A New Model of the Fractional Order Dynamics of the Planetary Gears
| Autor: | Ćemal B. Dolićanin, Ljiljana Veljović, Vera Nikolić-Stanojević |
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| Rok vydání: | 2013 |
| Předmět: |
Engineering
Article Subject General Mathematics Degrees of freedom (physics and chemistry) 02 engineering and technology System of linear equations 01 natural sciences Noise (electronics) Computer Science::Robotics 0203 mechanical engineering Analytical mechanics 0103 physical sciences Boundary value problem 010301 acoustics business.industry lcsh:Mathematics Mathematical analysis General Engineering lcsh:QA1-939 Physics::Classical Physics Vibration Nonlinear system 020303 mechanical engineering & transports Classical mechanics lcsh:TA1-2040 lcsh:Engineering (General). Civil engineering (General) business Rotation (mathematics) |
| Zdroj: | Mathematical Problems in Engineering, Vol 2013 (2013) |
| ISSN: | 1563-5147 1024-123X |
| Popis: | A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained. |
| Databáze: | OpenAIRE |
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