Modeling and methods for gear shaping process and cutting force prediction of variable transmission ratio rack

Abstract Variable transmission ratio rack shows great potentials in the automobile industry as a key component of vehicle variable transmission ratio steering gear to balance steering portability and steering sensitivity. The current processing method for variable transmission ratio rack is orbital forging, which has the advantages of high performance and high processing efficiency. However, orbital forging can only process small size rack and its processing accuracy is limited. Therefore, this paper proposes a novel processing method, i.e., gear shaping, to achieve high quality processing of variable transmission ratio rack by overcoming above limits of orbital forging. Firstly, an accurate envelope motion model between the tool and the workpiece is established based on the mapping relation of the speed as well as the feed of each machine axis between envelope motion and actual gear shaping process, so as to envelope final complex changing tooth shape of variable transmission ratio rack. Namely, the speed of each machine axis is determined strictly according to the linkage relationship of each machine axis with a variable transmission ratio function involved. Then, a specific tooth profile mathematical model of variable transmission ratio rack is obtained through simultaneous solution of the envelope motion model and the tool model. Meanwhile, since cutting force is a critical factor of gear shaping process, this paper proposes a new method for cutting force prediction which involves two innovative calculation algorithms for two major components (contact length b and chip area a) of the classical metal cutting force calculation model. Firstly, based on discrete representation, a new calculation algorithm of contact length b including specific dynamic selection criteria of cutting contact points is presented. Secondly, in order to precisely calculate chip area a, this paper proposes a discrete calculation algorithm with two pivotal cutting points selecting criteria involved. Finally, based on the classical metal cutting force calculation model, accurate predictions of cutting force in gear shaping process of variable transmission ratio rack are achieved. Gear shaping experiments as well as cutting force measurements are conducted and errors between the predictions and the experimental measurements of cutting force are obtained, which remain between 1% and 19%. Therefore, it is concluded that the envelope motion model and methods for cutting force prediction in gear shaping process of variable transmission ratio rack presented in this paper are feasible.