Basic Gear Formulas (pg 1)

Basic Gear Formulas

2.00 This section covers the recommended tooth proportions and design data for fine pitch spur and helical gears.

2.01 Basic rack - The basic rack shown in figure 2.1 is used to illustrate the tooth proportions covered by this standard. When small numbers of teeth, or special center distance situations are encountered, it is intended that long and short addendum proportions be used. This standard permits freedom of choice in making the minor changes in the tooth proportions to meet special design conditions as long as the resulting gears are fully conjugate to the basic rack. Such changes may be indicated when a special contact ratio or top land is desired.

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2.02 Spur gears - The basic rack shown in figure 2.1 and the tooth proportions shown in Table 2.1 provide the basic design data for a spur gear tooth.

2.03 Helical gears - The helical teeth covered by this standard are conjugated in the normal plane to the basic rack shown in figure 2.1 and Table 2.1.

2.04 Standard center distance is given by the equation shown in Table 2.1.

2.05 Center distance systems - There are two center distance systems in use. These are the standard center distance system and the enlarged center distance system. The choice of which is used will depend on the number of teeth in the meshing gears and on other design requirements. When an enlarged pinion is to be meshed with a gear at the center distance that is standard for the numbers of teeth, the gear diameter and tooth thickness must be decreased by the amount of the pinion enlargement.

2.06 Standard center-distance system - ( Long and Short addendums.) In this system the center of distance is made standard for the number of teeth, and the pressure angle remains constant. The outside diameter and root diameter of the gear is decreased the same amount that the pinion diameter is increased.

2.07 Spur pinion enlargement - Enlargement of spur pinions of 20 degree pressure angle and diametrical pitches from 20 thorough 120. Spur pinions having fewer than the minimum numbers of teeth shown in Table 2.2 should be enlarged to avoid objectionable undercut. Pinions of 20 degree pressure angle should be enlarged in accordance with the recommendations given in Table 2.3. The mating gear or the center distance should be adjusted as discussed in paragraph 2.05. Pinions of finer than 120 diametrical pitch require special consideration since the proportionally larger clearance requires hobs which tend to produce greater undercut. In general, pinions cut by the shaping process will not have as much undercut as those cut by hobbing.

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TOOTH PROPORTIONS
(All Values in Millimeters)
Item	Spur	Helical
Addendum (a)	M	M_n
Dedendum (b)	M + c = 1.16M	M_n + c = 1.16m_n
Working Depth (h_k)	2.000M	2.000M_n
Whole Depth (h_t)	2.16M	2.16M_n
Clearance (c) (standard)	.1M to .3M	.1M to .3M_n
Tooth Thickness (t)
Formulas
Metric Module (M)	D/N
Circular Pitch (p)
Pitch Diameter (D)	NM
Outside Diameter (D_n)	(N+2)M
Center Distance (C)
Where M = Metric Module M_n = Normal Metric Module t_n = Normal Tooth Thickness at PitchDiameter	p = Circular Pitch p_n = Normal Circular Pitch = Helix Angle	N = Number of Gear Teeth n = Number of Pinion Teeth D = Pitch Diameter

TOOTH PROPORTIONS
(All Values in Inches)
Item	Spur	Helical
Addendum (a)
Dedendum (b)
Working Depth (h_k)
Whole Depth (h_t)
Clearance (c) (standard)
(Shaved or Ground teeth)
Tooth Thickness (t)
Formulas
Circular Pitch (p)
Pitch Diam. Pinion (d)
Pitch Diam. Gear (D)
Outside Diam. Pinion (d_o)
Outside Diam. Gear (D_o)
Center Distance (C)
Where P = Transverse Diametrical Pitch P_n = Normal Diametrical Pitch t_n = Normal Tooth Thickness at Pitch Diameter	P_n = Normal Circular Pitch = Helix Angle n = Number of Pinion Teeth N = Number of Gear Teeth