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)
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
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