Investigation of nonlinear characteristics of a gear transmission system in a multi-ring braiding machine considering contact temperature

In the multi-ring braiding equipment, gear transmission system is an extremely important part, its operation process will be affected by a variety of factors. Considering the influence of contact temperature on the dynamic behavior of the gear transmission system, a mathematical model of the gear system is established in order to observe the nonlinear characteristics of the system. And the bifurcation diagrams, the maximum Lyapunov exponents diagrams, phase diagrams, Poincaré mapping diagrams, and the power spectrum diagrams are analyzed. Using the final iteration results to study the nonlinear characteristics of the gear system and the model is evaluated to show the key regions of sensitivity. The results show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> </mml:math> must be controlled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>w</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>0.32</mml:mn> </mml:mrow> </mml:math> .The amplitude response of the system is strong when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>200</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>240</mml:mn> </mml:mrow> </mml:math> . Compared to the bifurcation diagram, the system exhibits chaotic behavior within the range of this frequency, and as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>w</mml:mi> </mml:msub> </mml:mrow> </mml:math> increase, the strong amplitude response of the system increases at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>200</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>240</mml:mn> </mml:mrow> </mml:math> .The nonlinear characteristics are greatly influenced by the incentive factors such as the contact temperature, and the analysis results are beneficial to the design and control of the braiding machine.