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Rack-and-pinion gear sets with variable transmission ratios have gradually become a standard core component in steering systems, as the harmony between portability and sensitivity in vehicle steering can be achieved with such applications. When the conventional meshing theory is adopted to calculate point clouds of variable-ratio tooth surfaces, drawbacks will occur with respect to unevenness in point cloud density, inaccessible tooth surface boundaries, and point cloud fusion at the interface between the working tooth surface and fillet. Thus, the generated point cloud of variable ratio tooth surfaces is inapplicable for computer-aided engineering (CAE) and plastic forming. In this study, the point cloud reconstruction of pinion tooth surfaces with variable transmission ratio was investigated. Meanwhile, based on the analysis of transient length in contact lines that occur during gear meshing, various criteria were proposed to determine the validity of the variable-ratio rack-and-pinion design in terms of whether continuous and reverse driving can be achieved. By adopting the proposed methods, the designed variable-ratio pinion tooth surfaces demonstrate point clouds with equidistant distributions and clear boundaries. CAE analysis results also indicate a good quality in gear meshing. The real-time gear meshing status of variable-ratio rack-and-pinion sets is characterized by the transient length of contact lines. The measured variation curves for the transmission ratios of a prototype demonstrate significant consistency with the theoretical curves, indicated by attaining transmission ratio errors within a reasonable range. The validity of the design methods proposed in this study has been verified by the aforementioned results.

Rack-and-pinion pair with variable transmission ratio can achieve the unity of vehicle steering portability and sensitivity, and effectively reduce vehicle steering energy consumption. Therefore, they have gradually become the standard core components of steering system. However, the gear surface of rack-and-pinion pair with variable transmission ratio is seriously worn under long-term service, which leads to the degradation of performance and cannot achieve the theoretically variable transmission ratio. To solve these problems, a new configuration of rack-and-pinion pair for commercial vehicle with herringbone pure rolling variable transmission ratio is proposed in this paper. The tooth surface mathematical model of the fully-conjugate variable transmission ratio is established based on the variable speed envelope principle, and the formula for calculating pure rolling point of tooth surface with variable transmission ratio is derived. The tooth point deviation equation of fully-conjugate variable transmission ratio is proposed, and the method of constructing pure rolling variable transmission ratio tooth surface is formed. The finite element analysis shows that the design of the pure rolling rack-and-pinion pair with variable transmission ratio has good tooth surface quality without the phenomenon of contact spot intermittent and edge contact during the meshing process, and the contact ellipse center of the tooth surface is located at the theoretical pure rolling point of the tooth surface. The measured transmission ratio curve of the samples is in good agreement with the theoretical variable transmission ratio curve, and the transmission ratio error is within a reasonable range. The contact strips of tooth surface impression test are consistent with those of finite element analysis, which indicates that the designed rack-and-pinion pair with variable transmission ratio has the characteristics of pure rolling and point contact. The tooth surface wear test shows that the wear of pure rolling gear surface with variable transmission ratio is obviously less than that of traditional gear surface with variable transmission ratio. The above tests and simulation indicate the correctness of the design method.