A load calculation method for a planetary roller bearing

Abstract

A load calculation method of a planetary gear needle bearing, first calculates the tangential force acting on the rim of the planetary gear 、 The radial force, the revolution centrifugal force, and the rotation centrifugal force of the needle of the needle bearing acting on the rim when rotating, then an equation of load-deformation influence coefficient of the planetary gear rim is established, the deformation of the planetary gear rim affected by the rotation of the needle bearing and the deformation of the planetary gear rim not affected by the rotation of the needle bearing are calculated respectively, the radial deformation of the planetary ring is selected by comparison, then the needle is sliced and discretized along the axis of the needle bearing, then the radial deformation of the planetary ring obtained in step four is used to calculate the total deformation between the slice unit and the raceway, and further calculate the contact force between the slice unit and the inner and outer raceways, finally a static equation set of the needle bearing is established, and the deformation of each needle position of the needle bearing is obtained by solving the equation set through Newton iteration method, so that the load distribution of the needle bearing can be calculated.

Description

Technical Field

[0001] This invention relates to the field of load calculation for needle roller bearings, and more particularly to a method for calculating the load of planetary gear needle roller bearings. Background Technology

[0002] Planetary gear systems are widely used in transmission applications across various industries, including vehicles, wind turbines, ships, and aerospace, due to their compact structure, large transmission ratio, high power density, and high transmission efficiency. Currently, with increasing demands for torque and power transmission, planetary gear bearings are becoming increasingly compact in their spatial structure, and the planetary needle roller bearings used typically employ thin-walled structures. Therefore, under gear meshing and impact, planetary gears are prone to large structural deformations, which in turn affect the contact performance of the planetary needle roller bearings.

[0003] Existing bearing contact and deformation analysis models typically treat the bearing rings as rigid, neglecting their structural deformation and only considering the contact deformation between the rolling elements and raceways. As thin-walled bearings, planetary needle roller bearings are directly affected by ring deformation, which directly impacts load distribution. Therefore, analyzing the contact performance of needle roller bearings using rigid rings leads to significant discrepancies between calculated and actual results. However, current technology lacks a method to comprehensively analyze and calculate the deformation of thin-walled planetary gear rims and the contact load of needle roller bearings, taking into account both rotational coupling and gear meshing impact. Summary of the Invention

[0004] The purpose of this invention is to provide a load calculation method for planetary gear needle roller bearings, which analyzes and calculates the deformation of thin-walled planetary gear rims and the contact load of needle roller bearings by comprehensively considering the coupling between rotation and gear meshing impact.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a load calculation method for a planetary gear needle roller bearing, wherein the planetary gear meshes simultaneously with the sun gear and the internal gear ring of the planetary gear train, and the inner bore of the planetary gear is mounted on a rotating shaft through a needle roller bearing. The method includes the following steps: Step 1: Establish a three-axis coordinate system on the planetary gear, with the z-axis of the coordinate system coinciding with the axis of the planetary gear. Define the annular region on the planetary gear from the inner bore to the tooth root as the rim of the planetary gear. Then, calculate the tangential force T, the radial force S, and the centrifugal force F acting on the rim. c1 And the centrifugal force F exerted on the rim by the needle rollers of the needle roller bearing during their rotation. c2 ; ; S = T × tan(α); F c1 =4mπ 2 n12 R n ; F c2 =2m2π 2 n2 2 D m ; In the above formula, T is the tangential force, S is the radial force, and F is the radial force. c1 For the centrifugal force of revolution, F c2 M is the centrifugal force of rotation, M is the driving torque of the sun gear, and K is the centrifugal force of rotation. p d1 is the load-sharing coefficient of the planetary gear train, d1 is the diameter of the sun gear, N is the number of planet gears, α is the pressure angle, m is the weight of the planet gears, n1 is the orbital speed of the planet gears, and R is the load-sharing coefficient of the planetary gear train. n Let m2 be the radius from the center of the planetary gear to the center of the sun gear, m2 be the mass of the needle roller, n2 be the rotational speed of the planetary gear, and D be the radius. m The diameter of the needle roller; Step 2: Establish the equation for the load-deformation influence coefficient of the planetary gear rim; ; ; ; ; ; ; In the above formula, R is the radius of the planetary ring, and C T i C is the deformation influence coefficient of tangential force. S i C is the deformation influence coefficient of radial force. M i C is the deformation influence coefficient of the driving torque. P ij C is the deformation influence coefficient of the support reaction force of the needle roller bearing. Fc1 i C is the deformation influence coefficient of the planetary gear revolution. Fc2 ij φ is the deformation influence coefficient of the needle roller bearing's rotation. j Let φ be the position angle of the j-th needle roller acting on the planetary gear rim. i Let be the position angle of the i-th deformation position on the planetary gear rim; Step 3: Calculate the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing. i And the deformation δ'' of the planetary gear rim unaffected by the rotation of the needle roller bearing i ; The deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing iThe formula for calculation is: ; In the above formula, P j Let δ1 be the support reaction force of the j-th needle roller row on the planetary gear rim, and 2T = Kδ1. 10 / 9 K = 2.89 × 10 4 ×l 0.82 ×D m 0.11 l is the length of the needle roller; For δ i The calculation formula is dimensionless: δ i =A(δ i ) 1.1 +B; ; Transform the dimensionless formula into a low-relaxation iterative scheme: δ i (k+1)= (1-Aω) δ i (k) + Bω, where ω is the relaxation iteration coefficient; Then, a low-relaxation iterative method is used to solve the problem until δ is reached. i ≤1×10 -6 At that time, the solution value is used as the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing. i ; Planetary gear rim deformation δ'' unaffected by needle roller bearing rotation i The formula for calculation is: ; For δ'' i The calculation formula is dimensionless: δ'' i =A1(δ'' i ) 1.1 +B1; ; Transform the dimensionless formula into a low-relaxation iterative scheme: δ'' i (k+1)= (1-A1ω1) δ'' i (k) + B1ω1, where ω1 is the relaxation iteration coefficient; Then, a low-relaxation iterative method is used to solve the problem until δ'' is reached. i ≤1×10 -6 At that time, the solution value is used as the deformation δ'' of the planetary gear rim that is not affected by the rotation of the needle roller bearing. i ; Step 4: Calculate the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing obtained in Step 3. i And the deformation δ'' of the planetary gear rim unaffected by the rotation of the needle roller bearing i For comparison, when δ'' i <0 and δ'' i <δ i When (max), δ'' i As the radial deformation of the planetary rings, otherwise δ i As the radial deformation of the planetary rings; Step 5: Discretize the needle rollers along the axis of the needle roller bearing. Then, based on the radial deformation of the planetary ring obtained in Step 4, calculate the combined deformation of the inner and outer rings between the sliced ​​unit and the raceway. δ' ki =δ ki -e r / 2-2c λ ; δ' ko =δ ko -e r / 2-2c λ ; In the above formula, e r c is the radial clearance of the bearing. λ For shaping; Then, the contact force Q generated between the slice unit and the inner and outer raceways is calculated separately. jo and Q ji : ; ; Step 6: Establish the static equations for the needle roller bearing: ; ; The static equations of the needle roller bearing are solved by Newton's iteration method to obtain the deformation at each needle position. Then, the load of the needle roller bearing is calculated based on the deformation.

[0006] According to the above technical solution, the beneficial effects of the present invention are: This invention considers factors such as planetary gear rim deformation, planetary gear train rotation coupling, and gear meshing impact, establishing an accurate planetary gear train mechanical model. Based on the principle of virtual work in elasticity and rolling bearing design methods, calculation formulas for the loads on the planetary gear rim and rolling elements are derived. Known parameters can be directly substituted into the formulas for calculation, making the load calculation more standardized and universal. The processing method for the deformation analysis of needle rollers and raceways during the modeling process can provide reference for the research of other types of bearings. Finally, considering the rotation coupling and gear meshing impact, the deformation of thin-walled planetary gear rims and the contact load of needle roller bearings are analyzed and calculated, accurately obtaining the load distribution of planetary gear needle roller bearings. Detailed Implementation

[0007] A method for calculating the load of a planetary gear needle roller bearing, wherein the planetary gear meshes with both the sun gear and the internal gear ring of a planetary gear train, and the inner bore of the planetary gear is mounted on a rotating shaft via a needle roller bearing, the method comprising the following steps.

[0008] Step 1: Establish a three-axis coordinate system on the planetary gear, with the z-axis of the coordinate system coinciding with the axis of the planetary gear. Define the annular region on the planetary gear from the inner bore to the tooth root as the rim of the planetary gear. Then, calculate the tangential force T, the radial force S, and the centrifugal force F acting on the rim. c1 And the centrifugal force F exerted on the rim by the needle rollers of the needle roller bearing during their rotation. c2 ; ; S = T × tan(α); F c1 =4mπ 2 n1 2 R n ; F c2 =2m2π 2 n2 2 D m ; In the above formula, T is the tangential force, S is the radial force, and F is the radial force. c1 For the centrifugal force of revolution, F c2 M is the centrifugal force of rotation, M is the driving torque of the sun gear, and K is the centrifugal force of rotation. p d1 is the load-sharing coefficient of the planetary gear train, d1 is the diameter of the sun gear, N is the number of planet gears, α is the pressure angle, m is the weight of the planet gears, n1 is the orbital speed of the planet gears, and R is the load-sharing coefficient of the planetary gear train. n Let m2 be the radius from the center of the planetary gear to the center of the sun gear, m2 be the mass of the needle roller, n2 be the rotational speed of the planetary gear, and D be the radius. m This is the diameter of the needle roller.

[0009] Step 2: Establish the equation for the load-deformation influence coefficient of the planetary gear rim; ; ; ; ; ; ; In the above formula, R is the radius of the planetary ring, and C T i C is the deformation influence coefficient of tangential force. S i C is the deformation influence coefficient of radial force. M i C is the deformation influence coefficient of the driving torque. P ij C is the deformation influence coefficient of the support reaction force of the needle roller bearing. Fc1 i C is the deformation influence coefficient of the planetary gear revolution. Fc2 ij φ is the deformation influence coefficient of the needle roller bearing's rotation. j Let φ be the position angle of the j-th needle roller acting on the planetary gear rim. i Let be the position angle of the i-th deformation position on the planetary gear rim.

[0010] Step 3: Calculate the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing. i And the deformation δ'' of the planetary gear rim unaffected by the rotation of the needle roller bearing i .

[0011] The deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing i The formula for calculation is: ; In the above formula, P j Let δ1 be the support reaction force of the j-th needle roller row on the planetary gear rim, and 2T = Kδ1. 10 / 9 K = 2.89 × 10 4 ×l 0.82 ×D m 0.11 , where l is the length of the needle roller.

[0012] For δ i The calculation formula is dimensionless: δ i =A(δ i ) 1.1 +B; .

[0013] Transform the dimensionless formula into a low-relaxation iterative scheme: δ i (k+1)= (1-Aω) δ i (k) + Bω, where ω is the relaxation iteration coefficient.

[0014] Then, a low-relaxation iterative method is used to solve the problem until δ is reached. i ≤1×10 -6 At that time, the solution value is used as the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing. i .

[0015] Planetary gear rim deformation δ'' unaffected by needle roller bearing rotation i The formula for calculation is: .

[0016] For δ'' i The calculation formula is dimensionless: δ'' i =A1(δ'' i ) 1.1 +B1; .

[0017] Transform the dimensionless formula into a low-relaxation iterative scheme: δ'' i (k+1)= (1-A1ω1) δ'' i (k) + B1ω1, where ω1 is the relaxation iteration coefficient.

[0018] Then, a low-relaxation iterative method is used to solve the problem until δ'' is reached. i ≤1×10 -6 At that time, the solution value is used as the deformation δ'' of the planetary gear rim that is not affected by the rotation of the needle roller bearing. i .

[0019] Step 4: Calculate the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing obtained in Step 3. i And the deformation δ'' of the planetary gear rim unaffected by the rotation of the needle roller bearing i For comparison, when δ'' i <0 and δ'' i <δ i When (max), δ'' i As the radial deformation of the planetary rings, otherwise δ i As the radial deformation of the planetary rings.

[0020] Step 5: Discretize the needle rollers along the axis of the needle roller bearing. Then, based on the radial deformation of the planetary ring obtained in Step 4, calculate the combined deformation of the inner and outer rings between the sliced ​​unit and the raceway. δ' ki =δ ki -e r / 2-2c λ ; δ' ko =δ ko -e r / 2-2c λ ; In the above formula, e r c is the radial clearance of the bearing. λ For shaping.

[0021] Then, the contact force Q generated between the slice unit and the inner and outer raceways is calculated separately. jo and Q ji : ; .

[0022] Step 6: Establish the static equations for the needle roller bearing: ; ; The static equations of the needle roller bearing are solved by Newton's iteration method to obtain the deformation at each needle position. Then, the load of the needle roller bearing is calculated based on the deformation.

[0023] This invention considers factors such as planetary gear rim deformation, planetary gear train rotation coupling, and gear meshing impact, establishing an accurate planetary gear train mechanical model. Based on the principle of virtual work in elasticity and rolling bearing design methods, calculation formulas for the loads on the planetary gear rim and rolling elements are derived. Known parameters can be directly substituted into the formulas for calculation, making the load calculation more standardized and universal. The method for handling the deformation analysis of needle rollers and raceways during the modeling process can provide reference and guidance for the research of other types of bearings.

Claims

1. A method for calculating the load of a planetary gear needle roller bearing, wherein the planetary gear meshes simultaneously with the sun gear and the internal ring gear of a planetary gear train, and the inner bore of the planetary gear is mounted on a rotating shaft via a needle roller bearing, characterized in that... The method includes the following steps: Step 1: Establish a three-axis coordinate system on the planetary gear, with the z-axis of the coordinate system coinciding with the axis of the planetary gear. Define the annular region on the planetary gear from the inner bore to the tooth root as the rim of the planetary gear. Then, calculate the tangential force T, the radial force S, and the centrifugal force F acting on the rim. c1 And the centrifugal force F exerted on the rim by the needle rollers of the needle roller bearing during their rotation. c2 ; ； S = T × tan(α); F c1 =4mπ 2 n1 2 R n ; F c2 =2m2π 2 n2 2 D m ; In the above formula, T is the tangential force, S is the radial force, and F is the radial force. c1 For the centrifugal force of revolution, F c2 M is the centrifugal force of rotation, M is the driving torque of the sun gear, and K is the centrifugal force of rotation. p d1 is the load-sharing coefficient of the planetary gear train, d1 is the diameter of the sun gear, N is the number of planet gears, α is the pressure angle, m is the weight of the planet gears, n1 is the orbital speed of the planet gears, and R is the load-sharing coefficient of the planetary gear train. n Let m2 be the radius from the center of the planetary gear to the center of the sun gear, m2 be the mass of the needle roller, n2 be the rotational speed of the planetary gear, and D be the radius. m The diameter of the needle roller; Step 2: Establish the equation for the load-deformation influence coefficient of the planetary gear rim; ； ； ； ； ； ； In the above formula, R is the radius of the planetary ring, and C T i C is the deformation influence coefficient of tangential force. S i C is the deformation influence coefficient of radial force. M i C is the deformation influence coefficient of the driving torque. P ij C is the deformation influence coefficient of the support reaction force of the needle roller bearing. Fc1 i C is the deformation influence coefficient of the planetary gear revolution. Fc2 ij φ is the deformation influence coefficient of the needle roller bearing's rotation. j Let φ be the position angle of the j-th needle roller acting on the planetary gear rim. i Let be the position angle of the i-th deformation position on the planetary gear rim; Step 3: Calculate the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing. i And the deformation δ'' of the planetary gear rim unaffected by the rotation of the needle roller bearing i ; The deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing i The formula for calculation is: ； In the above formula, P j Let δ1 be the support reaction force of the j-th needle roller row on the planetary gear rim, and 2T = Kδ1. 10 / 9 K = 2.89 × 10 4 ×l 0.82 ×D m 0.11 l is the length of the needle roller; For δ i The calculation formula is dimensionless: d i =A(δ i ) 1.1 +B; ； Transform the dimensionless formula into a low-relaxation iterative scheme: δ i (k+1)= (1-Aω) δ i (k) + Bω, where ω is the relaxation iteration coefficient; Then, a low-relaxation iterative method is used to solve the problem until δ is reached. i ≤1×10 -6 At that time, the solution value is used as the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing. i ; Planetary gear rim deformation δ'' unaffected by needle roller bearing rotation i The formula for calculation is: ； For δ'' i The calculation formula is dimensionless: δ'' i =A1(δ'' i ) 1.1 +B1; ； Transform the dimensionless formula into a low-relaxation iterative scheme: δ'' i (k+1)= (1-A1ω1) δ'' i (k) + B1ω1, where ω1 is the relaxation iteration coefficient; Then, a low-relaxation iterative method is used to solve the problem until δ'' is reached. i ≤1×10 -6 At that time, the solution value is used as the deformation δ'' of the planetary gear rim that is not affected by the rotation of the needle roller bearing. i ; Step 4: Calculate the deformation δ of the planetary gear rim affected by the rotation of the needle roller bearing obtained in Step 3. i And the deformation δ'' of the planetary gear rim unaffected by the rotation of the needle roller bearing i For comparison, when δ'' i <0 and δ'' i <δ i When (max), δ'' i As the radial deformation of the planetary rings, otherwise δ i As the radial deformation of the planetary rings; Step 5: Discretize the needle rollers along the axis of the needle roller bearing. Then, based on the radial deformation of the planetary ring obtained in Step 4, calculate the combined deformation of the inner and outer rings between the sliced ​​unit and the raceway. d' ki =d ki -e r / 2-2c λ ; d' ko =d ko -e r / 2-2c λ ; In the above formula, e r c is the radial clearance of the bearing. λ For shaping; Then, the contact force Q generated between the slice unit and the inner and outer raceways is calculated separately. jo and Q ji : ； ； Step 6: Establish the static equations for the needle roller bearing: ； ； The static equations of the needle roller bearing are solved by Newton's iteration method to obtain the deformation at each needle position. Then, the load of the needle roller bearing is calculated based on the deformation.

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