This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modif...This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.展开更多
Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analyti...Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.展开更多
A lack of accurate description of the meshing characteristics and the corresponding frictional mechanism of the harmonic drive gear has limited progress toward modeling the hysteresis stiffness. This paper presents a ...A lack of accurate description of the meshing characteristics and the corresponding frictional mechanism of the harmonic drive gear has limited progress toward modeling the hysteresis stiffness. This paper presents a method for detection and quantification of the meshing characteristics of the harmonic drive gear based on computer vision. First, an experimental set-up that integrates a high speed camera system with a lighting system is developed, and the image processing is adopted to extract and polish the tooth profiles of the meshed teeth pairs in each acquired video sequence. Next, a physical-mathematical model is established to determine the relative positions of the selected tooth pair in the process of the gear engagement, and the combined standard uncertainty is utilized to evaluate the accuracy of the calculated kinematics parameters. Last, the kinematics analysis of the gear engagement under the ultra-low speed condition is performed with our method and previous method, and the influence of the input rotational speed on the results is examined. The results validate the effectiveness of our method, and indicate that the conventional method is not available in the future friction analysis. It is also shown that the engaging-in phase is approximately a uniform motion process, the engaging-out phase is a variable motion process, and these characteristics remain unchanged with the variation of the input rotational speed. Our method affords the ability to understand the frictional mechanism on the meshed contact surfaces of the harmonic drive gear, and also allows for the dynamic monitoring of the meshing properties.展开更多
基金Project(51675061)supported by the National Natural Science Foundation of China。
文摘This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51405400 & 51375403)the Fundamental Research Funds for the Central Universities (Grant Nos. 2682015ZD12 & 2682016CX125)the Fundamental Research Funds for State Key Laboratory of Traction Power (Grant Nos. 2015TPL_T14 & 2014TPL_T10)
文摘Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.
基金supported by the National Natural Science Foundation of China(Grant No.11272171)the Beijing Natural Science Foundation(Grant No.3132030)the Education Ministry Doctoral Fund of China(Grant No.20120002110070)
文摘A lack of accurate description of the meshing characteristics and the corresponding frictional mechanism of the harmonic drive gear has limited progress toward modeling the hysteresis stiffness. This paper presents a method for detection and quantification of the meshing characteristics of the harmonic drive gear based on computer vision. First, an experimental set-up that integrates a high speed camera system with a lighting system is developed, and the image processing is adopted to extract and polish the tooth profiles of the meshed teeth pairs in each acquired video sequence. Next, a physical-mathematical model is established to determine the relative positions of the selected tooth pair in the process of the gear engagement, and the combined standard uncertainty is utilized to evaluate the accuracy of the calculated kinematics parameters. Last, the kinematics analysis of the gear engagement under the ultra-low speed condition is performed with our method and previous method, and the influence of the input rotational speed on the results is examined. The results validate the effectiveness of our method, and indicate that the conventional method is not available in the future friction analysis. It is also shown that the engaging-in phase is approximately a uniform motion process, the engaging-out phase is a variable motion process, and these characteristics remain unchanged with the variation of the input rotational speed. Our method affords the ability to understand the frictional mechanism on the meshed contact surfaces of the harmonic drive gear, and also allows for the dynamic monitoring of the meshing properties.
