Although a cylindrical worm reducer is generally used in various fields and forms throughout the industry, and manufacturing processes are standardized and optimized, a double enveloping worm reducer is very difficult to standardize due to manufacturers'' prevention of technology outflow. This paper was aimed to provide a better understanding of the Hindley worm drive method, which has an important effect on the double enveloping worm reducer.
To derive a design equation for the tooth profile of double enveloping worm gear that requires two contact lines and three or more tooth profile contacts, the literature on the major parameters of the double enveloping worm gear design was reviewed. Hindley''s classic Multi-Cutting method with trapezoidal tooth profile in the axial plane has problems such as reduced precision of tooth profile and increased lead time due to tool point contact machining. Thus, a formula was induced to quantify the design equation of double enveloping worm tooth flank based on tool line contact machining, which is a new type of Hindley´s Side-Cutting method, and the design equation of gear tooth flank corresponding to the worm.
To verify the validity of the tooth profile design, the Side-Cutting method was designed to allow up to 6 starts on worm and up to 5 teeth in engagement, and a program to enter visual parameters was created to visualize the results of the tooth profile design such as worm gear blank shapes. Without several processes of 3D modeling and CAM like the classic Multi-Cutting Method, the tooth profile of double enveloping worm generated G-code to allow machining in 5 axis machines. And regarding the tooth profile of double enveloping gear, a program like the Multi-Cutting Method design program was developed that visualizes 3D modeling in CATIA, a three-dimensional design program, in which 3D point data is printed in the form of a csv Excel file as discrete points.
A static, dynamic finite element analysis of 3D modeling was made for the entire double enveloping worm reducer on the assembly of 50 mm center distance of worm and gear, 60 teeth on the gear, single start worm, and 3 teeth in engagement to verify the contact and strength design of double enveloping tooth profile and its influence to the reducer gearbox. In particular, a dynamic analysis of 3 teeth in engagement was performed tracking changes in the state of stable contact between the gears, bending strength, and contact pressure to verify the adequacy of the design.
Since the double enveloping tooth profile is very complex and the precision of tooth profile is important, the double enveloping worm gear model was created with 120 mm center distance of worm and gear, 60 teeth on the gear, single start worm, and 5 teeth in engagement based on the optimized precision machining. The Multi-Cutting method based on 3D modeling performed toolpath work on worm and gear in CAM, and G-code was generated to implement the tooth profile of double enveloping worm gear. The reverse design with the Side-Cutting method was carried out for the worm tooth profile and its 3D modeling using a three-dimensional design program as well. Besides, gears performed several processes of the Multi-Cutting method. To make sure the reliability of tooth profile machining, the machining of double enveloping worm gear was performed using simultaneous five-axis turn-mill machining equipment, and 3D modeling, precision, and machining time of the two methods were compared and analyzed.