A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profle is proposed. The radial deformation function of the fexspline (FS), obtained through Finite Element ...A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profle is proposed. The radial deformation function of the fexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profle is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.展开更多
The current research of wind turbine drivetrain is mainly concentrated in dynamic characteristics of gearbox with a specific suspension of main shaft, such as one-point and two-point suspension. However, little attent...The current research of wind turbine drivetrain is mainly concentrated in dynamic characteristics of gearbox with a specific suspension of main shaft, such as one-point and two-point suspension. However, little attention is paid to the e ects of these suspension configurations on the dynamic responses of wind turbine gearbox. This paper investigates the influences of suspension configurations of main shaft on the dynamic characteristics of drivetrain. For evaluating the dynamic behaviors of drivetrain with multi-stage transmission system more realistically, a dynamic modeling approach of drivetrain is proposed based on Timoshenko beam theory and Lagrange's equation. Considering the flexibility and di erent suspension configurations of main shaft, time-varying mesh sti ness excitation, time-varying transmission error excitation and gravity excitation, etc., a three-dimensional dynamic model of drivetrain is developed, and the dynamic responses of drivetrain are investigated. Results show that with the one-point suspension of main shaft, the resonance frequencies in gearbox, especially at the low-speed stage, obviously shift to the higher frequency range compared to the gearbox without main shaft, but this trend could be inversed by increasing main shaft length. Meanwhile, the loads in main shaft, main shaft bearing and carrier bearing are greatly sensitive to the main shaft length. Hence, the load sharing is further disrupted by main shaft, but this e ect could be alleviated by larger load torque. Comparing to the one-point suspension of main shaft, there occurs the obvious load reduction at the low-speed stage with two-point suspension of main shaft. However, those advantages greatly depend on the distance between two main bearings, and come at the expense of increased load in upwind main shaft unit and the corresponding main bearing. Finally, a wind field test is conducted to verify the proposed drivetrain model. This study develops a numerical model of drivetrain which is able to evaluate the e ects of di erent suspension configurations of main shaft on gearbox.展开更多
A compound oscillatory roller reducer(CORR)with a first-stage gear transmission and a second-stage oscillatory roller transmission is presented.The transmission principle of oscillatory roller transmission is introduc...A compound oscillatory roller reducer(CORR)with a first-stage gear transmission and a second-stage oscillatory roller transmission is presented.The transmission principle of oscillatory roller transmission is introduced,and the tooth profile equation of the inner gear is derived.The analytical model of mesh force considering the installation errors and manufacturing errors is proposed.Then,parametric studies considering different errors on the mesh force are conducted.Results show that the design parameters are significant factors for mesh force.The mesh force is reduced by 17%as the eccentricity of disk cam increases from 2.5 mm to 4 mm.When the radius of the movable roller increases from 7 mm to 20 mm,the mesh force decreases by 8%.As the radius of disk cam increases from 125 mm to 170 mm,the mesh force is decreased by 26.5%.For the impacts of errors,the mesh force has a noticeable fluctuation when these errors exist including the manufacturing error of disk cam,the installation error of disk cam and the manufacturing error of movable roller change.The prototype of the reducer is manufactured and preliminary run-in test proved the feasibility of the transmission principle.展开更多
The reliability and service life of wind turbines are influenced by the complex loading applied on the hub, especially amidst a poor external wind environment. A three-point elastic support, which includes the main be...The reliability and service life of wind turbines are influenced by the complex loading applied on the hub, especially amidst a poor external wind environment. A three-point elastic support, which includes the main bearing and two torque arms, was considered in this study. Based on the flexibilities of the planet carrier and the housing, a coupled dynamic model was developed for a wind turbine drive train. Then, the dynamic behaviors of the drive train for different elastic support parameters were computed and analyzed. Frequency response functions were used to examine how different elastic support parameters influence the dynamic behaviors of the drive train. Results showed that the elastic support parameters considerably influenced the dynamic behaviors of the wind turbine drive train. A large support stiffness of the torque arms decreased the dynamic response of the planet carrier and the main bearing, whereas a large support stiffness of the main bearing decreased the dynamic response of planet carrier while increasing that of the main bearing. The findings of this study provide the foundation for optimizing the elastic support stiffness of the wind turbine drive train.展开更多
基金Supported by Guangdong Provincial Key-Area Research and Development Program(Grant No.2019B090917002).
文摘A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profle is proposed. The radial deformation function of the fexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profle is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.
基金Supported by National Natural Science Foundation of China(Grant Nos.51775061,51575061)Chongqing Municipal Research Program of Frontier and Application Foundation of China(Grant No.cstc2018jcyj AX0087)
文摘The current research of wind turbine drivetrain is mainly concentrated in dynamic characteristics of gearbox with a specific suspension of main shaft, such as one-point and two-point suspension. However, little attention is paid to the e ects of these suspension configurations on the dynamic responses of wind turbine gearbox. This paper investigates the influences of suspension configurations of main shaft on the dynamic characteristics of drivetrain. For evaluating the dynamic behaviors of drivetrain with multi-stage transmission system more realistically, a dynamic modeling approach of drivetrain is proposed based on Timoshenko beam theory and Lagrange's equation. Considering the flexibility and di erent suspension configurations of main shaft, time-varying mesh sti ness excitation, time-varying transmission error excitation and gravity excitation, etc., a three-dimensional dynamic model of drivetrain is developed, and the dynamic responses of drivetrain are investigated. Results show that with the one-point suspension of main shaft, the resonance frequencies in gearbox, especially at the low-speed stage, obviously shift to the higher frequency range compared to the gearbox without main shaft, but this trend could be inversed by increasing main shaft length. Meanwhile, the loads in main shaft, main shaft bearing and carrier bearing are greatly sensitive to the main shaft length. Hence, the load sharing is further disrupted by main shaft, but this e ect could be alleviated by larger load torque. Comparing to the one-point suspension of main shaft, there occurs the obvious load reduction at the low-speed stage with two-point suspension of main shaft. However, those advantages greatly depend on the distance between two main bearings, and come at the expense of increased load in upwind main shaft unit and the corresponding main bearing. Finally, a wind field test is conducted to verify the proposed drivetrain model. This study develops a numerical model of drivetrain which is able to evaluate the e ects of di erent suspension configurations of main shaft on gearbox.
基金Supported by Research and Development Plans in Key Areas of Guangdong(Grant No.2019B090917002)Key Research and Development Project of Chongqing Science and Technology Program(Grant No.cstc2018jszx-cyztzxX0038).
文摘A compound oscillatory roller reducer(CORR)with a first-stage gear transmission and a second-stage oscillatory roller transmission is presented.The transmission principle of oscillatory roller transmission is introduced,and the tooth profile equation of the inner gear is derived.The analytical model of mesh force considering the installation errors and manufacturing errors is proposed.Then,parametric studies considering different errors on the mesh force are conducted.Results show that the design parameters are significant factors for mesh force.The mesh force is reduced by 17%as the eccentricity of disk cam increases from 2.5 mm to 4 mm.When the radius of the movable roller increases from 7 mm to 20 mm,the mesh force decreases by 8%.As the radius of disk cam increases from 125 mm to 170 mm,the mesh force is decreased by 26.5%.For the impacts of errors,the mesh force has a noticeable fluctuation when these errors exist including the manufacturing error of disk cam,the installation error of disk cam and the manufacturing error of movable roller change.The prototype of the reducer is manufactured and preliminary run-in test proved the feasibility of the transmission principle.
基金The authors are grateful for the financial support given by the National Natural Science Foundation of China （Grant Nos. 51405043 and 51575060） and the Innovation Project of the City of Chongqing （Grant Nos. cstc2015zdcy-ztzx70010 and cstc2015zdcy-ztzx70012）.
文摘The reliability and service life of wind turbines are influenced by the complex loading applied on the hub, especially amidst a poor external wind environment. A three-point elastic support, which includes the main bearing and two torque arms, was considered in this study. Based on the flexibilities of the planet carrier and the housing, a coupled dynamic model was developed for a wind turbine drive train. Then, the dynamic behaviors of the drive train for different elastic support parameters were computed and analyzed. Frequency response functions were used to examine how different elastic support parameters influence the dynamic behaviors of the drive train. Results showed that the elastic support parameters considerably influenced the dynamic behaviors of the wind turbine drive train. A large support stiffness of the torque arms decreased the dynamic response of the planet carrier and the main bearing, whereas a large support stiffness of the main bearing decreased the dynamic response of planet carrier while increasing that of the main bearing. The findings of this study provide the foundation for optimizing the elastic support stiffness of the wind turbine drive train.
