Question

Planetary gear sets are convenient spatially compact devices that can provide gear reduction to truck wheels. Consider using the planetary gear set from a Toyota Prius EVT for gear reduction to a truck wheel. This planetary gear set has 30 teeth on the sun gear, 78 teeth on the ring gear, and 23 teeth on the planet gears. Assume the ring is locked to the vehicle frame so it cannot rotate. If the drive shaft delivers 10 kW of rotational power at 1000 rpm to the sun, what is the speed rotational speed of the wheel if it is directed connected to the planetary carrier (yoke)? What torque is applied to the 9. wheel?

Answer 1

The carrier connected to planetary gear set of the Toyota Prius EVT would rotate at approximately 277.78 RPM, exerting a torque of about 345.24 N·m on the truck wheel, given the sun gear rotates at 1000 RPM and the ring gear is locked.

Step-by-step explanation:

To calculate the rotational speed of the truck wheel when the sun gear is input with 1000 RPM with the ring locked, we can use the formula for the planetary gear ratio:

With the ring gear locked, the gear ratio (R) is given by:

R = 1 + (Teeth on Ring Gear / Teeth on Sun Gear)

Substituting the given values:

R = 1 + (78 / 30) = 3.6

Therefore, the carrier's rotational speed will be:

Carrier speed = Sun speed / R

Carrier speed = 1000 RPM / 3.6 ≈ 277.78 RPM

To calculate the torque applied to the wheel, we use the power equation:

Torque = Power / (Angular speed in radians per second)

Power = 10 kW = 10,000 Watts

Angular speed = 277.78 RPM * (2π / 60 s)

Torque ≈ 10,000 / (277.78 * (2π / 60)) ≈ 345.24 N·m

Hence, the carrier will have a rotational speed of approximately 277.78 RPM and exert a torque of about 345.24 N·m on the wheel.