what makes the "diff"(erence)

Make a line of friends standing hand in hand. Let the person at the outside start to run. The one at the inside stands still. You will see that the further you go to the outside of the line the harder the person needs to run to keep the line straight. The same happens when a car makes a corner. The wheel at the outside needs to run faster as the wheel at the inside to make that same corner in the same line.

A differential is a device to allow two things to spin at different rates while being driven by a single source. Each wheel is connected to a halfshaft (HS). As you know, as you turn, the outside wheel must turn faster than the inside wheel. Hence, the outside HS must turn faster than the inside. To handle this, the driveshaft supplies torque to the HS via a differential. The diff allows the torque to be split between the two HS, but allows them to turn at different rates if needed.

To make this possible the diff is invented. As the word already says there are diffe(rent) rotation speeds possible between two wheels or drive shafts when powered by one source. A car without diff's (solid axles) is hard to control on our off-road tracks and is giving extra strain to the tyres and drive train.

Ball differentials:
These are often used in the smaller 1:10 scale off-road cars. Because of the high loads produced by the engines nowadays, these units will not function for long with the same performance in a 1:8 scale buggy. The BMT company from Italy was the last one in the 90's to use ball diff's in a 1:8 scale buggy. Although they were adjustable, the range in which this was possible was very small. Therefore most drivers switched over to conventional gear diff's.

Gear differentials are splitted in:
Open differentials (Bevel gears, Planetary gears), limited slip and Torsen diffs.

Bevel gears:

These differentials use gears who are running in an angle of 90 degrees at each other. The output drive shafts are connected to two large main "sun" gears. Four little "satellite" gears are making the connection between the two "sun" gears.

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Planetary gears:
These gears run in the same line as the output drive shafts. The output shafts and the other gears are connected side by side

TORSEN differentials:
This is a special kind of gear differential. It also uses planetary gears but they have special helicoilidal worm spirals.

Between open differential like bevel and planetary, there is no major difference except of the way they are constructed. The working stays the same. The drive axles associated with an open differential are interconnected by gears, designed to divide equal torque between drive axles. This arrangement will not support any substantial torque difference between the drive axles and, as a consequence, offers very little resistance to differentiation. Virtually any attempt to deliver an increased amount of torque to one of the drive axles will result in rotation of the gear set as evidenced by differential rotation between drive axles. For example, if one of the drive wheels should lose traction, any attempt to deliver additional torque to the other drive wheel having better traction will result in undesirable 'spin up' of the wheel having poorer traction. The maximum amount of torque conveyed by the drive axles collectively is limited to approximately twice the amount of torque supported by the drive wheel having the least traction. The overall result is that the car is stable when one wheel is off the ground, because there is no traction at that specific moment. There is only overall traction when four wheels are on the ground.
This makes the car stable when driving on high grip tracks like artificial grass.
These diffs need normal maintenance.
You can use silicone grease or oil to alter the diff's working.
More about that will follow soon.

Torque sensing diffs, direct torque to each HS based on available traction. In other words, there is some feedback from the wheels to the differential to guide the torque distribution. The Torsen name comes from TORque SENsing.

The Torsen design is based on worm gears, rotating on different axes. Each side gear is a worm gear splined to the HS. There are 2 or 3 sets of planetary worm gears (called element gears), perpendicular to the side gear axis. Each set consists of two worm gears, connected via spur gears, and mated with each side gear. Thus, the two side gears are interconnected via the element worm gears.

As traction at each wheel changes, the pressure between the element worm and side gears change, causing the element pairs to counter-rotate, biasing the torque to the other side. Unlike the other designs, torque sensors (TS) work in just about all conditions. Even if the wheels are turning at different rates (turing, going over bumps, etc), they still shuffle the torque around based on traction.

The above is identical to the way a Torsen diff functions. A Torsen diff will only transfer torque to the wheel with the most grip when there's still some resistance on the other side. Once that's lost it will "unload" just like a normal gear diff.

In other words, the opposite reaction of a Torsen diff only happens when one wheel has less grip, not total loss of grip. Otherwise, you wouldn't be able to control them over bumps and jumps. The amount of torque that's transferred also varies from model to model. Not all brands behave the same. The more torque a Torsen diff can transfer the more relative grip you'll have at the sacrifice of forward drive. The ones that transfer more torque also feel less aggressive.
Driving with Torsen diffs also require more careful car setup and throttle control. The diffs have a lot of extra forward drive and power over tracks sections where a normal diff would slightly back off. From experience the center diff makes the greatest difference in forward drive. Personally, I think you also need a front Torsen to pull things straight and stabilize the car for easier driving. In the rear you can put in a normal open gear diff.
Torsen diffs need special care and maintenance.