Pitch Cylinders imaginary friction cylinders which by pure rolling together

Pitch cylinders imaginary friction cylinders which by

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Pitch Cylinders:imaginary friction cylinders, which by pure rolling together, transmit the same motion as a pair of gears Pitch Circle:circle corresponding to a section of the equivalent pitch cylinder by a plane normal to wheel axis Pitch Diameter:diameter of pitch cylinder Pitch Surface: surface of pitch cylinder Pitch Point:point of contact of two pitch circles Pressure Angle:angle b/t the normal to the tooth profile at the pitch circle and the tangent to the pitch circle at that point Line of Centers:line through centers of rotation of a pair of mating gears Pinion:smaller & usually the driving gear in a pair of mated gears Addendum Circle:circle passing through the tips of the teeth Addendum:radial height of the teeth above the pitch circle- standard value is one module Dedendum or Root Circle: circle passing through the roots of the teeth Dedendum: radial depth of a tooth below the pitch circle Clearance:radial difference between addendum and dedendum of a tooth Full Depth of Teeth:total depth of tooth space (addendum +dedendum) Working Depth of Teeth:maximum depth of which a tooth penetrates into the tooth space of the mating gear (sum of addendums of two gears) Space Width:width of tooth space along pitch circle Tooth Thickness:thickness of the tooth measured along the pitch circle Backlash:difference between the space width and the tooth thickness along the pitch circle Face Width:length of tooth parallel to the gear axis Top Land:surface at the top of the tooth Bottom Land:surface at bottom of the booth between the adjacent fillets Flank:tooth surface between the pitch circle & bottomland including fillet Fillet:curved portion of the tooth flank at the root circle Calculations Pitch:pitch of 2 mating gears must be the same Circular Pitch (p):distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth p= (pi*d)/T p= circular pitch, d= pitch diameter, and T= number of teeth Diametral Pitch (DP):number of teeth per unit length of a pitch circle diameter in inches DP= T/d Limitations of diametral pitch are in terms of teeth per unit length rather than units of length Module (m):ratio of pitch diameter in mm to the number of teeth- used in SI units in place of diametral pitch m= d/t → p= (pi*d)/T → p= pi*m Gear Ratio (GR):ratio of the number of teeth on the driven gear to that on the driving gear GR= (T: # teeth on driven)/(t:number of teeth on pinion or driver) Speed or Velocity Ratio (VR):ratio of the angular velocity of the driven gear to angular velocity on driving gear
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Let d= pitch diameter, T= number of teeth, w= angular velocity (rad/s), N= angular velocity (rpm) VR= angular velocity of driven/ angular velocity of driver VR= pitch diameter driver/ pitch diameter driven VR= number of teeth driver/ number of teeth driven
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