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.

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 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.


Figure 14.5 Basic spur gear geometry.

Spur Gear Geometry


Figure 14.6 Nomenclature of gear teeth.

Gear Teeth


Figure 14.7 Standard diametral pitches compared with tooth size.

Standard Tooth Size

Table 14.1 Preferred diametral pitches for four tooth classes


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

Gear Geometry Formulas


Figure 14.9 Pitch and base circles for pinion and gear as well as line of action and pressure angle.

Pitch and Base CirclesPressure angle

What is best pressure angle for

torque transmission?

Standard pressure angles

= ?


Figure 14.10 Construction of the involute curve.

Involute Curve


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 A1, construct the straight line A

1B

1, perpendicular

with 0A1, and likewise beginning at A

2 and A

3.

3. Along A1B

1, lay off the distance A

1A

0, thus establishing C

1. Along

A2B

2, lay off twice A

1A

0, thus establishing C

2, etc.

4. Establish the involute curve by using points A0, C

1, C

2, C

3,...

Gears made from the involute curve have at least one pair of teeth in contact with each other.


Figure 14.12 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:


Figure 14.13 Illustration of backlash in gears.

Backlash

Table 14.3 Recommended minimum backlash for coarse-pitched gears.


Figure 14.14 Externally meshing gears.

Meshing Gears

Figure 14.15 Internally meshing gears.


Figure 14.16 Simple gear train.

Gear Trains

Figure 14.17 Compound gear train.


Example 14.7

Figure 14.18 Gear train used in Example 14.7.


Planetary Gear Trains

Figure 14.19 Illustration of planetary gear train. (a) With three planets; (b) with one planet (for analysis only).

Important planet gear equations:


Gear Design Formulae

Design for Bending Stress - next.


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 DiameterN = speed RPMV = 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 PowerDesign 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

Figure 14.20 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.


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 C

H 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 C

pf.


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.

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.

Documents

gear teeth slide

involute curve slide

spur gear geometry slide

helical gears b

collection of spur gears

collection of bevel

collection of helical

spur gear drive