Aim. Development of mathematical model for process of teeth profiling of spur helical gear by disk cutting tool by the radial and round kinematic modify formation method on the basis conception of forming of teeth flanks by spatial helix coaxial formative lines. Method. Researches are based on methods and substantive provisions of the theory of parts surfaces formation by cutting instruments, in particular formation of spur gear teeth, the tooth system theory, kinematics analysis, analytical and differential geometry. Results. The design of formation process of surfaces of teeth of cylindrical helical wheels is conducted by disk milling cutters by the new method of formation at the continuous rotation of the cut gear. It is suggested to carry out gear cutting with a kinematics changeable angular velocity with the rotation of eccentric arbor with the set disk milling cutter that provides the receipt of wheels teeth with necessary thickness. The systems of equalizations of helix formative coaxial lines and equalizations of spatial tooth flanks of spur helical gears are got. Scientific novelty. Bases of profiling of teeth surfaces of spur helical gear are worked out by the radial and round kinematic modify formation method. Profiling of teeth sides is executed true spiral coaxial by formative lines. The necessity of profiling of teeth surfaces of helical wheels is set due to the kinematics change of angular velocity of appeal of instrument. The correlations got in theory complement theoretical positions of formation of surfaces of details cutting instruments and them technological providing. It is offered at the synthesis of teeth surfaces of sine-similar profile of the increased loading ability complex to combine kinematics, geometrical responses of hooking and technological parameter of gear cutting process. Practical significance. The design of process of forming of teeth surfaces of cylindrical helical wheels will provide rational practical application of the radial and round kinematic modify formation method for making of large module of cylindrical gear-wheels of gearing of transport vehicles due to the increase of the productivity of treatment at the receipt of surfaces of teeth with modified relatively by a involute profile that forecast diminishes the dynamic loading in hooking and assists the decline of sound-level in a transmission.
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