| Spring overrunning clutch has the characteristics of light weight,simple structural composition,high reliability,suitable for high-speed heavy load transmission system,has been used in foreign advanced high-speed helicopters.Its torsion-transferring element variable-section spring is a slender flexible beam structure,which has the initial deflection rate in three-dimensional space,the structural characteristics of variable section and the mechanical characteristics of nonlinear distributed load and continuous displacement constraint,making it unsuitable for mechanical modeling and solution by linear elastic theory.There is a lack of research results to accurately solve the stress-strain field of the spring cross-section under steady-state torsion transfer of the spring clutch and the nonlinear dynamic response of the clutch in steady state and transient state,which restricts the improvement of the design theory and application promotion of high-speed heavy-duty spring clutches.In this paper,we describe the coordinate transformation between the undeformed and deformed configurations by two independent and continuous Euler angles based on the geometrically exact beam theory for the full Lagrangian configuration of the Euler-Bernoulli spatially flexible beam unit and describe the geometric nonlinearity and initial deflection curvature of the beam unit by Jaumann strain rate,rotation matrix and orthogonal imaginary rotation.The six-degree-of-freedom nonlinear equations of motion for the spatial beam unit considering geometric nonlinearity and initial deflection rate are established,and the finite element unit formulation applicable to the geometrically nonlinear spatial beam is derived.Meanwhile,the transient engagement characteristics of the spring clutch and the steady-state dynamics of the coupling with the gear system are analyzed and revealed according to the structural characteristics and usage scenarios of the spring.This study can provide a theoretical basis for the design and application of variable-section spring-loaded overrunning clutches.The main research elements of the thesis include:(1)In order to accurately describe the problem of large deformation of a helical spring in space,the spring wire is modelled as a space beam structure with initial winding curvature based on the Euler-Bernoulli assumption and exact geometric transformation relations,using geometrically objective,co-rotating Jaumann strain rate,according to differential geometry and geometrically exact beam theory.The local strain field of the spatially flexible beam is constructed and the non-linear control equations on the six degrees of freedom of the spatial beam are derived by extending Hamilton’s principle.(2)The linear weak form of the tangential stiffness matrix applicable for numerical calculations is derived from the general function relationship between the form and displacement variables.The loads generated by the spring in clutch operation are analyzed and equivalently converted into unit load vectors by means of the energy principle.A numerical calculation program based on the non-linear finite element method is written in MATLAB.The distribution of internal forces and deformations in the spring cross-section is obtained by static analysis of the variable-section spring and the influence of different structural parameters on the mechanical properties of the spring is analyzed.The structural vibration of variable-section springs is studied and the inherent properties of variable-section springs under clutch conditions are analyzed using the finite element method.A numerical method for calculating the torsional stiffness of springs under complex loading conditions is proposed,laying the foundation for the study of the dynamics of spring clutches and the design work on springs.(3)The characteristics of the different stages of the overrunning clutch engagement process are analyzed,a torsional motion model with two degrees of freedom of the investigated overrunning clutch is established,the transient response of the variable section spring overrunning clutch engagement process is studied and obtained,the torque transmission law during the spring clutch engagement process is described using multi-parameter equations and the influence of the clutch design parameters on the torque transmission during the spring expansion process is analyzed.(4)For the "spring clutch — high speed gear" system,the torque transferred by the clutch is designed as a segmental function,and the non-linearities of the gear pair in the system are taken into account.The torsional dynamics of the spring clutch in a conventional system is investigated.Using the dynamic transmission error of the gear pair and the clutch torsion angle as indicators,a sweep analysis of the torsional vibration dynamic characteristics of the system in the speed range of 500 to 50,000 rpm was carried out to identify the jump phenomenon and the subharmonic and harmonic resonance regions under the dynamic response of the system.In order to determine the influence of physical parameters on the dynamic response of the system,the torsional stiffness and damping ratio of the clutch and the inertia ratio of the clutch to the pinion were investigated on the dynamic response of the system.(5)An experimental platform with dynamic characteristics to regulate the engagement and overrunning function of the overrunning clutch has been established.The dynamic engagement characteristics of the spring-loaded overrunning clutch were tested,and the angular velocity curves of the driving and driven ends were obtained to verify the validity of the theoretical calculation model.The torsional mechanical characteristics of the spring-loaded overrunning clutch were also tested to verify the validity of the torsional stiffness model of the spring-loaded overrunning clutch.The stress values generated by the torsional deformation of a variable-section spring were tested using a resistance strain gauge to verify the accuracy of the theoretical calculation. |
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