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A transmission is as effective as the shortest gear in it. What does it mean?
Table of Content
Coming to the Part 2 of Gears and Transmission, here we will take one step ahead into the world of gears. A gear, in simple terms, is a wheel with teeth profiles along it's circumference.
Today we will take a look into the basic parts of the gear and understand the anatomy of a gear.
There are a few different terms that you'll need to know if you're just getting started with gears, as listed below. In order for gears to mesh, the diametral pitch and the pressure angle need to be the same.
Axis: The axis of revolution of the gear, where the shaft passes through
Teeth: The jagged faces projecting outward from the circumference of the gear, used to transmit rotation to other gears. The number of teeth on a gear must be an integer. Gears will only transmit rotation if their teeth mesh and have the same profile.
Pitch Circle: The circle that defines the "size" of the gear. The pitch circles of two meshing gears need to be tangent for them to mesh. If the two gears were instead two discs that drove by friction, the perimeter of those discs would be the pitch circle.
Pitch Diameter: The pitch diameter refers to the working diameter of the gear, a.k.a., the diameter of the pitch circle. You can use the pitch diameter to calculate how far away two gears should be: the sum of the two pitch diameters divided by 2 is equal to the distance between the two axes.
Diametral Pitch: The ratio of the number of teeth to the pitch diameter. Two gears must have the same diametral pitch to mesh.
Circular Pitch: The distance from a point on one tooth to the same point on the adjacent tooth, measured along the pitch circle. (so that the length is the length of the arc rather than a line).
Module: The module of a gear is simply the circular pitch divided by pi. This value is much easier to handle than the circular pitch, because it is a rational number.
Pressure Angle: The pressure angle of a gear is the angle between the line defining the radius of the pitch circle to the point where the pitch circle intersects a tooth, and the tangent line to that tooth at that point. Standard pressure angles are 14.5, 20, and 25 degrees. The pressure angle affects how the gears contact each other, and thus how the force is distributed along the tooth. Two gears must have the same pressure angle to mesh.
Now that we know the basic anatomy of a gear, let's look into the transmission capabilities of a gear.
Gear Ratio
Gears can be used to reduce or enhance the speed or torque of a driving shaft, as previously stated. To drive an output shaft at a specified speed, you must employ a gear system with a specific gear ratio.
The gear ratio of a system is the ratio of the input shaft's rotational speed to the output shaft's rotational speed. In a two-gear system, there are several ways to compute this. The first method is to count the number of teeth on each gear (N). The equation for calculating the gear ratio (R) is as follows:
R = N2/N1
The number of teeth on the gear connected to the output shaft is N2, while the number of teeth on the input shaft is N1. In the first figure, the left gear has 16 teeth, whereas the right gear has 32 teeth. The ratio is 32:16 if the left gear is attached to the input shaft, which can be simplified to 2:1. This indicates that the right gear rotates once for every two revolutions of the left gear.
The gear ratio can also be computed using the pitch diameter (or even the radius) using the same equation:
R = D2/D1
Where D2 is the output gear's pitch diameter and D1 is the input gear's pitch diameter.
The gear ratio can also be used to calculate the system's output torque. Torque is described as an object's inclination to rotate along its axis; in other words, the turning power of a shaft. Larger objects can be turned by a shaft with more torque. The gear ratio R is also equal to the ratio of the output shaft torque to the input shaft torque. Although the 32 tooth gear spins slower than the input shaft in the example above, it produces double the turning power.
The total ratio of a larger system of gears with many gears and shafts is still the ratio of the input and output shaft speeds; there are just more shafts in between. It is simpler to get the total ratio by first determining the gear ratio of each pair. Then, starting with the set driving the output shaft and working backward, multiply the first number in the ratio (the input shaft's speed) by the values corresponding to the ratio of the next gear set, and use the result as your new input speed for a net ratio. This may be a bit confusing, so an example is provided below.
Assume you have a gear train with three sets of gears: one set from a motor with a 2:1 ratio, another set with a 3:2 ratio arising from the output shaft of the first set, and the third set driving the system's output with another 2:1 ratio. Start with the last gear ratio, 2:1, to compute the total system's gear ratio. The ratio of the input shaft of the second set of gears to the overall system output shaft is 3:1 since the smaller gear on the 3:2 set and the larger gear on the 2:1 set are currently "equal" due to the ratios. We do that again, multiplying the ratio of the first gear set by 3 (to get 6:3), and combining it with our net ratio (currently 3:1), to get the overall ratio of the system, 6:1.
Summary
The number of teeth on a gear must be an integer. Gears will only transmit rotation if their teeth mesh and have the same profile.
For two gears to mesh, the gears must have same diametral pitch.
The gear ratio of a system is the ratio of the input shaft's rotational speed to the output shaft's rotational speed.
Understanding gear ratio is important when building any transmission system. The amount of output torque can be manipulated using multiple gear arrangements. Keep following Mech n Flow for more interesting stuff.
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