bondgear@epix.net

ENGINEERING FORMULAS and TABLES LEGEND

Diametral Pitch	P
Circular Pitch	P'
Outside Diameter	D
Pitch Diameter	D'
Number of Teeth	N

FORMULAE

TO GET	HAVING	FORMULA
Diametral Pitch	Circular Pitch	P = 3.1416/P'
Diametral Pitch	Pitch Diameter & No. of Teeth	P = N/D'
Diametral Pitch	Outside Diameter & No. of Teeth	P = (N+2)/D
Circular Pitch	Diametral Pitch	P' = 3.1416/P
Circular Pitch	Pitch Diameter & No. of Teeth	P' = D'/.3183*N
Circular Pitch	Outside Diameter & No. of Teeth	P' = D/(.3183*N)+2
Pitch Diameter	No. of Teeth & Diametral Pitch	D' = N/P
Pitch Diameter	No. of Teeth & Outside Diameter	D' = (D*N)/(N+2)
Pitch Diameter	Outside Diameter & Diametral Pitch	D' = D - (2/P)
Pitch Diameter	No. of Teeth & Circular Pitch	D' = NP'.3183
Pitch Diameter	Outside Diameter & Circular Pitch	D' = D - (P'*.6366)
Outside Diameter	No. of Teeth & Diametral Pitch	D = (N+2)/P
Outside Diameter	Pitch Diameter & Diametral Pitch	D = D'+(2/P)
Outside Diameter	Pitch Diameter & No. of Teeth	D = (N+2)D/N
Outside Diameter	No. of Teeth & Circular Pitch	D = (N+2)P'.3183
Outside Diameter	Pitch Diameter & Circular Pitch	D = D'+(P'*.6366)
Number of Teeth	Pitch Diameter & Diametral Pitch	N = D'*P
Number of Teeth	Outside Diameter & Diametral Pitch	N = (D*P) - 2
Number of Teeth	Pitch Diameter & Circular Pitch	N = D'*3.1416/P'

HORSEPOWER and TORQUE HP = Torque (inch lbs.) X RPM / 63025 Torque (inch lbs.) = HP X 63025 / RPM Gear Line Marble

Strength of Gearing

SPUR GEARING and WORM GEARING

As is the case with most problems in engineering, there is more than one approach to the problem of calculating the strength of Spur Gears, however the Lewis Formula, modified to compensate for various speeds, serves as an excellent guide.
For the purpose of calculating strength of Worm Gearing we recognize that there are many varying factors which affect performance and capacity of this type of drive (such as sliding friction and wear). However, all things taken into consideration and using reasonably good practice as to installation and maintenance, the Lewis Formula for Spur Gearing serves as a practical guide.

Lewis Formula for Spur & Worm Gearing

W = (S X F X Y) / P X 600 / (600 + V) and HP = W X V / 33,000

MITER AND BEVEL GEARING

Strength of Miter and Bevel gearing is determined in a somewhat similar manner, using the Lewis Formula with modifications to correct it to angular gearing.

Lewis Formula for Miter and Bevel Gearing

W = (S X F X Y) / P X (C - F) / C X 600 / (600 + V) X V / 33,000
( Note: The Y factor (outline factor) for Miter and Bevel Gearing is modified by calculating a "theoretical" N (Number of Teeth or N') which will give you a number of teeth in an equivalent Spur Gear . N' = No. of Teeth / Cos a)

W	Load transmitted in lbs. at the pitch line
P	Diametral Pitch
F	Face Width in inches
Y	Factor for different Numbers Forms of teeth (See Table I)
HP	Horsepower
V	Velocity at the Pitch Line in feet per minute
S	Safe Working Stress of Material (See Table II)
a	The Pitch Cone Angle of the gear Where: Tan ag = Ng/Np
C	The Pitch Cone Radius = Pitch Diameter/2*Sin a

**TABLE I**
No. of Teeth	Y Factor - 14-1/2 Deg Involute	Y Factor - 20 Deg Involute	No. of Teeth	Y Factor - 14-1/2 Deg Involute	Y Factor - 20 Deg Involute
12	0.210	0.245	27	0.314	0.349
13	0.220	0.261	30	0.320	0.358
14	0.226	0.276	34	0.327	0.371
15	0.236	0.289	38	0.336	0.383
16	0.242	0.295	43	0.346	0.396
17	0.251	0.302	50	0.352	0.408
18	0.261	0.308	60	0.358	0.421
19	0.273	0.314	75	0.364	0.434
20	0.283	0.320	100	0.371	0.446
21	0.289	0.327	150	0.377	0.459
23	0.295	0.333	300	0.383	0.471
25	0.305	0.339	RACK	0.390	0.484
No. ofTeeth	Y Factor - 14-1/2 DegInvolute	Y Factor - 20 DegInvolute	No. ofTeeth	Y Factor - 14-1/2 DegInvolute	Y Factor - 20 DegInvolute

**TABLE II**
STEEL	15,000 lbs.
CAST IRON	9,000 lbs.
BRONZE	12,000 lbs.

Charles Bond Company

11 Green Street - P.O. Box 105

Christiana, PA 17509-0105

Phone: (800)-922-0125 or (610)-593-5171

FAX: (610)-593-5378

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We have made every attempt to assure the accuracy of the information on our web site, however we are NOT responsible for any errors. Furthermore, we reserve the right to make changes to our products, at anytime, without prior notice.

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