Research on Mapping Rules of Hob Geometric Errors and Gear Geometric Precision

Abstract

High precision gear is an necessary support of high-end equipment to meet the requirements of high-speed, heavy-duty,impact, low noise(mute) and other extreme environments. In order to improve the accuracy of hobbing manufacture, to partly achieve"replacing grinding with rolling", and to reduce processing costs, focusing on the insufficient quantitative mapping rules between hob geometry errors and gear geometric error, the quantitative mapping rule research between gear hob tooth profile error, helix error, gear hob installation angle of the radial runout error and the gear tooth profile error, base pitch error with the consideration of machine tool movement error are carried out respectively. Utilizing the counterpart rack law, the gear tooth profile equation enveloping from involute curve hob tooth profile equation is generated, quantitative mapping relational model of hob pitch error and pitch deviation based on differential geometry and envelope principle is builded. At the same time quantitative mapping relational model between hob helix error,radial runout error of hob installation angle and the gear tooth profile error are established respectively. According to the geometric relations between gear tooth profile error and gear base pitch error, the mapping rule of base pitch error is calculated based on the factors mentioned above. A joint equation model between the above three main errors of gear hob and the tooth profile error based on Gaussian distribution with the consideration of machine tool movement error are builded. At last the correctness of the above model by comparing the result of model simulation method with empirical data is verified, so the essential mapping rules of hob error and the main factors which affect tooth geometric precision such as tooth profile error, base pitch error with the consideration of machine tool movement error are revealed, thus a theoretical foundation for roll cutting gear with higher precision is layed.