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

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 14.7.4),10,11 Practice problems Ch 14- 3, 5, 8, 16, 18, 20, 23.

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

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

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

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

Spur Gear Geometry Figure 14.5 Basic spur gear geometry.

Gear Teeth Figure 14.6 Nomenclature of gear teeth.

Standard Tooth Size Table 14.1 Preferred diametral pitches for four tooth classes Figure 14.7 Standard diametral pitches compared with tooth size.

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

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

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

Involute Curve Figure 14.10 Construction of the involute curve.

Construction of the Involute Curve 1. Divide the base circle into a number of equal distances, thus constructing A0, A1, A2,... 2. Beginning at A1, construct the straight line A1B1, perpendicular with 0A1, and likewise beginning at A2 and A3. 3. Along A1B1, lay off the distance A1A0, thus establishing C1. Along A2B2, lay off twice A1A0, thus establishing C2, etc. 4. Establish the involute curve by using points A0, C1, C2, C3,... Gears made from the involute curve have at least one pair of teeth in contact with each other.

Contact Parameters Figure 14.11 Illustration of parameters important in defining contact.

Length of line of action: Contact ratio: Figure 14.12 Details of line of action, showing angles of approach and recess for both pinion and gear.

Backlash Figure 14.13 Illustration of backlash in gears. Table 14.3 Recommended minimum backlash for coarse-pitched gears.

Meshing Gears Figure 14.14 Externally meshing gears. Figure 14.15 Internally meshing gears.

Gear Trains Figure 14.16 Simple gear train. Figure 14.17 Compound gear train.

Example 14.7 Figure 14.18 Gear train used in Example 14.7.

Important planet gear equations: Planetary Gear Trains Important planet gear equations: Figure 14.19 Illustration of planetary gear train. (a) With three planets; (b) with one planet (for analysis only).

Design for Bending Stress - next. Gear Design Formulae Design for Bending Stress - next.

(Modified from Design Data, PSG Tech,1995) 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) Wt = S*bw*Y*600 / (Pd. [600 + V]) Where, Wt = Tooth Load, Lbs S = Safe Material Stress (static) psi. bw = Face Width, In. Y = Tooth Form Factor (Lewis Form Factor See Table 14.7 p-648) Pd = Diametral Pitch D = Pitch Diameter N = speed RPM V = Pitch Line Velocity, (FPM). = 0.2618 * D* N

Gear Design (contd.) 2. Horse Power Rating (HP_L) = Wt *D* N / 126051 3. 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. Given Design HP, we can find tooth load for a given tooth face width. Then can find, Pd … etc. For Non-Metallic (e.g. polymer) Gears, tooth load: W = S*F*Y* {(150 /[200 + V]) + 0.25} / Pd

Gear Quality Table 14.4 Quality index Qv for various applications. Figure 14.20 Gear cost as a function of gear quality. The numbers along the vertical lines indicate tolerances. Table 14.4 Quality index Qv for various applications.

Form Cutting Figure 14.21 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.

Pinion-Shaped Cutter Figure 14.22 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.

Gear Hobbing Figure 14.23 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.

Allowable Bending Stress Figure 14.24 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.

Allowable Bending and Contact Stress Table 14.5 Allowable bending and contact stresses for selected gear materials.

Allowable Bending Stress Figure 14.24 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.

Allowable Contact Stress Figure 14.25 Effect of Brinell hardness on allowable contact stress number for two grades of through-hardened steel.

Stress Cycle Factor Figure 14.26 Stress cycle factor. (a) Bending stress cycle factor YN.

Stress Cycle Factor Figure 14.26 Stress cycle factor. (a) pitting resistance cycle factor ZN.

Reliability Factor Table 14.6 Reliability factor, KR.

Hardness Ratio Factor Figure 14.27 Hardness ratio factor CH for surface hardened pinions and through-hardened gears.

Loads on Gear Tooth Figure 14.24 Loads acting on an individual gear tooth.

Loads and Dimensions of Gear Tooth Figure 14.29 Loads and length dimensions used in determining tooth bending stress. (a) Tooth; (b) cantilevered beam.

Bending and Contact Stress Equations Lewis Equation AGMA Bending Stress Equation Hertz Stress AGMA Contact Stress Equation

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

Spur Gear Geometry Factors Figure 14.30 Spur gear geometry factors for pressure angle of 20° and full-depth involute profile.

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.

Load Distribution Factor where

Pinion Proportion Factor Figure 14.31 Pinion proportion factor Cpf.

Pinion Proportion Modifier Figure 14.32 Evaluation of S and S1.

Mesh Alignment Factor Figure 14.33 Mesh alignment factor.

Dynamic Factor Figure 14.34 Dynamic factor as a function of pitch-line velocity and transmission accuracy level number.