Study On Direct Digital Modeling For Double- Enveloping Hourglass Worm Drive

Double-enveloping hourglass worm gearing is characterized with high load-carrying capability and good lubrication condition, which is widely applied in heavy-duty machinery. Due to its sensitivity to the manufacturing errors and load-carrying deformation, the tooth form is sometimes modified to ensure its meshing performance. However, the results of the tooth modification cannot be represented accurately by computer simulation technique. The main reason is that it is very difficult to solve the conjugate equation with the tooth modification and the effect of tooth modification on their solid models is not accurate considered. Based on the manufacturing process of Double-enveloping hourglass worm gearing, the direct digital modeling method (DDMM) is developed. The worm and the gear are modeling by Boolean operation in DDMM. It is avoidable to solve the complex conjugate equations. At the same time, it is convenience to consider the tooth modification in their solid models by DDMM. Therefore, the designer can directly predict the effect of tooth modification on contact zone. It shortens the lead time of worm gearing and reduces its cost.This dissertation aims to explore the feasibility, validity and practicability of DDMM from two aspects: direct digital modeling theory and realization technique by computer simulation. The main research focuses on following hands.(1) Based on the manufacturing process of double-enveloping hourglass worm gearing, the mathematical models of the worm and the gear are established by direct digital modeling method. According to evaluation method of surface error, the normal distances between modeling surfaces by DDMM and theoretical surface of the worm and the gear are calculated. It verifies the feasibility of DDMM in solid modeling of double-enveloping hourglass worm gearing.(2) Non-linear elastic contact algorithm is applied to analyze the contact zone and stress distribution on tooth surface of double-enveloping hourglass worm gearing, which is respectively modeled by DDMM and theoretical surfaces. After the comparison of the results of contact analysis, the relation among the modeling step, modeling accuracy and efficiency is obtained.(3) In order to overcome the limitation of representation method for solid model, a new method for solid model is adopted to carry out to simultaneously satisfy the model precisions and modeling efficiency by DDMM. The prototype of DDMM is developed to perform solid model of double-enveloping hourglass worm gearing.