Abstract: Abstract: The hydro-mechanical differential turning system is the double power flow turning system made up of a hydraulic transmission, mechanical transmission, and planetary transmission. It can allow tracked vehicles to accomplish a continuously step-less turning process and exhibits high working efficiency and light operation force. The turning system has good application prospects for tracked tractors, construction machinery, armored vehicle and other heavy machinery. Because the turning system contains several parameters, constraint and coupling are among these parameters. The system parameter design is addressed by a multi-parameter, multi-goal, nonlinear optimization question. Known from literature, the optimized parameters include the characteristic coefficient of planet row, parameters of the hydraulic closed-loop system (rated pressure, motor displacement), rear transmission ratio of the motor, the fixed axis transmission ratio, and other parameters. The turning dynamic, turning flexibility, and turning speed of a tracked vehicle are the evaluation objectives of system parameter optimization. The turning dynamic is evaluated by dynamic factors of engine, hydraulic closed-loop system and ground. The turning flexibility is evaluated by the minimum turning radius. The turning speed is evaluated by the minimum turning time or maximum angular velocity. The optimization math model of the hydro-mechanical differential turning system parameters, including the turning dynamics、turning flexibility, and turning speed of tracked vehicle, is established based on the theory of parameter optimization and an evaluation index. The ground characteristic, engine characteristic, and characteristics of the hydraulic closed-loop system are constraint conditions in the optimization process. Using the basic theory of genetic algorithms, the mutual constraint and coupling among these system parameters are solved by dividing the question space using analytic hierarchy process. In connection with every optimized parameter, its question space is determined. Based on the optimization evaluation objectives and constraint conditions, the weighting coefficient of every evaluation objective and the solution size of every optimized parameter are set. The gradation genetic algorithm is carried out in accordance with the question space, and the optimization process is finished. The population size of the lower hierarchy question space is generated by the population size of upper hierarchy question space. The invalid parameters group scheme is avoided. When the calculation is carried out in the previous step of the process, the union of every solution of the hierarchy is adopted. When the calculation is carried out in the next step of the process, every individuality of the hierarchy is sequenced in the light of pareto superior relation. The fitness of the population is determined by the number being inferior to this individuality. The parameter optimization is finished according to optimization precision. Referencing the design requirements of an actual tracked vehicle, based on several groups of weighting coefficients, the parameters of a hydro-mechanical differential turning system for a tracked vehicle are optimized. In light of the known parameters of actual tracked vehicle and the optimized parameters of a hydro-mechanical differential turning system, the dynamic factor of engine, dynamic factor of hydraulic closed-loop system, and dynamic factor of ground are simulated and calculated. The results show that the parameters of a hydro-mechanical differential turning system for a tracked vehicle can meet its performance requirements, and the optimization method can meet the actual engineer design requirements of a hydro-mechanical differential turning system for tracked vehicles.