How does a car differential work?

The principle

A car differential. One engine drives two wheels on the same axle. Going straight they turn at the same speed, but they can’t always turn together. The differential is the small box of gears in the middle of the axle that lets them differ.

Step 1: In a turn, the wheels differ. In a fairly tight turn the outer wheel might roll about 6.8 m around the bend while the inner one rolls only about 5.3 m. So if both wheels turn about 400 rpm going straight, in the turn the inner one turns about 350 rpm and the outer about 450 rpm. It is like runners on a bend: the one in the outside lane has to run further in the same time. With a solid axle, one tyre would have to scrub and skip along the road.

Step 2: The ring gear turns the box. The shaft from the engine ends in a small gear that turns a big ring gear. The ring gear is bolted to a box (the carrier), so the whole box spins. Inside it, small spider gears sit on a pin and ride around with the box. They mesh with two side gears, one on each wheel’s shaft. Going straight, the spider gears don’t spin on their pin at all: they just carry both side gears around, so both wheels turn the same.

Step 3: Spider gears spin in a turn. In a turn the inner wheel is held back a little. The spider gears now start to spin on their pin, and that lets the other side gear run ahead by exactly the same amount. 350 + 450 = 2 x 400 rpm: the box always turns at the average of the two wheels. Nothing scrubs and the car turns smoothly.

Step 4: The problem: ice. An open differential (the simple kind, in most ordinary cars) always gives both wheels about the same turning force. That is fine on dry road. But if one wheel is on ice, the ice can only hold back a little, say about 70 Nm, before the wheel slips. So that wheel gets about 70 Nm, and the wheel on dry road gets the same 70 Nm, not more. That is far too little to move the car. The ice wheel spins at about double speed (about 800 rpm here) while the other stands still. It is like a tug of war where one side lets go: the other side can’t pull harder than the rope is held. So the open differential splits the force equally, but lets all the speed go to the easy wheel.

Step 5: Limited-slip fixes it. A limited-slip differential (LSD) adds something that resists one wheel spinning much faster than the other: in this example, stacks of clutch plates next to the side gears, pressed together by springs and by the engine’s own push. It does not split the force equally (that is what the open differential does). The plates act like a brake on the spinning wheel, and the slower wheel with grip gets the ice wheel’s force plus what the plates hold back. A common way to rate an LSD is its bias ratio: a 3:1 unit can give the gripping wheel up to about 3 times the force of the slipping one. So in this example the ice wheel still gets about 70 Nm, but the wheel with grip gets about 210 Nm, and the car pulls away. Put simply, the LSD holds the two wheels closer to the same speed, and holding the spinning wheel back is exactly how the gripping wheel gets more force. A fully locked differential goes all the way: both wheels always turn at the same speed. Many factory LSDs are around 2:1 and sporty ones about 3:1; real numbers depend on the car.

Open differential or limited-slip?

• Open differential: simple, cheap, light and smooth, and it needs almost no care. Downside: if one wheel loses grip (ice, mud, a wheel in the air), both wheels get almost no force.
• Limited-slip (LSD): keeps driving the wheel with grip, so it helps on ice and when accelerating hard out of a bend. Downside: more parts, more cost, some kinds need special oil and wear over time, and it can make tight, slow turns feel a bit stiffer.