Someone once asked me if I was trying to reinvent the wheel. I don’t know where that phrase was coined, as the concept of using a wheel to redirect motion has been in existence for thousands of years. Beyond adding wheels to a cart, the design of a rope and a pulley is one of the early wheel applications. Once the idea of adding pegs to the wheel was contemplated, the result was the first gear design. This was further refined into the gear tooth forms that we know today.
As valuable as gearing is to the mechanical world, this topic is usually covered as one single lecture of an Introduction to Machine Design course during just one semester of an engineering student’s four-year education. As such, the amount of knowledge and understanding of gearing by both new engineers and those in industry for many years remains limited. This leads to many questions about the application and design of gears. Some questions are misconceptions and others just leave you shaking your head.
Torque is a simple engineering concept. It is the product of a force and the distance from the centroid. As such, the distance at which the force is applied has more impact than the force itself. For example, if a 100-pound force is applied at one foot, the result is 100-foot pounds of torque. However, if the same 100-pound force is applied at two feet, then the result is 200-foot pounds. It is typically easier to move the force to a further distance than it is to increase the force at the same distance.
As application engineers, we are frequently asked if a particular gear can handle a specific speed. The answer to this question typically starts with, “it depends.” “Can this gear operate at 20,000 rpm?” If the question is, can this gear spin at 20,000 rpm, then the answer is yes. The gear will spin at the same speed as the motor to which it is attached. However, if the question is, “Can this gear handle the torque that I need to transmit at this speed?”, then the answer is probably no. Torque and speed are inversely proportional. As the speed increases, the torque transmitted decreases. This means that either the gear will need to increase dimensionally in order to handle the same torque at a higher speed or the material will need to be changed in order to handle the higher forces needed to produce the torque. Although the gear designer may be able to develop a gear that fits the design window and can transmit the desired torque at a specific speed, there are other criteria that need to be considered. For example, are the bearings rated for these speeds and loads, what type of lubrication is suitable for these speeds, do I have proper shaft alignment for these speeds?
Ordinarily torque is validated in either a static or a dynamic condition. For gearing, the maximum allowable static torque is the value at which a gear tooth will shear if the applied force is exceeded. This value is independent of speed, duty cycle, or desired life of the gear. The maximum allowable dynamic torque is the value at which a given force applied for a specific duty cycle will permit the gear to operate for a specific life span without degradation of the tooth shape. These independent values will determine the mode of failure for the gear dependent on the torque applied. If the static torque is exceeded, then the gear will fail by fracture of the tooth. If the dynamic torque is exceeded, then the gear will fail due to surface wear. It is common for gears with small numbers of teeth to have a maximum static torque that is significantly higher than the maximum dynamic torque. Conversely, gears with more than 50 teeth typically have a higher maximum dynamic torque. When heat treating a gear, you typically increase the maximum dynamic torque but there is a slight decrease in the maximum static torque.
Another consideration for torque is the bore of the gear. When the bore is too small, typically less than 10 percent of the outer diameter, the torque transmitted through the shaft will cause the shaft to fail. Conversely, if the bore is too large, the torque can cause failure to the gear. When a bore has a keyway, it is possible to not have sufficient material remaining between the bore diameter and the hub outer diameter or the root diameter. It is recommended that minimum distance between the corner of the keyway and the hub diameter is equal to the tooth height of the gear. For example, if the gear is a module 2, then the minimum wall thickness between the hub outer diameter and the inner bore diameter is 4.5 millimeters. It is recommended that the minimum distance between the corner of the keyway and the root diameter is twice the tooth height. If the gear is a module 1.5, then this distance should exceed 6.75 millimeters.
There are many considerations that a gear designer must review while developing the best gear system for their application but, ultimately, manufacturability will be the final and most important one. Just because you can draw a gear design in CAD does not mean that it can handle the torque that your system requires.
