Digitization modeling and CNC machining for cone-generated double-enveloping worm drive

  • Zhi Liu
  • Hong Lu
  • Shaojun Wang
  • Guoming Yu


Digitization modeling and CNC machining method of cone-generated double-enveloping worm drive are proposed in this study. The modeling coordinate frame is developed, and coordinate transformation matrices are also built for different coordinate systems. Next, the common normal vectors and relative velocity vectors of the conical cutter and worm and worm and worm wheel are derived by using differential geometry, kinematic analysis, and coordinate transformation method; then, the mathematical models of the worm drive are established applying spatial meshing principle. In addition, the solving algorithms for the complex multivariate nonlinear constrained mathematical models of the worm drive are developed according to the worm drive’s surface-generating characteristic; then, the meshing point cloud that represents the tooth profile of the worm drive are calculated based on the developed algorithms; finally, the digital CAD models of the worm drive could be constructed on the basis of the point cloud in the modeling software system. The CNC machining code is generated based on the accurate digital CAD models, and the surfaces of the worm drive could be machined in the CNC machining center. The modeling and machining experiment results demonstrate the validity and accuracy of the proposed modeling and CNC machining method for cone-generated double-enveloping worm drive.


Enveloping surface Cone-generated Double-enveloping Digital CAD model CNC machining Algorithm 


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The authors gratefully acknowledged the support of the National Natural Science Foundation of China (NO.51675393), Hubei Province Natural Science Foundation of China (No.2016CFB148), Hubei Province Young Talents Science Foundation of China (No.Q20162902), and HuangGang Normal University Science Project of China (No.2015002003, No.201711503). The authors would also like to thank the editors and reviewers for their insightful suggestions and helpful comments for improving the manuscript.


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© Springer-Verlag London Ltd., part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mechanical and Electronic EngineeringHuanggang Normal UniversityHuanggangChina
  2. 2.School of Mechanical and Electronic EngineeringWuhan University of TechnologyWuhanChina
  3. 3.Southeast Missouri State UniversityCape GirardeauUSA

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