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            Gear Information

           Nomenclature and Formulas

Types of Gears

Spur Gears have teeth that are straight and parallel to the axis of rotation.
Helical Gears have teeth that spiral around the body of the gear at an angle.
Internal Gears have teeth on the inside of a hollow cylindrical shape.
External Gears have teeth on the outside of a cylindrical shape.
Bevels & Miters have teeth on the outside of a conical-shaped body. Most commonly used on shafts intersecting at 90 degrees.
Worm Gears usually "wrap" slightly around a WORM which is a cylindrical body like screw threads.

Terminology

Addendum: Height of the tooth above the Pitch Circle.
Backlash: Distance by which a tooth space exceeds the thickness of the engaging tooth at the operating pitch circles.
Center Distance: Distance between the centerlines of mating gears on parallel shafts.
Dedendum: Distance along tooth below the Pitch Circle.
Diametral Pitch: Measure of tooth size in the English system. Expressed as the number of teeth per inch of pitch diameter. As tooth size increases, the D.P. decreases.
Face Width: Length of a tooth in an axial plane.
Outside Diameter: Distance from the top of one tooth to the top of the diametrically opposite tooth.
Pitch Circle: A circle defined by the number of teeth and the Diametral Pitch.
Pressure Angle: Angle between the normal to the tooth profile at the pitch circle and the tangent to the pitch circle at that point.
Root Diameter: Distance from the bottom of one tooth to the bottom of a diametrically opposite tooth.
Tooth Profile: One side of the tooth in cross section between the outside circle and the root circle.
Tooth Surface: The side of a gear tooth.
Undercut: Condition where the tooth cutting process removes material from the lower section of the tooth profile to prevent interference with the tip of the mating gear's teeth.
Whole Depth: Depth of a tooth space from the outside diameter to the root diameter.

Formulas-Spurs, Internal Spurs, & Bevels

To find the following for Spur Gears: When you know the following: Use this Formula
Diametral Pitch (P) Pitch Diameter(PD) & Number of Teeth(N) P = N/PD
Diametral Pitch (P) Circular Pitch (Pc) P = 3.14 / Pc
Diametral Pitch (P) Outside Diameter (OD) & Number of Teeth (N) P = (N+2) / OD
Pitch Diameter (PD) Number of Teeth (N) & Diametral Pitch (P) PD = N / P
Outside Diameter (OD) Number of Teeth (N) & Diametral Pitch (P) OD = (N+2) / P
Number of Teeth (N) Pitch Diameter (PD) & Diametral Pitch (P) N = PD x P
Addendum (a) Diametral Pitch (P) A = 1 / P
Dedendum (d) Whole Depth (W) & Addendum (a) d = W—a
Tooth Thickness(T) at the Pitch Diameter Diametral Pitch (P) T = 1.5708 / P
Minimum Face Width (F) Circular Pitch (Pc) Min.F = Pc x 3
Center Distance (C) Diametral Pitch (P) & Number of Teeth in both Gears (N1 + N2) C = (N1 + N2) / 2P
Circular Pitch (Pc) Diametral Pitch (P) Pc = 3.1416 / P
Whole Depth(hw) for 20 DP & finer Diametral Pitch (P) Hw = 2.2 / P + .002
Whole Depth(hw) for Coarser than 20 DP Diametral Pitch (P) Hw = 2.157 / P
To find the following for Bevel Gears When you know the following: Use this Formula:
Pitch Diameter of Pinion (PDp) Number of pinion teeth (n) &Diametral Pitch (P) PDp = n / P
Pitch Diameter of Gear (PDg) Number of gear teeth (N) & Diametral Pitch (P) PDg = N / P
Outside Diameter of Pinion (ODp) Pinion Pitch Diameter (PDp),Pinion Addendum (ap), & Pitch Angle (g) ODp = PDp + 2ap x cosg
Outside Diameter of Gear (ODg) Gear Pitch Diameter (PDg),Gear Addendum (ag), & Pitch Angle (G) ODg = PDg + 2ag x cosG

Formulas-Helicals & AGMA/ISO/DIN/JIS

To find the following for Helical Gears: When you know the following: Use this Formula
Normal D.P. (Pn) Tranverse P (P) & Helix Angle (A) Pn = P / Cos A
Normal D.P. (Pn) Number of Teeth (N) & Helix Angle (A) Pn = N / (D x Cos A)
Transverse Pitch (P) Normal Diametral Pitch (Pn) & Helix Angle (A) P = Pn x Cos A
Pitch Diameter (PD) Number of Teeth (N), Normal D.P.(Pn), & Helix Angle (A) PD = N / (Pn x Cos A)
Outside Diameter (OD) Pitch Diameter (D) & Addendum (a) OD = D + (2 x a)
Outside Diameter (OD) Normal Diametral Pitch (Pn) & Pitch Diameter (D) OD = D + 2 / Pn
Helix Angle (A) for Parallel Shafts Number of Teeth (N), Pitch Diameter (PD), & Normal Diametral Pitch (Pn) Cos A = N / (Pn x PD)
Addendum (a) Normal Diametral Pitch (Pn) ‘a= 1 / Pn
Lead of Tooth Helix (L) Pitch Diameter (PD) & Helix Angle (A) L = PD x pi x cot A
Approximate Normal Tooth Thickness (T) Normal Diametral Pitch (Pn) T = 1.571 / Pn
Whole Tooth Depth (W) Normal Diametral Pitch (Pn) W = 2.157 / Pn
Center Distance (C) Pitch Diameters of both gears(PD1, PD2) C = (PD1 + PD2) / 2
Designation Description AGMA390.03
Standard		 Previous AGMA 236.04
Standard		 ISO DIN3963/1978 JISJapan
AAUltra-highaccuracy Highest possible accuracy 14 or 15 Precision 3=AGMA 13/14.20 DP or finer   DIN 2=AGMA 15DIN 3=AGMA 14  
AHigh accuracy Used extensively for turbine & aerospace gearing 12 or 13 Precision 2=AGMA12.20 DP or finer ISO 4=AGMA 13ISO 5=AGMA 12 DIN 4=AGMA 13DIN 5=AGMA 12 JIS 0=AGMA 13JIS 1=AGMA 12
BMedium-highaccuracy May be achieved by hobbing & shaping with best machy. 10 or 11 Precision 1=AGMA 10/11.20 DP or finer ISO 6=AGMA 11ISO 7=AGMA 10 DIN 6=AGMA 11DIN 7=AGMA 10 JIS 2=AGMA 11JIS 3=AGMA 10
CMediumAccuracy Achieved by hobbing or shaping with 1st rate machy.& operators 8 or 9 Commercial 3 =AGMA 8.Commercial 4 =AGMA 9.20 DP or finer ISO 8=AGMA 9ISO 9=AGMA 8 DIN 8=AGMA 9DIN 9=AGMA 8 JIS 4=AGMA 9JIS 5=AGMA 8
DLow accuracy Typically for low-speed gears 6 or 7 Commercial 2 =AGMA 6/7.20 DP or finer   DIN 10 or 11  

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