D a1,2 = d 1,2 + 2m (a. + x 1,2 - Δ y) - for internal gearing the interference check is done as well for km 0 is accomplished by addendum lowering d a2 = d a2 - 2km. Gear Catalog 135 ENGINEERING INFORMATION SPUR GEARS. FILLET RADIUS (r f) is the radius of the fillet curve at the base. SPUR GEAR FORMULAS FOR FULL DEPTH INVOLUTE TEETH Diametral Backlash Diametral Backlash Pitch (Inches) Pitch (Inches) 3.013 8-9.005 4.010 10-13.004.
Notes on Spur GearsNotes on Spur Gears Definitions Addendum: The radial distance between the Pitch Circle and the top of the teeth. Arc of Action: That arc of the Pitch Circle between the first point of contact between gear teeth and the last. Arc of Approach: That arc of the Pitch Circle between the first point of contact between gear teeth and the the Pitch Point. Arc of Recession: That arc of the Pitch Circle between the Pitch Point and the last point of contact between gear teeth.
Backlash: Play between mating teeth. Base Circle: The circle from which is generated the involute curve upon which the tooth profile is based. Center Distance: The distance between centers of two gears. Chordal Addendum: The distance between a chord, passing through the points where the Pitch Circle crosses the tooth profile, and the tooth top.
Chordal Thickness: The thickness of the tooth measured along a chord passing through the points where the Pitch Circle crosses the tooth profile. Circular Pitch: Inches of Pitch Circle circumference per tooth. Circular Thickness: The thickness of the tooth measured along an arc following the Pitch Circle Clearance: The distance between the top of a tooth and the bottom of the space into which it fits on the meshing gear. Contact Ratio: The ratio of the length of the Arc of Action to the Circular Pitch. Dedendum: The radial distance between the bottom of the space between teeth and the top of the teeth.
Diametral Pitch: Teeth per inch of diameter. Sometimes written (incorrectly) as Diametrical Pitch. Face: The working surface of a gear tooth, located between the pitch diameter and the top of the tooth. Face Width: The width of the tooth measured parallel to the gear axis. Flank: The working surface of a gear tooth, located between the pitch diameter and the bottom of the space between gear teeth Gear: The larger of two meshed gears.
If both gears are the same size, they're both called 'gears'. Land: The top of the tooth. Line of Action: That line along which the point of contact between gear teeth travels, between the first point of contact and the last. Module: Teeth per millimeter of Pitch Diameter. Pinion: The smaller of two meshed gears. Pitch Circle: The circle, the radius of which is equal to the distance from the center of the gear to the pitch point.Pitch Diameter: Diameter of the pitch circle Pitch Point: The point of tangency of the pitch circles of two meshing gears, where the Line of Centers crosses the pitch circles. Pressure Angle: Angle between the Line of Action and a line perpendicular to the Line of Centers.
Profile Shift: An increase in the Outer Diameter and Root Diameter of a gear, introduced to lower the practical tooth number or acheive a non-standard Center Distance. For a description of Profile Shift, see. Ratio: Ratio of the numbers of teeth on mating gears. Root Circle: The circle that passes through the bottom of the tooth spaces.
Root Diameter: The diameter of the Root Circle. Stub Gear: A gear with Stub Teeth. Stub Tooth: A gear tooth with only 80% of the usual working depth. Undercut: A gear tooth which is thinner at the base than at the Pitch Circle. Caused by too few teeth (too course a Diametral Pitch) for a given Pitch Diameter. Whole Depth: The distance between the top of the teeth and the bottom of the spaces between teeth. Working Depth: The depth to which a tooth extends into the space between teeth on the mating gear.
General NotesGears that are smaller than 32 teeth for a 14.5° Pressure Angle, or 18 teeth for a 20° Pressure Angle, have a Root Circle smaller than the Base Circle, resulting in the teeth being undercut. Undercutting is avoided by the use of Profile Shift, the shifting the the Addendum and Dedendum outward without altering the location of the base circle. Profile shift is also used to attain non-standard center distances. Gears with shifted profiles will run properly with standard gears.Standard Pressure Angle is 20°, but 14.5° is traditional.
14.5° was chosen because the sine is almost exactly ¼, which simplified design in the pre-computer age.There are no 'standards' for pitch, but industry has settled on certain common values. Common Diametral Pitches include 48, 32, 24, 20, 18, 16, and 12. Common Modulusises (Modulae? Moduli?) include 0.5, 0.8, 1.00, 1.25, 1.50, 2.50, and 3.FormulaeI prefer the term 'formulae' to 'formulas'.