Spur gears – Gear teeth are parallel to the axis of rotation. For power transfer between parallel shafts.

Helical gears – Gear teeth are inclined to the axis of rotation. Allows more continuous tooth engagement with less noise (vs. spur gears). Helical gears will have thrust loads. Allows power transfer between parallel and non-parallel shafts. See fig. 13-2

Bevel gears -- Gear teeth are formed on a conical surface and are used mainly to transmit power with intersecting shafts. See figure 13-3.

Worm gears -- A worm gear set consists of a worm (resembling a screw thread) and the gear (a specialized helical gear) usually on shafts intersecting at 90 degrees. A worm gear gives very high gear reduction ratios. See figure 13-4.

Nomenclature -- See figure 13- 5

Pitch circle – a theoretical circle on which all calculations are based. See figure 13-5.

Pitch diameter, d - diameter of pitch circle (in.) [for SI mm]

Pinion – smaller of two mating gears; the larger is called the gear

Circular pitch, p = sum of tooth thickness and width of space

Diametral pitch, P - ratio of the number of teeth to the pitch diameter

Addendum, a – radial distance between the pitch circle and the top of the gear tooth.

Dedendum, b -- radial distance between the bottom land and the pitch circle.

Backlash -- the amount by which the width of a tooth space exceeds the thickness of the engaging tooth measured on the pitch circle.

Basic Gear Geometry Equations:

P = N/d Eqn. 13-1

modulus for S I units Eqn. 13-2

p = d/N = m Eqn. 13-3

pP = Eqn. 13-4

Where N is the number of teeth; m is module (mm);

d – pitch diameter (in) or for SI (mm); p – circular pitch (in)

P – diametral pitch, (teeth/in)

Conjugate Gear Action

On mating gears, when the tooth profiles are designed so as to produce a constant angular velocity ratio, these gears are said to have conjugate action

The standard tooth profile that provides conjugate gear action is the involute profile (There are others, but not used often)

Involute Properties

Generating a involute tooth profile see figures 13-7, 13- 8

Base circle - circle on which the involute is generated

Fundamentals [Spur Gears]

Pitch line velocity

or

Where r’s are the gear pitch circle radii

d’s are the gear pitch circle diameters

’s are the gear angular velocities

See figure 13-9and figure 13-10

Gear pitch circles are tangent at the pitch point

Pressure line (line of action) – the direction in which the resultant force acts between the gear

Dedendum height is 1.25/P to 1.35/P (P is the diametral pitch)

E Base pitch is related to circular pitch

Where is the pressure angle the angle between the pressure line and a line joining the centers of the two gears

See example 13 - 1

Contact Ratio

Tooth contact begins and ends at the two addendum circles

Generally want more than one tooth in contact at the same time

Contact ratio

Eqn. 13- 8&9

Where m_{c} is the contact ratio; q_{t} is the sum of the arc of approach and arc of recess; L_{ab} is the length of the line of action (see fig. 13-15 for visual of these terms)

Interference

See figure 13-16 for interference action in gear teeth

Sometimes undercutting is used to eliminate interference; this can weaken the tooth

Equation for the minimum number of teeth on a pinion and gear without interference, N_{p}

m = N_{G} /N_{p} the ratio of gear teeth to pinion teeth

The Forming of Gear Teeth

See figures 13-17; 13-18; and 13-19

Milling

Shaping

Hobbing

Finishing can be important to gears operating at high speed

Straight Bevel Gears

See figure 13-20 for geometry

Pitch angle - see figure 13-20

Or Eqn. 13-14

Tredgold’s approximation

Figure 13-20 shows that he shape of the teeth, when projected on the back cone, is the same as a spur gear having a radius equal to the back-cone distance r_{b }

N’

where N’ is the virtual number of teeth of this imaginary gear and p is the circular pitch at the large end of the teeth

Parallel Helical Gears

Helical gears used to transmit power between parallel shafts

The helix angle is the same on both gears

One gear must have a right-hand helix and the other left-handed

Helical gears subject the shaft to radial and thrust loads

Because of the nature of the contact between helical gear the contact ratio is of minor importance [it is the contact area (~ face width) that becomes significant]

Herringbone gear – a gear with a double helix to avoid thrust loads. Like two helical gears of opposite hand mounted side by side on the same shaft.