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Spur Gears
Introduction..... Standards..... Terminology..... Spur Gear Design..... Materials..... Basic Equations..... Module..... Pressure Angle..... Contact Ratio..... Forces- Torques etc..... Strength Durability calcs..... Design Process..... Internal Gears..... Table of Lewis Form Factors..... Introduction Gears are machine elements used to transmit rotary motion between two shafts, normallywith a constant ratio. The pinion is the smallest gear and the larger gear is called the gear wheel.. A rack is a rectangular prism with gear teeth machined along one side- it is in effect a gear wheel with an infinite pitch circle diameter. In practice the action of gears in transmitting motion is a cam action each pair of mating teeth acting as cams. Gear design has evolved to such a level thatthroughout the motion of each contacting pair of teeth the velocity ratio of the gears is maintained fixed and the velocity ratio is still fixed as each subsequent pair of teeth come into contact. When the teeth action is such that the driving tooth moving at constant angular velocity produces a proportional constant velocity of the driven tooth the action is termed a conjugate action. The teethshape universally selected for the gear teeth is the involute profile. Consider one end of a piece of string is fastened to the OD of one cylinder and the other end of the string is fastened to the OD of another cylinder parallel to the first and both cylinders are rotated in the opposite directions to tension the string(see figure below). The point on the string midway between the cylinder P ismarked. As the left hand cylinder rotates CCW the point moves towards this cylinder as it wraps on . The point moves away from the right hand cylinder as the string unwraps. The point traces the involute form of the gear teeth.

The lines normal to the point of contact of the gears always intersects the centre line joining the gear centres at one point called the pitch point. For each gear thecircle passing through the pitch point is called the pitch circle. The gear ratio is proportional to the diameters of the two pitch circles. For metric gears (as adopted by most of the worlds nations) the gear proportions are based on the module. m = (Pitch Circle Diameter(mm)) / (Number of teeth on gear). In the USA the module is not used and instead the Diametric Pitch d pis used d p = (Number ofTeeth) / Diametrical Pitch (inches)

Profile of a standard 1mm module gear teeth for a gear with Infinite radius (Rack ). Other module teeth profiles are directly proportion . e.g. 2mm module teeth are 2 x this profile

Many gears trains are very low power applications with an object of transmitting motion with minium torque e.g. watch and clock mechanisms, instruments, toys, music boxes etc.These applications do not require detailed strength calculations.


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AGMA 2001-C95 or AGMA-2101-C95 Fundamental Rating factors and Calculation Methods for involute Spur Gear and Helical Gear Teeth BS 436-4:1996, ISO 1328-1:1995..Spur and helical gears. Definitions and allowable values of deviations relevant to corresponding flanks of gear teeth BS 436-5:1997, ISO1328-2:1997..Spur and helical gears. Definitions and allowable values of deviations relevant to radial composite deviations and runout information BS ISO 6336-1:1996 ..Calculation of load capacity of spur and helical gears. Basic principles, introduction and general influence factors BS ISO 6336-2:1996..Calculation of load capacity of spur and helical gears. Calculation of surface durability(pitting) BS ISO 6336-3:1996..Calculation of load capacity of spur and helical gears. Calculation of tooth bending strength BS ISO 6336-5:2003..Calculation of load capacity of spur and helical gears. Strength and quality of materials

If it is necessary to design a gearbox from scratch the design process in selecting the gear size is not complicated - the various design formulea have all been...
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