The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30,2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS6.029 Simulation of Gear Systems with Dynamic Analysis Y. Temis 1 E. Kozharinov 2 D. Kalinin 3 CIAM, BMSTU CIAM CIAM Moscow, Russia Moscow, Russia Moscow, Russia Abstract: In the present paper, two different methodologies for simulate the dynamic behavior of gears are described and compared. The nonlinear torsion vibrations of geared systems are studied at resonance frequency with the contact loss of the meshing teeth. In the proposed model a time-varying mesh stiffness of tooth pairs and a viscous damping proportional to the meshing stiffness are considered. Gear errors of each meshing tooth pair are also included. Dynamic motion of the spur gear pair over wide range of excitation frequency using the finite element method was simulated. Results of bending stress distribution during overall operation speeds were obtained by FEA. It may serve as a tool for aiding the gear fault diagnosis. Keywords: gear mesh, dynamic model, FEM, friction damper I. Introduction. Dynamic loads on the teeth, resulting from the operation of gears are one of the important factors determining the reliability and durability of the transmission. Therefore, the analysis of dynamic loads in gear mesh and the level of vibration in aircraft transmissions and drives is relevant. A qualitative assessment of the dynamic state of heavily gear necessary to develop mathematical models of meshing gears helps evaluate dynamic processes in gear mesh, transmission errors, stiffness of supports and structural elements, and other factors that are sources of vibration excitation in the transmissions. Theoretical description of dynamic processes in meshing of gears is usually based on two principal methods. In shock method for estimating the dynamic loads, the proposed A.I. Petrusevich and M.D. Genkin [1] and further developed M.S. Polotskiy, the process of meshing is considered as two independent phenomena - the medial edge and strikes, which is typical for transmission at relatively low speeds. Vibrating method for calculating dynamic loads in mesing developed in papers of N.A. Kovalev [2], suggests as the main source of excitation - a periodic variation in the meshing stiffness intermating and related parametric torsional vibration. Based on this method were explained resonance phenomena in gears found the zone of instability and the effects of transmission parameters shown to decrease with the approach of parametric oscillations overlap factor to an integer and supercritical range. In papers Kahraman [4] and Parker [3] used a model with lumped parameters in which the gearing seems as hard drives connected to the elastic- damping coupling. With modern methods of designing aircraft gears, vibration excitation sources such as impact processes, caused by premature meshing tooth top as a result of strain and deflection of the basic step are sidelined. This is due to an increase in manufacturing precision of aviation gear (now modern machines are moving to accuracy class 3), as well as the development of methods for selecting tooth profile modification, compensating the deviation of the deformed shape of a tooth from the theoretical. As a result, the main source of excitation of vibration in geared system is a time-varying mesh stiffness characterized primarily contact ratio ε. II. Model formulation. In the present section the analytical model of motion of a spur gear system is described. The most difficult problem in gear dynamic modeling is to evaluate the level of dynamic loads in the transmission elements. Most precisely such a solution can be obtained by a numerical method for solving dynamic elasticity problems, such as finite element method in a dynamic setting. However, using the finite element method is effective only for the simplest model of a gear pair. Evaluation of the dynamic properties of the entire powertrain is usually carried out by means of analytical models of dynamic systems with lumped parameters [12]. The properties of each subsystem of such a model for a more accurate result is obtained by dynamic simulation in the FEM. A dynamic model of gear train in generally represents a system of the inertial masses connected to each other through elastic and damping elements (fig. 1). Stiffness characteristic for elastic coupling usually evaluated through nonlinear finite element model or based on results of experimental data. Fig. 1. The lumped-parameter dynamic model of a spur gear. To assess the qualitative behavior of a nonlinear system of gears meshing considered two mass dynamic model of a pair of gears (lumped-parameter dynamic model), in which
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Simulation of Gear Systems with Dynamic · PDF filestiffness for spur gear pair with the contact ratio of the overlap . ... The software package Matlab Simulink® used to solve the
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The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30,2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS6.029
Simulation of Gear Systems with Dynamic Analysis
Y. Temis1 E. Kozharinov
2 D. Kalinin
3
CIAM, BMSTU CIAM CIAM
Moscow, Russia Moscow, Russia Moscow, Russia
Abstract: In the present paper, two different
methodologies for simulate the dynamic behavior of gears
are described and compared. The nonlinear torsion
vibrations of geared systems are studied at resonance
frequency with the contact loss of the meshing teeth. In the
proposed model a time-varying mesh stiffness of tooth
pairs and a viscous damping proportional to the meshing
stiffness are considered. Gear errors of each meshing tooth
pair are also included. Dynamic motion of the spur gear
pair over wide range of excitation frequency using the
finite element method was simulated. Results of bending
stress distribution during overall operation speeds were
obtained by FEA. It may serve as a tool for aiding the gear