A gear train is a mechanical device that transmits energy from one part of a system to another in such a way that force, torque, speed and displacement may be alerted. The inertia and friction of the gears are neglected in the ideal case. Consider a gear system as shown in the Fig.1.
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| Fig1 |
The number of teeth on the surface of the gears is proportional to the radii r1 and r2 of the gears.
The distance travelled along the surface of each gear is same.
The work done by one gear is same as the other.
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Remarks:
1) The number of teeth N are proportional to the radius r of a gear.
2) The distance travelled on each gear is same.
3) Work done = Tθ by each gear is same.
1.1 Gear Train with Inertia and Friction
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| Fig2 |
In practice, gears do have inertia and friction which cannot be neglected. Consider such practical gear arrangement connected to the load, shown below.
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| Fig3 |
T = applied torque θ1, θ2 = angular displacement
T1 , T1 = Torque transmitted to gears J1, J2 = Inertia of gears
N1, N2 = Number of teeth B1, B2 = Friction coefficients.
Torque equation of side 1 is,
Torque equation of side 2 is,
Substituting in equation 2,
Substituting value of T1 in equation 1
and B1e = equivalent friction referred to primary side
1.2 Belt or Chain Drives
Belt and chain drives perform same function as that of gear train. Assuming that there is no slippage between belt and pulleys we can write,
1.3 Leavers
The lever system is shown in the Fig.5 This transmits translational motion and forces, similar to gear trains.
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| Fig5 |
By low of moment,
