Automobille Engineering

How does a Differential work ?

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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.

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

GDJP Gas Turbine Working Principle

Gas Turbine Engine for Jet Propulsion

Following figure shows of gas turbine engine of an aircraft. In order to make the flight move forward this engine should produce a force in forward direction.

Fig.1 Jet force required by aircraft is produced by a gas turbine engine

This force is produced by jet effect of this exit fluid. When a high velocity fluid is ejected from aircraft engine it will produce a reaction force which will power the aircraft flight. This force is known as jet force. By applying Newton’s 2nd law of motion to jet engine control volume, one can easily deduce magnitude this jet force as follows.

It is momentum out minus momentum in. So if jet velocity is high it means high thrust force! This is why exit portion of a jet engine has got decreasing area, assuming the flow is subsonic. Or the exit portion acts like nozzle which increase jet velocity.

Continuous Production of High Velocity Jet

If we can produce high velocity jet continuously, the engine will be continuous jet force. We will produce this by a combustion process, by injecting fuel into air. This will produce flames with very high velocity.

Fig.2 Combustion produces flames at high energy, which is then transformed to high velocity flames

But for a sustainable combustion process we need the inlet air to the combustion chamber to be at high temperature and pressure.

Use of Compressor

Surrounding air is brought to high temperature and pressure state with help of diffuser plus compressor arrangement. Air gets into the engine by forward motion of engine and sucking effect of compressor. Diffuser increases pressure and temperature of the fluid to some extent by converting some part of kinetic energy. After that compressor comes where both pressure and temperature of the air is raised by by energy supply from compressor.

Fig.3 Diffuser and compressor together raise pressure and temperature of the incoming air

So at outlet of the compressor we will have air at high pressure and temperature. But compressor requires some power input to do this compression process.

Turbine - A Source of Power to Compressor

Power required compressor is given by a turbine which is situated right after the combustion chamber. The turbine absorbs some amount of energy from the high energy fluid and transmits it to the compressor.

Fig.4 The complete gas turbine, which is self sustainable in operation

Nozzle - Production of High Velocity Jet

Now the fluid with high energy can be expanded in a nozzle section to produce a high velocity jet.In nozzle air will expand to surrounding pressure. Thus the process of producing high velocity jet at outlet has become a self sustainable. We will get continuous supply of high velocity jet and thrust force to this aircraft, thanks to synchronized working of all these components.

Thermal Cycle of Gas Turbine - Brayton Cycle

Variation of state of fluid from inlet to exit of gas turbine engine is shown in Fig.5 in a T-s diagram. Point 1 is the inlet condition of a gas turbine engine, which is same as state of surrounding air. Due to diffuser effect pressure and temperature of the fluid increases slightly, entropy remains same assuming this is an adiabatic reversible process (1-2). Next in compressor stage also same process continues, temperature and pressure rise to a level where combustion process is sustainable (2-3). Now fuel injection and heat addition to the fluid, this process happens almost at constant pressure, here pressure raises to very high level (3-4). Right after that, turbine will absorb some amount energy which is required by the compressor. So here temperature and pressure of the fluid comes down (4-5). Now the last section, which produces high velocity jet. This is again a constant entropy process, where internal energy of the fluid gets converted into kinetic energy. Here pressure expands to the surrounding pressure (5-6).

Fig.5 Variation of state of fluid as it executes Brayton cycle

It should be noted here that the exit stream never go back to the inlet condition, at inlet it sucks fresh steam of air in. So this is an open cycle process, but since both this points are having same pressure we can assume pseudo constant pressure process (6-1) in between in order to complete the cycle.