Abstract
In the research of gear transmission, the vibration and noise problem has received many concerns all the times. Scholars use tooth modification technique to improve the meshing state of gearings in order to reduce the vibration and noise. However, few of researchers consider the influence of measured manufacturing errors when they do the study of tooth modification. In order to investigate the efficiency of the tooth modification in the actual project, this paper proposes a dynamic model of a helical gear pair including tooth modification and measured manufacturing errors to do a deterministic analysis on the dynamical transmission performance. In this analysis, based on the measured tooth deviation, a real tooth surface (including modification and measured tooth profile error) is fitted by a bicubic B-spline. With the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) on the real tooth surface, the loaded transmission error, tooth surface elastic deformation, and load distribution can be determined. Based on the results, the time-varying mesh stiffness and gear mesh impact are computed. Taking the loaded transmission error, measured cumulative pitch error, eccentricity error, time-varying mesh stiffness, and gear mesh impact as the internal excitations, this paper establishes a 12-degree-of-freedom (DOF) dynamic model of a helical gear pair and uses the Fourier series method to solve it. In two situations of low speed and high speed, the gear system dynamic response is analyzed in the time and frequency domains. In addition, an experiment is performed to validate the simulation results. The study shows that the proposed technique is useful and reliable for predicting the dynamic response of a gear system.
Highlights
In the gear machining process, the design deviation, manufacturing error, and fixing error of the machine cutting tool can cause a change in conjugate conditions and produce a tooth profile error, pitch error, eccentric error, etc. ese errors affect the contact characteristics of gears, worsen the stability and bearing capability of gear transmission, and cause enormous noise and vibration. us, many scholars pay close attention to the prediction and control of gear vibration and noise in their transmission designs [1,2,3,4,5,6,7,8]
Hu et al [15] researched the effect of tooth modification of a high-speed gear system and set the variation of the tooth profile error and pitch error as a sine function
Wei et al [17] established a coupled nonlinear dynamics model which is used for planetary gear transmission systems in wind turbines and incorporates the effects of the time-varying mesh stiffness, dynamic transmission error, gear mesh impact, and input
Summary
In the gear machining process, the design deviation, manufacturing error, and fixing error of the machine cutting tool can cause a change in conjugate conditions and produce a tooth profile error, pitch error, eccentric error, etc. ese errors affect the contact characteristics of gears, worsen the stability and bearing capability of gear transmission, and cause enormous noise and vibration. us, many scholars pay close attention to the prediction and control of gear vibration and noise in their transmission designs [1,2,3,4,5,6,7,8]. Chen et al [20] proposed a rotational nonlinear dynamic model of a planetary gear transmission system, which included the time-varying mesh stiffness and synthetic mesh error with random fluctuation; the synthetic mesh error was resolved into a sine signal and white noise. E main objective is to do dynamics analysis of a helical gear pair based on the real tooth surface (including tooth modification and tooth profile error) and the measured cumulative pitch error, so that the transmission performance of the machined gear system can be predicted. E internal excitations, including time-varying mesh stiffness, gear mesh impact, loaded transmission error, measured cumulative pitch error, and eccentric errors, will be considered in the analysis. The proposed method is compared with the traditional method and verified by a noise and vibration experiment
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