Diff'rent strokes
Racecar Engineering|December 2021
Racecar looks at the different types of mechanical differential, their benefits and limitations
JAHEE CAMPBELL-BRENNAN

Whatever the axle configuration, or number of axles, between any driven wheels of an automotive powertrain (with a caveat for some EVs and hybrids) you will find a differential gear set.

The technology was conceived as a solution to two problems of the early, combustion-engined automobile associated with transmission of power from the engine to the road and manoeuvrability.

As a combustion engine has one rotational output and the requirement to power two driven wheels, the differential firstly serves as a mechanism of splitting the rotation of the crankshaft to drive the left and right wheels of an axle. The second, and more interesting, function it serves us as motorsport engineers is to provide a method of introducing a speed differential between opposing wheels.

To understand the requirement for this speed differential, we need to look to the foundations of vehicle dynamics.

As a vehicle travels around a corner at a given cornering speed, the inside and outside wheels are logically travelling on different radii due to their distances from the vehicle's centre of rotation. The inside wheel is closer to the centre of rotation than the outside wheel and therefore must have a relatively lower forward velocity to maintain a free rolling condition, without slip.

In the early days of automobiles featuring rudimentary solid axle configurations, the physics that enable these free rolling conditions are blocked by the fact the wheels are mechanically coupled to each other. This mismatch of speeds stimulates the inside and outside tyres to generate longitudinal forces in opposition of the yawing moment requested by the driver's steering inputs.

The result is a dynamically limited vehicle - a significant portion of the total yawing moment generated by the chassis is absorbed in the process of overcoming these longitudinal forces and not yawing the vehicle. In the automotive world, this leads to a poor handling car with a laboured turn in and excessive tyre wear. In motorsport, it means poor tyre management, slow lap times and frustrated drivers.

Open differentials

As we explore the science of differentials, we will explore an interesting variation of the technology in a form of a limited slip differential (LSD), but we must start with some focus on the original implementation of the automotive differential. What we call'open'.

The open differential is a relatively simple mechanism consisting of a number of intermeshed bevel gears with input from the driveshaft and two outputs to each axle halfshaft. The driveshaft supplies torque to the differential housing, which carries two pinion gears meshed with side gears located at the end of each halfshaft.

Under normal conditions, such as straight line driving, these pinion gears do not rotate on their shafts as the housing rotates, driving the halfshafts via the side gears with equal velocity as the housing.

But, under conditions where one wheel needs to rotate faster than the other, the slower halfshaft reduces velocity relative to the housing, while the faster shaft speeds up.

The fundamental kinematic relationship within a differential is described as follows: WF + WS = 2wh

With open differentials, the inside and outside wheels can spin completely independently of each other through the induced rotation of the pinion gears. This allows free rotation, which solves the cornering issues, but introduces a new problem in the context of vehicle dynamics that can be equally as damaging to performance as operating with a fully coupled, solid axle.

With an open differential, one could hold a single wheel of the axle static while the entirety of the engine's power travels to the unrestricted wheel. If this scenario rings any bells, this is analogous to an on-limit cornering situation in which lateral weight transfer has an outside wheel heavily loaded and the inside wheel very lightly loaded.

Once power is applied on the exit of a corner in this scenario, due to its reduced vertical load, the inside wheel will break traction first and quickly receive close to 100 per cent of the engine's power. The result is a spinning inside wheel and greatly reduced acceleration.

The solution to this was realised in the implementation of a new style of differential that blurred the lines of an open and solid axle by introducing a coupling action dependent on external factors, maintaining the independence of the wheels, but in a controlled way.

And so, the limited slip differential was conceived. Various references point the introduction of the LSD to a collaboration between Porsche and ZF in the 1930s, but safe to say the technology has been around for a long time. In motorsport today, the LSD presents itself in two main forms - mechanical and geared.

Mechanical LSD

The first and most common type is the mechanical, or clutch-style LSD. These use the basic architecture of an open differential, but with the addition of a series of clutch plates constrained to the differential housing and pressure plates splined to each axle halfshaft.

These clutch packs work in a similar action as the clutch and flywheel of an engine. In normal conditions, where each wheel is rotating with the same velocity, an amount of pressure is exerted on the clutch pack through engine torque from the driveshaft, clamping the clutch and pressure plates together and creating a partial couple between the wheels.

As a speed differential occurs across the axle due to a loss of traction on one wheel, the mechanics of the differential exert a greater pressure on the clutch pack of the faster spinning axle, which generates a braking torque, shifting the distribution of the engine's power towards the slower axle.

'In our mechanical differentials, we have a device called the thrust ring/explains Harald Hinterwallner, director of design and engineering at Drexler.'As soon as there is a driving torque on the differential, this thrust ring experiences an axial force, compressing the clutch pack and locks the differential. In this condition, the torque from the driveshaft is distributed in a greater proportion to the wheel with more traction!

Due to the nature of meshed bevel gears, the resultant force at the gear teeth has an axial component as well as a radial component. In practice, this means the faster halfshaft will generate a larger clamping pressure in the clutch packs, braking the shaft and biasing torque towards the inside wheel.

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