When I was a child, one piece of equipment that was found on every playground was the merry-go-round. It was a simple device consisting of a round platform balanced on a central rotating base. Around the outside of the platform was handles that acted as both the method of propulsion and as a support to keep from flying off the ride due to centripetal force. This simple device combined the questions of: “How much load do I need to apply to make it spin? How fast can I make it go? Can I resist the force to pull me off?” When designing gears, similar questions need to be asked in order to select the appropriate gear system for the application.
Much like the interstate highways, there are recommended maximum speeds for gearing. All gears can operate as fast as the shaft on which they are mounted, as long as they are not engaged with their mating gear. Once the gear becomes part of a meshed pair, there are firm limits on the maximum speed that a gear can operate. For worm gear pairs, the practical speed limit is 1,800 rpm. These gears require a lower speed than others because a concentrated section of the worm is in constant engagement with the worm wheel. Due to this small area being exposed to continuous friction, the heat buildup in the worm will exceed the ability of the lubricant to cool it at speeds above 1,800 rpm. For bevel gears, the practical speed limit is 3,600 rpm. For these gears, the limit is also due to friction and lubrication. When these gears operate at speeds above 3,600 rpm the lubricant cannot form the protective film that is necessary to limit surface wear. If the gears are submerged in an oil bath, the teeth at high speeds will agitate the oil. resulting in the creation of an oil foam. If the gears are subjected to an applied oil mist, the centripetal force will throw the oil away from the mesh. For spur and helical gears, the practical speed limit is 6,000 rpm.
Another limiting factor for gearing is the torque capacity. Torque and speed have a proportionally inverse relationship. As the speed increases, the torque capacity of a gear pair decreases. Therefore, a gear system that needs to handle a large torque should be designed to operate at a lower speed (Figure 1).
Torque is related to the force (load) applied at the pitch line as defined by:
T = F x L
where
T = torque (NM)
F = The applied load at the pitch line (Newtons)
L = 1/2 of the pitch diameter (Meters)
If we dissect this equation, we can see that if the force applied at the pitch line remains constant, we can increase the pitch diameter in order to increase the torque (Figure 2). Conversely, if we increase the applied torque and keep the pitch diameter constant, then the force at the pitch line increases. Understanding these relationships, you can see that if you have an application where you need to increase the output torque capacity of a gear drive, you can increase the number of teeth of the output gear. However, this will alter the output speed as the ratio of the gear teeth will also change. For example, if you have an application where the drive gear is a 20-tooth helical gear and the driven gear is a 30-tooth helical gear, the speed ratio will be 30/20 or 3:2. By increasing the driven gear to 45 teeth, you could increase the output torque by 50 percent but the speed of the output would drop to 4:2.
For a rack and pinion system, these factors are very important to consider. In this case, the rack is stationary and therefore the maximum allowable force is determined by the shear strength at the tooth root. If you choose a pinion that has a small pitch diameter, then the applied torque will impart a large force on the rack. However, if you increase the pitch diameter of the pinion to lower the imparted force on the rack, there will be a larger offset from the rack pitch line to the centerline of the motor shaft.
A final consideration regarding speed, load, and torque in regard to your gear application is the desired lifespan of the gears. For most industrial applications, it is assumed that the gears will require a life of 26,000 hours. This is based on a lifespan of 10 hours per day, five days per week, 52 weeks per year, for 10 years. If you are operating a race car that has an engine or transmission lifespan of only 100 hours, then the torque, speed, and force calculations will be significantly different. As noted above, the practical speed limit for helical gears in an industrial automation application is 6,000 rpm; however, in an IndyCar, they are run up to 12,000 rpm.
