Report

Shigley’s Mechanical Engineering Design 9th Edition in SI units Richard G. Budynas and J. Keith Nisbett Chapter 15 Bevel and Worm Gears Prepared by Kuei-Yuan Chan Associate Professor of Mechanical Engineering National Cheng Kung University Copyright © 2011 by The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 15 Bevel and Worm Gears Chapter Outline 15-1 Bevel Gearing—General 15-2 Bevel-Gear Stresses and Strengths 15-3 AGMA Equation Factors 15-4 Straight-Bevel Gear Analysis 15-5 Design of a Straight-Bevel Gear Mesh 15-6 Worm Gearing—AGMA Equation 15-7 Worm-Gear Analysis 15-8 Designing a Worm-Gear Mesh 15-9 Buckingham Wear Load Bevel Gearing-General • Bevel gears may be classified as follows Straight bevel gears Spiral bevel gears Zerol bevel gears Hypoid gears Spiroid gears • Straight bevel gears are usually used for pitch-line velocities up to 1000 ft/min (5 m/s) when the noise level is not an important consideration. • Spiral bevel gears are recommended for higher speeds and where the noise level is an important consideration. • The Zerol bevel gear is a patented gear having curved teeth but with a zero spiral angle. • Hypoid gears are similar to bevel gears but with the shafts offset. • For larger offsets, the pinion begins to resemble a tapered worm and the set is then called spiroid gearing. 3 Bevel-Gear Stress and Strength • Fundamental Contact Stress Equation • Permissible Contact Stress Number (Strength) Equation • Bending Stress • Permissible Bending Stress Equation 4 AGMA Equation Factors • Overload Factor Ko (KA) • Dynamic Factor Kv 5 AGMA Equation Factors (Cont.) • Size Factor for Pitting Resistance Cs (Zx) • Size Factor for Bending Ks (Yx) • Load-Distribution Factor Km (KHβ) • Crowning Factor for Pitting Cxc (Zxc) • Pitting Resistance Geometry Factor I (ZI) 6 AGMA Equation Factors (Cont.) • Bending Strength Geometry Factor J (YJ) • Stress-Cycle Factor for Pitting Resistance CL (ZNT) • Stress-Cycle Factor for Bending Strength KL (YNT) • Hardness-Ratio Factor CH (ZW) • Temperature Factor KT (Kθ) • Reliability Factors CR (ZZ) and KR (YZ) 7 AGMA Allowable Stress Numbers 8 Straight-Bevel Gear Analysis 9 Design of a Straight-Bevel Gear Mesh • A useful decision set for straight-bevel gear design is Function Design factor Tooth system Tooth count Pitch and face width Quality number Gear material, core and case hardness Pinion material, core and case hardness 10 A priori decisions Design variables Worm Gearing-AMGA Equation • Crossed helical gears, and worm gears too, usually have a 90◦ shaft angle, though this need not be so. The relation between the shaft and helix angles is Where ∑ is the shaft angle • The pitch worm diameter d falls in the range where C is the center-to-center distance. • AGMA reports the coefficient of friction f as • The heat loss rate Hloss from the worm-gear case in ft · lbf/min is where e is efficiency, and Hin is the input horsepower from the worm 11 Worm Gearing-AMGA Equation(Cont.) • AGMA relates the allowable tangential force on the worm-gear tooth (Wt ) all to other parameters by 12 Worm-Gear Analysis • Compared to other gearing systems worm-gear meshes have a much lower mechanical efficiency. When the worm drives the gearset, the mechanical efficiency eW is given by With the gear driving the gearset, the mechanical efficiency eG is given by • To ensure that the worm gear will drive the worm, where values of fstat can be found in ANSI/AGMA 6034-B92. • The magnitude of the gear transmitted force WtG can be related to the output horsepower H0, the application factor Ka , the efficiency e, and design factor nd by • The largest lead angle λmax associated with normal pressure angle φn. 13 Designing a Worm-Gear Mesh • A usable decision set for a worm-gear mesh includes Function: power, speed, mG, Ka Design factor: nd Tooth system Materials and processes Number of threads on the worm: NW Axial pitch of worm: px Pitch diameter of the worm: dW Face width of gear: FG Lateral area of case: A 14 A priori decisions Design variables Buckingham Wear Load • Buckingham showed that the allowable geartooth loading for wear can be estimated from where Kw = worm-gear load factor dG = gear-pitch diameter Fe = worm-gear effective face width 15