Study And Simulation On Design The Tooth Profile Of Non-circular Gear Based On The Force-Arm Function Method

Non-circular gears can realize the variable speed ratio transmission between two shafts accurately and efficiently.Non-circular gears have wide applications in the field of automatic machinery.The kinematic characteristics of mechanism determine that the non-circular gears mainly bear the changing loads.However,the design method of tooth profile is commonly based on the geometric and meshing characteristics.Without considering the load characteristics of the mechanism,it may be lead to an unbalanced force on every gear teeth,and it is easy to cause the failure of the gear.As an exploration of solving the above problems.The force-arm function method is proposed in this dissertation.It’s a new method to design the tooth profile of planar non-circular gears.The force-arm function method takes the load characteristics of mechanism as one of the design conditions.The relationship among the load,the force conditions and the shape of tooth profile is established.On the condition of satisfying the fundamental law of gearing,this dissertation strives to let the contact force on every gear teeth can be balanced,therefore it can improve the transmission performance and the gear strength.This dissertation mainly contain the principle of the force-arm function method,the force-arm function’s design and the simulation of non-circular gear’s tooth profile design based on the force-arm function method.In this dissertation,the principle of design the tooth profile of non-circular gears based on the force-arm function method is proposed.The force-arm function and the force-arm curve are defined,and the mathematical expressions which is only includes the force-arm function and the centrode of non-circular gears are deduced.What’s more,the geometric characteristics of the tooth profile based on the force-arm function method are analyzed.This is the basic theory that can be applied to the non-circular gears when design the tooth profile based on the force-arm function method.In order to make the contact force isn’t change suddenly and get the tooth profile which is continuous,smooth and have no inflection points,this dissertation discusses the design conditions that the force-arm function should be satisfied.On the basis of above results,threemethods to design the force-arm function are put forward in this dissertation,namely the synthesis load method,the constant pressure angle method and the predetermined curve method.And then the basic principles of above design methods are explained.In this dissertation,the design conditions of non-circular gear’s tooth profile based on the force-arm function method are investigated.In order to meet the minimum instantaneous contact ratio and non-interferential condition of the tooth profile,the determination method of the tooth profile parameters such as the non-circular gear’s analogy module,addendum,dedendum and number of teeth are analyzed.The equal arc length method and equal angle method are proposed to determine the location of tooth profile on the non-circular gears,and the design processes of tooth profile about the above two methods are given.On the basis of the above research works,this dissertation works out a computer program by using the MATLAB software.Based on the force-arm function method,a computer program can realize a simulation of designing the tooth profile of non-circular gears.By entering the design parameters into the human-computer interface,it can realize the calculation and output the data of tooth profile.What’s more,it can illustrate the correctness of tooth profile and realize the meshing simulation of a pair of non-circular gears.The simulation results showed that as long as the design parameters are reasonable,the force-arm function method can design the feasible tooth profile of non-circular gears.Above conclusions can verify the effectiveness of the force-arm function method.