This research deals with the study of some kinematic characteristics, which can be used to ensure the loading capacity of the rack drives, including its hydrodynamic component. A brief analysis of the spatial rack drives in terms of their load capacity is realized. When mutually enveloping tooth surfaces are synthesized, it is possible to appear singular contact points appear on the active tooth surfaces. Two kinds of singular points exist, depending on the normal vector to the meshed tooth surfaces in their common points: singular points of firstorder (called ordinary nodes), and singular points of second-order. Singular points of first order should be registered and eliminated from the mesh region since increased specific friction, worsen lubrication, and heat transfer are present, which result in a decreased loading
capacity of the gear set A special accent is placed on the registration and elimination of singular points on the tooth surfaces of the synthesized rack drives. Analytical expressions are written defining total transference velocity and its normal component to an instantaneous contact line at an arbitrary contact point.
- F. Litvin, Theory of Gearing. Publishing house Nauka, Moscow, 584, (1968), (in Russian).
- A. Georgiev. Elements of Geometric Theory and Some Questions of Design and Manufacture of Hypoid - Worm Gears. Sc. D. Thesis, IMI, Izhevsk, 258, (1965).
- A. Georgiev, V. Goldfarb. On Node Lines of Mesh in Orthogonal Spiroid Gears with Convex-Concave Threads Profile of the Cylindrical Worm. Problems of Research, Design, and Manufacture of Gears. A summary of reports for the V zonal conference, 114-119, (1974).
- V, Ganshin. Analytical and Experimental Study of Spiroid Transmission with an Involute Worm. Sc. D. Thesis, Ministry of Heavy Power and Transport Engineering, Moscow, 161, (1970).
- I. Dusev, V. Vasiliev. Analytical Theory of Spatial Gearing and its Application to the Study of Hypoid Gears. Novocherkaskiy Polytechnic Institute, 147, (1968).
- Litvin, F. Theory of Gearing. NASA Reference Publication 1212, AVSCOM Technical Report 88-C-035, US Government Printing Office, Washington, 1989, 470, (1989).
- S. Lagutin. Once Again on the Problems of Singularities and Undercutting of Teeth. Proc. of the Int. Conf. “Theory and Practice of Gears”, Izhevsk, 193-199, (1998).
- S. Lagutin. Spatial Gearing and ASynthesis of Worm Gears with a Localized Contact, Proc. of the Int. Conf. “Theory and Practice of Gears”, Izhevsk, 185-192, (1998).
- K. Minkov, Mechanical and Mathematical Modeling of Hyperbolic Gears. Sc. D. Thesis, Sofia, 330, (1986), (in Bulgarian).
- V. Abadjiev, V. Gearing Theory and Technical Applications of Hyperboloid Drives, Sc. D. Thesis, Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, 309, (2007),(in Bulgarian)
- W. Nelson, Spiroid Gearing Part 1 - Basic Design Practices. J. Machine Design, 136-144, (1961).
- V. Abadjiev, D. Petrova, E. Abadjieva. Mathematical Modelling for Synthesis and Design of Non-Orthogonal Wormgears with a Straight-Line Tooth Contact, III European Conference on Computational Mechanics Solids, Structures and Coupled Problems in Engineering, Portugal, (2006), (Published on CD).
- V. Abadjiev, E, Abadjieva. Two Approaches for Elimination of the Ordinary Nodes from the Planoid Meshing. Scientific Papers of the Jubilee Scientific Conference 2006 of the Rousse University, International Scientific Conference AMTECH 44(2), Rousse University, 674-678, (2005).
- E. Abadjieva, V. Abadjiev V. On the Synthesis of Hypoid Gears with Linear Contact. Part 1 – Geometric Synthesis Practices in the Pitch Contact Point. 10th Jubilee National Congress on Theor. and Appl. Mech., 1, 1-6, (2005).
- E. Abadjieva, V. Abadjiev V. On the Synthesis of Hypoid Gears with Linear Contact. Part 2 – Geometric Synthesis of the Planoid Gearing. 10th Jubilee National Congress on Theor. and Appl.Mech., 1, 7-11, (2005).
- E. Abadjieva, Mathematical Models of the Kinematic Processes in Spatial Rack Mechanisms and Their Application, Ph. D Thesis, Institute of Mechanics, Sofia, 165, (2010), (in Bulgarian)
- G. Korn, T. Korn, Mathematical Guide for Scientists and Engineers. Definitions, Theorems, Formulas. Nauka Publishing House, Moscow, 831, (1973).
- I. Krivenko, S. Chervenkova. To the Calculation of the Total Length of the Contact Lines of the Worm Gears. Proc. of Higher Educational Institutions. Mashinostroenie. Scientific and Technical Journal, 10, 42-46, (1978).
- V. Abadjiev, K. Minkov. On the Geometry of the Helical Surfaces of Spiroid Gears. Theor. and Appl. Mech., Publishing House at BAN, 2, 17-27,(1981).