TORQUE RATIO
To understand the torque ratio of gears, it is necessary to understand the principle of leverage as it applies to gears. If you recall, we discussed applying torque to a bolt earlier in the lesson. To discuss torque ratio between gears, we must think of the force from a shaft to a gear, from that gear to another gear, and from the second gear to the shaft it is mounted on. To do this, we will refer to the items as an input shaft and gear and an output gear and shaft. The input is the driving member, and the output is the driven member.
Let's first look at the input member. The shaft and gear are bringing the turning force into the gear train. For our purpose, we will say that an engine or motor is driving the input shaft and is applying 25 pound-feet of torque on the shaft.
To begin with, we can think of each tooth on a gear as being the same as the lever or wrench we discussed earlier. Remember, when two gears are in mesh, only one or parts of two teeth are touching each other at any one time. Therefore, we must remember that the entire load between two gears is on these teeth.
For our discussion here, we will think of the driving gear as having just the one tooth that is going to do the work. Further, to help understand it a little better, we will say that the gear is 2 feet in diameter so the one tooth will be exactly 12 inches long. We said that there was a torque of 25 pound-feet applied to the shaft.
This means that if the torque was in the direction of rotation, it could lift 25 pounds out on the 12-inch mark or at the end of the tooth. This is just the reverse of what we explained with the wrench. Here, the shaft is turning the gear; with the wrench, we wanted to turn the shaft, except we used a bolt instead for our example.
By remembering the laws of leverage, we know that a smaller gear will deliver more torque than a larger gear. At the 6-inch mark (the size of a 12-inch gear instead of a 24-inch gear), the tooth could lift 50 pounds because of a greater leverage. You can prove this yourself by holding a stick straight out at arm's length. Have someone hang a small weight on the very end of the stick. You will notice how hard it is to hold the weight. Now have the person take the weight off the end of the stick and hang twice as much weight on the center. You will see that it requires the same effort to hold twice the weight in the center as it does to hold the single weight on the end.
From this, we can see that a small driving gear in comparison to the driven gear can deliver more torque (drive a heavier load) than a big gear. After you have gained experience, you will notice that the driving gear in almost all gear trains is smaller than the driven gear. An exception to this is if you want increased speed instead of torque, then the input or driving gear would be bigger than the driven gear.
Now we will mesh this one tooth of the driving gear with one tooth of a driven gear. Both gears are the same size.
When thinking of the driven member of a gear train, we think of it exactly the same as a bolt with a wrench on it. The longer the wrench is, the easier it is to turn the bolt.
We said that the input gear could apply a force of 25 pounds on the end. This, then, is the amount of force it will apply to the tooth of the driven gear. Because the tooth of the gear is 1 foot long, a torque of 25 pound-feet will be applied against the shaft on which the driven gear is mounted.
Again, remembering our discussion of the wrench, we know that more effort is required to turn the bolt with a short wrench than with a long wrench. Therefore, if we applied the input force of 25 pounds against an output tooth 24 inches long, we would get twice as much torque on the shaft as on a tooth 12 inches long.
Here again, we can compare the output gear to the knob you use to wind your watch. As the knob is made bigger, it is easier to wind the watch. The same principle applies with the driven gear in a gear train. When the driven gear is bigger than the driving gear, you can increase torque.
How does all of this apply to you as a wheeled vehicle mechanic? Well, let's look at a few things about a wheeled vehicle that depend on gears.
To begin with, the vehicle engine can only produce so much power. When it is running fast, it produces more power than when it is idling. The power developed by the engine is sent to the vehicle in the form of twisting motion or torque at the flywheel at the end of the crankshaft.
When the vehicle is started from a standstill, a great deal of torque is required to get it in motion. In addition, the engine is not running at high speed at this time. Therefore, torque from the engine is applied to a small driving gear which, in turn, drives a large driven gear. This increases torque and helps the engine get the vehicle started.
After a vehicle is in motion, less torque is required to keep it in motion. When this occurs, the driving gear and driven gear can be nearer to the same size. In other words, we want the gear train to develop speed more than torque.
When the vehicle comes to a hill, the ratio will have to be changed again. Now the driving gear will have to be smaller than the driven gear to increase the torque. In doing so, we are giving up speed to increase torque.
To sum up torque ratio, we can compare it with gear ratio.
If the driving gear has 12 teeth and is driving a large driven gear with 24 teeth, we have a gear ratio of 2:1. In other words, the driving gear has to rotate two times to make the driven gear rotate once. In this gear train, we double the torque and cut the speed in half.
If the driving gear is the same size as the driven gear, the gear ratio is 1:1. The input and output torque and speed are the same.
If the input gear has 24 teeth and the output gear has 12 teeth, the gear ratio is 0.5:1. In this gear train, we are reducing torque and increasing speed. |