Abstract
Variable transmission ratio racks show great potential in rice transplanters as a key component of variable transmission ratio steering to balance steering portability and sensitivity. The objective of this study was to develop a novel geometrical design method to achieve quick, high-quality modeling of the free curvilinear tooth profile of a variable transmission ratio rack. First, a discrete envelope motion 3D model was established between the pinion-sector and the variable transmission ratio rack blank based on the mapping relationship between the rotation angle of the pinion-sector and the displacement of the rack, according to the variable transmission ratio function. Based on the loop Boolean subtraction operation, which removed the pinion-sector from the rack blank during all moments of the discrete motion process, the final complex changing tooth shape of the variable transmission ratio rack was enveloped. Then, since Boolean cutting residues made the variable ratio tooth surface fluctuant and eventually affected the precision of the model, this study proposed a modification method for establishing a smooth and continuous tooth profile. First, a novel fitting algorithm used approximate variable ratio tooth profile points extracted from the Boolean cutting marks and generated a series of variable ratio tooth profiles by utilizing B-spline with different orders. Next, based on a transmission stability simulation, the variable ratio tooth profile with optimal dynamic performance was selected as the final design. Finally, tests contrasting the transmission stability of the machining samples of the initial variable ratio tooth profile and the final variable ratio tooth profile were conducted. The results indicated that the final variable ratio tooth profile is more effective than the initial variable ratio tooth profile. Therefore, the proposed variable ratio tooth profile modeling and modification method for eliminating Boolean cutting residues and improving surface accuracy is proved to be feasible. Keywords: rice transplanter, steering, variable ratio tooth profile, variable ratio curve, Boolean subtraction operation, transmission stability DOI: 10.25165/j.ijabe.20201305.4884 Citation: Niu Z R, Li J L, Xin S, Zou L L, Li Y H, Hou J L, et al. Geometrical design of variable ratio tooth profile based on Boolean subtraction operation and a novel modification method. Int J Agric & Biol Eng, 2020; 13(5): 125–133.
Highlights
A steering system with a constant transmission ratio is unable to provide the comfortable steering ratio that rice transplanters need in a paddy field with high moisture and low carrying capacity
Variable ratio steering systems are divided into three categories at present, including the steer-by-wire system (SBW), the electronic controlled steering system (ECS) and the mechanical variable ratio steering system (MVRS)
There are three generation processes to determine variable ratio tooth profile (VRTP): (1) the involute pinion-sector is designed by CAD software; (2) the discrete motion relationship between the variable ratio rack and the pinion-sector is digitally expressed according to a variable transmission ratio function; and (3) VRTP is generated with the Boolean subtraction operation modeling method
Summary
A steering system with a constant transmission ratio is unable to provide the comfortable steering ratio that rice transplanters need. The ECS has successfully integrated a mechanical steering system and a set of double planetary gear mechanisms driven by an electric motor to provide an additional wheel angle to regulate transmission ratio, so it is more practicable[4], but the extra gear mechanism increases manufacturing difficulty and energy consumption. Both the SBW and the ESC use the steering motor to provide limited steering force, but the force is not sufficient to meet the steering requirements of rice transplanters under severe. The feasibility of the method was subsequently verified through a transmission stability test using the processed samples
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
