ABSTRACT
Contents 11.1 Introduction 264 11.2 Design of Shafts for Static Loading 264 11.3 Fatigue Design of Shafts 267 11.4 Additional Shaft Design
Considerations 271 11.5 Critical Speed of Rotating Shafts 272 11.6 Keys, Roll Pins, Splines and
Set Screws 275 11.7 Retaining Rings and Pins 278 11.8 Flywheels 279 11.9 Couplings 285 11.10 Summary 288
Examples 11.1 Static Design of a Shaft 266 11.2 Fatigue Design of a Shaft 269 11.3 Fatigue Design of a Shaft
Under Combined Loading 269 11.4 Critical Shaft Speed 274 11.5 Key Design 276 11.6 Flywheel Design 282 11.7 Flywheel Stresses 283
Design Procedures 11.1 Shafts 271 11.2 Keys 275 11.3 Flywheels 282
Symbols A area, m2
A˜ constant defined in Eq. (11.26) B˜ constant defined in Eq. (11.27) C1 integration constant Cf coefficient of fluctuation, Eq. (11.80) Ct ring correction factor c distance from neutral axis to outer fiber, m d diameter, m dm mean spline diameter, m ds set screw diameter, m E modulus of elasticity, Pa g gravitational acceleration, 9.807 m/s2
h height, m I area moment of inertia, m4
Im mass moment of inertia, kg-m2
J polar area moment of inertia, m4
Kc stress concentration factor Ke kinetic energy, N-m Kf fatigue stress concentration factor k spring rate, N/m kf surface finish factor kr reliability factor ks size factor l length, m ls spline length, m M moment, N-m Mf performance index, J/kg ma mass, kg n number of teeth ns safety factor P normal force, N Pt retaining force, N p pressure, Pa pf interference pressure, Pa qn notch sensitivity factor r radius, m Se modified endurance limit, Pa S′e endurance limit, Pa Sse shear modified endurance limit, Pa Ssy shear yield strength, Pa Su ultimate strength, Pa Sut ultimate tensile strength, Pa Sy yield strength, Pa T torque, N-m Tl load torque, N-m Tm mean torque, N-m t time, s th thickness, m U potential energy, N-m u velocity, m/s W load, N w width, m x, y, z Cartesian coordinates, m δ deflection, m θ cylindrical polar coordinate, deg θωmax location within a cycle where speed is
maximum, deg θωmin location within a cycle where speed is
minimum, deg ν Poisson’s ratio ρ density, kg/m3
σ normal stress, Pa σe critical stress using distortion-energy
theory, Pa σφ normal stress acting on oblique plane, Pa τ shear stress, Pa
τφ shear stress acting on oblique plane, Pa φ oblique angle, deg ω angular speed, rad/s ωφ fluctuation speed, rad/s
Subscripts a alternating c compression i inner m mean o outer r radial s shear θ circumferential ω speed 1,2,3 principal axes
This chapter begins by discussing the design of shafts, making extensive use of the material from Sections 2.8 through 2.12 and Ch. 4 to develop stresses. The failure theories presented in Section 6.7 are used for static failure prediction in Section 11.2; the material in Ch. 7 is used to develop design rules for fatigue of shafts in Section 11.3. Here, combinations of loading are presented, whereas previously each type of loading was considered independently. It is important that this material be understood before proceeding with this chapter. The critical speed of rotating shafts is discussed in Section 11.5. The dynamics and the first critical speed are important, since the rotating shaft becomes dynamically unstable and large vibrations are likely to develop.
