# Bending stress in gears

I have a double step up gearbox with two equal ratios gear pairs. Their the same modules and both gears have the same form factor as well as the pinions. With a input speed of 4000 and a output of 14000rpm. Pinion 1 is spinning at roughly 6500rpm with a velocity of 15m/s. It has a bending stress of 400mpa. Whereas pinion 2 is turning at 14000rpm and a velocity of 28m/s. It has a bending stress of 350mpa. Pinion 1 has the highest being stress of the 4 gears, why is this the case when pinion 2 is turning quicker and has a higher velocity of mesh? All gears have the same width.

Transmitted load is higher in gear 1 to pinion 1 than gear 2 to pinion 2 which is output.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Jan 26, 2023 at 9:39

Because energy/power is the invariant which is transmitted through the gearbox (i.e. the power remains the same, while rpm , torque and forces change) , it might help if you think about it in terms of Power/Energy.

The basic concept is that Power going through a shaft is given as

$$P = M \cdot \omega = F\cdot u$$

where:

• M is the torque through the shaft
• $$\omega$$ is the angular velocity $$(=\frac{2\pi \; n}{60})$$
• F is the force at the point of contact of the tooth
• u is the linear velocity of the meshing gear.

The second form is more applicable, because as you can see because $$P = constant$$, this results in $$F=\frac{P}{u}$$. Which means that as the velocity increases, the force decreases.

However the force is responsible for the bending stress. So for higher velocities you should expect smaller bending stress (all things being equal).

• Great that makes sense, thanks a lot that really helped me, I noticed the velocitys but didnt understand enough to think about the force or how the power was the same through each gear. Would it be possible to assume there is a loss of torque through the gearbox as the speed is increased? So high torque in, lower torque out.
– Rhys
Jan 26, 2023 at 20:46
• Yes there is a trade-off between torque and angular velocity
– NMech
Jan 26, 2023 at 22:21