Gear Ratios and Speed Background Material

Transcription

1 VEX Robotics Lab 3 How Do Gear Ratios Affect and Torque? Introduction In this investigation, students will learn the relationships between gear ratio, axle speed, and torque. Students will use the Vex Robotics System in a laboratory setting and conduct scientific inquiry-based experiments to determine the effect of gear ratio on an axle s speed and strength. Students will use the Vex starter kit to construct a gearbox that will allow them to test these mechanical principles. Students will gain an understanding of math and science concepts related to gears, angular speed, and torque. Gear Ratios and Background Material In simple systems, the gear ratio is the ratio of the number of teeth on a driven gear to the number of teeth on a driving gear. The driving gear is the origin of the rotation, and is usually powered by a motor. The driven gear is influenced by the driving gear, and is usually connected to a wheel. First, let s explore what happens when the driving gear is larger than the driven gear. Imagine that a gear attached to a motor (a driving gear) has 50 teeth. Imagine that this gear is turning a second gear (a driven gear) that has 10 teeth, and that the driven gear is on a wheel s axle. Since the calculation for gear ratio is teeth on driven gear: teeth on driving gear, the gear ratio in this case is 1:5. Now, each full rotation of the driving gear will cause 5 complete rotations of the driven gear. As a result, a wheel placed on the driven axle will rotate 5 times faster than a wheel placed on the motor s axle. So, the simple addition of a gear allows an engineer to immediately change the maximum speed of a device! But note that the gear ratio also influences the axle s torque. The rotational strength of the driven axle is now 5 times smaller than the rotational strength of the driving axle. Also note that the effect that gear ratio has on speed and torque is linear- a gear ratio of 5:1 changes both the speed and torque by a factor of 5. If the driving axle is smaller than the driven axle, the gear ratio will have the opposite effect on the device. Now, a full rotation of the driving gear will not cause a full rotation of the driven gear, which means that the angular speed of the driven axle will decrease. However, the torque of that driven axle will now increase. As before, the relationship between gear ratio and these two factors is linear. Gear Ratios and Torque Background Material

2 Torque is a measure of the rotational influence that a force has on an object. It is measured by multiplying the force by its distance from the object s center of rotation. This may sound confusing at first, but a common example will add clarity to the concept. Imagine trying to close a heavy door. If you concentrate your effort near the door s hinges, you will find that it is quite difficult. But if you instead focus your strength near the other edge of the door, you will see that a gentler force can get the job done. Feel free to try this out! When you are pushing near the hinges, the distance from the fulcrum, which is called the lever arm, is very short. When you are pushing near the edge of the door, the lever arm is much longer. Since the torque, or the influence on the door s rotation, is equal to the product of the force and the lever arm, a weaker force can create the same rotation just by being distant from the center of rotation. In motors, torque is a measure of rotational strength. Imagine a plow attempting to push a heavy object. The wheels on the plow must have great rotational strength, or torque, to power the vehicle forward. Similarly, a motor lifting a heavy object must have great rotational strength. Torque Background Material

3 Materials Constructed Gear Box and ing Crate Please note: I used a crate and of pennies because I thought they're easily available. Feel free to substitute whatever lifting apparatus and/or weights you prefer. An especially good solution is a strong spring scale (20-60 lb. maximum). By anchoring the spring scale, then tying it to the string, you do not need to use a crate or weights. Rolls of pennies, Stopwatch String Radio Transmitter Link for gearbox construction: Link for crate construction: Procedure 1. Follow the instructions to build the lifting crate and the first stage of the gearbox (you may already have this completed from lab 2) as given in the links above. 2. If you have previously downloaded programs to your microcontroller, take this time to download the default code. 3. Record the time it takes for the wheel to make ten full revolutions. Calculate the rotational speed in rev/s. Convert the value to rev/min (rpm) 4. Place 1 roll of pennies in the lifting crate and tie it to the spool on the motor s axle. 5. Test the system to see if the gear box is capable of lifting the load. 6. Continue to add of pennies to the crate until the gearbox can no longer raise the load. Record the maximum weight that the gearbox could lift.

4 7. Modify the gearbox so the wheel is on the second axle as shown below. Determine the gear ratio between driven and driving axles. 8. Use the gear ratio and the data from the first axle to calculate the maximum weight that the axle could lift if the spool were placed on it. 9. Tie the lifting crate to the spool and measure the maximum weight that the gearbox can lift using this axle. How does this measured value compare to your theoretical value? 10. Modify the gearbox so the spooling wheel is on the third axle. 11. Predict and then calculate the rpm for this axle. Predict the maximum weight that this axle can lift. 12. If an appropriate set of weights is available, test the theoretical value you just calculated. 13. Repeat the steps for the final axle. Predict and measure rpm. Predict maximum weight. If possible, measure maximum weight Analysis Graph your results: RPM vs. Gear Ratio ing Capability vs. Gear Ratio Find the best-fit line Find the slope of the best-fit line

5 Data Gear Ratio Trial 1 Trial 2 DATA COLLECTION Trial 3 (1:X) (rpm) rev/sec rev/sec rev/sec rev/sec (Eng weight) (metric weight) Trial 1 Trial 2 Trial 3 SAMPLE GRAPHS Axle vs. Gear Ratio Axle (rpm) Gear Ratio (1:X)

6 ing Capability vs. Gear Ratio ing Capability ( of pennies) Gear Ratio (1:X)