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Difficulty: HardDriveshafts and Differentials

During a drivetrain inspection of a rear-wheel-drive vehicle equipped with a standard open differential, the vehicle is raised on a lift with the transmission in Park, holding the driveshaft and differential carrier stationary. If a technician manually rotates the left rear wheel two full revolutions in the forward direction, what will be the resulting motion of the right rear wheel?

  1. A
    It will rotate two full revolutions in the forward direction.
  2. B
    It will rotate forward at a speed multiplied by the final drive axle ratio.
  3. It will rotate two full revolutions in the reverse direction.Answer
  4. D
    It will remain completely stationary while internal clutch packs slip to absorb the input motion.

Answer

The right rear wheel will rotate two full revolutions in the reverse direction.
In a standard open differential, the two axle side gears mesh with spider (pinion) gears mounted inside the carrier case. When the driveshaft is held stationary by the transmission parking pawl, the ring gear and differential carrier cannot turn. Turning one axle shaft forces its side gear to rotate the spider gears on their stationary cross-shaft. These spider gears act as reversing idlers, driving the opposite side gear and wheel at the exact same rotational speed and displacement, but in the opposite (reverse) direction.

Step-by-Step Solution

1
Analyze the state of the differential carrier and ring gear.
The transmission in Park mechanically locks the driveshaft, preventing the pinion gear, ring gear, and differential carrier case from rotating (Ncarrier=0N_{\text{carrier}} = 0).
Establishing carrier movement is essential to determine whether gear action is rotational transfer or internal differentiation.
2
Apply the mechanical kinematic relationship of an open differential bevel gear set.
Carrier rotational speed is the average of the two axle shaft speeds: Ncarrier=Nleft+Nright2N_{\text{carrier}} = \frac{N_{\text{left}} + N_{\text{right}}}{2}. With Ncarrier=0N_{\text{carrier}} = 0, the relationship simplifies to Nright=−NleftN_{\text{right}} = -N_{\text{left}}.
The differential spider gears pivot on their stationary cross-shaft, acting as idler gears between the left and right side gears.
3
Calculate the magnitude and direction of the right wheel's displacement.
Rotating the left wheel +2+2 turns (forward) forces the right wheel to rotate −2-2 turns (reverse).
The 1:1 gear ratio between identical side gears ensures equal displacement in the opposite direction.

Key Concept

Open Differential Planetary Gear Kinematics with Locked Carrier
Estimated Time:1m 30s
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Topics

Driveshafts and Differentials

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