Research On The Safety Domain And Safety Characteristics Of Spur Gear Pair

The gear transmission devices are widely used in the different mechanical equipments.The gear pair should have higher reliability and safety to meet the development needs of the higher speed and more power of the mechanical equipments.The backlash and the time-varying meshing stiffness,etc.make the gear pair have complex nonlinear vibration characteristics.Thus,the methods of establishing safety domains and the transfer laws of safety features in the established safety domains are studied,which can provide the theoretical basis for the safe and warning of the spur gear pair.The main contents are as follows:1.The spur gear pair,considering load distribution,tooth surface friction,time-varying meshing stiffness,meshing damping,backlash,external load force and error,is taken as the research object.The contact ratio of the system is calculated according to the system parameters.The tooth profile is divided into two double teeth meshing areas and a single tooth meshing area,and the time of different meshing areas participating in meshing is obtained according to the contact ratio.The nonlinear dynamic equations of the multi-state meshing spur gear pairs,considering drive-side teeth engaging,tooth disengagement and back-side teeth contacting,and single and double teeth meshing,are established.The system is the basis of the establishment of safety domains and the studies of safety features.2.The methods for establishing four types of safety domains of gear pairs is firstly proposed.The first type of safety domain is a single factor security condition.The calculation formulas of the contact stress on the tooth surface,the deformation of the tooth and the bending stress of the tooth root of the teeth are derived according to the positions of the meshing point.The safety conditions to prevent the tooth surface contact fatigue,prevent the tooth plastic deformation,and prevent the tooth root bending fatigue are respectively established based on the conditions of tooth surface contact fatigue,plastic deformation of gear teeth and tooth root bending fatigue.The second type of safety domain is the contacting safety domain,which is considered the above three safety conditions at the same time.The third type of safety domain is the meshing safety domain,which is established by the three states of the system caused by the tooth backlash are tooth surface meshing,disengagement and tooth back contact.The meshing safety domain is graded into three levels: safe,quasi-safe and unsafe.The fourth type of safety domain is the comprehensive safety domain considered the contact and meshing safety,which is diviede into eight different safety levels.3.The identification methods of the safety characteristic are proposed for the established safety domains.The state space of the gear pair is constituted by the relative displacement and the relative speed of the teeth.The safety characteristic of the system in the different safety domains is judged according to the relationship between the state variables and the safety domains.The safe basin is calculated based on an improved cell mapping algorithm.The coexistence attractors and their safety characteristics in the safe basin are identified by the multi-initial phase diagram and the Poincaré map.The influences of the system parameters on the safety characteristic under the contact safety domain,the meshing safety domain and the comprehensive safety domain are studied by the safety basin and other methods.4.The construction method of the safety & bifurcation dendrogram is proposed.The transition processes of the system safety characteristic and the erosion mechanisms of the safety basin when the system parameters change are studied by the methods of the safety & bifurcation,the multi-initial values bifurcation diagram and the multi-initial values top Lyapunov exponents.The system's multi-stable responses and their safety characteristics under the common effects of the multi-initial excitations and the system parameters are studied.The coexistence solutions and the hidden bifurcation points of the system are fully revealed.The bifurcation points are classified into the types of one-to-one and one-to-two according to whether they are sensitive to the initial values.5.The integrity of the system motions in the safe basin is firstly studied by the global integrity measure,the integrity factor and its high mountain map.