Research On The Optimization Design Of Planetary Reducer With Few Tooth Number Difference

With the advantages of high efficiency,high transmission ratio,high load capacity and compact structure,planetary reducers with few tooth number difference are widely used in robots,mining,ships,aerospace,etc.Due to their simple structure and easy miniaturization,they can be applied to electromechanical servo systems that have emerged in recent years.The trial methodolgoy is usually used to calculate the parameters when designing a gear reducer,but the parameters are not optimal.Due to the low design efficiency and high cost,their application in many fields are restricted.The enclosed graph method and the genetic multi-objective optimization method are used for parameter design of the planetary reducer with little difference tooth numbers including the following four aspects:(1)Through the preliminary market research,it is determined that the planetary reducers with little difference tooth numbers,large reduction ratio,high efficiency and low cost are selected as the target.(2)A planetary reducer with little difference tooth numbers is designed.By analyzing its transmission operations,the factors on transmission performances are clarified,and a strength check method for the internal engaged gear pair when considering the multi-tooth-meshing effect is proposed.(3)Mathematical models were established for the main constraints and limit curves and the nonlinear equations were solved using an iterative method.The enclosed graph was drawn and the gear displacement coefficients were selected according to the requirements.(4)A genetic algorithm was used to optimize the parameters.4 variables including displacement coefficient,meshing angel,tooth height factor and tooth width,3 target functions including efficiency,volume and safety coefficient,7 constraints including overlapping degree and others were selected,and initial values were decided by extrapolation.An optimized solution was obtained.(5)A testing stand for the reducer was designed.Parameters such as torque and velocity were measured and data was analyzed.It shows that the measurements fit well with the optimization results.It is demonstrated that,compared with the conventional enclosed graph methodology,the mutil-variable optimization was realized by the genetic algorithm,with local optimization circumvented,and optimized planetary reducers with few tooth number difference have big potentials in better performances like transmission efficiency.