Stability and bifurcation analysis of a bevel gear system supported by finite-length squeeze film dampers
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ORIGINAL PAPER
Stability and bifurcation analysis of a bevel gear system supported by finite-length squeeze film dampers Weitao Chen . Siyu Chen
. Jinyuan Tang . Haonan Li
Received: 20 December 2019 / Accepted: 25 May 2020 Springer Nature B.V. 2020
Abstract To analyze the dynamic characteristics of gear systems supported by squeeze film dampers (SFD), the nonlinear oil-film force of SFD is usually obtained by the short bearing approximation (SBA), long bearing approximation (LBA) or finite difference method (FDM). However, the SBA and LBA methods only hold for the cases of infinitely short and infinitely long SFD, which may be not true in practice. Additionally, the FDM method is generally applied to the case of the regular film boundary. Hence, the present work proposes a finite element method to achieve the film pressure of finite-length SFDs (FLSFD) based on the variational principle. The proposed method is not plagued with the boundary conditions and is verified by the comparison with the classic methods. Then, a seven-degree-of-freedom dynamic model of a bevel gear system with FLSFD is developed incorporating the nonlinear film force. Based on Gram–Schmidt QR-decomposition, a strategy to calculate the Lyapunov spectrum of the highdimensional gear system is presented, and the characteristic multipliers of the system are obtained by solving the eigenvalues of the monodromy matrix. The Lyapunov exponents, characteristic multipliers, and bifurcation diagrams, as well as phase portraits and
W. Chen S. Chen (&) J. Tang H. Li State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China e-mail: [email protected]
Poincare´ sections, are utilized to qualify the nonlinear behaviors of the bevel gear system with and without FLSFD. The results show that the application of FLSFD can effectively reduce the occurrences of saddle-node bifurcation, Hopf bifurcation, and perioddoubling, and suppress nonlinear characteristics like the bistable response and jump phenomenon. Keywords Finite-length squeeze film damper Finite element method Bevel gear system Stability analysis Bifurcation type
1 Introduction The gear system is one of the most common mechanical devices and is extensively applied in various industries, such as reducers, automobiles, and aircraft engines. The gear dynamics directly determines the performance and reliability of mechanical devices [1]. The existence of manufacture errors, load fluctuations, time-varying meshing stiffness, transmission error excitation, and bearing nonlinear force inevitably causes vibration, noise, and other undesirable dynamic characteristics in gear systems [2]. Bevel gears are critical parts of the power transmission device of aeroengine. Its transmission performance directly influences the vibration and reliability of the engine. With the accelerating demands of high speed, light-weight,
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and heavy-load in aero-engine, it is urgent to predic
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