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The recurrence analysis method is used in the mechanical diagnosis of a gear transmission system using time domain data. The recurrence is a natural behavior of a periodic motion system, which tells the state of the system, after running some time, and will approach a certain past state. In this paper, some statistical parameters of recurrence qualification analysis are extensively evaluated for the use of mechanical diagnosis, based on fairly short acceleration time series; recurrence results are compared with those obtained from Fourier analysis, and the identification procedures for the failure gear transmission by recurrences is also presented. It is found that, using only fairly short time series, some statistical parameters in quantification recurrence analysis can give clear-cut distinction between a healthy and damaged state.

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This study relates to the research on improving analytical models of gears. A new analytical model of gear shaft with 5 DOF was proposed. Equations of vibration were derived without small-angle approximation and were presented in a form that could be implemented in Simulink. In order to determine the effect of the additional DOF, four popular models having 2 DOF, 4 DOF, 6 DOF and 8 DOF were investigated, too. The proposed model has 12 DOF in total. This number of DOF could be increased; this, however, would result in a greater difference between the considered models, thus making it more difficult to evaluate the impact of the additional DOF of shafts. As a benchmark, the dynamic meshing force in the considered analytical models was calculated. Simulations were carried out with and without friction. Additionally, for the 12 DOF model, the effects of the position of the centre of gear and the centre of mass were investigated.

When gears change their distance along the off-line of action (OLOA) direction, this affects the distance between the working surfaces of the meshing teeth along the line of action (LOA). This effect is usually neglected in studies. To include this effect precise equations are derived for spur gears. The analysis is carried out for the general case of spur gears with shifted profiles frequently used in the industry. The influence of OLOA gear displacement on LOA direction is also a function of gears parameters. An analysis is conducted, and the impact of parameters such as module, pressure angle, gear ratio, and the number of teeth is determined. As an example, a simulation of a 12 DOF analytical model is presented. The movement of gears along OLOA is caused by a frictional force that can be high during tooth degradation e.g. scuffing. Results show that when the movement of gears along the OLOA direction is significant, its influence on the distance between the mating teeth should not be neglected.