A body under net force is under tranlational motion and a body under net torque is under rotational motion; but they both have something in common and that is both have kinetic energy. This energy can be exploited to do some useful work. The mechanical energy of an object can be used to move another object. Some examples can be a rotating shaft of a motor, which can be used to move a vehicle for public transport. But for this to happen the force, the torque, the mehanical energy or the mechanical power needs to be transmitted from one moving or rotating body to another body.
How mechanical force or torque or energy or power is transmitted from one body to another body? There are many ways, many mechanisms like pulley, chain, gears etc. So what is a Gear? Gear is a device, a mechanism through which mechanical force, torque, energy or power is transmitted from one object to another. To draw an analogy gear has same role for mechanical energy that electrical wire has for electrical energy. No not just that role of gear is much more than that. Gears act to increase or decrease the velocity from one moving element to another moving element. This way they has analogy with transformers in electrical domain.
A gear is a circular object with a large number of teeth on it and two gears physically engage with each other to transmit mechanical power. This is illustrated in the following picture (http://www. osha. gov/SLTC/etools/machineguarding/animations/gears. html).
Figure 1: Two gears engaged with each other In the subsequent sections we will briefly talk about different terminology about gears and about different types of gears: In the most coomon configuration a gear is engaged with another gear. However, it can engage with any other device which has compatible teath.
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One interesting arrangement is a linear object with teath, which is also termed as Rack. If a gear is engaged with a rack then forms what is known a Rack and a Pinion. It should however, be noted that a rack can be seen as a segment of a gear with infinite radius. Now let us talk about two gears of unequal size engages with each other as in figure 1, above. This combination produces “mechanical advantage” i. e. angular spee and torque of the second gear is different from that of the first gear. Let us explore this important concept about gears. Mchanical advantage
The physical interlocking of the teeth in a pair of gears ensures that circumference of these gears move at the same linear speed. As the angualr speed is circumferential speed divided by its radius; the bigger gear moves at smaller angular speed than the smaller gear engaged with it. Let us look at it from the number of teath consideration. Because the teeth of two engaging gears are locked one to one, by the time all the teeth of the smaller gear have passed the point of contact only a fraction of the teath of the bigger gear has done that. In other words he smaller gear rotates faster than the bigger gear.
This results in the following formula (Angular Speed A) x (Number of teeth A) = (Angular Speed B) x (Number of teeth B) or, (Angular Speed A)/ (Angular Speed B) = (Number of Teath B) / (Number of Teath B) This ratio is nothing but Gear Ratio. Similarly, one can dertermine torque ratio. The bigger gear experiences larger torque and vice versa. The torque ratio is equal to the ratio of the radii of the two gears and is inverse of the velocity ratio. Larger torque implies smaller velocity and vice versa. This fact is in confirmity with the law of conservation of energy.
In this discussion we have ignored the friction, which dissipates the energy. Velocity ratio being a geometrical term remain unaffected by friction, however there is loss in torque ratio due to friction and thus actual torque ratio is always less than inverse of the velocity ratio. Because, gear is not perfectly circular due to presence of teath on the circumference, there is something called ‘pitch radius’, which is some sort of average between the radius at the root of the teath and at the outer of the teath and is used for these calculations for velocity ratio.
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Torque ratio etc. The pitch radius depends on the point of contact of the two gears. Also this point of contact keeps changing over time. Due to this the velocity ratio and torque ratio is not constant and instead keeps changing over the period of engagement. These ratios (velocity and torque ratios) that we have discussed so far are gross values and changes from point to point on the gear teath. However, the shape of the tooth can be made such that the velocity ratio remains constant with time on short and long term basis.
This is done in good quality gears, because fluctuations in the velocity ratio causes undue vibration, put extra stress on the teeth, which can in turn break as the laod and the speed are many times very high. Keeping the velocity ratio constant is also desired from the precision considerations in devices like delicate instruments, eatches, clocks etc. Now let us compare gears with other mechanisms of mechanical power transmission. Gears and other Means of Power Transmission: There are other mechanisms for mechanical power transmission such as chains, belts, pulleys etc.
Each of these has its own advantages and limitations. However, none is as diverse as gears. The problem of slippage is often encountered with these devices and the gears have edge over othe mechanisms. Similarly gears have constant velocity ratio, which is not the case with other devices. However, gears are generally more costly, but this higher cost is initial investment only and is paid back many more times due to very high life of gears than other devices. In the subsequent sections we will talk about different types of gears. Spur gear
These are the most simple common gear. This is nothing but a disk with teath projecting radially and the leading edges of the teeth are aligned parallel to the axis of rotation. These gears are used for power transmission between parallel shafts. Such a gear is shown in figur 1, above. Helical gear This is a refinement over spur gear. In this gear the leading edge of the teeth is set at an agle to the axis of rotation and not not parallel to the axis of rotation as in case of spur gear. Because the gear is curved, this makes the tooth to be a segment of a helix.
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Such a tooth engages more gradually than do spur gear teeth. Therefore, this gear runs smoothly and produces much lesser noise than the spur gear. Besides, helical gear can tranmit power between non-parallel shafts as well. A pair of helical gears can be engage in two ways – the shafts can be oriented at at either the sum or the difference of the helix angles of the gears. These configurations of the shafts are known as parallel or crossed, respectively. The parallel configuration is the mechanically more sound than the crossed configuration.
In this configuration, the helices of a pair of engaging teeth meet at a common tangent, and therefore, the contact between the tooth surfaces will, is a curve, which extends some distance across their face widths. On the other hand, the helices do not meet tangentially in the crossed configuration, and between tooth surfaces only point contact is achieved. Because of this (the small area of contact), crossed helical gears are and can be used with light loads only. Generally, helical gears come in pairs.
The helix angle of one is the negative of the helix angle of the other in this pair and this pair is termed as having a right handed helix and a left handed helix of equal angles. When engaged in the ‘parallel’ mode, these equal and opposite angles add to zero i. e. the angle between shafts is zero or the the shafts are parallel. When engaged in the ‘crossed’ configuration, the angle between shafts is twice the helix angle of individual gears. However, it should be borne in mind that parallel configuration of gears and paralles shafts are two different things i. e. parallel configuration of axes may not always lead to parallel shafts.
The helical gear is shown in figure 2, below (http://en. wikipedia. org/wiki/Image:Helical_Gears. jpg).
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Figure 2: Helical gears in parallel and crossed configurations Double Helical Gear This gear is known as herringbone gear as well. This was invented to overcome the problem of axial thrust caused by helical gear. Here teath are of V shape. In this, each gear can be visualized as two standard and mirror image, helical gears stacked. This configuration cancels out the thrust because each half of the gear thrusts in the opposite direction. These can be interchanged with spur gears without changing the bearings.
