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Hamrock Fundamentals of Machine Elements Chapter 14 Just stare at the machine. There is nothing wrong with that. Just live with it for a while. Watch it the way you watch a line when fishing and before long, as sure as you live, you’ll get a little nibble, a little fact asking in a timid, humble way if you’re interested in it. That’s the way the world keeps on happening. Be interested in it. Robert Pirsig, Zen and the Art of Motorcycle Maintenance

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Hamrock Fundamentals of Machine Elements Thursday April 12, 2012 Qz#3 – 25 minutes Test 3 – Thursday April 26? Design mtgs- Lecture – Ch 14 – Reading- sections 1-4, 6, 7 (exclude ),10,11 Practice problems Ch 14- 3, 5, 8, 16, 18, 20, 23.

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Hamrock Fundamentals of Machine Elements Spur Gears Figure 14.1 Spur gear drive. (a) Schematic illustration of meshing spur gears; (b) a collection of spur gears.

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Hamrock Fundamentals of Machine Elements Helical Gears Figure 14.2 Helical gear drive. (a) Schematic illustration of meshing helical gears; (b) a collection of helical gears.

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Hamrock Fundamentals of Machine Elements Bevel Gears Figure 14.3 Bevel gear drive. (a) Schematic illustration of meshing bevel gears; (b) a collection of bevel gears.

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Hamrock Fundamentals of Machine Elements Worm Gears Figure 14.4 Worm gear drive. (a) Cylindrical teeth; (b) double enveloping; (c) a collection of worm gears.

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Hamrock Fundamentals of Machine Elements Figure 14.5 Basic spur gear geometry. Spur Gear Geometry

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Hamrock Fundamentals of Machine Elements Figure 14.6 Nomenclature of gear teeth. Gear Teeth

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Hamrock Fundamentals of Machine Elements Figure 14.7 Standard diametral pitches compared with tooth size. Standard Tooth Size Table 14.1 Preferred diametral pitches for four tooth classes

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Hamrock Fundamentals of Machine Elements Figure 14.8 Transmitted power as a function of pinion speed for a number of diametral pitches. Power vs. Pinion Speed

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Hamrock Fundamentals of Machine Elements Table 14.2 Formulas for addendum, dedendum, and clearance (pressure angle, 20°; full-depth involute). Gear Geometry Formulas

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Hamrock Fundamentals of Machine Elements Figure 14.9 Pitch and base circles for pinion and gear as well as line of action and pressure angle. Pitch and Base Circles Pressure angle What is best pressure angle for torque transmission? Standard pressure angles = ?

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Hamrock Fundamentals of Machine Elements Figure Construction of the involute curve. Involute Curve

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Hamrock Fundamentals of Machine Elements Construction of the Involute Curve 1.Divide the base circle into a number of equal distances, thus constructing A 0, A 1, A 2,... 2.Beginning at A 1, construct the straight line A 1 B 1, perpendicular with 0A 1, and likewise beginning at A 2 and A 3. 3.Along A 1 B 1, lay off the distance A 1 A 0, thus establishing C 1. Along A 2 B 2, lay off twice A 1 A 0, thus establishing C 2, etc. 4.Establish the involute curve by using points A 0, C 1, C 2, C 3,... Gears made from the involute curve have at least one pair of teeth in contact with each other.

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Hamrock Fundamentals of Machine Elements Figure Illustration of parameters important in defining contact. Contact Parameters

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Hamrock Fundamentals of Machine Elements Figure Details of line of action, showing angles of approach and recess for both pinion and gear. Line of Action Length of line of action: Contact ratio:

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Hamrock Fundamentals of Machine Elements Figure Illustration of backlash in gears. Backlash Table 14.3 Recommended minimum backlash for coarse- pitched gears.

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Hamrock Fundamentals of Machine Elements Figure Externally meshing gears. Meshing Gears Figure Internally meshing gears.

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Hamrock Fundamentals of Machine Elements Figure Simple gear train. Gear Trains Figure Compound gear train.

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Hamrock Fundamentals of Machine Elements Example 14.7 Figure Gear train used in Example 14.7.

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Hamrock Fundamentals of Machine Elements Planetary Gear Trains Figure Illustration of planetary gear train. (a) With three planets; (b) with one planet (for analysis only). Important planet gear equations:

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Hamrock Fundamentals of Machine Elements Gear Design Formulae Design for Bending Stress - next.

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Hamrock Fundamentals of Machine Elements Spur Gear Design (Modified from Design Data, PSG Tech,1995) DESIGN OF SPUR GEAR 3 (or so) steps: 1. Determine Horse Power based on Lewis Formula Metallic Spur Gears: (Tangential)Tooth Load (force) W t = S*b w *Y*600 / (P d. [600 + V]) Where, W t = Tooth Load, Lbs S = Safe Material Stress (static) psi.Safe Material Stress b w = Face Width, In. Y = Tooth Form Factor (Lewis Form Factor See Table 14.7 p-648)Tooth Form Factor P d = Diametral Pitch D = Pitch Diameter N = speed RPM V = Pitch Line Velocity, (FPM). = * D* N

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Hamrock Fundamentals of Machine Elements Gear Design (contd.) 2. Horse Power Rating (HP_L) = W t *D* N / Calculate Design Horse Power Design HP = HP_L * Service Load factor 4. Select the Gear / pinion with horse power capacity equal to or more than Design HP.Service Load factor Given Design HP, we can find tooth load for a given tooth face width. Then can find, P d … etc. For Non-Metallic (e.g. polymer) Gears, tooth load: W = S*F*Y* {(150 /[200 + V]) } / P d

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Hamrock Fundamentals of Machine Elements Gear Quality Figure Gear cost as a function of gear quality. The numbers along the vertical lines indicate tolerances. Table 14.4 Quality index Q v for various applications.

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Hamrock Fundamentals of Machine Elements Form Cutting Figure Form cutting of teeth. (a) A form cutter. Notice that the tooth profile is defined by the cutter profile. (b) Schematic illustration of the form cutting process. (c) Form cutting of teeth on a bevel gear.

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Hamrock Fundamentals of Machine Elements Pinion-Shaped Cutter Figure Production of gear teeth with a pinion-shaped cutter. (a) Schematic illustration of the process; (b) photograph of the process with gear and cutter motions indicated.

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Hamrock Fundamentals of Machine Elements Gear Hobbing Figure Production of gears through the hobbing process. (a) A hob, along with a schematic illustration of the process; (b) production of a worm gear through hobbing.

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Hamrock Fundamentals of Machine Elements Allowable Bending Stress Figure Effect of Brinell hardness on allowable bending stress number for steel gears. (a) Through-hardened steels. Note that the Brinell hardness refers to the case hardness for these gears.

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Hamrock Fundamentals of Machine Elements Allowable Bending and Contact Stress Table 14.5 Allowable bending and contact stresses for selected gear materials.

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Hamrock Fundamentals of Machine Elements Allowable Bending Stress Figure Effect of Brinell hardness on allowable bending stress number for steel gears. (b) Flame or induction-hardened nitriding steels. Note that the Brinell hardness refers to the case hardness for these gears.

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Hamrock Fundamentals of Machine Elements Allowable Contact Stress Figure Effect of Brinell hardness on allowable contact stress number for two grades of through-hardened steel.

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Hamrock Fundamentals of Machine Elements Stress Cycle Factor Figure Stress cycle factor. (a) Bending stress cycle factor Y N.

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Hamrock Fundamentals of Machine Elements Stress Cycle Factor Figure Stress cycle factor. (a) pitting resistance cycle factor Z N.

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Hamrock Fundamentals of Machine Elements Reliability Factor Table 14.6 Reliability factor, K R.

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Hamrock Fundamentals of Machine Elements Hardness Ratio Factor Figure Hardness ratio factor C H for surface hardened pinions and through-hardened gears.

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Hamrock Fundamentals of Machine Elements Loads on Gear Tooth Figure Loads acting on an individual gear tooth.

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Hamrock Fundamentals of Machine Elements Loads and Dimensions of Gear Tooth Figure Loads and length dimensions used in determining tooth bending stress. (a) Tooth; (b) cantilevered beam.

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Hamrock Fundamentals of Machine Elements Bending and Contact Stress Equations Lewis Equation AGMA Bending Stress Equation Hertz Stress AGMA Contact Stress Equation

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Hamrock Fundamentals of Machine Elements Lewis Form Factor Table 14.7 Lewis form factor for various numbers of teeth (pressure angle, 20°; full-depth involute).

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Hamrock Fundamentals of Machine Elements Spur Gear Geometry Factors Figure Spur gear geometry factors for pressure angle of 20° and full-depth involute profile.

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Hamrock Fundamentals of Machine Elements Application and Size Factors Table 14.8 Application factor as function of driving power source and driven machine. Table 14.9 Size factor as a function of diametral pitch or module.

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Hamrock Fundamentals of Machine Elements Load Distribution Factor where

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Hamrock Fundamentals of Machine Elements Pinion Proportion Factor Figure Pinion proportion factor C pf.

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Hamrock Fundamentals of Machine Elements Pinion Proportion Modifier Figure Evaluation of S and S 1.

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Hamrock Fundamentals of Machine Elements Mesh Alignment Factor Figure Mesh alignment factor.

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Hamrock Fundamentals of Machine Elements Dynamic Factor Figure Dynamic factor as a function of pitch-line velocity and transmission accuracy level number.

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