Non-Linear Dynamic Feature Analysis of a Multiple-Stage Closed-Loop Gear Transmission System for 3D Circular Braiding Machine

Aiming at the particularity of a multiple-stage closed-loop gear transmission system for 3D circular braiding machine, the model of gear transmission system in radial braiding machine was simplified. The non-linear dynamic equations of a n-elements closed-loop gear transmission system with symmetrical structure including static transmission error, the random disturbance of meshing damping and backlash were considered. For convenience of calculation n = 3, the equations were solved numerically by using Runge-Kutta. The dynamic transmission error(DTE) with different backlash, dynamic meshing forces with and without the random disturbance of meshing damping, the amplitude of dynamic transmission error at n = 1000 r/min and b = 2.65 × 10−5 m, root mean square(RMS) of DTE and the mean value of DTE of the first pair of gears were analyzed. The simulation results show that different backlash and the random disturbance of meshing damping have a great influence on the dynamic displacement error and meshing force of the gear pair, and RMS and the mean value of DTE changes at different rotational speeds. The results will provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine and have great practical significance for improving the braiding quality.

[1]  Robert G. Parker,et al.  Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration , 2008 .

[2]  Roland Hinterhölzl,et al.  Finite element simulation of the braiding process for arbitrary mandrel shapes , 2015 .

[3]  Piaras Kelly,et al.  Complete simulation process chain for the manufacturing of braided composite parts , 2017 .

[4]  Sheng Li,et al.  A tribo-dynamic model of a spur gear pair , 2013 .

[5]  Rajendra Singh,et al.  Non-linear dynamics of a spur gear pair , 1990 .

[6]  Ming J. Zuo,et al.  Effects of friction and stochastic load on transient characteristics of a spur gear pair , 2018, Nonlinear Dynamics.

[7]  Wen-Jun Zhang,et al.  Stochastic Vibration Model of Gear Transmission Systems Considering Speed-Dependent Random Errors , 1998 .

[8]  Zhansheng Liu,et al.  Nonlinear Dynamic of a Geared Rotor System With Nonlinear Oil Film Force and Nonlinear Mesh Force , 2012 .

[9]  David Branscomb,et al.  Modeling of the tensioning system on a braiding machine carrier , 2012 .

[10]  Arvid Naess,et al.  Stochastic spur gear dynamics by numerical path integration , 2007 .

[11]  Wei Zhang,et al.  Finite element analyses on transverse impact behaviors of 3-D circular braided composite tubes with different braiding angles , 2015 .

[12]  L. L. Lebel,et al.  Automated braiding of a complex aircraft fuselage frame using a non-circular braiding model , 2017 .

[13]  S. J. Harris,et al.  Stress corrosion cracking of GRP pultruded rods in acid environments , 1983 .

[14]  Dongil Shin,et al.  Nonlinear analysis of a geared rotor system supported by fluid film journal bearings , 2020, Journal of Sound and Vibration.

[15]  Bernt J. Leira,et al.  Stochastic dynamics of a nonlinear time-varying spur gear model using an adaptive time-stepping path integration method , 2019, Journal of Sound and Vibration.

[16]  Song He,et al.  Construction of Semianalytical Solutions to Spur Gear Dynamics Given Periodic Mesh Stiffness and Sliding Friction Functions , 2008 .

[17]  Rajendra Singh,et al.  Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system , 1991 .

[18]  Donald R. Houser,et al.  Mathematical models used in gear dynamics—A review , 1988 .

[19]  T. Wehrkamp-Richter,et al.  Damage and failure of triaxial braided composites under multi-axial stress states , 2017 .

[20]  Maciej Kumosa,et al.  Initiation of Stress Corrosion Cracking in Unidirectional Glass/Polymer Composite Materials , 2001 .

[21]  P. Hamelin,et al.  Analysis of 2D and 3D circular braiding processes: Modeling the interaction between the process parameters and the pre-form architecture , 2013 .

[22]  Sébastien Baguet,et al.  Nonlinear couplings in a gear-shaft-bearing system , 2010 .

[23]  Kang Huang,et al.  Nonlinear dynamic modelling and analysis for a spur gear system with time-varying pressure angle and gear backlash , 2019, Mechanical Systems and Signal Processing.

[24]  Peter Middendorf,et al.  Influence of the cover factor of 2D biaxial and triaxial braided carbon composites on their in-plane mechanical properties , 2017 .

[25]  J. H. van Ravenhorst,et al.  A yarn interaction model for circular braiding , 2016 .

[26]  J. H. van Ravenhorst,et al.  Circular braiding take-up speed generation using inverse kinematics , 2014 .

[27]  Seung‐Yeol Jeon,et al.  Prediction of the braid pattern on arbitrary-shaped mandrels using the minimum path condition , 2014 .

[28]  Maciej Kumosa,et al.  Stress corrosion of aligned glass fibre-polyester composite material , 1985 .

[29]  Xiaopeng Li,et al.  Nonlinear response analysis of gear-shaft-bearing system considering tooth contact temperature and random excitations , 2019, Applied Mathematical Modelling.