| Traditional involute cylindrical gears are widely used in the field of mechanical transmission,but there are also obvious deficiencies.For example,spur gears have low contact ratio and low load carrying capacity.Helical gears have large axial forces and require high rigidity for shafting support.The herringbone gears are complicated to process and easy to cause single-sided meshing conditions.With the continuous upgrading of mechanical equipment,it is urgent to develop a new kind of curvilinear cylindrical gear with superior performance.At present,the circular-arc-tooth-trace cylindrical gears(CC-gears)have superior transmission performance,overcoming the shortage of traditional involute gears theoretically.However,the CC-gears are difficult to be machined efficiently.In the process of researching the CC-gears,it is found that the elliptic-arc-tooth-trace cylindrical gears(EC-gears)also have excellent transmission characteristics and can be processed efficiently and quickly.Based on the CC-gears,this paper first proposes the EC-gears.The pinion-and-rack meshing model specifies the geometric characteristics of the EC-gears.The tooth profiles are the same involute in any cross section,and the expanded tooth traces on reference cylinder are symmetrical elliptical arc.According to the space geometry,the equation of tooth surface is deduced,and the three dimensional automatic modeling program is compiled with the Solidworks secondary development technology.By using theory of gear meshing,the conjugate tooth surface equation and meshing line equation are established,and the contact characteristics are carried out by solid models.Based on original definition of contact ratio,the theoretical formulas of transverse contact ratio and the longitudinal contact ratio are derived.Moreover,the calculation formulas of bending fatigue strength and contact fatigue strength are deduced by force analysis of EC-gear pair.Through the finite element simulation,the force characteristics of spur gears,helical gears and EC-gears are compared and analyzed.The results show that the EC-gears have the advantages of large bearing capacity and high comprehensive strength.The concept of tooth width to tool diameter is given,and the mechanism of the influence of minor axis on contact stress and bending stress of EC-gears is studied.Meanwhile,in order to improve the anti-eccentric load ability of the gear,the method of adjustmenting the minor axis of tooth trace is proposedjand the influence of modification coefficient on the strength of the gear is analyzed.The EC-rack is transformed into cutting tools by counterpart rack,and the tilting rotary cutter processing method is proposed.The convex and concave tooth surfaces are processed by inner and outer cutting edge tools separately.The relationship between cutting tools and gear blank is of generating motion.According to the theory of surface envelope,the kinematic model of tools and gear is established,and the single parameter equation of tooth surface is deduced.Special milling equipment is developed,and the EC-gear is processed by the machine.In this paper,a new type of curvilinear cylindrical gears is presented,and the geometric parameter and tooth surface equation are defined.The contact line of the gear pair is verified by three dimensional solid models.The comprehensive strength of EC-gear is better than that of traditional cylindrical gears by theoretical analysis and mechanical simulation.The tilting rotary cutter processing method is put forward,and the correctness of the processing method is preliminarily verified by numerical analysis.A special milling equipment is designed to realize the efficient milling of EC-gears.The basic parameters of gears are measured on the gear laser measuring instrument,and the correctness of the geometrical shape of the machined gear is verified.The EC-gears have excellent transmission performance and can be machined efficiently,and This new type of gear have important application value and broad development prospects. |
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