearing inner diameter; , are the minimum and maximum values ​​and target values ​​of the bearing outer diameter; , are the minimum and maximum values ​​and target value of the bearing width; Number of rolling elements; is the rolling element diameter; is the rolling element length; is the pitch diameter; , is the minimum and maximum value of the rolling element aspect ratio; design bearing life Not less than the specified service life of 20 years; contact stress The permissible contact stress shall not exceed ;Static load capacity Not exceeding the allowable safety factor ; Step 4) is to adjust the inner diameter of the main bearing of the fan upwind and downwind , , outer diameter , , contact angle , and the length of the rolling element , , rolling element diameter , , number of rolling elements , , roller semi-cone angle , As the optimization variable, ， ， , They are the optimization variables of the main bearings in the upwind and downwind directions of the fan respectively.

2. The single-row tapered roller bearing optimization method according to claim 1, characterized in that: The fatigue life model of the single row tapered roller bearing is: ， ， is the fatigue life of the main bearing under the fatigue load spectrum, The fatigue life of the main bearing under a certain load condition, is the time proportion of the corresponding load condition, The calculated life of the slice unit of the inner ring of the main bearing, The calculated life of the main bearing outer ring slice unit, is the contact fatigue life between rolling element and inner raceway, is the contact fatigue life between rolling element and outer raceway, Indicates the number of rolling elements. is the number of rotations of the rolling element, Represented as outer ring, Indicated as inner ring, Number the rolling element; Among them, the improved LP theory is used to divide the rolling element into Slice units, The inner and outer ring raceways The basic dynamic load rating of a slice unit is ， in, It is the reduction factor considering the stress concentration phenomenon on the rolling element profile; is the contact angle; is the rolling element diameter; is the roller contact length; is a dimensionless parameter; middle For the contact surface, , They correspond to the inner and outer circles respectively; ， in, is the pitch diameter; is the equivalent dynamic load of the bearing inner ring raceway slice unit when the main bearing is in working condition with only the inner ring rotating and the outer ring fixed; ， The equivalent dynamic load of the bearing outer ring slice unit when the outer ring is stationary relative to the external load: ， ， ， is the calculated life of a single raceway, ， is the basic dynamic load rating of the rolling element, ， When the bearing rolling elements are in contact with the inner and outer raceways, the fatigue life calculation method of the rolling element segments and raceway segments is the same as that of the bearing rings. is the contact load between the rolling element and the corresponding raceway at different positions, where The index is 4 for the rolling element numbering. When the contact between the rotating ring and the rolling element relative to the applied load is line contact, the index is 4. When the contact between the stationary ring and the rolling element relative to the applied load is line contact, the index is 4.

5.

3. The single-row tapered roller bearing optimization method according to claim 1, characterized in that: The step 5) is: First, input loads, material properties, performance requirements, and related parameters as optimization conditions; Then, the value range of the optimization variable is determined according to the input conditions, and key parameters such as the initial population size, number of iterations and crossover rate of the genetic algorithm are set; Then, the genetic algorithm is used to iteratively optimize the optimization variables, and after each iteration, it is evaluated whether the termination condition is met. If not, the crossover rate is gradually increased to enhance population diversity and improve search efficiency. Finally, the optimal solution and its fitness value under different crossover rates are recorded and output, thus completing the entire optimization process.

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