Activity 1.1.3 Gears – FT
You do not have to look far to see gears. You might not think of an object such as a computer as having a lot of moving parts, but the CD tray on your computer is likely controlled by gears. A traditional watch is full of gears. The watch has one source of power or input that must move multiple hands continuously and at different speeds. Some watches also keep track of the day of the month. This may be low-tech by today’s standards, but imagine the challenge of choosing just the right gears to keep a watch synchronized. In a watch the gears are used to manipulate rotational speed. Gears are also used in many applications to control torque and ...view middle of the document...
Method 2: The gear ratio can be determined using the diameter of each gear. Assume that the diameter of gear A is 2.5 in. (din) and the diameter of gear B is 5 in. (dout).
Method 3: The gear ratio can be determined by recording and comparing the angular velocity or speed at which each gear is turning. The lower case Greek letter ω is used to represent angular velocity. A common way to measure angular velocity is using revolutions per minute (rpm). Assume that the rpm of the input gear is 446 rpm and the rpm of the output gear is 223 rpm.
Method 4: The gear ratio can be determined by recording the torque at each gear. Divide the torque at the output gear (τout) by the torque at the input gear (τint). A common way to measure torque is to use foot pounds (ft·lb). Assume that the torque force at the driver gear is 4 ft·lb and the force at the driven wheel is 8 ft·lb of torque.
The above equations all solve for the gear ratio of the driver gear to the driven gear. Based upon these formulas, the following is true.
Solving for Speed and Torque
In most applications you will know the speed and torque provided by your driver or input gear. You will mesh another gear to achieve a specific output speed or output torque to accomplish a task. Below are some examples that illustrate this.
Example 1: A motor is driving an axle with a 6-in.-diameter drive gear. The speed of the motor is 20 rpm. A gear must be attached that increases the speed to 100 rpm. What size diameter should the attached gear be?
Example 2: A motor is driving an axle with a 30-tooth drive gear. You know that the maximum output torque of the motor is only 90 ft·lb. A gear must be attached that will increase the torque force to 300 ft·lb in order to lift a heavy object. How many teeth should the attached gear have?
A gear train consists of two or more gears assembled in order to transfer energy from one axis to others. | |
When two gears are meshed together, each will rotate in an opposite direction. If the desired rotation for two gears is the same, an idler gear is introduced. In Figure 3 the two outside gears will move at the same speed and direction and will have the same torque because of the idler gear between them. If they were attached without the idler gear, they would have matching speed and torque, yet would be rotating in opposite directions. | |
Simple Gear Trains
A simple gear train connects two or more gears in a row, each gear having its own axle. | |
Build a Simple Gear Train
In a group build a simple gear train that consists of four meshed gears each with its own axle. At least three gears should have different sizes. Once the gears are arranged, assume that the first gear, gear A, is the driver as seen in Figure 4. Attach a crank to gear A and compare the speeds of gears B, C, and D as you turn gear A.
Complete the following tables based upon the simple gear train that you created.
Number of Teeth per Gear...