Calculation and Verification of Teeth Top and Teeth Bottom Interference of Rack and Pinion

For the meshing of pinions and racks, the analysis of interference between the tops of pinion teeth and the bottoms of rack teeth, as well as the interference between the bottoms of pinion teeth and the tops of rack teeth, was conducted. The discriminants for avoiding the interference between the top cylindrical surface of the pinion and the bottom plane of the rack, the interference between the bottom circular arc of the rack and the surface of the pinion, the interference between the root cylindrical surface of the pinion and the top plane of the rack, and the interference between the transition curve of the pinion and the surface of the rack were derived. At the same time, the radius of the start circle of involute of the helical pinion and the discriminant for avoiding the undercut were derived. Finally, an example of calculation and verification was given, and the three-dimensional model of rack and pinion assembly was established by SolidWorks software to verify the correctness of the formula. These discriminants provide important basis for the design of pinion-and-rack related mechanical products.