Considered one of the fastest land animals, the cheetah can achieve speeds of 100+ kilometers per hour (kph). It can accelerate from zero to 95 kph within three seconds. However, it can only sustain this speed for about 25 to 30 seconds, which results in a distance traveled of 300 to 400 meters before it needs to rest. A caribou can travel 80 kilometers per day at a steady pace of 16 kph with the ability to run at 60 kph for short distances. These two animals reflect similar needs for machinery that uses gearing.
Consider the gearing in a race car. The gears need to operate at high speeds, under severe conditions, for short periods of time with a relatively short lifespan. The engine might be operating at a speed of 9,000 rpm, for a distance of 500 miles at a time, for approximately 40 races in one season. Now consider a gasoline-powered vehicle designed for daily use. In this case, the engine will operate at a speed varying between 1,200 and 4,000 rpm, for a distance of 10 to 50 miles, but the lifetime number of trips will be more than 30,000. Based on these criteria, the gear design in each engine will be vastly different.
When designing a gear system, one of the critical questions is, “At what speed will the gears operate?”
The answer to this question has a significant impact on the maximum allowable load and the possible length of life. Since speed and torque have a proportional inverse relationship, the faster a gear spins, the less torque it can carry. In addition to the speed, the desired life of the gear will impact the torque capacity. If a gear is to be used for a short burst of time, then the speed and load can be valued higher than if the gear system is to be used continuously for prolonged periods of time.
The standard design life for gearing and similar mechanical drive components is 26,000 hours. This resolves into approximately three years of continuous operation, 24 hours per day, every day of the week. It resolves into approximately nine years of operations if used eight hours per day, every day of the week; and it resolves into 12.5 years of operations if used eight hours per day, five days per week.
When determining the maximum load on a gear, you need to review two separate calculations. The first is the maximum allowable load due to bending failure, and the second is the maximum allowable load due to surface durability. The maximum allowable load due to bending failure is the maximum force which, when applied to the gear, will cause immediate structural failure of the gear, typically occurring at the tooth root. The maximum allowable load due to surface durability is the maximum force which, when applied to the gear continuously, will cause significant wear which will reduce the lifespan of the gear, typically by wearing away the tooth surface.
To determine if the applied force is lower than the maximum allowable bending force, you must first calculate the actual tangential force, Ft. This calculation is as follows:
Where:
Ft (kgf) is the transmitted tangential force at the pitch circle
P (kW) is the power.
T (kgf • m) is the torque.
v (m/s) is the tangential speed of working pitch circle.
Where:
db (mm) is the working pitch diameter.
n (rpm) is the rotational speed.
The JGMA 401-01:1974 formula for determining the maximum allowable bending force in spur and helical gearing is:
Where:
Ftlim (kgf) is the maximum allowable load.
σFlim (kgf/mm2) is the maximum allowable bending stress at the tooth root
mn is the normal module.
b (mm) is the effective face width.
YF is the tooth profile factor.
Yε is the load sharing factor .
Yβ is the helix angle factor.
KL is the life factor.
KFX is the size factor of root stress.
KV is the dynamic load factor.
KO is the overload factor .
SF is the safety factor for bending failure.
These factors are available from tables produced by JGMA and republished by KHK USA.
For the maximum allowable force due to surface durability the JGMA 402-01:1976 formula is:
Where:
Ftlim (kgf) is the maximum allowable load.
σHlim (kgf/mm2) the maximum allowable Hertz stress.
d01 (mm) is the pitch diameter.
bH (mm) is the effective face width.
ZH is the zone factor.
ZM is the material factor .
Zε is the contact ratio factor.
Zβ is the helix angle factor .
KHL is the life factor.
ZL is the lubricant factor.
ZR is the surface roughness factor.
ZV is the lubrication speed factor.
ZW is the hardness ratio factor.
KHX is the size factor.
KHβ is the longitudinal load distribution factor .
KV is the dynamic load factor.
KO is the overload factor .
SH is the safety factor for pitting.
These factors are available from tables produced by JGMA and republished by KHK USA.
In order for a gear to be properly sized for the applied load, the desired speed and design life, the transmitted tangential force at the pitch circle Ft must be less than the values for Ftlim for both the bending and the surface durability conditions.ß
Conclusion
In summary, gears can operate at any speed if their design accounts for the applied loading and an assumed design life. If the design life of a gear system is going to be more than a few minutes, then the load and operating speeds need to be carefully assessed using industry formulas in order to ensure a useful design. Otherwise, catastrophic, or premature, failure should be expected.
