User:Dream mind/Gears

Gears are toothed wheels which are used to transmit motion or power to other gears or toothed parts by meshing without any slip.When two gears are meshed together the smaller gear is called a pinion and the bigger one is called a gear irrespective of which is driving the other.

When pinion is the driver, it results in step down drive in which the output speed decreases and the torque increases. On the other hand, when the gear is the driver, it results in step up drive in which the output speed increases and the torque decreases

History
Types

Gear tooth system Its very necessary to study gear tooth system when designing a gear.A gear tooth system is defined by its unique tooth proportions,pressure angles etc.

Law of gearing
Before we take a look at the actual gearing systems let us see what is the fundamental law that governs the gearing system.The law of gearing states that the angular velocity ratio of all gears of a meshed gear system must remain constant i.e if $$\omega\ _1$$ and $$\omega\ _2$$ are the angular velocities and $$D_1$$ and $$D_2$$ are the diameters of two gears meshed together then $${\omega _1\over \omega _2}={D_1\over D_2}$$

Gear profiles
Gear profiles should satisfy the law of gearing.

The profiles best suited for this law are:


 * 1) Involute
 * 2) Cyloidal
 * 3) Circular arc or Novikov

Gear Nomenclature
Various nomenclatures related to a gear are sown in the figure


 * Let us consider a spur gear and define the following terms-
 * Pitch circle:It is defined as the circle having radius as the mean of the maximum radius(to the tip of the gear teeth) to the radius of the base of a gear teeth.
 * Addendum:It is the distance between the top of a gear teeth and the pitch circle.
 * Dedendum:It is defined as the distance between the pitch circle and the root of a teeth.
 * Flank:It is the face of a gear teeth which comes in contact with the teeth of another gear.So,a flank is an important part of a gear.
 * Fillet:Fillets in the root regiion are of less important since they don't actually come in contact with other gear tooth.
 * Circular pitch:Circular pitch is the sum of width of a teeth and a space betweent the tooth of a gear.Circular pitch is an important parameter as it indicates the size of the tooth of a gear.If $$P_c$$is the circular pitch,Z is the number of teeth on a gear and D is the pitch diameter then,$$P_c={\pi D\over Z}$$

So the size of a teeth is given by $$m={D\over Z}$$ where m is the unit of size called module.And hence for two meshed gears we must have the same size of tooth,then we can have the following relations, $$m={D_1\over Z_1}={D_2\over Z_2}={P_c\over \pi}$$---(1)

In case of a rack the diameter and the number of tooth tend to infinity but still the module remain finite.
 * Cuircular thickness or tooth thickness: It is the thickness of the tooth measured on the pitch circle.It should be noted that this thickness is measured as the arc along the pitch circle and should not be taken as the displacement
 * Diametrical Pitch: It is defined as the number of tooth per inch of the diameter of the pitch circle of a gear.It is incicated by the letter P.Therefore, $$P={Z\over D}$$---(2)

So using equation (1) and (2), we can have $$P_c P= \pi$$