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1、Ken Youssefi,Mechanical Engineering Dept.,1,Force Analysis Spur Gears,The equation in SI units,Ken Youssefi,Mechanical Engineering Dept.,2,Force Analysis Helical Gears,Ken Youssefi,Mechanical Engineering Dept.,3,Force Analysis Bevel Gears, = Pressure angle (20o),Ken Youssefi,Mechanical Engineering D
2、ept.,4,Force Analysis Worm Gear Sets,Three orthogonal components of W without considering friction,considering friction,Relations between forces acting on the worm and the gear,Ken Youssefi,Mechanical Engineering Dept.,5,Force Analysis Worm Gear Sets,Two useful relations, friction force and transmit
3、ted loads.,Efficiency of worm gear sets,Ken Youssefi,Mechanical Engineering Dept.,6,Stress Analysis Spur Gears,Bending Strength,Lewis equation (1892 Wilfred Lewis, Philadelphia Engineers Club),Bending stress is maximum at the root of the tooth,F,W t,Ken Youssefi,Mechanical Engineering Dept.,7,Modifi
4、cation of Lewis Equation,Assumptions made in deriving Lewis equation,The load is applied to the tip of a single tooth.,The radial component of the load, Wr , is negligible.,The load is distributed uniformly across the full face width.,Stress concentration in the tooth fillet is negligible.,Lewis equ
5、ation, where,Ken Youssefi,Mechanical Engineering Dept.,8,Modification of Lewis Equation,Modifications according to AGMA standards (American Gear Manufacturers Association),W t tangential transmitted load Ka application factor KV dynamic factor KS size factor KI Idler factor (use 1.42 if designing an
6、 idler gear) Pd transverse diameteral pitch F face width of the narrower member Km load-distribution factor KB rim-thickness factor J geometry factor for bending strength which includes root fillet stress concentration factor Kf,Lewis equation,Ken Youssefi,Mechanical Engineering Dept.,9,Bending Stre
7、ss Modifying Factors,Geometry factor J,Ken Youssefi,Mechanical Engineering Dept.,10,Bending Stress Modifying Factors,Dynamic factor Kv,Application factor, Ka,Ken Youssefi,Mechanical Engineering Dept.,11,Bending Stress Modifying Factors,AGMA has not established standards for size factor and recommend
8、s that Ks be set to 1.,Size factor Ks,Load Distribution factor Km,Ken Youssefi,Mechanical Engineering Dept.,12,AGMA Bending Strength Equation,Sfb is the allowable fatigue bending stress, psi,KR is the reliability factor,KT is the temperature factor,KL is life factor,Allowable Stress,Reliability fact
9、or KR,Ken Youssefi,Mechanical Engineering Dept.,13,AGMA Bending Strength Equation,Stress cycle factor KL,Ken Youssefi,Mechanical Engineering Dept.,14,AGMA Bending-Fatigue Strength, Sfb,Ken Youssefi,Mechanical Engineering Dept.,15,Surface Strength Analysis,The basic surface deterioration,Scoring,If t
10、he surface asperity welding and tearing cause a transfer of metal from one surface to the other, the resulting surface damage is called scoring. If the local welding of asperities becomes so extensive that the surfaces no longer slide on each other, the resulting failure is called seizure.,Ken Youss
11、efi,Mechanical Engineering Dept.,16,Surface Strength Analysis,Abrasive wear,Abrasive wear is a surface damage caused by the presence of abrasive particles in the lubricant. Large particles tend to scratch and gouge the surface, where small (dust like) particles polish the tooth surface to a mirror f
12、inish.,Scoring, abrasive wear and corrosion wear are due to the failure of lubrication system.,Ken Youssefi,Mechanical Engineering Dept.,17,Surface Strength Analysis,Surface Fatigue Failure, due to repeated contact load,Proper lubricating system can minimize the surface damage due to wear and corros
13、ion. But, surface fatigue can occur even with proper lubrication and its the most common mode of gear failure and is characterized by pitting and spalling of the tooth surface. The damage is caused by repeated contact stresses.,Ken Youssefi,Mechanical Engineering Dept.,18,AGMA Surface Stress Equatio
14、n,Cp elastic coefficient, (lb/in2)0.5 Wt transmitted tangential load Ca overload factor (same as Ka) Cv dynamic factor (same as Kv) Cs size factor (same as Ks) Cm load-distribution factor (same as Km) Cf surface condition factor d pitch diameter of the pinion F face width of the narrowest member I g
15、eometry factor,Ken Youssefi,Mechanical Engineering Dept.,19,AGMA Surface Stress Equation,AGMA Elastic coefficient CP,Ken Youssefi,Mechanical Engineering Dept.,20,AGMA Surface Strength Equation,Sfc is the allowable contact stress, psi,CR is the reliability factor (same as KR),CT is the temperature fa
16、ctor (same as KT),CL is the surface-life factor,CH is the hardness ratio factor,Ken Youssefi,Mechanical Engineering Dept.,21,AGMA Surface Strength Equation,Pitting resistance stress cycle factor ZN,Ken Youssefi,Mechanical Engineering Dept.,22,AGMA Surface Strength Equation,AGMA allowable surface fatigue strength,Ken Youssefi,Mechanical Engineering Dept.,23,AGMA Spur Gear Design Equations,Surface strength design equation, Stress = strength,Design steps,Select material,
