Machine Elements in Mechanical Design FIFTH EDITION CHAPTER

Machine Elements in Mechanical Design FIFTH EDITION CHAPTER 10 Helical Gears, Bevel Gears, and Wormgearing Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Forces on Helical Gear Teeth • Forces § WN is the true normal force that acts perpendicular to the face of the tooth in the plane normal to surface of the tooth. § Wt is tangential force that acts in transverse plane and tangent to pitch circle of helical gear and causes torque to be transmitted from driver to driven gear. Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Forces on Helical Gear Teeth • Forces § Wr is the radial force that acts toward center of the gear perpendicular to pitch circle and to tangential force. § Wx is the axial force that acts parallel to axis of gear and causes a thrust load that must be resisted by bearings carrying the shaft. Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Helical Gear Teeth • Stresses: equation for computing bending stress number for helical gear teeth for spur gear teeth in Equation (9 – 16). Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Helical Gear Teeth • Pitting resistance: same procedure as for spur gears in Equation (9– 23). Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Table 10 -1 Geometry Factors for Pitting Resistance, I, for Helical Gears with 20° Normal Pressure Angle and Standard Addendum Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Table 10 -1 (continued) Geometry Factors for Pitting Resistance, I, for Helical Gears with 20° Normal Pressure Angle and Standard Addendum Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Table 10 -2 Geometry Factors for Pitting Resistance, I, for Helical Gears with 25° Normal Pressure Angle and Standard Addendum Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Table 10 -2 (continued) Geometry Factors for Pitting Resistance, I, for Helical Gears with 25° Normal Pressure Angle and Standard Addendum Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Forces on Straight Bevel Gears • Because of conical shape of bevel gears and of involute-tooth form, a threecomponent set of forces acts on bevel gear teeth. § Tangential § Radial § Axial Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Bearing Forces and Bending Moments on Shafts Carrying Bevel Gears • Because of three-dimensional force system that acts on bevel gears, calculation of forces on shaft bearings cumbersome. § Provide rigid mountings and stiff shafts when using bevel gears • Because there are forces acting in two planes on bevel gears, there is bending in two planes. Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Stresses In Straight Bevel Gear Teeth • Primary Standard in the United States § AGMA Standard 2003 -C 10, Rating the Pitting Resistance and Bending Strength of Generated Straight Bevel, Zerol Bevel and Spiral Bevel Gear Teeth Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Stresses In Straight Bevel Gear Teeth • Bending and Contact Stress § § § § Pitch diameter Pitches Tangential force Bending stress number Overload factor Size factor for bending strength Load distribution factor Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Stresses In Straight Bevel Gear Teeth • Bending and Contact Stress § Dynamic factor § Geometry factor for bending strength § Allowable bending strength number Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Table 10 -4 Gears Allowable Stress Numbers for Bevel Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Stresses In Straight Bevel Gear Teeth • Bending and Contact Stress § Contract stress number § Allowable contact stress number Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Stresses In Straight Bevel Gear Teeth • Practical Considerations for Bevel Gearing § Factors similar spur and helical gears considered in design of systems using bevel gears. § Accuracy of alignment and accommodation of thrust loads are critical. Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Forces, Friction, and Efficiency in Wormgear Sets • Force System: perpendicular components; tangential, radial, axial forces § § § Pitch line speed Velocity ratio Coefficient of friction Output torque from wormgear drive Friction force Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Forces, Friction, and Efficiency in Wormgear Sets • Force System § § § Power loss due to friction Input power Efficiency Factors affecting efficiency Self-locking wormgear sets Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Emerging Technology and Software for Gear Design • Emerging Gearing Technologies § American Gear Manufacturers Association (AGMA) § International Organization for Standardization (ISO) § Power Transmission Engineering § Gear Technology Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Emerging Technology and Software for Gear Design • Emerging Gearing Technologies § Non-standard gearing and gear tooth forms § Peening • • Cast spheres Cut wire Beads Crushed glass, coal slag, hard rock, garnet Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved

Emerging Technology and Software for Gear Design • Emerging Gearing Technologies § Peening • • Wheel blasting Air blasting Sand blasters Vibratory finishing Machine Elements in Mechanical Design , Fifth Edition Robert L. Mott Copyright © 2014 by Pearson Education, Inc. All Rights Reserved