Gear manufacturing error is one of the main sources of vibration and noise in gears; its influence on the dynamic transmission behaviour of gear systems is a research hotspot. In the current study on the effect of the manufacturing errors, the processing methods of the errors are mostly rough or hypothetical, so the analysis results cannot provide high reference value. This paper proposes a distinctive method to analyse the vibration response of helical gears in the presence of random manufacturing errors and modifications. The presented study performs tooth contact analysis (TCA) with the real tooth surface containing the random tooth profile error and the modification and performs loaded tooth contact analysis (LTCA) based on the superposition of the random pitch error and the initial gap between mating teeth obtained by TCA. Furthermore, the dynamic excitations, including time-varying mesh stiffness and meshing impact, are computed using the above-mentioned TCA and LTCA. The processing method for the manufacturing errors in this paper is reasonable and close to the actual situation of gear engagement. Using this proposed method, statistical analysis was carried out under machining accuracy grades 5, 6 and 7 to show the effect of the different distributions of random manufacturing errors on the gear vibration. The analysis results are of practical significance and provide references for the design and vibration control of gear drive systems.

Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.

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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.