# Working of a Limited Slip Differential

Limited slip differentials (LSD) are used in automobile to overcome the traction difference problem of drive wheels. In this article working of LSD is explained in a logical manner.

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Detailed webpage version of the video is given below.

## Problem with the Standard Differential

Consider a situation where a vehicle fitted with a standard differential moves straight, and one drive wheel is on a surface with good traction and the other wheel is on a slippery track. In a standard differential the left and right axle rotations are completely independent. Since one wheel is on a slippery track, the standard differential will make that wheel spin in excessive speed, while the good traction wheel will remain almost dead. This means high power supply to the slippery wheel and low power flow to the good traction wheel. So the vehicle won’t be able to move.

Fig.1 In a standard differential power from the engine is transferred to the wheel with low traction

One way to overcome this problem is to limit the independency or relative motion between the left and right axles. Limited slip differentials are introduced for this purpose. One of the most commonly used LSD technology is clutch-pack based.

## Constructional Features of LSD

First we will go through constructional features of LSD.

The basic components of a standard differential are shown below. It has got pinion gear, ring gear, case, spider gears and side gears.

Fig.2 The basic components of a standard differential

To understand working of a standard differential please check this link . Apart from its basic components a Limited slip differential has got a series of friction and steel plates packed between the side gear and the casing. Friction discs are having internal teeth and they are locked with the splines of the side gear. So the friction discs and the side gear will always move together.

Fig.3 It is clear from the figure that steel plates are locked with the case and friction disc with the side gear

Steels plates are having external tabs and are made to fit in the case groove. So they can rotate with the case.

If any of the clutch pack assembly is well pressed, the frictional force within them will make it move as a single solid unit. Since steel plates are locked with the case and friction discs with the side gear, in a well pressed clutch pack casing and the clutch pack will move together. Or motion from the casing is directly passed to the corresponding axle.

Space between the side gears is fitted with a pre-load spring. Pre load spring will always give a thrust force and will press clutch pack together.

Fig.4 Pre-load spring in an LSD will always give a thrust force; The blue arrow represents thrust force

## Separating action of Bevel gears

You can note that spider and side gear are bevel gears. It has got one specialty. When torque is transmitted through a bevel gear system axial forces are also induced apart from the tangential force. The axial force tries to separate out the gears.

Fig.5 During power transmission through a bevel gear system axial forces are also induced

You can note that side gear and axle are 2 separate units. The side gear has got a small allowance for axial movement.

Fig.6 Side gear and axle are two separate units as shown; So the side gear can have small axial movement

So during high torque transmission through spider-side gear arrangement, a high separating thrust force is also transmitted to the clutch pack. This force presses and locks the clutch pack assembly against wall of the casing.

## Working of Limited Slip Differential

Now back to the initial problem. Since one wheel is on a high traction surface, the torque transmitted to it will be higher. So the thrust force developed due to the bevel gear separation action also will be high at that side. Thus clutch pack at high traction wheel side will be pressed firmly and clutch pack will be locked. So power from the differential casing will flow directly to high traction axle via clutch pack assembly.

Fig.7 Thrust force induced due to the bevel gear separation action is high for the high traction wheel

On the other hand clutch pack on the low traction wheel side is not engaged yet, so power flow will be limited to that side. So the vehicle will be able to overcome the traction difference problem.

Fig.8 Low thrust force at low traction wheel will allow steel plate and friction disc to slip

However while taking a turn the LSD can act like a normal differential. In this case thrust force developed due to bevel gear separation action won’t be that high. So the plates in clutch pack will easily overcome frictional resistance and will be able to slip against each other. Thus the right and left wheel can have different speed just like an open differential.

Following are the other commonly used technologies used to overcome the drive wheel traction difference problem.

• Clutch pack - Pressure disk type
• Torsen®
• Cone Differential
• Hydraulic Locking Type

# How does a Differential work ?

The differential is an integral part of all four wheelers. Differential technology was invented centuries ago and is considered to be one of the most ingenious inventions human thinking has ever produced. In this video, we will learn, in a logical manner, why a differential is needed in an automobile and its inner workings.

A detailed webpage version of the video lecture is given below.

## Why the Differential gear is used?

Wheels receive power from the engine via a drive shaft. The wheels that receive power and make the vehicle move forward are called the drive wheels. The main function of the differential gear is to allow the drive wheels to turn at different rpms while both receiving power from the engine.

Fig.1 Power from the engine is flowed to the wheels via a drive shaft

Consider these wheels, which are negotiating a turn. It is clear that the left wheel has to travel a greater distance compared to the right wheel.

Fig.2 While taking a right turn the left wheel has to travel more distance; this means more speed to left wheel

This means that the left wheel has to rotate at a higher speed compared to the right wheel. If these wheels were connected using a solid shaft, the wheels would have to slip to accomplish the turn. This is exactly where a differential comes in handy. The ingenious mechanism in a differential allows the left and right wheels to turn at different rpms, while transferring power to both wheels.

## Parts of a Differential

We will now learn how the differential achieves this in a step-by-step manner using the simplest configuration. Power from the engine is transferred to the ring gear through a pinion gear. The ring gear is connected to a spider gear.

Fig.3 Motion from the pinion gear is transferred to the spider gear

The spider gear lies at the heart of the differential, and special mention should be made about its rotation. The spider gear is free to make 2 kinds of rotations: one along with the ring gear (rotation) and the second on its own axis (spin).

Fig.4 Spider gear is free to make 2 kinds of rotations

The spider gear is meshed with 2 side gears. You can see that both the spider and side gears are bevel gears. Power flow from the drive shaft to the drive wheels follows the following pattern. From the drive shaft power is transferred to the pinion gear first, and since the pinion and ring gear are meshed, power flows to the ring gear. As the spider gear is connected with the ring gear, power flows to it. Finally from the spider gear, power gets transferred to both the side gears.

Fig.5 The basic components of a standard differential

## Differential Operation

Now let’s see how the differential manages to rotate the side gears (drive wheels) at different speeds as demanded by different driving scenarios.

### The vehicle moves straight

In this case, the spider gear rotates along with the ring gear but does not rotate on its own axis. So the spider gear will push and make both the side gears turn, and both will turn at the same speed. In short, when the vehicle moves straight, the spider-side gear assembly will move as a single solid unit.

Fig.6 While the vehicle moves straight, the spider gear does not spin; it pushes and rotate the side gears

### The vehicle takes a right turn

Now consider the case when the vehicle is taking a right turn. The spider gear plays a pivotal role in this case. Along with the rotation of the ring gear it rotates on its own axis. So, the spider gear is has a combined rotation. The effect of the combined rotation on the side gear is interesting.

Fig.7 To get peripheral velocity at left and right side of spider gear we have to consider both rotation and spin of it

When properly meshed, the side gear has to have the same peripheral velocity as the spider gear. Technically speaking, both gears should have the same pitch line velocity. When the spider gear is spinning as well as rotating, peripheral velocity on the left side of spider gear is the sum of the spinning and rotational velocities. But on the right side, it is the difference of the two, since the spin velocity is in the opposite direction on this side. This fact is clearly depicted in Fig.7. This means the left side gear will have higher speed compared to the right side gear. This is the way the differential manages to turn left and right wheels at different speeds.

### The vehicle takes a left turn

While taking a left turn, the right wheel should rotate at a higher speed. By comparing with the previous case, it is clear that, if the spider gear spins in the opposite direction, the right side gear will have a higher speed.

Fig.8 While taking left turn the spider gear spins in opposite direction

## Use of more Spider gears

In order to carry a greater load, one more spider gear is usually added. Note that the spider gears should spin in opposite directions to have the proper gear motion. A four-spider-gear arrangement is also used for vehicles with heavy loads. In such cases, the spider gears are connected to ends of a cross bar, and the spider gears are free to spin independently.

Fig.9 Double spider gear arrangement is usually used to carry more loads

## Other functions of the Differential

Apart from allowing the wheels to rotate at different rpm differential has 2 more functions. First is speed reduction at the pinion-ring gear assembly. This is achieved by using a ring gear which is having almost 4 to 5 times number of teeth as that of the pinion gear. Such huge gear ratio will bring down the speed of the ring gear in the same ratio. Since the power flow at the pinion and ring gear are the same, such a speed reduction will result in a high torque multiplication.

You can also note one specialty of the ring gear, they are hypoid gears. The hypoid gears have more contact area compared to the other gear pairs and will make sure that the gear operation is smooth.

The other function of the differential is to turn the power flow direction by 90 degree.

## Drawback of a Standard Differential

The differential we have gone through so far is known as open or standard differential. It is capable of turning the wheels at different rpm, but it has got one major drawback. Consider a situation where one wheel of the vehicle is on a surface with good traction and the other wheel on a slippery track.

Fig.10 A standard differential vehicle on different traction surfaces will not be able to move

In this case a standard differential will send the majority of the power to the slippery wheel, so the vehicle won’t be able to move. To overcome this problem, Limited Slip Differentials are introduced. We will learn more about them in a separate article.