Method for calculating load sharing factor of planetary gear mechanism

Abstract

The present application relates to a kind of load sharing coefficient calculation method of planetary gear mechanism, including building planetary gear mechanism assembly finite element model;In turn define the material properties of finite element model, the stiffness of spring unit, the boundary condition of finite element model: fixed bolt hole on the split shell connected with motor;Define the initial temperature of finite element model;Load 1-3 is applied;Adjust all components to ideal assembly position;Determine the 1st meshing position of planetary gear mechanism;Define calculation condition;Carry out finite element analysis;Calculate the load sharing coefficient of planetary gear mechanism in the 1st meshing position;Carry out planetary gear mechanism gear meshing position adjustment and the load sharing coefficient calculation of corresponding position;Considering the manufacturing error and assembly error of component, repeat the above steps to carry out planetary gear mechanism load sharing coefficient calculation.The present application realizes the high-precision prediction of planetary gear mechanism load sharing coefficient;More reasonable to evaluate the load sharing coefficient of planetary gear mechanism;It improves the calculation speed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of mechanical transmission, and particularly relates to a load sharing coefficient calculation method of a planetary gear mechanism. BACKGROUND

[0002] The planetary gear mechanism is increasingly applied in transmission systems, such as automatic transmissions, coaxial electric drive bridges, and transfer cases, etc. The planetary gear mechanism utilizes multiple planetary gears evenly distributed around the sun gear to share the load, thereby reducing the load borne by each planetary gear. The planetary gear mechanism utilizes the high load bearing capacity of the internal meshing and the large space volume of the internal gear ring to reduce the radial and axial dimensions of the mechanism, thereby ensuring compact structure and high load bearing capacity. The planetary gear mechanism utilizes the coaxial input shaft and output shaft to shorten the axial dimension of the transmission system. Therefore, the transmission system with the planetary gear mechanism has the advantages of small volume, light weight, compact structure, large power transmission, and high load bearing capacity. In order to fully utilize the advantages of the planetary gear mechanism, the load sharing coefficient of the planetary gear mechanism should be as close to 1.0 as possible. However, due to the inevitable manufacturing errors, installation errors, elastic deformation of parts, and temperature factors, it is difficult to achieve the ideal load sharing coefficient, and thus the planetary gears in the planetary gear mechanism inevitably have uneven stress.

[0003] The prior art discloses a load sharing coefficient calculation method of a planetary gear train of a new energy vehicle. The finite element method is applied to calculate the stress of the planetary gears under two conditions of manufacturing error and no manufacturing error, and the stress ratio under the two conditions is used to evaluate the load sharing of the planetary gears. However, the following disadvantages exist. 1. The nodes on the outer surface of the internal gear ring are constrained, and the outer surface of the internal gear ring is assumed to be a rigid surface. The advantage is fast calculation speed, but the stiffness of the external supporting parts in contact with the internal gear ring is not considered. In fact, the external supporting parts are mostly made of aluminum alloy material, and the thermal expansion amount after temperature rise is greater than that of the internal gear ring. The thermal expansion amount and the stiffness of the supporting parts are beneficial to the load sharing of the planetary gears, resulting in a large deviation between the calculated load sharing coefficient and the actual value. 2. The stress of the planetary gears at one time is calculated to evaluate the load sharing performance. In fact, the stress of the planetary gears at different times is different, and the corresponding load sharing coefficient also has a large deviation. Therefore, this evaluation method is not reasonable.

[0004] The prior art also discloses a load sharing test load coefficient calculation method of a planetary gear box. The test measurement technology is applied to test the tooth root strain of the internal gear ring, obtain the peak value of each group of strain gauges and the average value of the peak values, and then use the ratio of the two to evaluate the load sharing of the planetary gears. The disadvantage is that it does not state whether single-axis strain gauges or strain flowers are used, and which type of strain is used for evaluation. The above factors all affect the specific value of the load sharing coefficient of the planetary gears, and further affect the load sharing performance evaluation of the planetary gear mechanism.

[0005] The prior art also discloses a planet transmission uneven load coefficient calculation based on a finite element method, the finite element method is applied, the contact relationship between parts is considered, the planet gear contact stress in two cases of having planet gear position error and not having planet gear position error is calculated, and the planet gear uniform load condition is evaluated by using the contact stress ratio in the two cases. The method has the following disadvantages: 1, the influence of the stiffness of the external supporting part in contact with the inner gear ring is not considered, the calculated contact stress deviation is large, and the evaluation effect of the planet gear mechanism uniform load performance is affected; 2, the contact stress is different when the gear is in different meshing positions, only the planet gear uniform load coefficient of one meshing position is calculated, not the maximum uniform load coefficient in the rotation process of the planet gear, and in fact, the planet gear uniform load coefficients are different in different meshing positions, therefore, the evaluation method of the uniform load coefficient is not reasonable.

[0006] Therefore, the uniform load coefficient of the planet gear mechanism should be effectively evaluated in the early stage of product development, so as to determine whether the design of the planet gear mechanism is reasonable and whether the manufacturing process requirements are met. SUMMARY

[0007] The purpose of the present application is to provide a planet gear mechanism uniform load coefficient calculation method to solve the problem of determining whether the design of the planet gear mechanism is reasonable and whether the manufacturing process requirements are met.

[0008] The purpose of the present application is achieved by the following technical solutions:

[0009] A planet gear mechanism uniform load coefficient calculation method, comprising the following steps:

[0010] S1, build a planet gear mechanism assembly finite element model:

[0011] The sun gear, planet gear, planet carrier, inner gear ring, shell, inner ring and outer ring of the bearing in the planet gear mechanism are respectively subjected to solid grid division, and the contacting parts are assembled together by defining the contact relationship therebetween;

[0012] S2, define the material properties of the finite element model:

[0013] The elastic modulus E, Poisson's ratio μ, material density ρ and thermal expansion coefficient α of the finite element model material of each part are defined;

[0014] S3, define the stiffness K of the spring unit in step S1:

[0015] S4, define the boundary conditions of the finite element model: fix the bolt holes on the split type shell connected with the motor;

[0016] S5, define the initial temperature of the finite element model: apply the initial temperature to all part finite element models in step S1;

[0017] S6, applying load 1: load 1 is a temperature load, i.e. a high temperature load is applied to all the finite element models of the components in step S1;

[0018] S7, applying load 2: load 2 is a torque M on the input shaft, which is applied to the input shaft by means of an RBE3 unit, the RBE3 unit selecting a point away from the center point of the end face of the input shaft at one end of the sun gear, and a master point selecting a node on the end face of the input shaft away from one end of the sun gear, M being applied to the RBE3 unit selection point;

[0019] S8, applying load 3: load 3 is a centrifugal force, i.e. the centrifugal force of all rotating components in step S1, as shown in the calculation formulas (3)-(9);

[0020]

[0021] w2 = 2πn2 (4)

[0022] In formulas (3)-(4): F2 is the centrifugal force of the grid element of the sun gear; m2 is the mass of the grid element of the sun gear; r2 is the rotational radius of the grid element of the sun gear; w2 is the angular velocity of the sun gear; n2 is the rotational speed of the sun gear;

[0023]

[0024] w3 = 2πn3 (6)

[0025]

[0026] In formulas (5)-(7): F3 is the centrifugal force of the grid element of the planet carrier; m3 is the mass of the grid element of the planet carrier; r3 is the rotational radius of the grid element of the planet carrier; w3 is the angular velocity of the planet carrier; n3 is the rotational speed of the planet carrier; z2 is the number of teeth of the sun gear; z R is the number of teeth of the inner ring;

[0027]

[0028]

[0029] In formulas (8)-(9): F4 is the centrifugal force of the grid element of the planet gear; m4 is the mass of the grid element of the planet gear; r4 is the revolution rotational radius of the grid element of the planet gear; w4 is the revolution angular velocity of the planet gear, w4 = w3; r 41 is the rotation radius of the grid element of the planet gear; w 41 is the rotation angular velocity of the planet gear; R4 is the revolution radius of the center line of the planet gear; r 42 is the pitch circle radius of the planet gear; r 22 is the pitch circle radius of the sun gear;

[0030] S9, adjust all parts to the ideal assembly position:

[0031] Regardless of the manufacturing error and assembly error of the parts, adjust each part in step S1 to the ideal assembly position;

[0032] S10, determine the first meshing position of the planetary gear mechanism: rotate the planetary gear to any rotationally symmetric plane position of the inner ring gear as the first meshing position of the planetary gear mechanism, to calculate the load sharing coefficient of the planetary gear mechanism at this time, and evaluate the rationality of the structure design of the parts;

[0033] S11, define the calculation condition: the calculation condition is composed of the boundary condition in step S4, the initial temperature in step S5, the load 1 in step S6, the load 2 in step S7, and the load 3 in step S8;

[0034] S12, perform finite element analysis: according to the calculation condition defined in step S11, consider the geometric nonlinearity to calculate the tangential force of the spring element of the simulated needle in the revolution direction of the planetary gear;

[0035] S13, calculate the load sharing coefficient of the planetary gear mechanism in the first meshing position:

[0036] Multiply the tangential force of each simulated needle spring element in the revolution direction of the planetary gear by the revolution radius of the planetary gear supported, that is, obtain the torque transmitted by the planetary gear shaft, and take the ratio of the maximum torque to the average torque of all torques as the load sharing coefficient of the planetary gear mechanism in the first meshing position, see formula (10) for details;

[0037]

[0038] In formula (10), s1 is the load sharing coefficient; f j is the tangential force of the jth spring element of the simulated needle in the revolution direction of the planetary gear; R 4j is the revolution radius of the planetary gear supported by the jth spring element;

[0039] S14, adjust the meshing position of the planetary gear mechanism and calculate the load sharing coefficient at the corresponding position:

[0040] Rotate the planetary gear to other non-rotationally symmetric plane positions in turn, and rotate the sun gear and the planet carrier according to the speed ratio, to obtain the second, third, …, xth meshing positions of the planetary gear mechanism. Repeat steps S11 to S13 at each position to calculate the load sharing coefficients s2, s3, …, sx of the corresponding meshing positions; x Take the maximum value of s1, s2, s3, …, sx as the load sharing coefficient of the planetary gear mechanism; x

[0041] ​S15, considering the manufacturing error and assembly error of the parts, repeating steps S11 to S14 to perform the planetary gear mechanism uniform load coefficient calculation.

[0042] Further, in step S1, the bearing rolling elements are simplified modeled by spring elements. For bearings with outer and inner rings, the nodes at both ends of the spring element simulating the rolling element are connected to the slave points of two RBE3 elements, which are located on the geometric center line of the bearing. The slave point of one RBE3 element is selected as the geometric center of the outer raceway, and the master point is selected as a node on the outer raceway. The slave point of the other RBE3 element is selected as the geometric center of the inner raceway, and the master point is selected as a node on the inner raceway. For needle bearings without outer and inner rings, the nodes at both ends of the spring element simulating the needle are also connected to the slave points of two RBE3 elements, which are located on the geometric center line of the needle bearing. The slave point of one RBE3 element is selected as a point on the center line of the needle bearing, and the master point is selected as a grid node in contact with the planetary gear part on the outer diameter side of the needle bearing. The slave point of the other RBE3 element is selected as another point on the center line of the needle bearing, and the master point is selected as a grid node in contact with the planetary gear shaft part on the inner diameter side of the needle bearing. The number of spring elements is equal to the number of bearings.

[0043] Further, in step S1, the bearing and the housing, and the supported parts are not considered to have interference, and are fitted with zero clearance.

[0044] Further, in step S3, the spring element stiffness K represents the combined stiffness of all rolling elements in a bearing, and the specific acquisition method is divided into steps S3-1 to S3-8.

[0045] S3-1, establish a finite element model of a single rolling element: including meshing three parts of the rolling element, the upper plate and the lower plate, and the mesh at the contact position needs to be finely divided to improve the load transmission accuracy and deformation calculation accuracy; the upper plate and the lower plate are assumed to be rigid bodies to obtain the stiffness of the pure rolling element; the parts are assembled together by defining the contact relationship between them;

[0046] S3-2, define the material properties of the finite element model of a single rolling element: define the elastic modulus E and Poisson's ratio μ of the rolling element;

[0047] S3-3, define the boundary conditions of the finite element model of a single rolling element: the boundary conditions include two types, one is to completely constrain the lower plate and fix it; the other is to constrain the upper plate along all degrees of freedom except its normal direction to ensure that the upper plate can only move along its normal direction;

[0048] S3-4, apply the load F1 borne by a single rolling element: F1 acts on the upper plate, and F1 along the normal direction of the upper plate causes the rolling element to produce compression deformation;

[0049] S3-5, defining the calculation condition of a single rolling element: the calculation condition includes the boundary condition in S3-3 and the load F1 in S3-4;

[0050] S3-6, performing finite element analysis of a single rolling element: the compression deformation X1 of the rolling element is calculated according to the calculation condition defined in S3-5, which is equal to the distance of the load F1 action point moving along the normal direction of the upper plate;

[0051] S3-7, calculating the stiffness K1 of a single rolling element: the stiffness K1 is specifically shown in the calculation formula (1);

[0052]

[0053] S3-8, calculating the stiffness K of the spring unit: K is equal to the comprehensive stiffness of all rolling elements in a bearing, and is specifically shown in the calculation formula (2);

[0054] K = K1 × (COSθ1 + COSθ2 + … + COSθ i ) (2)

[0055] In the formula, θ i is the angle of the i-th rolling element relative to the first rolling element with the intersection point of the bearing center line and the plane formed by all rolling element center points as the center, the first ball can be any ball in the bearing, θ1 = 0, and θ i < 90.

[0056] Further, the stiffness of the spring unit needs to be defined in the radial direction of the bearing by means of a cylindrical coordinate system, the origin of the coordinate system is located on the bearing center line, the r-axis of the coordinate system is along the radial direction of the bearing, the z-axis is along the direction of the bearing center line, and the t-axis is determined according to the right-hand rule by the r-axis and the z-axis.

[0057] Further, in step S5, the initial temperature is defined as room temperature.

[0058] Further, in step S6, the high-temperature load applied on the finite element model of all parts in step S1 is the same, and the temperature value is greater than the normal working temperature value of the planetary gear mechanism.

[0059] Further, in step S7, the torque M is the maximum design input torque of the planetary gear mechanism.

[0060] Further, in steps S10 and S14, the included meshing positions are evenly distributed between two adjacent symmetrical planes of the ring gear.

[0061] Further, in step S15, the manufacturing error is equivalent to the position error of the center line of one of the planetary gears in the tangential direction of the orbit of the planetary gears, i.e., the equivalent tangential position error, as shown in the calculation formula (11); the assembly error is equivalent to the position error of the center line of one of the planetary gears in the radial direction of the orbit radius of the planetary gears, i.e., the equivalent radial position error, as shown in the calculation formula (12); and the manufacturing error and the assembly error are applied to the planetary gears by using the comprehensive equivalent position error, and the calculation of the comprehensive equivalent position error is shown in the formula (13), and specifically, the planetary gears are offset from the ideal assembly position by a distance of the comprehensive equivalent position error to evaluate whether the design of the planetary gear mechanism meets the manufacturing process requirements;

[0062]

[0063]

[0064]

[0065] In the formulas (11)-(13), Δw1 is the equivalent tangential position error, p1 is the eccentric error of the sun gear, p2 is the eccentric error of the planetary gear, p3 is the eccentric error of the inner ring gear, p4 is the eccentric error of the planet carrier, p5 is the eccentric error of the shaft hole of the planetary gear shaft, θ is the gear pressure angle, Δw2 is the equivalent radial position error, a1 is the assembly error of the sun gear, a2 is the assembly error of the planetary gear, a3 is the assembly error of the inner ring gear, a4 is the assembly error of the planet carrier, a5 is the assembly error of the shaft hole of the planetary gear shaft, and Δw is the comprehensive equivalent position error.

[0066] Compared with the prior art, the present application has the following beneficial effects:

[0067] 1. The present application establishes a full-flexible planetary gear mechanism uniform load coefficient finite element model containing a sun gear, a planetary gear, a planet carrier, an inner ring gear, a shell and a bearing, which is more close to the physical prototype; the constraint is applied to the split type shell bolt hole connected with the motor, which is far away from the planetary gear mechanism, so that the influence on the force of the planetary gear is minimized; the load includes torque load, centrifugal force load when revolving and transmitting, and temperature load, which is more comprehensive, so that the environment of the planetary gear mechanism is more consistent with the real environment, and the above measures effectively realize high-precision prediction of the uniform load coefficient of the planetary gear mechanism.

[0068] 2、The present application multiplies tangential force transmitted by planetary gear by revolution radius of planetary gear to obtain torque transmitted by planetary gear, and introduces influence of manufacturing error and assembly error on transmission torque through revolution radius change of planetary gear; the ratio of torque transmitted by one planetary gear to average value of all planetary gear transmission torque is used to evaluate load sharing of planetary gear mechanism, and torque reduction of planetary gear caused by friction in torque transmission is considered, therefore, it is more reasonable to use torque transmitted by planetary gear to evaluate load sharing coefficient of planetary gear mechanism;

[0069] 3、Compared with the prior art using dedendum stress, dedendum strain and tooth surface contact pressure to evaluate load sharing coefficient of planetary gear mechanism, the present application uses torque transmitted by planetary gear to evaluate, which can effectively ignore influence of local structure of dedendum, microscopic modification of tooth surface and other microscopic structures, and the calculated load sharing coefficient is more reasonable, which can more reasonably evaluate planetary gear mechanism and reduce unnecessary structure change;

[0070] 4、The present application uses spring unit to simulate bearing rolling element and gives real support stiffness, which effectively reduces size of finite element model and improves calculation speed. BRIEF DESCRIPTION OF DRAWINGS

[0071] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows, and it should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation to the scope, and other related drawings can be obtained by those skilled in the art without paying creative labor on the premise of not deviating from the concept of the present application.

[0072] Figures 1-6 is a schematic diagram of a planetary gear mechanism;

[0073] Figure 7 is a schematic diagram of a bearing outer ring RBE3 unit;

[0074] Figure 8 is a schematic diagram of a bearing inner ring RBE3 unit;

[0075] Figure 9 is a schematic diagram of a RBE3 unit of a planetary gear part in contact with an outer diameter side of a needle bearing;

[0076] Figure 10 is a schematic diagram of a RBE3 unit of a planetary gear shaft part in contact with an inner diameter side of a needle bearing;

[0077] Figure 11 is a schematic diagram of a single rolling element stiffness finite element analysis model;

[0078] Figure 12 is a schematic diagram of a comprehensive stiffness calculation auxiliary diagram of all rolling elements of a ball bearing;

[0079] Figure 13 is a centrifugal force calculation auxiliary schematic diagram;

[0080] Figure 14 is a planetary gear mechanism meshing position schematic diagram;

[0081] Figure 15 is a planetary gear mechanism uniform load coefficient schematic diagram when each part in the planetary gear mechanism is in a theoretical assembly position;

[0082] Figure 16 is a manufacturing error and assembly error application schematic diagram;

[0083] Figure 17 is a planetary gear mechanism uniform load coefficient schematic diagram when manufacturing error and assembly error are considered. DETAILED DESCRIPTION

[0084] The application will be further described below in conjunction with the embodiments:

[0085] The application will be further described below in conjunction with the embodiments and the drawings. It can be understood that the specific embodiments described herein are only used to explain the application, and not to limit the application. In addition, it should be noted that, for the convenience of description, only the parts related to the application are shown in the drawings, not all the structures.

[0086] It should be noted that: similar labels and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the application, the terms "first", "second" and the like are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0087] The planetary gear mechanism uniform load coefficient calculation method of the application comprises the following steps:

[0088] S1, build a planetary gear mechanism assembly finite element model:

[0089] The sun gear, planetary gear, planet carrier, inner ring, shell, inner ring and outer ring of the bearing in the planetary gear mechanism are respectively subjected to solid grid division, and the contacting parts are defined as contact relationship and assembled together.

[0090] As Figures 1-4As shown, the sun gear 1001 and the input shaft 1002 are integrated structures, divided into solid grids; the planetary gears include three first-stage reduction planetary gears (first-stage reduction planetary gear I 1001, first-stage reduction planetary gear II 1003, first-stage reduction planetary gear III 1005) and three second-stage reduction planetary gears (second-stage reduction planetary gear I 1002, second-stage reduction planetary gear II 1004, second-stage reduction planetary gear III 1006), all divided into solid grids, the first-stage reduction gear I 1001 and the second-stage reduction gear I 1002, the first-stage reduction gear II 1003 and the second-stage reduction gear II 1004, and the first-stage reduction gear III 1005 and the second-stage reduction gear III 1006 are connected together through common nodes to simulate the interference assembly relationship; the planet carrier includes three planetary gear shafts (planetary gear shaft I 3001, planetary gear shaft II 3002, planetary gear shaft III 3003) and a differential case 4000, all divided into solid grids, and each planetary gear shaft is assembled together with the differential case 4000 through a defined contact relationship; the shell supporting the planetary gear mechanism includes two split shells (shell I 5001, shell II 5002), both divided into solid grids, and connected together through a rigid element RBE2 defined at the bolt hole 5003 position; the inner ring 7001 is located inside the shell II 5002 and is a floating part, which needs to be divided into a solid grid, and the inner ring 7001 is assembled together with the shell II 5002 through a defined contact relationship.

[0091] As shown in Figure 5 , Figure 6 As shown, the bearings include bearing I 6001 supporting the input shaft, bearing II 6002, bearing III 6003 supporting the differential case, ball bearing IV 6004, needle bearing I 6005 supporting the planetary gear, needle bearing II 6006, needle bearing III 6007, the outer ring and the inner ring of the bearing I 6001, the bearing II 6002, the bearing III 6003, and the ball bearing IV 6004 are all divided into solid grids; in order to improve the calculation efficiency without affecting the calculation accuracy, the rolling elements are simulated by spring elements, which correspond to the jointc element in the Abaqus software. As shown in Figure 7 , Figure 8 As shown, taking the bearing 6001 as an example, the bearing has an outer ring and an inner ring, and the nodes at both ends of the spring element simulating the rolling element are connected to the slave points of two RBE3 elements, and the two slave points are located on the geometric center line 6008 of the bearing 6001, one slave point of one RBE3 element 6009 is selected as the geometric center 6011 of the outer ring raceway 6010, and the master point is selected as the node on the outer ring raceway 6010, and the other RBE3 element 6012 is selected as the geometric center 6014 of the inner ring raceway 6013, and the master point is selected as the node on the inner ring raceway 6013.

[0092] As shown in Figure 9 ,Figure 10 As shown in the drawings, taking the needle bearing 16005 as an example, the bearing has no outer ring and inner ring, and the nodes at both ends of the spring unit simulating the needle are also connected to the two RBE3 unit slave points, and the two slave points are located on the geometric center line of the needle bearing 16005. One slave point of the RBE3 unit 6015 is selected as a point 6016 on the center line of the needle bearing 16005, and the master point is selected as a grid node at a position 6017 in contact with the outer diameter side of the planetary gear. The slave point of the other RBE3 unit 6018 is selected as another point 6019 on the center line of the needle bearing 16005, and the master point is selected as a grid node at a position 6020 in contact with the inner diameter side of the planetary gear shaft. In the embodiment, the number of spring units is 7, which is equal to the number of bearings.

[0093] The bearings 16001, 16002, 16003, and the ball bearing 16004 are not considered to have interference with the shell and the supported components, and are zero gap fit.

[0094] S2, define the material properties of the finite element model:

[0095] Define the elastic modulus E, Poisson's ratio μ, material density p, and thermal expansion coefficient a of the material of each component finite element model;

[0096] The materials of the shell 15001 and the shell 15002 are aluminum alloy AlSi9Cu3, E = 71000 MPa, μ = 0.33, p = 2700 kg / m 3 , and a = 0.0000212 / ℃; the material of the differential shell 4000 is nodular cast iron QT600, E = 17500 MPa, μ = 0.3, p = 7090 kg / m 3 , and a = 0.0000118 / ℃; the others are iron alloy, E = 210000 MPa, μ = 0.3, p = 7800 kg / m 3 , and a = 0.0000127 / ℃.

[0097] S3, define the stiffness K of the spring unit in step S1:

[0098] The stiffness K of the spring unit represents the comprehensive stiffness of all rolling elements in a bearing. The specific acquisition method is divided into steps S3-1 to S3-8. Taking the ball bearing 16004 as an example to illustrate the calculation and application process of K.

[0099] S3-1, establish a finite element model of a single rolling element: as Figure 11As shown, three components of the ball 6021, the upper plate 6022 and the lower plate 6023 are meshed, and the mesh at the contact position needs to be finely divided to improve the load transfer accuracy and deformation calculation accuracy; the upper plate 6022 and the lower plate 6023 are assumed to be rigid bodies to obtain the stiffness of the simple ball; the components are assembled together by defining the contact relationship.

[0100] S3-2, define the material properties of the finite element model of the single rolling body: define the elastic modulus E of the ball 6021 as 210000 MPa, and the Poisson's ratio μ as 0.3.

[0101] S3-3, define the boundary conditions of the finite element model of the single rolling body: the boundary conditions include two types, one is to constrain the lower surface of the lower plate 6023, and fix it; the second is to constrain the upper plate 6022 along all degrees of freedom except its normal direction, so that the upper plate can only move along its normal direction.

[0102] S3-4, apply the load F1 borne by the single rolling body: as shown in Figure 11 F1 acts on the upper plate 6022, F1 causes the ball to compress and deform along the normal direction of the upper plate 6022, and F1 = 5000 N.

[0103] S3-5, define the calculation condition of the single rolling body: the calculation condition includes the boundary condition in S3-3 and the load F1 in S3-4.

[0104] S3-6, perform finite element analysis of the single rolling body: calculate the compression deformation X1 of the ball according to the calculation condition defined in step S3-5, which is equal to the distance of the load F1 acting point moving along the normal direction of the upper plate 6022, X1 = 0.08652 mm.

[0105] S3-7, calculate the stiffness K1 of the single rolling body: the stiffness K1 is shown in formula (1), and the calculated K1 = 57790 N / mm;

[0106]

[0107] S3-8, calculate the stiffness K of the spring unit: K is equal to the comprehensive stiffness of all balls in a bearing, and the specific calculation formula (2) is as follows:

[0108] K = K1 × (COSθ1 + COSθ2 + … + COSθ i ) (2)

[0109] In the formula, θ i is the angle of the i-th ball relative to the first ball with the intersection of the center line of the ball bearing and the plane passing through the centers of all balls as the center, the first ball can be any ball in the bearing, θ1 = 0, and θ i < 90°.

[0110] As shown in Figure 12 ball bearing IV 6040C includes 9 balls in total, the center line of ball bearing IV 6040C intersects with the plane formed by the centers of all the balls at the center 6024, the angle between two adjacent balls is 40°, i = 5; the first ball is located at the bottom end of the bearing, θ1=0; θ2=θ3=40°, θ4=θ5=80°, K1, θ i Substitute the specific value into formula (2), the calculated spring stiffness K=166400 N / mm; as shown in Figure 12 The spring unit stiffness K needs to be defined in the radial direction of the bearing by means of the cylindrical coordinate system 6025, the origin of the coordinate system is located at the center 6024, the r axis is along the radial direction of the bearing, the z axis is along the center line direction of the bearing, and t is determined according to the right-hand rule by the r axis and the z axis.

[0111] Repeat steps S3-1 to S3-8 to calculate the combined stiffness of the rolling elements of other bearings, and assign the corresponding spring units. The combined stiffness of the rolling elements of bearing I 6001 is K=217656 N / mm, the combined stiffness of the rolling elements of bearing II 6002 is K=166400 N / mm, the combined stiffness of the rolling elements of bearing III 6003 is K=386660 N / mm, and the combined stiffness of the rolling elements of needle bearing I 6005, needle bearing II 6006 and needle bearing III 6007 is K=10344668 N / mm.

[0112] S4, define the boundary conditions of the finite element model: fix the bolt holes 5004 on the split shell connected to the motor.

[0113] S5, define the initial temperature of the finite element model: apply the initial temperature to all the finite element models of the components in step S1, i.e. room temperature 25℃.

[0114] S6, apply load 1: load 1 is a temperature load, i.e. apply a high temperature load to all the finite element models of the components in step S1, and the high temperature load applied to all the finite element models of the components is the same, with a size equal to 120℃.

[0115] S7, apply load 2: load 2 is the torque M on the input shaft 1002, with a size equal to the maximum designed input torque 300 Nm of the planetary gear mechanism, which is applied to the input shaft by means of RBE3 unit 1003, as shown in Figure 5 The RBE3 unit selects the center point 1004 of the input shaft end face away from the sun gear end, the main point selects the node on the input shaft end face 1005 away from the sun gear end, and M is applied to the RBE3 unit from point.

[0116] S8, apply load 3: load 3 is the centrifugal force, which specifically includes the centrifugal force of all rotating components in step S1, and the specific formulas are (3)-(9);

[0117]

[0118] w2=2πn2 (4)

[0119] In formulas (3)-(4): F2 is the centrifugal force of the grid cell of the sun gear and the input shaft; m2 is the mass of the grid cell of the sun gear and the input shaft; r2 is the rotation radius of the grid cell of the sun gear and the input shaft; w2 is the angular velocity of the sun gear and the input shaft; n2 is the rotational speed of the sun gear and the input shaft.

[0120]

[0121] w3=2πn3 (6)

[0122]

[0123] In formulas (5)-(7): F3 is the centrifugal force of the planet carrier's grid element; m3 is the mass of the planet carrier's grid element; r3 is the rotation radius of the planet carrier's grid element; w3 is the angular velocity of the planet carrier; n3 is the rotational speed of the planet carrier; z2 is the number of teeth on the sun gear; z R This represents the number of teeth on the internal gear ring.

[0124]

[0125]

[0126] In formulas (8)-(9): F4 is the centrifugal force of the planetary gear's grid element; m4 is the mass of the planetary gear's grid element; r4 is the radius of revolution of the planetary gear's grid element; w4 is the angular velocity of the planetary gear's revolution, w4 = w3; r 41 The radius of rotation of the grid cell of the planetary gear; w 41 R is the rotational angular velocity of the planetary gear; R4 is the revolution radius of the planetary gear's centerline; r 42 r is the pitch circle radius of the planetary gear. 22 Let be the pitch circle radius of the sun gear.

[0127] like Figure 13 As shown, take a certain unit s on the sun gear u Taking an example to illustrate the centrifugal force calculation process, the calculation process for centrifugal force loads on other units and other components is the same as that for unit s. u Same; Unit s u Mass m2 = 3.14 × 10 -15 kg, and its distance from the geometric center line 6008 of the rotating shaft bearing I6001 is r2 = 24.6 × 10 kg. -3m, the angular velocity w2 = 2 x π x n2 / 60 = 1675.5 / s around the center line 6008, the centrifugal force can be obtained from the formula (3)-(4)

[0128] S9, adjust all parts to the ideal assembly position:

[0129] Without considering the manufacturing error and assembly error of the parts, adjust each part in step S1 to the ideal assembly position.

[0130] S10, determine the first meshing position of the planetary gear mechanism: as shown in Figure 14 , rotate the two-stage reduction planetary gear 2002 to the position of any rotationally symmetric plane 7002 of the inner ring gear 7001 as the first meshing position of the planetary gear mechanism, so as to calculate the load sharing coefficient of the planetary gear mechanism at this time, and evaluate the rationality of the structure design of the parts.

[0131] S11, define the calculation condition: the calculation condition is composed of the boundary condition in step S4, the initial temperature in step S5, the load 1 in step S6, the load 2 in step S7, and the load 3 in step S8.

[0132] S12, perform finite element analysis: according to the calculation condition defined in step S11, simulate the tangential force of the spring unit of the needle roller 6005, the needle roller 6006, and the needle roller 6007 in the revolution direction of the two-stage reduction planetary gear I 2002, the two-stage reduction planetary gear II 2004, and the two-stage reduction planetary gear III 2006, considering geometric nonlinearity.

[0133] S13, calculate the load sharing coefficient of the planetary gear mechanism in the first meshing position:

[0134] Multiply the tangential force of each simulated needle roller spring unit in the revolution direction of the planetary gear by the revolution radius of the supported planetary gear, that is, obtain the torque transmitted by the planetary gear shaft, and take the ratio of the maximum torque to the average torque of all torques as the load sharing coefficient of the planetary gear mechanism in the first meshing position, see formula (10);

[0135]

[0136] In formula (10), s1 is the load sharing coefficient; f j is the tangential force of the jth spring unit of the simulated needle roller in the revolution direction of the planetary gear; R 4j is the revolution radius of the planetary gear supported by the jth spring unit.

[0137] In this embodiment, f1 = 8660 N, f2 = 9061 N, f3 = 9497 N, R 41 = R 42 = R 43=75mm, and from formula (10), we can get s1 =1.047.

[0138] S14. Adjust the meshing position of the planetary gear mechanism and calculate the load sharing coefficient for the corresponding position:

[0139] like Figure 14 As shown, the second-stage reduction planetary gear I2002 is rotated sequentially along the internal gear ring 7001 to positions 7003, 7004, ... 7037, with each position evenly distributed between the symmetry planes 7002 and 7038. Simultaneously, the sun gear, planet carrier, and other planetary gears are rotated according to the speed ratio to obtain the 2nd, 3rd, ... 36th meshing positions of the planetary gear mechanism. Steps S11 to S13 are repeated at each position to calculate the load sharing coefficients s2, s3, ... s at the corresponding meshing positions. 36 Take s1, s2, s3, ... s 36 The maximum value is used as the load sharing coefficient of the planetary gear mechanism.

[0140] The load sharing coefficients for the driven gears I 2002, II 2004, and III 2006 of the second-stage reduction gears at different meshing positions are as follows: Figure 15 As shown in the figure, the highest points of the three curves are basically close, namely 1.068, 1.068 and 1.070 respectively. Therefore, when each component of the planetary gear mechanism is in the ideal assembly position in step S9, the maximum load-sharing coefficient is 1.070, which is close to 1. Based on this, it can be judged that the component structure design is reasonable.

[0141] S15. Considering the manufacturing and assembly errors of the components, repeat steps S11 to S14 to calculate the load-sharing coefficient of the planetary gear mechanism:

[0142] Manufacturing error is equivalent to the position error of one of the planetary gear centerlines along the tangent of the planetary gear revolution, i.e., the equivalent tangential position error, as shown in calculation formula (11); assembly error is equivalent to the position error of one of the planetary gear centerlines along the radius of the planetary gear revolution, i.e., the equivalent radial position error, as shown in calculation formula (12); manufacturing error and assembly error are applied to the planetary gear by a comprehensive equivalent position error, and the comprehensive equivalent position error is calculated by formula (13). Specifically, the distance of the planetary gear from the ideal assembly position by a comprehensive equivalent position error is used to evaluate whether the planetary gear mechanism design meets the manufacturing process requirements;

[0143]

[0144]

[0145]

[0146] In the formulas (11)-(13), Δw1 is an equivalent tangential position error, p1 is a sun gear eccentricity error, p2 is a planet gear eccentricity error, p3 is an inner ring gear eccentricity error, p4 is a planet carrier eccentricity error, p5 is a planet gear shaft hole eccentricity error, θ is a gear pressure angle, Δw2 is an equivalent radial position error, a1 is a sun gear assembly error, a2 is a planet gear assembly error, a3 is an inner ring gear assembly error, a4 is a planet carrier assembly error, a5 is a planet gear shaft hole assembly error, and Δw is a comprehensive equivalent position error.

[0147] In the embodiment, the part manufacturing errors and assembly errors are shown in Table 1, the gear pressure angle θ is 21°, and the specific values are substituted into the formulas (11)-(13) to obtain Δw1=0.051 mm, Δw2=0.052 mm, and Δw=0.073 mm, and the corresponding application process is as shown in Figure 16 Based on the step S9, the first-stage planet gear 2001 and the second-stage planet gear 2002 are offset by the same distance in the same direction, specifically, the two gears are moved by Δw1 in the opposite direction of revolution, and are moved by Δw2 in the radial direction of the inner ring gear 7001 towards the inner ring gear 7001.

[0148] Table 1: Part error values

[0149]

[0150] The steps 11 to 14 are repeated to calculate the planet gear mechanism uniform load coefficients, and the corresponding second-stage reduction driven gears I 2002, II 2004 and III 2006 at different meshing positions have the uniform load coefficients as shown in Figure 17 As can be seen from the figure, the highest points of the two curves corresponding to the second-stage reduction driven gears II 2004 and III 2006 are basically close, and are 1.208 and 1.275 respectively, and the highest point of the curve corresponding to the second-stage reduction driven gear I 2002 is 0.773, which is relatively small, therefore, after considering the manufacturing errors and assembly errors of the planet gear mechanism parts, the maximum uniform load coefficient of the planet gear mechanism is 1.275, which is relatively large, and the subsequent floating design of the inner ring gear should be optimized to reduce the maximum uniform load coefficient of the planet gear mechanism.

[0151] The present application is more consistent with the physical conditions from the modeling of the planet gear mechanism to the definition of the boundary conditions and load conditions; the planet gear mechanism uniform load coefficient is evaluated by the torque transmitted by the planet gear, the torque belongs to the macroscopic quantity, and is less affected by the microcosmic modification of the gear tooth surface, and the torque evaluation is more reasonable than the microcosmic parameter evaluation such as the root stress and the tooth surface contact stress in the prior art; the spring element is used to simulate the bearing rolling body stiffness, which accurately simulates the rolling body stiffness and effectively reduces the finite element calculation scale of the planet gear mechanism.

[0152] Note that the above merely describes preferred embodiments of the present application and the principles of the technology applied. Those skilled in the art will understand that the present application is not limited to the specific embodiments described herein, and that various obvious changes, modifications and substitutions can be made without departing from the scope of the present application. Therefore, although the present application has been described in detail through the above embodiments, the present application is not limited to the above embodiments, and can include more other equivalent embodiments without departing from the concept of the present application, and the scope of the present application is determined by the scope of the claims.

Claims

1. A method of calculating a load sharing factor of a planetary gear mechanism, characterized by, Comprise the following steps: S1, set up planetary gear mechanism assembly finite element model: Respectively to the sun gear, planetary gear, planet carrier, inner ring gear, shell, bearing inner ring and outer ring in planetary gear mechanism entity grid division, and define the contact between the components is in contact with each other together; Bearing rolling body is simplified by spring element modeling, for the bearing with outer ring and inner ring, the nodes at both ends of spring element simulating rolling body are connected to the slave points of two RBE3 units, and the two slave points are located on the geometric center line of the bearing, one slave point of RBE3 unit selects the geometric center of outer ring raceway, and the master point selects the node on the outer ring raceway, and the other slave point of RBE3 unit selects the geometric center of inner ring raceway, and the master point selects the node on the inner ring raceway; for needle bearing without outer ring and inner ring, the nodes at both ends of spring element simulating needle are also connected to the slave points of two RBE3 units, and the two slave points are located on the geometric center line of needle bearing, one slave point of RBE3 unit selects a point on the geometric center line of needle bearing, and the master point selects the grid node of the part of planetary gear contacting the outer diameter side of needle bearing, and the other slave point of RBE3 unit selects another point on the geometric center line of needle bearing, and the master point selects the grid node of the part of planetary gear shaft contacting the inner diameter side of needle bearing; the number of spring elements is equal to the number of bearings; the clearance between the bearing and the shell and the supported components is zero; S2, define the material properties of finite element model: Define the elastic modulus E, Poisson's ratio μ, material density ρ and thermal expansion coefficient α of the finite element model of each part; S3, define the stiffness K of spring element in step S1: the stiffness K of spring element represents the comprehensive stiffness of all rolling bodies in a bearing, and the specific acquisition method is divided into steps S3-1 to S3-8; S3-1, establish the finite element model of single rolling body: including grid division of rolling body, upper plate and lower plate three parts, and the grid at the contact position needs to be finely divided to improve the load transmission accuracy and deformation calculation accuracy; the upper plate and the lower plate are assumed to be rigid bodies to obtain the stiffness of the single rolling body; the parts are assembled together by defining the contact relationship between them; S3-2, define the material properties of single rolling body finite element model: define the elastic modulus E and Poisson's ratio μ of the rolling body; S3-3, define the boundary conditions of single rolling body finite element model: the boundary conditions include two types, one is to completely constrain the lower plate and fix it; the other is to constrain the upper plate along all degrees of freedom except its normal direction to ensure that the upper plate can only move along its normal direction; S3-4, apply the load F1 borne by single rolling body: F1 acts on the upper plate, and F1 makes the rolling body produce compression deformation along the normal direction of the upper plate; S3-5, define the calculation condition of single rolling body: the calculation condition includes the boundary condition in S3-3 and the load F1 in S3-4; S3-6, carry out finite element analysis of single rolling body: calculate the compression deformation X1 of the rolling body according to the calculation condition defined in step S3-5, which is equal to the distance of the load F1 acting point moving along the normal direction of the upper plate; S3-7, calculating the stiffness K1 of a single rolling element: the stiffness K1 is specifically shown in the calculation formula (1); S3-8, calculating the stiffness K of the spring unit: K is equal to the comprehensive stiffness of all rolling elements in a bearing, and is specifically shown in the calculation formula (2); K = K1 x (COS θ1 + COS θ2 +... + COS θn) (1) i ) (2) In the formula, θ i Let θ1 be the angle between the i-th rolling element and the first rolling element, centered at the intersection of the plane formed by the bearing centerline and the center points of all rolling elements. The first ball can be any ball in the bearing, θ1 = 0, θ... i <90; The stiffness of the spring unit needs to be defined in the radial direction of the bearing using a cylindrical coordinate system. The origin of the cylindrical coordinate system is located on the bearing center line. The r-axis of the coordinate system is along the radial direction of the bearing, and the z-axis is along the bearing center line. The t is determined by the r-axis and z-axis according to the right-hand rule. S4, defining the boundary conditions of the finite element model: fixing the bolt holes on the split shell connected with the motor; S5, defining the initial temperature of the finite element model: applying the initial temperature on all the finite element models of the components in step S1; the initial temperature is defined as room temperature; S6, applying load 1: the load 1 is a temperature load, i.e. applying a high temperature load on all the finite element models of the components in step S1; The high temperature load applied on all the finite element models of the components in step S1 is the same, and the temperature value is greater than the normal working temperature value of the planetary gear mechanism; S7, applying load 2: the load 2 is a torque M on the input shaft, which is applied to the input shaft by means of an RBE3 unit, the RBE3 unit selects a center point on the end face of the input shaft away from the end of the sun gear as a slave point, and selects a node on the end face of the input shaft away from the end of the sun gear as a master point, and M is applied to the slave point of the RBE3 unit; the torque M is the maximum designed input torque of the planetary gear mechanism; S8, applying load 3: the load 3 is a centrifugal force, and the centrifugal force of all the rotating components in step S1 is specifically shown in the calculation formulas (3)-(9); w2=2πn2 (4) In the formulas (3)-(4): F2 is the centrifugal force of the grid element of the sun gear; m2 is the mass of the grid element of the sun gear; r2 is the rotating radius of the grid element of the sun gear; w2 is the angular velocity of the sun gear; n2 is the rotating speed of the sun gear; w3=2πn3 (6) In formulas (5)-(7): F3 is the centrifugal force of the grid unit of the planet carrier; m3 is the mass of the grid unit of the planet carrier; r3 is the rotational radius of the grid unit of the planet carrier; w3 is the angular velocity of the planet carrier; n3 is the rotational speed of the planet carrier; z2 is the number of sun gear teeth; z R is the number of ring gear teeth; In formulas (8)-(9): F4 is the grid cell centrifugal force of the planetary gear; m4 is the grid cell mass of the planetary gear; r4 is the grid cell revolution radius of the planetary gear; w4 is the revolution angular velocity of the planetary gear, w4 = w3; r 41 is the grid cell rotation radius of the planetary gear; w 41 is the rotation angular velocity of the planetary gear; R4 is the revolution radius of the planetary gear center line; r 42 is the pitch radius of the planetary gear; r 22 is the pitch radius of the sun gear; S9, adjusting all the components to the ideal assembly position: Without considering the manufacturing error and assembly error of the components, adjusting all the components in step S1 to the ideal assembly position; S10, determining the first meshing position of the planetary gear mechanism: rotating the planetary gear to any rotationally symmetric plane position of the inner ring gear as the first meshing position of the planetary gear mechanism, so as to calculate the load sharing coefficient of the planetary gear mechanism at this time, and evaluate the rationality of the structural design of the components; in step S10, the meshing positions are evenly distributed between two adjacent symmetric planes of the inner ring gear; S11, defining the calculation condition: the calculation condition is composed of the boundary conditions in step S4, the initial temperature in step S5, the load 1 in step S6, the load 2 in step S7, and the load 3 in step S8; S12, performing finite element analysis: according to the calculation condition defined in step S11, considering the geometric nonlinearity, the tangential force of the spring unit of the simulated rolling pin in the revolution direction of the planetary gear is calculated; S13, calculating the load sharing coefficient of the planetary gear mechanism at the first meshing position: The tangential force of each simulated rolling pin in the revolution direction of the planetary gear is multiplied by the revolution radius of the supported planetary gear, so as to obtain the torque transmitted by the planetary gear shaft, and the ratio of the maximum torque to the average torque of all the torques is taken as the load sharing coefficient of the planetary gear mechanism at the first meshing position, and the calculation formula (10) is specifically shown; In formula (10), s1 is a uniform load coefficient; f j is a tangential force of the jth spring unit of the roller pin in the direction of revolution of the planetary gear; R 4j is the revolution radius of the planetary gear supported by the jth spring unit. S14, adjusting the gear meshing position of the planetary gear mechanism and calculating the load sharing coefficient at the corresponding position: The planetary gear is rotated to other non-rotationally symmetrical plane positions in sequence, and the sun gear and the planet carrier are rotated according to the speed ratio, so that the second, third,..., x meshing positions of the planetary gear mechanism are obtained, and steps S11 to S13 are repeated at each position to calculate the load sharing coefficients s2, s3,..., sx of the corresponding meshing positions. x ; the maximum value of s1, s2, s3,..., sx x is taken as the load sharing coefficient of the planetary gear mechanism. S15, considering the manufacturing error and assembly error of the parts, repeating steps S11 to S14 to perform the planetary gear mechanism uniform load coefficient calculation; The manufacturing error is equivalent to the position error of the center line of one of the planetary gears in the tangential direction of the planetary gear orbit tangent, i.e., the equivalent tangential position error, as shown in the calculation formula (11); the assembly error is equivalent to the position error of the center line of one of the planetary gears in the radial direction of the planetary gear orbit radius, i.e., the equivalent radial position error, as shown in the calculation formula (12); the manufacturing error and the assembly error are applied to the planetary gear by using the comprehensive equivalent position error, and the calculation of the comprehensive equivalent position error is shown in the formula (13); specifically, the planetary gear is offset from the ideal assembly position by a distance of the comprehensive equivalent position error, so as to evaluate whether the planetary gear mechanism design meets the manufacturing process requirements; In the formulas (11)-(13), Δw1 is the equivalent tangential position error; p1 is the sun gear eccentric error; p2 is the planetary gear eccentric error; p3 is the inner ring gear eccentric error; p4 is the planetary carrier eccentric error; p5 is the planetary gear shaft hole eccentric error; θ is the gear pressure angle; Δw2 is the equivalent radial position error; a1 is the sun gear assembly error; a2 is the planetary gear assembly error; a3 is the inner ring gear assembly error; a4 is the planetary carrier assembly error; a5 is the planetary gear shaft hole assembly error; and Δw is the comprehensive equivalent position error.

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