Method for analyzing service life of support bearing of RV speed reducer

Abstract

A method for analyzing the service life of a support bearing of an RV speed reducer mainly relates to the field of reliability analysis of key parts of the RV speed reducer, and comprises the following steps: firstly, determining the model and working condition of the RV speed reducer and design parameters of the support bearing, then determining the loading condition of two-stage transmission related components, and analyzing and solving the dynamic force of the support bearing according to the stress of an eccentric shaft; based on a Miner linear cumulative damage rule and a life calculation theory, precise equivalence of axial and radial periodic variable loads of the support bearing is realized, and on this basis, a RV reducer support bearing rated life calculation formula is established. The mathematical relationship between the rated service life of the support bearing and the service life under different working conditions is determined through an S-N curve, a Miner linear cumulative damage rule, the equivalent rotating speed and the equivalent torque, a high-precision calculation formula for the service life of the support bearing of the RV speed reducer is established, and the calculation formula is suitable for predicting the service life of the support bearing of the RV speed reducer under the actual working condition of an industrial robot. And an RV reducer life calculation theoretical system is supplemented.

Description

Technical Field

[0001] The invention belongs to the technical field of reliability analysis of key components of RV reducers, and in particular relates to an analysis method for dynamic forces exerted on planetary carrier support bearings of RV reducers and establishment of a service life calculation formula thereof. Background Art

[0002] RV reducer is a precision transmission device developed based on the traditional pin-cycloid planetary gear transmission. It is mainly composed of a cycloid wheel, a pin wheel, an eccentric shaft, an involute gear and a bearing. It has the advantages of high precision, high rigidity, strong load-bearing capacity, high transmission efficiency, compact design, good stability and long life. It is widely used in industrial robots, machine tools, automation equipment and conveyor belt systems.

[0003] As a precision control component at the joint of an industrial robot, the characteristics of the RV reducer directly affect the mechanical characteristics of the industrial robot. At present, the research on the RV reducer mainly focuses on the influence of the cycloid wheel modification, component stiffness, manufacturing error and assembly error on its inherent characteristics and dynamic transmission error, and concentrates on the comprehensive performance of the RV reducer, while there is still a great lack of research on the load analysis and life of its key components. Among the components that make up the RV reducer, the bearing is the weakest part. The stability of the industrial robot and the positioning accuracy of the RV reducer are directly related to the load condition and service life of the support bearing. Under heavy load and high-speed operation, the life of the support bearing may account for the main weight of the service life of the RV reducer. However, the current research has not yet established the reliability theory of the support bearing of the RV reducer, and the complex mechanical structure and high precision of the RV reducer increase the difficulty of dynamic force analysis and life research of the support bearing, resulting in the inability to accurately predict the life of the support bearing under the actual working conditions of the RV reducer. Therefore, it is very necessary to design a service life analysis method for the support bearing of the RV reducer. Summary of the invention

[0004] RV reducers use clean grease lubrication and low friction when working. Therefore, except for operating in harsh environments, RV reducers are unlikely to fail in the form of fracture. Under normal operating conditions, the main reason for the failure of RV reducers is the fatigue failure of the parts structure caused by the fatigue of the metal materials of the support bearings and the swing arm bearings. The support bearings have high speeds, small working spaces, and poor heat dissipation. During operation, they are subjected to periodic cyclic variable loads. The roller surface and raceway surface are prone to pitting and pitting, which leads to fatigue failure of the support bearings and a significant decrease in the repeated positioning accuracy of the RV reducer. The robotic arm cannot run according to the specified trajectory. At the same time, insufficient force analysis of the support bearings will lead to design selection errors, thereby shortening the service life of the RV reducer and affecting the operation of the equipment. Therefore, it is necessary to analyze the dynamic force of the support bearings of the RV reducer and calculate the service life of the support bearings in order to solve the following problems: predict the fatigue life of the support bearings to avoid premature failure; select appropriate support bearing types and materials for different working conditions; provide references for subsequent experimental tests; and provide guidance for optimizing bearing parameters, such as contact angles and roller sizes. At present, the research on RV reducers mainly focuses on the influence of cycloid wheel modification, component stiffness, manufacturing error and assembly error on its inherent characteristics and dynamic transmission error, and concentrates on the comprehensive performance of RV reducers, while there is still a great lack of research on the load analysis and life of support bearings. The current research has not yet established the reliability theory of RV reducer support bearings, and the complex mechanical structure and high precision of RV reducers increase the difficulty of dynamic force analysis and life research of support bearings, resulting in the inability to accurately predict the service life of support bearings under actual working conditions of RV reducers.

[0005] In order to make up for the defects of the prior art in the reliability analysis of RV reducer support bearings, the purpose of the present invention is to provide a service life analysis method for RV reducer support bearings, which can more accurately solve and equivalently calculate the cyclic variable load borne by the support bearings, establish a service life calculation formula for the RV reducer support bearings, improve the prediction accuracy of the support bearing life, and supplement the RV reducer reliability analysis theory.

[0006] In order to achieve the above object, the technical solution adopted by the present invention comprises the following steps:

[0007] Step 1, preparation work, load analysis of the relevant components (center wheel, planetary gear, cycloid wheel, pin gear) of the first-stage involute planetary gear transmission and the second-stage small-tooth-difference cycloid pinwheel transmission of the RV reducer, laying the foundation for solving the dynamic force of the supporting bearing. The specific process is as follows:

[0008] Step 1.1, determine the rated output torque T according to the RV reducer model out , according to the transmission principle of RV reducer, determine the corresponding input torque T in , analyze the load conditions of the center wheel and the planetary wheels:

[0009] Establish the balance relationship between the input torque and the central wheel torque, and solve the tangential force F exerted by the planetary gear on the central wheel tsi :

[0010] mxD tsi r i -T in =0 (1)

[0011] Establish the balance relationship between the eccentric shaft torque and the planetary gear torque, and apply the tangential force F of the center gear to the planetary gear. tis Solve the torque T exerted by the eccentric shaft on the planetary gear es :

[0012] mxD tis r s -T es =0 (2)

[0013] Establish the equilibrium relationship between the tangential force of the eccentric shaft on the planetary gear and the tangential force of the center gear on the planetary gear, and solve the tangential force F exerted by the eccentric shaft on the planetary gear tes :

[0014] F tes -F tis =0 (3)

[0015] Establish the equilibrium relationship between the radial force of the eccentric shaft on the planetary gear and the radial force of the center gear on the planetary gear, and solve the radial force F exerted by the eccentric shaft on the planetary gear res , radial force F exerted by the center wheel on the planetary gear ris :

[0016] F res -F ris =0 (4)

[0017] F ris =F res =F tis tanα (5)

[0018] Among them, m represents the number of eccentric shafts, r i Indicates the radius of the center wheel, r s It represents the radius of the planetary gear, and α represents the pressure angle of the standard involute planetary gear. Both are structural parameters of the RV reducer and are only related to the RV reducer itself.

[0019] Step 1.2, force analysis of the cycloid wheel and the pin gear. When the pin gear is stationary and the eccentric shaft rotates as a fixed axis, the cycloid wheel is subjected to the meshing force of the pin gear. The meshing force is synthesized at the node P of the cycloid wheel and decomposed into ∑P ix and ∑P iy ,∑P ixis the component of meshing force along the tangent direction of the cycloid wheel pitch circle, ∑P iy is the component of the meshing force along the pitch diameter of the cycloid wheel. In order to determine the size of the meshing force, the cycloid wheel in the transmission mechanism is assumed to be stationary for a moment, and a torque T is applied to the pinion housing. s Under the action of this torque, the meshing teeth produce elastic deformation, which can be solved according to Hooke's law:

[0020] The meshing force of the pin gear on the cycloid wheel ∑P ix and ∑P iy :

[0021]

[0022] ΣP iy =K y ΣP ix (7)

[0023] In the formula, K y It is used to express the expression related to the short amplitude coefficient K, specifically:

[0024]

[0025] Establish the balance relationship between the force of the swing arm bearing on the cycloid wheel and the force of the pin gear on the cycloid wheel, and solve the force F of the swing arm bearing on the cycloid wheel j1 、F j2 、F j3 , F j1 F is the force of the swing arm bearing on the cycloidal wheel in the tangent direction of the swing arm bearing distribution circle, j2 F is the horizontal component of the force exerted by the swing arm bearing on the cycloid wheel, j3 is the vertical component of the force exerted by the swing arm bearing on the cycloid wheel:

[0026]

[0027] In the formula, r p Indicates the radius of the pinwheel pitch circle, Z c Indicates the number of cycloid gear teeth, R p represents the radius of the pinwheel distribution circle, e represents the eccentricity between the center of the cycloid wheel and the center of the RV reducer, Z p Indicates the number of pin teeth, r0 indicates the radius of the eccentric shaft distribution circle, both of which are RV reducer structural parameters and are only related to the RV reducer itself;

[0028] Step 1.3, force analysis of the swing arm bearing. The force acting on the cycloid wheel by the swing arm bearing is F j1 、F j2 、F j3 According to the common point force balance, the tangential force F of the swing arm bearing along its distribution circle can be obtained: tWith radial force F rzb :

[0029] F t =F j1 +F j2 cosθ-F j3 sinθ (11)

[0030] F rzb =F j2 sinθ+F j3 cosθ (12)

[0031] In the formula, θ represents the angle between the line connecting the center of the swing arm bearing and the center of the cycloid wheel and the horizontal direction. It is a structural parameter of the RV reducer and is only related to the RV reducer itself.

[0032] Step 2, based on the stress analysis of the two-stage transmission related components of the RV reducer completed in step 1, start to solve the load conditions of the eccentric shaft and the support bearing, and complete the equivalent of the cyclic variable load of the support bearing through the Miner linear cumulative damage law and life calculation theory, in preparation for the life solution part. The specific process is as follows:

[0033] Step 2.1, when the RV reducer is running, the support bearing must bear the force and high speed of the eccentric shaft, and resist the radial load from the planetary carrier. The dynamic force of the support bearing is solved by analyzing the force of the eccentric shaft. The specific force relationship is:

[0034] The resultant force of the planetary gear, swing arm bearing and support bearing along the eccentric shaft axis is 0:

[0035] F tse +2(F j1 +F j2 cosθ-F j3 sinθ)+F oex1 +F oex2 =0 (13)

[0036] In the tangential force direction, the resultant moment of the planetary gear, swing arm bearing and support bearing at the geometric center of the rear support bearing installation position is 0:

[0037]

[0038] The resultant force of the planetary gear, swing arm bearing and support bearing along the eccentric axis distribution circle diameter line is 0:

[0039] -F rse +F oey1 +F oey2 =0 (15)

[0040] In the radial force direction, the combined moment of the planetary gear, swing arm bearing and support bearing at the geometric center of the rear support bearing installation position is 0:

[0041]

[0042] Front support bearing radial force F oex1 、F oey1 and the radial force F of the rear support bearing oex2 、F oey2 The solution is:

[0043]

[0044] Front support bearing radial variable load F r and axial variable load F a The final solution is as follows:

[0045]

[0046]

[0047] In the formula, O represents the geometric center of the installation position of the planetary gear on the eccentric shaft, O1 represents the geometric center of the installation position of the front support bearing on the eccentric shaft, O2 represents the geometric center of the installation position of the front swing arm bearing on the eccentric shaft, O3 represents the geometric center of the installation position of the rear support bearing on the eccentric shaft, O4 represents the geometric center of the installation position of the rear swing arm bearing on the eccentric shaft, l OO4 represents the distance from O to O4, l O1O4 represents the distance from O1 to O4, l O2O4 represents the distance from O2 to O4, l O3O4 Indicates the distance from O3 to O4, Z i Indicates the number of teeth on the center gear, Z s Indicates the number of planetary gear teeth, which are all structural parameters of the RV reducer and are only related to the RV reducer itself; Y represents the axial dynamic load coefficient, and its value is related to the ratio of the radial load to the axial load on the supporting bearing. The specific coefficient values ​​of different types of bearings can be obtained according to the corresponding bearing manual or the manual provided by the manufacturer;

[0048] Step 2.2, the equivalent of the periodic variable load of the support bearing, according to Miner's linear cumulative damage law and the bearing life calculation theory, the life components of the support bearing under several different load conditions can be obtained, and the calculation method of the equivalent load of the support bearing can be reversely deduced:

[0049] According to Miner's linear cumulative damage law, the life components of the RV reducer support bearing under cyclic variable load conditions are as follows:

[0050]

[0051] Use L zs represents the total life revolutions of the supporting bearing under cyclic variable load, then the equivalent load P m It can be expressed as:

[0052]

[0053] In the formula, P1, P2 to P n Indicates the equivalent loads corresponding to different types of loads, M1, M2 to M n Indicates the number of times the support bearing operates under different types of loads, and the transition element. Both are related to the actual operation of the RV reducer. It mainly considers the working conditions of the RV reducer during emergency stop, start-up and stable operation. There is no need to determine the specific value of each element, which will be simplified in subsequent calculations; C d Indicates the basic dynamic load rating of the supporting bearing, which is only related to the design parameters of the bearing itself;

[0054] According to step 2.1, the load on the RV reducer support bearing changes with a period of 2π, so the equivalent load P m The expression can be expressed as:

[0055]

[0056] According to the supporting bearing radial variable load F r And the axial variable load F a From the mathematical expression, we can see that the two have a common coefficient T out , assuming that the integral result is a constant I, which is only related to the design parameters of the RV reducer itself, then the equivalent result of the periodic variable load of the support bearing is:

[0057]

[0058] Where X represents the radial dynamic load coefficient, and its value is related to the ratio of the radial load to the axial load on the supporting bearing. The specific coefficient value of different types of bearings can be obtained from the corresponding bearing manual or the manual provided by the manufacturer;

[0059] Step 3, after completing the dynamic force analysis of the support bearing and the cyclic variable load equivalent according to steps 1 and 2, start solving the life parameters of the RV reducer support bearing. The main parameters are the basic rated dynamic load, equivalent load (solved in step 2.2) and bearing speed. The specific process is as follows:

[0060] Step 3.1, solve the basic dynamic load rating of the support bearing, the basic dynamic load rating C d It is used to measure the dynamic load that the bearing can withstand under normal operating conditions. It is only related to the design parameters of the supporting bearing itself and is solved as follows:

[0061]

[0062] Where b m is the coefficient for improving geometric accuracy, and its value is related to the bearing type. It is 1.3 for radial contact bearings, angular contact ball bearings, self-aligning ball bearings and outer spherical bearings, 1.1 for bearings with filling grooves, 1.1 for cylindrical roller bearings, tapered roller bearings and machine-made sleeve needle roller bearings, 1 for stamped outer ring needle roller bearings, and 1.15 for self-aligning roller bearings; λ is the reduction coefficient caused by rolling element edge stress and non-uniform stress distribution, and its value is related to the bearing type. It is 0.95 for single-row radial contact groove ball bearings, 0.90 for single-row and double-row angular contact groove ball bearings, 1 for single-row and double-row self-aligning ball bearings, 0.95 for magneto bearings, 0.90 for thrust ball bearings, and 0.45 for tapered roller bearings; i ls Indicates the number of rolling element rows; D we Indicates the nominal roller diameter, D pw represents the pitch diameter of the roller group, α0 represents the nominal contact angle of the support bearing, and γ is f c The value of is based on the nominal contact angle of the bearing, the nominal roller diameter and the pitch diameter of the roller group; f c It represents the coefficient related to the geometric shape, manufacturing accuracy and material of the bearing parts, and its value depends on λ and γ; Z represents the number of bearing rollers;

[0063] Step 3.2, support bearing speed analysis. Currently, the RV reducers used on industrial robots are all fixed with pinion housings, and the planetary carrier is used as the output end. The support bearing speed is solved by combining the use of RV reducers, reduction ratio analysis and transmission principle:

[0064] According to the mechanical structure and transmission principle of the RV reducer, the transmission ratio i of the RV reducer can be obtained. rv :

[0065]

[0066] The support bearing speed is the difference between the eccentric shaft speed and the planet carrier speed:

[0067]

[0068] Where n3 6 represents the support bearing speed, n1 represents the input shaft speed, i 12 Indicates the transmission ratio of the first-stage involute planetary gear transmission, i 34 Indicates the transmission ratio of the two-stage small-tooth-difference cycloid pinwheel transmission;

[0069] Step 4: Establishment of the calculation formula for the rated life and service life of the RV reducer support bearing. Based on the analysis of steps 1, 2, and 3, the key parameters of the dynamic force of the support bearing and the life of the support bearing are solved. The calculation formula for the rated life of the support bearing is established, and the equivalent torque T is introduced. m The variable torque under actual working conditions is equivalent to a fixed torque, and the equivalent speed n is introduced m The variable speed under actual working conditions is equivalent to a constant speed value. The mathematical relationship between the service life and rated life of the support bearing is preliminarily obtained by combining the concepts of equivalent speed and equivalent torque, fatigue strength theory and Miner's linear cumulative damage law. The specific process is as follows:

[0070] Step 4.1, mathematical expression for the rated life of the RV reducer support bearing:

[0071]

[0072] Where L0 is the rated life of the support bearing expressed in hours, and n0 is the rated output speed of the RV reducer;

[0073] Step 4.2, establish the relationship between the rated life and service life of the RV reducer support bearing, based on the mathematical expression of the rated life of the support bearing established in step 4.1, combined with the equivalent speed n m and equivalent torque T m The concept of (subscript m is only used to indicate the concept of equivalent), fatigue strength theory and Miner linear cumulative damage law are used to obtain the mathematical relationship between the service life and the rated life of the support bearing. The i involved in the following calculation process is only used to indicate the different operating conditions of the RV reducer (with i ls 、i rv 、i 12 、i 34 Its value varies according to the specific working conditions. In the subsequent calculation process, the relevant elements will be gradually simplified. The specific calculation process is:

[0074] Calculation method of equivalent speed and equivalent torque of RV reducer support bearing:

[0075]

[0076] In the upper part of formula (31), i ranges from 1 to J, where J represents the total number of load cycles. The value of J is mainly affected by the operating conditions of the RV reducer during emergency stop, start-up, and stable operation. For a specific life test platform, the T used in the test will be given. m The value of T does not need to be determined by analyzing the value of J. m, J is only used here to assist in explaining the concept of equivalent torque (for example: if the RV reducer support bearing is subjected to 5 different loads in the startup stage and another different load in the stable stage, then for the RV reducer from startup to stability, the value of J is 6. The example here is only used to illustrate the value of J and does not restrict the use of the present invention); q represents the material fatigue strength index, and its value has been standardized based on a large amount of experimental data and empirical formulas. The typical value of the fatigue strength index under specific conditions can be found; T i It represents the torque corresponding to the operation condition of the i-th RV reducer, and is an auxiliary explanatory element, which is simplified in the calculation process from equation (33) to equation (34);

[0077] In the lower part of formula (31), the value of i ranges from 1 to R, where R is the total number of speed cycles. The value of R is mainly affected by the operating conditions of the RV reducer during emergency stop, start-up and stable operation. For a specific life test platform, the number of n used in the test will be given. m The value of n does not need to be determined by analyzing the value of R. m Here, R is used only to assist in explaining the concept of equivalent speed (for example, if the RV reducer support bearing experiences 5 different speeds in the startup phase and another different speed in the stable phase, then for the RV reducer from startup to stability, the value of R is 6. The example here is only used to illustrate the value of R and does not restrict the use of the present invention); v represents the fatigue damage related index, and its value can be determined according to the specific material type; n i It represents the speed corresponding to the operation condition of the i-th RV reducer, and is an auxiliary explanatory element. It is simplified in the calculation of equations (33) to (34);

[0078] Combining the material fatigue strength curve and Miner's linear cumulative damage law, the life calculation model of key components of RV reducer can be obtained:

[0079]

[0080] In formula (32), the value of i ranges from 1 to l, l represents the total number of load types borne by the RV reducer, T0 represents the torque corresponding to the RV reducer under rated operating conditions, m' represents the material constant in the functional relationship of the finite life fatigue stage in the SN curve, and the value of m' needs to be determined through experiments. For steel, in bending fatigue and tension and compression fatigue, the value of m' is 6 to 20. When steel parts are subjected to fatigue bending, for medium-sized parts and large-sized parts, m'=9;

[0081] The life expressed in revolutions is converted into life expressed in time, and the relationship between the rated life and service life of the supporting bearing is preliminarily obtained through the life calculation model of key components of the RV reducer:

[0082]

[0083] In formula (33), L i represents the life corresponding to the i-th RV reducer operation condition, and L represents the service life of the RV reducer support bearing;

[0084] Step 5, according to the life relationship obtained in step 4, combined with the characteristics that the equivalent load is proportional to the output torque, the concepts of equivalent torque and equivalent speed, the relationship between the service life and the rated life is solved, and the method for calculating the service life based on the rated life of the support bearing and the detailed service life mathematical expression expressed by the equivalent speed and equivalent speed are obtained:

[0085]

[0086]

[0087] The beneficial results of the present invention are:

[0088] The present invention can obtain the dynamic force changes of key components (cycloidal wheel, pin wheel, eccentric shaft, swing arm bearing and support bearing) of the RV reducer under different operating conditions. At the same time, the present invention completes the equivalence of the cyclic variable load of the support bearing with higher accuracy through the life calculation theory and Miner linear cumulative damage law. The life calculation formula established on the basis of the dynamic force calculation and equivalent results obtained by the method of the present invention can significantly improve the prediction accuracy of the support bearing life, and has a guiding role in the reliability analysis of key components of the RV reducer. At the same time, the present invention establishes a mathematical relationship between the rated life and service life of the support bearing, which provides convenience for the subsequent analysis of the influencing factors of the fatigue life of the support bearing of the RV reducer and the structural optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the embodiments of the present invention, the drawings required for the embodiments are briefly introduced below. Obviously, the drawings described below are only exemplary, and for those of ordinary skill in the art, other implementation drawings can be derived from the provided drawings without creative work.

[0090] Figure 1 It is a flow chart of the service life analysis method of the RV reducer support bearing implemented by the present invention.

[0091] Figure 2 This is the force analysis diagram of the first-stage involute planetary gear transmission of the RV-80E reducer.

[0092] Figure 3 This is the force analysis diagram of the two-stage small-tooth-difference cycloidal pinwheel transmission of the RV-80E reducer.

[0093] Figure 4 This is the force analysis diagram of the swing arm bearing of the RV-80E reducer.

[0094] Figure 5(a) is a curve diagram of the dynamic force variation of the RV-80E reducer arm bearing as the eccentric shaft revolves, obtained through step 1.3, and Figure 5(b) is a surface diagram of the dynamic force variation of the RV-80E reducer arm bearing as the eccentric shaft simultaneously rotates and revolves, obtained through step 1.3.

[0095] Figure 6 This is the force analysis diagram of the eccentric shaft and support bearing of the RV-80E reducer.

[0096] FIG7(a) is a curve diagram showing the dynamic force variation of the support bearing of the RV-80E reducer as the eccentric shaft revolves, obtained through step 2.1. FIG7(b) is a surface diagram showing the dynamic force variation of the support bearing of the RV-80E reducer as the eccentric shaft rotates and revolves simultaneously, obtained through step 2.1.

[0097] Figure 8 This is the relationship between the equivalent load of the RV-80E reducer support bearing and its component forces obtained in step 2.2.

[0098] Fig. 9 This is the transmission principle diagram of the RV-80E reducer.

[0099] The reference numerals are as follows: center wheel 1 , planetary wheel 2 , eccentric shaft 3 , cycloid wheel 4 , pin gear 5 , swing arm bearing 6 , support bearing 7 , pin gear housing 8 , planet carrier 9 . DETAILED DESCRIPTION

[0100] RV reducers use clean grease lubrication and low friction when working. Therefore, except for operating in harsh environments, RV reducers are unlikely to fail in the form of fracture. Under normal operating conditions, the main reason for the failure of RV reducers is the fatigue failure of the parts structure caused by the fatigue of the metal materials of the support bearings and the swing arm bearings. The support bearings have high speeds, small working spaces, and poor heat dissipation. During operation, they are subjected to periodic cyclic variable loads. The roller surface and raceway surface are prone to pitting and pitting, which leads to fatigue failure of the support bearings and a significant decrease in the repeated positioning accuracy of the RV reducer. The robotic arm cannot run according to the specified trajectory. At the same time, insufficient force analysis of the support bearings will lead to design selection errors, thereby shortening the service life of the RV reducer and affecting the operation of the equipment. Therefore, it is necessary to analyze the dynamic force of the support bearings of the RV reducer and calculate the service life of the support bearings in order to solve the following problems: predict the fatigue life of the support bearings to avoid premature failure; select appropriate support bearing types and materials for different working conditions; provide references for subsequent experimental tests; and provide guidance for optimizing bearing parameters, such as contact angles and roller sizes. At present, the research on RV reducers mainly focuses on the influence of cycloid wheel modification, component stiffness, manufacturing error and assembly error on its inherent characteristics and dynamic transmission error, and concentrates on the comprehensive performance of RV reducers, while there is still a great lack of research on the load analysis and life of support bearings. The current research has not yet established the reliability theory of RV reducer support bearings, and the complex mechanical structure and high precision of RV reducers increase the difficulty of dynamic force analysis and life research of support bearings, resulting in the inability to accurately predict the life of support bearings under actual working conditions of RV reducers.

[0101] In order to make up for the defects of the prior art in the reliability analysis of the support bearing of the RV reducer, the present invention provides a service life analysis method for the support bearing of the RV reducer, which comprehensively considers the meshing force between the center wheel and the planetary wheel of the RV reducer, the meshing force between the cycloid wheel and the pin gear, the support reaction force of the eccentric shaft spline along the tangent direction and radial direction of its distribution circle, and the support reaction force of the swing arm bearing along the tangent direction and radial direction of its distribution circle on the dynamic force of the support bearing of the RV reducer. On this basis, the bearing life calculation theory and Miner's linear cumulative damage law are used to establish an accurate cyclic variable load equivalent method for the support bearing, which comprehensively considers the influence of various components and design parameters of the RV reducer on the equivalent load. Finally, considering that the RV reducer will inevitably be in a situation of instantaneous load increase and rapid speed change when the industrial robot suddenly stops and starts, the equivalent torque and equivalent speed are introduced, and the fatigue strength theory and Miner linear cumulative damage law are combined to establish the RV reducer support bearing service life calculation formula. The relationship between the support bearing service life and the rated life is established through the basic formula for calculating the life of key components of the RV reducer. This supplements the RV reducer reliability analysis theory, which plays a guiding role in the subsequent analysis of influencing factors and multi-objective optimization of RV reducer design parameters.

[0102] The RV reducer of the embodiment is an 80E reducer, and the support bearing used is a non-standard tapered roller bearing, and the main structural parameters are: the nominal roller diameter is 15mm, the effective roller length is 10mm, the number of rollers is 15, the nominal contact angle is 10°, the pitch circle diameter of the roller group is 25.5mm, the outer diameter is 35mm, the inner diameter is 15mm, the outer ring width is 11.8mm, and the inner ring width is 13.8mm; the number of planetary gear teeth used is 12, and the radius is 10.5mm; the number of center gear teeth used is 36, and the radius is 31.5mm; the eccentricity of the cycloid wheel center relative to the center of the RV reducer is 1.45mm, the radius of the pin gear distribution circle is 76.5mm, the number of pin gear teeth is 40, the number of cycloid wheel teeth is 39, the radius of the eccentric shaft distribution circle is 42mm, the rated output torque is 784Nm, the rated output speed is 15r / min, and the number of eccentric shafts is 3.

[0103] The present invention is described in detail below in conjunction with the accompanying drawings and embodiments. If not specifically described, the "support bearing" in the present invention refers to the front support bearing, that is, the support bearing closer to the input shaft.

[0104] Reference Figure 1 , a method for analyzing the service life of a support bearing of an RV reducer, comprising the following steps:

[0105] Step 1, preparation work, load analysis of the relevant components (center wheel 1, planetary wheel 2, cycloid wheel 4, pin gear 5 and swing arm bearing 6) of the first-stage involute planetary gear transmission and the second-stage small-tooth-difference cycloid pinwheel transmission of the RV reducer, laying the foundation for the dynamic force solution and life calculation of the support bearing 7. The specific process is as follows:

[0106] Step 1.1, refer to Figure 2 , determine the rated output torque T of the RV-80E reducer out , T out The value is 784Nm. On this basis, the corresponding input torque T is determined according to the transmission principle of the RV reducer. in , analyze the load conditions of center gear 1 and planet gear 2:

[0107] The center of the planetary gear is O i As a reference, establish the input torque and the torque balance relationship of the center wheel 1, and solve the tangential force F exerted by the planetary gear 2 on the center wheel 1 tsi :

[0108] mxD tsi r i -T in =0 (36)

[0109] Center wheel center O s As a reference, the torque balance relationship between the eccentric shaft 3 and the planetary gear 2 is established, and the tangential force F of the center wheel 1 on the planetary gear 2 is tis Solve the torque T exerted by the eccentric shaft 3 on the planetary gear 2 es :

[0110] mxD tis r s -T es =0 (37)

[0111] Establish the equilibrium relationship between the tangential force of the eccentric shaft 3 on the planetary gear 2 and the tangential force of the center wheel 1 on the planetary gear 2, and solve the tangential force F exerted by the eccentric shaft 3 on the planetary gear 2 tes :

[0112] F tes -F tis =0 (38)

[0113] Establish the equilibrium relationship between the radial force of the eccentric shaft 3 on the planetary gear 2 and the radial force of the center wheel 1 on the planetary gear 2, and solve the radial force F exerted by the eccentric shaft 3 on the planetary gear 2 res , radial force F exerted by center wheel 1 on planet wheel 2 ris :

[0114] F res -F ris =0 (39)

[0115] F ris =F res =F tis tanα (40)

[0116] In the formula, m represents the number of eccentric shafts 3, r i Indicates the radius of center wheel 1, r s represents the radius of planetary gear 2, α represents the pressure angle of the standard involute planetary gear, which is 20°; through step 1.1, the force analysis of each related component in the first-level involute planetary gear transmission can be completed, which is one of the necessary conditions for solving the dynamic force of the support bearing;

[0117] Step 1.2, refer to Figure 3 , the force analysis of the cycloid wheel 4 and the pin gear 5 is carried out. The pin gear housing 8 is fixed, the pin gear 5 is immobile, and when the eccentric shaft 3 rotates along a fixed axis, the cycloid wheel 4 is subjected to the meshing force of the pin gear 5. The meshing force is synthesized at the node P of the cycloid wheel 4, and the meshing force is decomposed into ∑P ix and ∑P iy ,∑P ix is the component of meshing force along the tangent direction of the cycloid wheel pitch circle, ∑P iy is the component of the meshing force along the cycloid wheel pitch diameter line direction. In order to determine the size of the meshing force, the cycloid wheel 4 in the transmission mechanism is assumed to be stationary for a moment, and a torque T is applied to the pin gear housing 8. s Under the action of this torque, the meshing teeth produce elastic deformation, which can be solved according to Hooke's law:

[0118] The meshing force ∑P of the pin gear 5 on the cycloid wheel 4 ix and ∑P iy :

[0119]

[0120] ΣP iy =K y ΣP ix (42)

[0121] In the formula, K y It is used to express the expression related to the short amplitude coefficient K, specifically:

[0122]

[0123] Establish the equilibrium relationship between the force of the swing arm bearing 6 on the cycloid wheel 4 and the force of the pin gear 5 on the cycloid wheel 4, and solve the force F acting on the cycloid wheel 4 by the swing arm bearing 6 j1 、F j2 、F j3 , F j1 F is the force of the swing arm bearing on the cycloidal wheel in the tangent direction of the swing arm bearing distribution circle, j2F is the horizontal component of the force exerted by the swing arm bearing on the cycloid wheel, j3 is the vertical component of the force exerted by the swing arm bearing on the cycloid wheel:

[0124]

[0125] In the formula, r p Indicates the radius of the 5th pitch circle of the pin gear, Z c Indicates the number of teeth of the cycloid wheel 4, R p represents the radius of the distribution circle of the pin gear 5, e represents the eccentricity between the center of the cycloid wheel 4 and the center of the RV reducer, Z p represents the number of pin teeth of the pin gear 5, and r0 represents the radius of the distribution circle of the eccentric shaft 3; through step 1.2, the force analysis of the two-stage small-tooth difference cycloidal pinwheel transmission can be completed. On this basis, the force calculation of the swing arm bearing is carried out to improve the preparation work for the dynamic force solution and life calculation of the support bearing;

[0126] Step 1.3, refer to Figure 4 , O c represents the center of the cycloid wheel 4, x1 and y1 represent the coordinate system rigidly connected to the swing arm bearing 6, and F rzb F represents the radial force of the swing arm bearing 6 along its distribution circle, t It represents the tangential force of the swing arm bearing 6 along its distribution circle. The force analysis of the swing arm bearing 6 is performed. The force of the swing arm bearing 6 acting on the cycloid wheel 4 is F j1 、F j2 、F j3 According to the common point force balance, the tangential force F of the swing arm bearing 6 along its distribution circle can be obtained: t With radial force F rzb :

[0127] F t =F j1 +F j2 cosθ-F j3 sinθ (46)

[0128] F rzb =F j2 sinθ+F j3 cosθ (47)

[0129] Where θ represents the angle between the line connecting the center of the swing arm bearing 6 and the center of the cycloid wheel 4 and the horizontal direction, which is the structural parameter of the RV reducer and is only related to the RV reducer itself; the tangential force F passing through the swing arm bearing 6 along its distribution circle is t With radial force F rzb The total dynamic force F of the swing arm bearing can be further solved zb According to the solution results, the dynamic force variation curve and surface of the swing arm bearing 6 as the eccentric shaft 3 rotates can be obtained, see Figure 5(a) ,5(b) Obviously, the load on the swing arm bearing 6 is a cyclic variable load with a period of 2π, and its total dynamic force is equal to F t The sizes are almost the same, indicating that F t The torque generated by the center of the distribution circle of the swing arm bearing 6 almost resists the torque of the cycloid wheel 4, which conforms to the transmission law of the cycloid wheel 4 and the eccentric shaft 3 of the RV reducer, and the preparation work is completed;

[0130] Step 2, based on the stress analysis of the two-stage transmission related components of the RV reducer completed in step 1, start to solve the load conditions of the eccentric shaft 3 and the support bearing 7, and complete the equivalent of the cyclic variable load of the support bearing 7 through the Miner linear cumulative damage law and life calculation theory, in preparation for the life solution part. The specific process is as follows:

[0131] Step 2.1, refer to Figure 6 , F t1 With F r1 They represent the tangential force and radial force of the front end swing arm bearing 6 (the swing arm bearing closer to the drive end) along its distribution circle, F t2 With F r2 They represent the tangential force and radial force of the rear end swing arm bearing along its distribution circle, respectively. a With F a2 They represent the axial forces of the front support bearing 7 and the rear support bearing respectively; when the RV reducer is running, the support bearing 7 must bear the force and high speed of the eccentric shaft 3, and resist the radial load from the planet carrier 9. The dynamic force of the support bearing 7 is solved by analyzing the force on the eccentric shaft 3. The specific mechanical relationship is:

[0132] The resultant force of the planetary gear 2, the swing arm bearing 6 and the support bearing 7 along the axis of the eccentric shaft 3 is 0:

[0133] F tse +2(F j1 +F j2 cosθ-F j3 sinθ)+F oex1 +F oex2 =0 (48)

[0134] In the tangential force direction, the resultant moment of the planetary gear 2, the swing arm bearing 6 and the support bearing 7 at the geometric center of the rear support bearing installation position is 0:

[0135] F tse l OO4 +F oex1 l O1O4 +(F j1 +F j2 cosθ-F j3 sinθ)(l O2O4 +lO3O4 )=0 (49)

[0136] The resultant force of the planetary gear 2, the swing arm bearing 6 and the support bearing 7 along the eccentric axis distribution circle diameter line is 0:

[0137] ∑F y =0, -F rse +F oey1 +F oey2 =0 (50)

[0138] In the radial force direction, the resultant moment of the planetary gear 2, the swing arm bearing 6 and the support bearing 7 at the geometric center of the rear support bearing installation position is 0:

[0139] -F rse l OO4 +F oey1 l O1O4 +(F j2 sinθ+F j3 cosθ)(l O3O4 -l O2O4 )=0 (51)

[0140] The radial force F of the front support bearing 7 oex1 、F oey1 and the radial force F of the rear support bearing oex2 、F oey2 The solution is:

[0141]

[0142] Front support bearing 7 radial variable load F r and axial variable load F a The final solution is as follows:

[0143]

[0144] Wherein, O represents the geometric center of the mounting position of the planetary gear 2 on the eccentric shaft 3, O1 represents the geometric center of the mounting position of the front support bearing 7 on the eccentric shaft 3, O2 represents the geometric center of the mounting position of the front swing arm bearing 6 on the eccentric shaft 3, O3 represents the geometric center of the mounting position of the rear support bearing on the eccentric shaft 3, O4 represents the geometric center of the mounting position of the rear swing arm bearing on the eccentric shaft 3, l OO4 represents the distance from O to O4, l O1O4 represents the distance from O1 to O4, l O2O4 represents the distance from O2 to O4, l O3O4 Indicates the distance from O3 to O4, Z c Indicates the number of teeth of the cycloid wheel 4, Z i Indicates the number of teeth on the center wheel, Zs represents the number of teeth of the planetary gear 2, and Y represents the axial dynamic load coefficient, whose value is related to the ratio of the radial load to the axial load on the support bearing. The specific coefficient values ​​of different types of bearings can be obtained according to the corresponding bearing manual or the manual provided by the manufacturer; according to the results, the dynamic force variation curve and surface of the support bearing 7 as the eccentric shaft 3 rotates are obtained, see Figure 7(a) , 7(b) Obviously, the radial force and axial force of the support bearing 7 are cyclic variable loads with a period of 2π. The main reason for the periodic change of the radial force on the support bearing 7 is the rotation of the planet carrier 9 and the eccentric shaft 3. The magnitude of the radial variable load of the bearing is basically the same as F oex1 Consistent, indicating F oex1 The torque generated by the center of the distribution circle of the eccentric shaft 3 basically resists the torque of the planet carrier 9, which is in line with the transmission principle of the RV reducer. The dynamic force of the support bearing 7 is solved through step 2.1. This solution method comprehensively considers the meshing force between the RV reducer center wheel 1 and the planetary wheel 2, the meshing force between the cycloid wheel 4 and the pin gear 5, the support reaction force of the eccentric shaft 3 spline along the tangential direction and radial direction of its distribution circle, and the support reaction force of the swing arm bearing 6 along the tangential direction and radial direction of its distribution circle on the dynamic force of the RV reducer support bearing 7. This analysis method is not only applicable to the RV-80E reducer, but also to other models of RV reducers;

[0145] Step 2.2, the equivalent of the cyclic variable load of the support bearing 7, comprehensively considering the influence of various components and design parameters of the RV reducer on the equivalent load, according to Miner's linear cumulative damage law and bearing life calculation theory, the life components of the support bearing 7 under several different load conditions can be obtained, and the calculation method of the equivalent load of the support bearing 7 can be reversely deduced:

[0146] According to Miner's linear cumulative damage law, the life components of the RV reducer support bearing 7 under cyclic variable load conditions are as follows:

[0147]

[0148] Use L zs represents the total life revolutions of the support bearing 7 under cyclic variable load, then the equivalent load P m It can be expressed as:

[0149]

[0150] In the formula, C d Indicates the basic dynamic load rating, P1, P2 to P n Indicates the equivalent load corresponding to different loads, M1, M2 to M nIndicates the number of times the support bearing operates under different loads and the transition element. Both are related to the actual operation of the RV reducer. They mainly consider the operating conditions of the RV reducer during emergency stop, start-up and stable operation. There is no need to determine the specific value of each element, which will be simplified in subsequent calculations. d Indicates the basic dynamic load rating of the supporting bearing, which is only related to the design parameters of the bearing itself;

[0151] According to step 2.1, the cyclic load on the support bearing 7 of the RV reducer changes with a period of 2π. Combined with the conclusion obtained by Miner's linear cumulative damage law, the equivalent load P of the support bearing m The expression is:

[0152]

[0153] According to the radial load F of the supporting bearing 7 r And the axial variable load F a From the mathematical expression, we can see that the two have a common coefficient T out , assuming that the integral result is a constant I, I is only related to the design parameters of the RV reducer itself, then the equivalent result of the periodic variable load of the support bearing 7 is:

[0154]

[0155] Where X represents the radial dynamic load coefficient, and its value is related to the ratio of the radial load to the axial load on the support bearing 7. The specific coefficient values ​​of different types of bearings can be obtained according to the corresponding bearing manual or the manual provided by the manufacturer. The relationship between the equivalent load of the support bearing 7 and its various components can be obtained through step 2.2, see Figure 8 , the equivalent load of the support bearing 7 is calculated by bringing in the design parameters of each component of the RV-80E reducer to be 3836.5N, which is one of the important parameters for the life calculation of the support bearing 7; the equivalent load calculation method of the support bearing 7 involved in the present invention is not limited to the 80E series RV reducer. Based on the method provided in the present invention, a person of ordinary skill in the art can obtain the dynamic force analysis results and equivalent load calculation results of the support bearing 7 of other types of RV reducers without making any creative work;

[0156] Step 3, after completing the dynamic force analysis and cyclic variable load equivalence of the support bearing 7 according to steps 1 and 2, start solving the life parameters of the RV reducer support bearing 7. The main parameters are the basic rated dynamic load, equivalent load (solved in step 2.2) and speed. The specific process is as follows:

[0157] Step 3.1, solve the basic dynamic load rating of the support bearing 7, the basic dynamic load rating C dIt is used to measure the dynamic load that the bearing can withstand under normal operating conditions. It is only related to the design parameters of the bearing itself and is solved as follows:

[0158]

[0159] The embodiment is an RV-80E reducer, and the support bearing 7 used is a single-row tapered roller bearing of non-standard design. The value of each element in the basic rated dynamic load calculation formula is determined according to the bearing type and design parameters. m The coefficient representing the improvement of geometric accuracy is related to the bearing type. The coefficient is 1.3 for radial contact bearings, angular contact ball bearings, self-aligning ball bearings and outer spherical bearings, 1.1 for bearings with filling grooves, 1.1 for cylindrical roller bearings, tapered roller bearings and machine-made ferrule needle roller bearings, 1 for stamped outer ring needle roller bearings, 1 for self-aligning roller bearings, and 1.15 for RV-80 reducer support bearings. m Take 1.1; λ represents the reduction coefficient caused by rolling element edge stress and non-uniform stress distribution, and its value is related to the bearing type. Single-row radial contact groove ball bearings take 0.95, single-row and double-row angular contact groove ball bearings take 0.90, single-row and double-row self-aligning ball bearings take 1, magneto bearings take 0.95, thrust ball bearings take 0.90, tapered roller bearings take 0.45, and RV-80 reducer support bearings take 0.45; i ls Indicates the number of rolling element rows, set to 1; f c It represents the coefficient related to the geometric shape, manufacturing accuracy and material of the bearing parts, and its value depends on λ and γ; Z represents the number of bearing rollers, and its value is 14; D we Indicates the nominal diameter of the roller, the value is 4.5mm; D pw Indicates the pitch diameter of the roller group, and its value is 25.5mm; α0 indicates the nominal contact angle of the support bearing 7, and its value is 15°; the basic rated dynamic load calculation of the RV-80E support bearing 7 is completed through step 3.1, and its value is 22.975KN, which is one of the main parameters in the life calculation;

[0160] Step 3.2, refer to Fig. 9 , analyze the rotation speed of the support bearing 7. At present, the RV reducers used on industrial robots are all fixed with the pinion housing 8, and the planet carrier 9 is used as the output end. The rotation speed of the support bearing 7 is solved by combining the use of the RV reducer, the reduction ratio analysis and the transmission principle:

[0161] According to the mechanical structure and transmission principle of RV-80E reducer, the transmission ratio i of RV reducer can be obtained. rv :

[0162]

[0163] according to Fig. 9As shown, the speed of the support bearing 7 is the difference between the speed of the eccentric shaft 3 and the speed of the planet carrier 9:

[0164]

[0165] Where n3 6 represents the speed of the supporting bearing 7, n1 represents the speed of the center wheel 1, i 12 Indicates the transmission ratio of the first-stage involute planetary gear transmission, i 34 Indicates the transmission ratio of the two-stage small-tooth-difference cycloid pinwheel transmission; through the speed analysis of step 3.2, the speed of each component of the RV-80E reducer under rated conditions can be obtained: the speed of the center wheel 1 is 1815rpm, the speed of the planetary wheel 2 is -585rpm, the speed of the eccentric shaft 3 is -585rpm, the speed of the cycloid wheel 4 is 15rpm, the speed of the pinion housing 8 is 0, and the speed of the planetary carrier 9 is 15rpm. Finally, the speed of the support bearing 7 is 600rpm. Speed ​​analysis is one of the main steps in life calculation. So far, the three main parameters related to life have been solved;

[0166] Step 4, the establishment of the calculation formula for the rated life and service life of the RV reducer support bearing 7. Based on the analysis of steps 1, 2 and 3, the dynamic force and life key parameters of the support bearing 7 are solved, and the calculation formula for the rated life of the support bearing 7 is established. When calculating the actual service life, the emergency stop and start of the industrial robot need to be considered. At this time, the RV reducer will inevitably be in a state of instantaneous load increase and rapid speed change, and the equivalent torque T needs to be introduced. m The variable torque under actual working conditions is equivalent to a fixed torque, and the equivalent speed n is introduced m The variable speed under actual working conditions is equivalent to a constant speed value. The mathematical relationship between the service life and the rated life of the support bearing 7 is preliminarily obtained by combining the concepts of equivalent speed and equivalent torque, fatigue strength theory and linear cumulative damage law. The specific process is as follows:

[0167] Step 4.1, mathematical expression for the rated life of the RV reducer support bearing 7:

[0168]

[0169] In the formula, L0 is the rated life of the support bearing 7 expressed in hours, n0 is the rated output speed of the RV reducer, and the value is 15r / min; according to the design parameters of the RV-80E reducer, the rated life of the support bearing 7 is calculated to be 10804.4h, which is about 4000 hours longer than the life of the swing arm bearing 6 under rated working conditions, which is in line with the actual situation and illustrates the accuracy of the rated life calculation formula;

[0170] Step 4.2, establish the relationship between the rated life and service life of the RV reducer support bearing. Based on the mathematical expression of the rated life of the support bearing 7 established in step 4.1, the mathematical relationship between the service life and the rated life of the support bearing 7 is obtained by combining the concepts of equivalent speed and equivalent torque (the subscript m is only used to indicate the concept of equivalent), fatigue strength theory and Miner's linear cumulative damage law. The i involved in the following calculation process is only used to indicate different operating conditions of the RV reducer (with i ls 、i rv 、i 12 、i 34 Its value varies according to the specific working conditions. In the subsequent calculation process, the relevant elements will be gradually converted. The specific process is as follows:

[0171] Calculation method of equivalent speed and equivalent torque of RV reducer support bearing 7:

[0172]

[0173] In the upper part of formula (31), i ranges from 1 to J, where J represents the total number of load cycles. The value of J is mainly affected by the operating conditions of the RV reducer during emergency stop, start-up, and stable operation. For a specific life test platform, the T used in the test will be given. m The value of T does not need to be determined by analyzing the value of J. m , J is only used here to assist in explaining the concept of equivalent torque (for example: if the RV reducer support bearing is subjected to 5 different loads in the startup stage and another different load in the stable stage, then for the RV reducer from startup to stability, the value of J is 6. The example here is only used to illustrate the basis for the value of J and does not restrict the use of the present invention); q represents the material fatigue strength index, and its value has been standardized based on a large amount of experimental data and empirical formulas. The typical value of the fatigue strength index under specific conditions can be found; T i It represents the torque corresponding to the operation condition of the i-th RV reducer, and is an auxiliary explanatory element, which is simplified in the calculation process from equation (33) to equation (34);

[0174] In the lower part of formula (31), the value of i ranges from 1 to R, where R is the total number of speed cycles. The value of R is mainly affected by the operating conditions of the RV reducer during emergency stop, start-up and stable operation. For a specific life test platform, the number of n used in the test will be given. m The value of n does not need to be determined by analyzing the value of R. m, R is used here only to assist in explaining the concept of equivalent speed (for example: if the RV reducer support bearing experiences 5 different speeds in the startup phase and another different speed in the stable phase, then for the RV reducer from startup to stability, the value of R is 6. The example here is only used to illustrate the basis for the value of R and does not restrict the use of the present invention); v represents the fatigue damage related index, and its value can be determined according to the specific material type; n i It represents the speed corresponding to the operation condition of the i-th RV reducer, and is an auxiliary explanatory element. It is simplified in the calculation of equations (33) to (34);

[0175] Combining the material fatigue strength curve and Miner's linear cumulative damage law, the basic formula for calculating the life of key components of the RV reducer can be obtained. This formula is applicable to all components of the RV reducer that are subject to variable loads, and is also applicable to support bearings 7:

[0176]

[0177] In formula (32), the value of i ranges from 1 to l, l represents the total number of load types borne by the RV reducer, T0 represents the torque corresponding to the RV reducer under rated operating conditions, m' represents the material constant in the functional relationship of the finite life fatigue stage in the SN curve, and the value of m' needs to be determined through experiments. For steel, in bending fatigue and tension and compression fatigue, the value of m' is 6 to 20. When steel parts are subjected to fatigue bending, for medium-sized parts and large-sized parts, m'=9. For the support bearing of the RV-80E reducer, the value of m' is 10 / 3;

[0178] Convert the life expressed in revolutions into life expressed in time, and use the basic formula for calculating the life of the RV reducer to preliminarily obtain the relationship between the rated life L0 and the service life L of the support bearing 7:

[0179]

[0180] In formula (33), L i represents the life span corresponding to the i-th RV reducer operation condition, the transition element, L represents the service life of the RV reducer support bearing. According to the relationship between the rated life and service life of the support bearing 7, it can be seen that under the condition of a given life span, the output speed and output torque of the RV reducer cannot be too large at the same time, and when the actual output torque is 4 times or more of the rated output torque, the output torque is significantly reduced, resulting in insufficient transmission capacity of the RV reducer, and the industrial robot cannot run according to the preset trajectory;

[0181] Step 5, according to the life relationship obtained in step 4, combined with the characteristics that the equivalent load is proportional to the output torque, the concepts of equivalent torque and equivalent speed, a method for calculating the service life based on the rated life of the support bearing 7 and a detailed mathematical expression of the service life expressed by the equivalent speed and the equivalent speed are obtained:

[0182]

[0183]

[0184] In the dynamic force solution stage, the influence of each component on the dynamic force of the support bearing 7 is considered in detail, and a load equivalence method with high accuracy is given. Compared with the traditional analysis method based on the average output torque acting on the three support bearings, the accuracy is significantly improved. Therefore, the service life calculation formula obtained in step 5 can more accurately calculate the service life of the RV reducer support bearing 7 under actual working conditions. In terms of test data, in order to maximize the influence of torque on the service life of the RV reducer, according to the principle of not destroying its failure mechanism under the start-up and stop allowable torque of the RV reducer, the test torque is set to 2.5 times the rated torque, that is, the equivalent torque T m =1960Nm, equivalent speed n m =13rpm, the theoretical test life time obtained by the service life calculation formula of the RV reducer support bearing 7 established according to formula (35) is 509.5 hours. Under the same test conditions, the theoretical life test time of the same RV reducer is only 11.5 hours longer than the actual life test time obtained by the RV reducer life test platform, and the error does not exceed 3%, which further illustrates the accuracy of the service life analysis method of the RV reducer support bearing. At the same time, according to the life calculation formula of the support bearing 7 obtained in step 5, the factors affecting the life can be easily seen, which plays a guiding role in the subsequent analysis of life influencing factors and multi-objective optimization of RV reducer design parameters.

[0185] The present invention can obtain the dynamic force changes of key components (cycloid wheel, pin wheel, eccentric shaft, swing arm bearing and support bearing) of the RV reducer under different operating conditions. The present invention completes the equivalence of the cyclic variable load of the support bearing with higher accuracy through the life calculation theory and Miner linear cumulative damage law. The life calculation model established on the basis of the dynamic force calculation and equivalent results obtained by the method of the present invention can significantly improve the prediction accuracy of the support bearing life, and has a guiding role in the reliability analysis of key components of the RV reducer.

[0186] The embodiments of the present invention are examples for the support bearings of the RV-80E reducer, so that those skilled in the art can understand or implement the present application. The dynamic force solution, cyclic variable load equivalence and service life calculation schemes are applicable to the reliability analysis of support bearings of different models of RV reducers. Any method based on the scheme of the present invention for fine-tuning or using similar means to the present invention to determine the service life of the support bearings should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the service life of a support bearing of an RV reducer, characterized in that: The following steps are involved: Step 1, preparation work, carry out load analysis on the relevant components of the first-stage involute planetary gear transmission and the second-stage small-tooth-difference cycloidal pinwheel transmission of the RV reducer, namely the center wheel, planetary wheel, cycloidal wheel, and pinwheel. The specific process is as follows: Step 1.1, determine the rated output torque T according to the RV reducer model out , according to the transmission principle of RV reducer, determine the corresponding input torque T in , analyze the load conditions of the center wheel and the planetary wheels: Establish the balance relationship between the input torque and the central wheel torque, and solve the tangential force F exerted by the planetary gear on the central wheel tsi : mF tsi r i -T in =0 (1) Establish the balance relationship between the eccentric shaft torque and the planetary gear torque, and apply the tangential force F of the center gear to the planetary gear. tis Solve the torque T exerted by the eccentric shaft on the planetary gear es : mF tis r s -T es =0 (2) Establish the equilibrium relationship between the tangential force of the eccentric shaft on the planetary gear and the tangential force of the center gear on the planetary gear, and solve the tangential force F exerted by the eccentric shaft on the planetary gear tes : F tes -F tis =0 (3) Establish the equilibrium relationship between the radial force of the eccentric shaft on the planetary gear and the radial force of the center gear on the planetary gear, and solve the radial force F exerted by the eccentric shaft on the planetary gear res , radial force F exerted by the center wheel on the planetary gear ris : F res -F ris =0 (4) F ris =F res =F tis tanα (5) Among them, m represents the number of eccentric shafts, r i Indicates the radius of the center wheel, r s represents the radius of the planetary gear, α represents the pressure angle of the standard involute planetary gear; Step 1.2, force analysis of the cycloid wheel and the pin gear. When the pin gear is stationary and the eccentric shaft rotates as a fixed axis, the cycloid wheel is subjected to the meshing force of the pin gear. The meshing force is synthesized at the node P of the cycloid wheel and decomposed into ∑P ix and ∑P iy ,∑P ix is the component of meshing force along the tangent direction of the cycloid wheel pitch circle, ∑P iy is the component of the meshing force along the pitch diameter of the cycloid wheel. In order to determine the size of the meshing force, the cycloid wheel in the transmission mechanism is assumed to be stationary for a moment, and a torque T is applied to the pinion housing. s Under the action of this torque, the meshing teeth produce elastic deformation, which can be solved according to Hooke's law: The meshing force of the pin gear on the cycloid wheel ∑P ix and ∑P iy : ΣP iy =K y ΣP ix (7) In the formula, K y It is used to express the expression related to the short amplitude coefficient K, specifically: Establish the balance relationship between the force of the swing arm bearing on the cycloid wheel and the force of the pin gear on the cycloid wheel, and solve the force F of the swing arm bearing on the cycloid wheel j1 、F j2 、F j3 Solve, F j1 F is the force of the swing arm bearing on the cycloidal wheel in the tangent direction of the swing arm bearing distribution circle, j2 F is the horizontal component of the force exerted by the swing arm bearing on the cycloid wheel, j3 is the vertical component of the force exerted by the swing arm bearing on the cycloid wheel: In the formula, r p Indicates the radius of the pinwheel pitch circle, Z c Indicates the number of cycloid gear teeth, R p represents the radius of the pinwheel distribution circle, e represents the eccentricity between the center of the cycloid wheel and the center of the RV reducer, Z p represents the number of pin teeth, r0 represents the radius of the eccentric shaft distribution circle; Step 1.3, force analysis of the swing arm bearing. The force acting on the cycloid wheel by the swing arm bearing is F j1 、F j2 、F j3 According to the common point force balance, the tangential force F of the swing arm bearing along its distribution circle can be obtained: t With radial force F rzb : F t =F j1 +F j2 cosθ-F j3 sinθ (11) F rzb =F j2 sinθ+F j3 cosθ (12) In the formula, θ represents the angle between the line connecting the center of the swing arm bearing and the center of the cycloid wheel and the horizontal direction; Step 2, based on the stress analysis of the two-stage transmission related components of the RV reducer completed in step 1, start to solve the load conditions of the eccentric shaft and the support bearing, and complete the equivalent of the cyclic variable load of the support bearing through the Miner linear cumulative damage law and life calculation theory, in preparation for the life solution part. The specific process is as follows: Step 2.1, when the RV reducer is running, the support bearing must bear the force and high speed of the eccentric shaft, and resist the radial load from the planetary carrier. The dynamic force of the support bearing is solved by analyzing the force of the eccentric shaft. The specific force relationship is: The resultant force of the planetary gear, swing arm bearing and support bearing along the eccentric shaft axis is 0: F tse +2(F j1 +F j2 cosθ-F j3 sinθ)+F oex1 +F oex2 =0 (13) In the tangential force direction, the resultant moment of the planetary gear, swing arm bearing and support bearing at the geometric center of the rear support bearing installation position is 0: The resultant force of the planetary gear, swing arm bearing and support bearing along the eccentric axis distribution circle diameter line is 0: -F rse +F oey1 +F oey2 =0 (15) In the radial force direction, the combined moment of the planetary gear, swing arm bearing and support bearing at the geometric center of the rear support bearing installation position is 0: Front support bearing radial force F oex1 、F oey1 and the radial force F of the rear support bearing oex2 、F oey2 The solution is: Front support bearing radial variable load F r and axial variable load F a The final solution is as follows: In the formula, O represents the geometric center of the installation position of the planetary gear on the eccentric shaft, O1 represents the geometric center of the installation position of the front support bearing on the eccentric shaft, O2 represents the geometric center of the installation position of the front swing arm bearing on the eccentric shaft, O3 represents the geometric center of the installation position of the rear support bearing on the eccentric shaft, O4 represents the geometric center of the installation position of the rear swing arm bearing on the eccentric shaft, l OO4 represents the distance from O to O4, l O1O4 represents the distance from O1 to O4, l O2O4 represents the distance from O2 to O4, l O3O4 Indicates the distance from O3 to O4, Z i Indicates the number of teeth on the center gear, Z s represents the number of planetary gear teeth; Y represents the axial dynamic load coefficient; Step 2.2, the equivalent of the periodic variable load of the support bearing, according to Miner's linear cumulative damage law and the bearing life calculation theory, the life components of the support bearing under several different load conditions can be obtained, and the calculation method of the equivalent load of the support bearing can be reversely deduced: According to Miner's linear cumulative damage law, the life components of the RV reducer support bearing under cyclic variable load conditions are as follows: Use L zs represents the total life revolutions of the supporting bearing under cyclic variable load, then the equivalent load P m It is expressed as: In the formula, P1, P2 to P n Indicates the equivalent loads corresponding to different types of loads, M1, M2 to M n Indicates the number of times the support bearing operates under different types of loads; C d Indicates the basic dynamic load rating of the supporting bearing; According to step 2.1, the load on the RV reducer support bearing changes with a period of 2π, so the equivalent load P m The expression is: According to the radial load F of the supporting bearing r And the axial variable load F a From the mathematical expression, we can see that the two have a common coefficient T out , assuming that the integral result is a constant I, which is only related to the design parameters of the RV reducer itself, then the equivalent result of the periodic variable load of the support bearing is: Where, X represents the radial dynamic load coefficient; Step 3: After completing the dynamic force analysis of the support bearing and the cyclic variable load equivalent according to steps 1 and 2, start solving the life parameters of the RV reducer support bearing. The parameters are the basic rated dynamic load, equivalent load and bearing speed. The specific process is as follows: Step 3.1, solve the basic dynamic load rating of the support bearing, the basic dynamic load rating C d It is used to measure the dynamic load that the bearing can withstand under normal operating conditions. It is only related to the design parameters of the supporting bearing itself and is solved as follows: Where b m The coefficient for improvement of geometric accuracy is 1.3 for radial contact bearings, angular contact ball bearings, self-aligning ball bearings and outer spherical bearings, 1.1 for bearings with filling grooves, 1.1 for cylindrical roller bearings, tapered roller bearings and machine-made sleeve needle roller bearings, 1 for stamped outer ring needle roller bearings, and 1.15 for self-aligning roller bearings; λ is the reduction coefficient caused by rolling element edge stress and non-uniform stress distribution, 0.95 for single-row radial contact groove ball bearings, 0.90 for single-row and double-row angular contact groove ball bearings, 1 for single-row and double-row self-aligning ball bearings, 0.95 for magneto bearings, 0.90 for thrust ball bearings, and 0.45 for tapered roller bearings; i ls i represents the number of rolling element rows; D we Indicates the nominal roller diameter, D pw represents the pitch diameter of the roller set, α0 represents the nominal contact angle of the support bearing, and Z represents the number of bearing rollers; Step 3.2, support bearing speed analysis. Currently, the RV reducers used on industrial robots are all fixed with pinion housings, and the planetary carrier is used as the output end. The support bearing speed is solved by combining the use of RV reducers, reduction ratio analysis and transmission principle: According to the mechanical structure and transmission principle of the RV reducer, the transmission ratio i of the RV reducer can be obtained. rv : The support bearing speed is the difference between the eccentric shaft speed and the planet carrier speed: Where n3 6 represents the support bearing speed, n1 represents the input shaft speed, i 12 Indicates the transmission ratio of the first-stage involute planetary gear transmission, i 34 Indicates the transmission ratio of the two-stage small-tooth-difference cycloid pinwheel transmission; Step 4: Establishment of the calculation formula for the rated life and service life of the RV reducer support bearing. Based on the analysis of steps 1, 2, and 3, the key parameters of the dynamic force of the support bearing and the life of the support bearing are solved. The calculation formula for the rated life of the support bearing is established, and the equivalent torque T is introduced. m The variable torque under actual working conditions is equivalent to a fixed torque, and the equivalent speed n is introduced m The variable speed under actual working conditions is equivalent to a constant speed value. The mathematical relationship between the service life and rated life of the support bearing is preliminarily obtained by combining the concepts of equivalent speed and equivalent torque, fatigue strength theory and Miner's linear cumulative damage law. The specific process is as follows: Step 4.1, mathematical expression for the rated life of the RV reducer support bearing: Where L0 is the rated life of the support bearing expressed in hours, and n0 is the rated output speed of the RV reducer; Step 4.2, establish the relationship between the rated life and service life of the RV reducer support bearing, based on the mathematical expression of the rated life of the support bearing established in step 4.1, combined with the equivalent speed n m and equivalent torque T m The concept of fatigue strength theory and Miner's linear cumulative damage law are used to obtain the mathematical relationship between the service life and the rated life of the support bearing. The specific calculation process is: Calculation method of equivalent speed and equivalent torque of RV reducer support bearing: In the upper part of formula (31), i ranges from 1 to J, where J represents the total number of load cycles; q represents the material fatigue strength index; T i Indicates the torque corresponding to the operation condition of the i-th RV reducer; In the lower part of formula (31), i ranges from 1 to R, where R is the total number of speed cycles; v represents the fatigue damage related index; n i Indicates the speed corresponding to the operation condition of the i-th RV reducer; Combining the material fatigue strength curve and Miner's linear cumulative damage law, the life calculation model of key components of RV reducer is obtained: In formula (32), the value of i ranges from 1 to l, l represents the total number of load types borne by the RV reducer, T0 represents the torque corresponding to the RV reducer under rated operating conditions, and m' represents the material constant in the functional relationship of the finite life fatigue stage in the SN curve; The life expressed in revolutions is converted into life expressed in time, and the relationship between the rated life and service life of the supporting bearing is preliminarily obtained through the life calculation model of key components of the RV reducer: In formula (33), L i represents the life corresponding to the i-th RV reducer operation condition, and L represents the service life of the RV reducer support bearing; Step 5, according to the life relationship obtained in step 4, combined with the characteristics that the equivalent load is proportional to the output torque, the concepts of equivalent torque and equivalent speed, the relationship between the service life and the rated life is solved, and the method for calculating the service life based on the rated life of the support bearing and the detailed service life mathematical expression expressed by the equivalent speed and equivalent speed are obtained:

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