Why use Castigliano's theorem

You can apply Castigliano's theorem if you should have some background with :

• Deflection of a beam/cylinder due to axial loading, bending, torsion.
• For calculating the normal moment of inertia.
• For calculating the polar moment of inertia.
• Deriving equations for linear changes in quantities.
• Using singularity functions but it is often used in conjunction with Castigliano’s Theorem.
• Determining the deflection of beams 
• Castigliano’s Theorem uses strain energies at the locations of forces to determine the deflections.
• For determining of deflections for objects with changing cross-sectional areas.

Muff coupling application

Applications of muff coupling are as follows :

• Piece couplings
• Grooved muff couplings for vertical applications
• Through bore muff couplings
• Stepped bore muff couplings
• Ribbed muff couplings
• 3 piece muff couplings

All of above can be made in different material like cast iron, carbon steel aluminium and stainless steel.

Difference between viscosity and friction

What is Friction?

The most common resistive force we experience every day is called friction is caused by the contact of two rough surfaces.

What is Viscosity?

Viscosity is just the friction between two fluid layers when the two layers move relative to each other.

Viscosity is kind of a special case of friction.

Friction and viscosity are two properties that matter a lot. Let us have a deep insight into the difference between viscosity and friction. 

Main difference :

Friction is used to refer to forces that resist relative motion, whereas viscosity refers specifically to resistive forces that occur between layers of fluid when fluids attempt to flow.

Difference between viscosity and friction : 

• Friction is due to the resistance of relative motion between two solid surfaces where viscosity is due to cohesion or adhesion between two surfaces.
• The viscous force depends on the velocity gradient and area of contact and frictional force independent of the area of contact and relative velocity.
• The force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding between them is called friction while the viscosity of a fluid is a measure of its resistance to gradual deformation through shear stress or tensile stress.
• Friction between solid matter does not depend on speed difference while friction in fluids depends on speed between adjacent layers by means of their viscosity.
• The viscosity of liquid decrease with increase in temperature, Where friction independent of temperature.

Similarity :

• Both properties came in to play whenever there is relative motion.
• Both oppose the relative motion.
• Both depend upon the nature of the surface.
• Both can be erased by intermolecular force.

You can also want to know the difference between related terms like the difference between viscosity and density.

Difference between viscosity and density

Viscosity and density are two very useful properties in describing the statics and dynamics of these substances while viscosity and density are both the same thing expressed in different forms truly different concepts.

What is Viscosity?

The viscosity is a measurement of the intermolecular forces and molecule shapes denote as μ.

What is Density?

The density is a measurement of the molecular weight of the composition denotes as ρ.

 Let us have a deep insight into the difference between viscosity an density. 

Difference : 

• Density says how much mass occupies a certain volume while viscosity is how well a liquid sticks together.
• Viscosity is the thickness or thinness of fluid while density refers to the space between its particles.
• Viscosity asked you the friction between two layers of the given fluid while density varies slightly with temperature. 
• Density and viscosity decrease with temperature, but viscosity has an exponential relationship and density has a linear relationship with temperature.
• Viscosity is applied for only fluids whereas density applied for all three types solid, liquid, gas.
• Viscosity is a physical property while density is a material property.
• Viscosity is how fast the particles move where density is how many particles are in it.
• A fluid with higher density will transition to turbulent flow quicker, and fluid with higher viscosity will have that transition later. so in a sense, they are inversely proportional.

Both of two properties are very different concepts, but together they can describe more than half of fluid's characteristics.

You can also want to know the difference between related terms like the difference between viscosity and friction.

Advantages of muff coupling

Muff coupling is also called sleeve coupling is the simplest type of rigid coupling that consists of a hollow cylinder whose inner diameter is the same as shaft. It is fitted over the ends of two shafts by means of a gif head key and power transmitted from one shaft to other by means of a key and a sleeve. Now, in this article, let us have a deep insight into the advantages of muff coupling.

Advantages of muff coupling : 

• Muff coupling is the simplest form of coupling with consisting of only two parts are sleeve and key.
• It is simple to design and manufacturer.
• It is cheaper than other types of coupling.
• It has compact construction with small radial dimensions.
• It has no projecting parts except the key head.
• The external surface of the sleeve is smooth this gives safety to the operator.

Muff coupling

What is muff coupling?

Answer :

• A coupling in which a hollow cylinder or muff is used to connect the abutting ends of two shafts.

In muff coupling, the muff is made into two halves and they are joined together by means of bolts. Where halves are made by cast iron and bolts are by mild steels. 

Muff coupling is also called sleeve coupling or box coupling.

Muff coupling is fall in the category of rigid coupling.

Features of muff coupling :

• Easy to manufacture.
• Components are easy to assemble and Dismantling.
• Their high torque capabilities make them suitable for higher RPM power transmission applications.
• Due to rigid connection lubrication is not required.
• Maintenance is minimal.
• Low operational cost due to no maintenance and no lubrication
• No moving part hence smooth and quiet operation.

Muff coupling is usually designed on shop floors by assuming standard proportions for the dimensions of the sleeve.

For the sleeve muff coupling the standard proportions used are as follows :

D = ( 2d + 13 ) mm 

L = 3.5 d

Where 

D = Outer diameter of the sleeve ( mm )

L = Axial length of the sleeve ( mm )

d = Diameter of the shaft ( mm )

What is coupling

This article is all about couplings and different types of coupling.

Coupling :

What is coupling?

Answer :

• A coupling can be defined as a mechanical device that permanently joins two rotating shafts to each other.

In other words, the coupling is a device for connecting parts of machinery.

The most common application of coupling is joining of shafts of two separately built or purchased units so that new machine can be formed.

Clutch and coupling doing work for the same purpose but the main difference between them is coupling is permanent connection while the clutch can connect or disconnect two shafts at the will of the operator.

The shafts to be connected by the coupling may have col-linear axes, intersecting axis or parallel axis with a small distance in between depending upon that different coupling are used.

Oldham coupling is used to connect two parallel shafts when they are at a small distance apart.

Hooke's coupling is used to connect two shafts having intersecting axes.

The axis is co-linear or in the same line, rigid or flexible coupling are used.

Advantage and disadvantage of woodruff key

Woodruff keys are semi-circular in shape, leaving a protruding tab when installed. A semi-circular pocket is a keyway in the shaft, the mating part is a longitudinal slot. They are used to improve the concentration of the shaft and the mating part, which is essential for operation at high speed. Let us have a deep insight into the pros and cons of woodruff key in this article. 

Advantages of woodruff key :

• It can be used on the tapered shaft because it can align by slight rotation in the seat.
• The extra depth of key in the shaft prevents its tendency to slip over the shaft.

Disadvantages of woodruff key :

• The extra depth of keyways in the shaft increases stress concentration and reduces its strength.
• The key does not permit axial movement between the shaft and the hub.

Types of keys in machine design

There are different types of keys are available and there are a number of standards. 
Many ways to classify the keys. so let we check it out types of keys below :

• Saddle key and Sunk key
• Square key and Flat key
• Taper key and Parallel key
• Key with and without Glib-head

There are some special types of keys are also available. some of the special types of keys are given below :

• Woodruff key
• Kennedy key or Feather key 

This special types of keys are used in the following applications depending upon the following factors :

• Power to be transmitted
• Tightness of fit
• Stability of connection
• Cost 

Saddle key :

A saddle key is a key which fits in the key ways of the hub only there are no keyways on the shaft.

Saddle keys are suitable for light duty only. They tend to work loose rock on the shaft under heavy duty.

There are two types of saddle keys :

• Hollow saddle key
• Flat saddle key  

Hollow saddle key :

Hollow saddle keys is a taper key which fits in key ways in the hub and the bottom of the key is a shaped to fit the curved surface of the shaft. 

It is held on by friction, therefore suitable for light loads.

Flat saddle key :

Flat saddle keys is a taper key which fits in key ways in the hub and is flat on the shaft.

It is likely to slip round the shaft under load, therefore suitable for comparatively light loads.  

In both types of saddle keys friction between the shaft, key and hub prevent the relative motion between the shaft and the hub.

In case of the flat key, the resistance of slip is more than that of the hollow key, therefore flat saddle key is slightly superior to hollow shaft key as far as the power transmitting capacity is concerned.

Sunk key :

A sunk key is a key in which half the thickness of the key fits into the keyways on the shaft and the remaining half in the keyways on the hub.

In these keys, keyways are required both on the shaft as well as the hub of the mating element.

This is the standard form of the key.

In sunk key, power is transmitted due to shear resistance of the key.

The sunk key is suitable for the heavy-duty applications because there is no possibility of the key to slip around the shaft.

Square key and flat key :

Sunk keys are used in two ways :

• Square 
• Rectangular cross-section

A sunk key with rectangular cross-section is called a flat key.

The flat key is more stability as compared with the square key.

Square keys are used in general industrial machinery while flat keys are more suitable for machine tool applications.

Taper key and Parallel key :

A parallel key which is uniform in width as well as height throughout the length of the key.

A tapper key is also uniform in width but tapper in height.

Standard tapper is 1 in 100.

Tapper is provided due to the following reason :

• Due to tapper, it is easy to remove the key and dismantle the joint easily.
• Tapper insures tightness of joint in operating conditions and prevent loosening of the parts.

Glib-head key :

Glib keys are tapered and notched machine keys that are used on power transmission keyed shafts to hold pulleys and gears tightly on the shaft.

Taper keys are often provided with glib-head to facilitate removal.

Glib head key has following advantages as compare with parallel key, taper key :

• The taper surface results in wedge action and increases frictional force and the tightness of the joint.
• The taper surface facilitates easy removal of the key, particularly with glib-head keys.

Feather key :

A feather key is a parallel key which is fixed either to the shaft or to the hub and which permits relative axial movement between them. 

The feather key is a particular type of sunk key with uniform width and height.

Feather key used where the parts mounted on the shaft are required to slide along the shaft such as clutches or gear shifting devices. 

Feather key is an alternative to splined connection.

Woodruff key :

A woodruff key is a sunk key in the form of an almost semicircular disk of uniform thickness.

Woodruff keys are used on tapered shaft in machine tools and automobiles.

Advantages of woodruff key :

• It can be used on tapered shaft because it can align by slight rotation in the seat.
• The extra depth of key in the shaft prevents its tendency to slip over the shaft.

Disadvantages of woodruff key :

• The extra depth of key ways in the shaft increases stress concentration and reduces its strength.
• The key does not permit axial movement between the shaft and the hub.

Keys in machine design

Keys :

What is the key ?

• A key can be defined as a machine element which is used to connect the transmission shaft to rotating machine elements like pulleys, gears, sprockets or flywheels.

Key joints consisting of shaft, hub and key.

Keys may be made of plain carbon steels like 45C8 or 50C8.

Functions of key :

• To transmit the torque from the shaft to the hub of the mating element and vice versa.
• To prevent relative motion between the shaft and the joined machine element like gear or pulley.
• In some cases, it is also used to prevent axial motion between two elements in case of father key or splined connection.

A drawback of the key joint :

• The main drawback of a key joint is due to keyway stress concentration in the shaft and the part becomes weak.

There are different types of keys are available and there is a number of standards.

How front wheel drive works

In this article we have discuss about front wheel drive and how to work front wheel drive and its assembly.

Assembly of front wheel drive train :

In most of front wheel drive train have a transaxle. A transaxle combines the transmission and differential into one single unit.  
Because of all components are in front of the car front wheel drive vehicle don't need long drive shafts to transfer torque to the wheels. instead of this half-shaft is used. Half-shaft is connects with the transaxle to the wheel assembly.
Half-shaft connect with the transaxel to the wheel assembly with the use of constant velocity joints, or CV-joints instead of U-joints. 
CV-joints use a ball bearing mechanism to reduce the friction and to allow more complex wheel movement.

Do front wheel drive cars have differentials

Do front wheel drive cars have differentials ?

Answer 

• Yes, front wheel drive cars have differentials.

In front wheel drive it is integrated into the transmission casing and is not immediately visible.

In FWD cars the two half-shafts ( for each wheel ) of the trans axle go directly into the differential hub.

If you want to know more about front wheel drive drive-train CHECK IT OUT below article :

• Front wheel drive train assembly 

Can front wheel drive cars drift

Can front-wheel-drive cars drift?

Answer :

• No, front-wheel-drive cars not drift 

A little bit of drift can be induced in a front-wheel-drive car by pulling on the handbrake and locking up the back wheels. this drift is called braking drift and this is not the same as a power drift where the back wheels break traction due to extra power through the drive train from the engine. 

Power drifts can only be done if there is power at rear wheels.  

But yes, using an FWD car, a braking drift can be done with handbrake which hardly lasts for a couple of seconds.

Front wheel drive vs Rear wheel drive

In this article we have to look out for what was actually a front wheel drive and rear wheel drive
what is the difference between them and comparison between them as a price wise performance wise etc. 
Most of the car buyer's in today scenario first think about what car to buy in this article they have clear their confusion and buy according to their need.

Front wheel drive :

FWD is the vehicle where the motor drives only the front wheels of a car. 
Now a days most of the car manufacturers offers front wheel drive because it is cheap and easy to design and also light weight as it is devoid of extra transmission and axle assemblies..

Rear wheel drive :

RWD is the vehicle where the motor drives only the rear wheels of a car. 
In rear wheel drive an engine in front it connected to a transmission then power to rear-axel via driveshaft which drives the rear wheels.

Now we have to discuss normal priorities like space, fuel economy, price and easier drive ability, efficiency.

Space :
In front the space is same but in the back, front wheel drive trumps rear wheel drive because of the high transmission tunnel which makes seating three in the back a hard and uncomfortable thing to do. 

Fuel Economy :
Front wheel drive cars have better economy because there is less power lost in transferring the power from engine to the wheels.
But now with the help of technology rear wheel drive cars are closing the gap.

Price :
It's just easier to built front wheel drive cars because everything is so nearby the engine.
So front wheel drive vehicles are mostly cheaper than that of the rear wheel drive vehicle.

Efficiency : 
FWD cars have less weight & thus better mileage due to no drive shaft. 
Also a transverse motor & transmission eliminates a gearing transfer, again reducing weight & friction because of that the FWD are better efficiency. 

Drive ability :

If you are a calm driver the front wheel drive is for you.
If you are a speed lover kind of driver then I would suggest Rear wheel drive because if you drive a front wheel drive car hard then it cause understeers which means that your steering is now turned fully to go left or right direction but you are still ploughing forward in the same direction.
But in case of RWD if you were driving car and you drive its up to limits it may or may not oversteer which means that your cars end is coming out of the perfect apex line depending on the amount of power you have.

Oversteer is controllable &

Understeer is not 

So for we can see above both cars can understeer but there is more probability of it being a front wheel drive car.
And after I have said that it also means that both cars oversteer too.

So for calm driver go for front wheel drive 
Harsh driver go for rear wheel drive. 
But depending on how good you drive and if you need the rest of the things mentioned above.

Verdict on what car you buy : 
A normal car that sees everyday use, a front wheel drive car (FWD) is a much better choice.
FWD cars feature better packaging of its components so this cars allowing more room for passenger comfort and cargo. FWD cars also tend to be lighter and use smaller more fuel efficient engines. 
So if you look for family cars you can go for front wheel drive.

If you are speed lover a rear wheel drive or (RWD) car offers better performance dynamics for the driving enthusiast then you can go for rear wheel drive.

A front wheel drive is better for a normal car.
A rear wheel drive car is capable of powerful pickup.
More important thing is you can drift the car if you want so and it is used in sports car.
Performance wise it is better than FWD. 

Depending upon the pros and cons you also make out you confusion easily : 
You can check it out advantages of front wheel drive & disadvantages of front wheel drive.

You can also check it out difference between front wheel drive and rear wheel drive 

Rear wheel drive

What is rear-wheel drive?

• A transmission system that provides power to the rear wheels of a motor vehicle. 

In rear wheel, drive power is transferred to the rear wheels to move the car.

For the better part of the twentieth century, nearly every vehicle on the road had the engine sending power to the rear wheels. 

The most common setup in a rear-wheel drive vehicle involves the engine at the front of the car connected to a driveshaft to the differential that sends power to the rear wheel of the car. 

Assembly of rear-wheel drive train :

In rear-wheel drive cars the transmission is attached to the rear of the engine by way of a flywheel. Transmission what really happens when you press down on the accelerator? To understand this the drive- train may control the amount of power that goes from your engine to your wheels. 

The driveshaft is connected to the transmission and transmits the spinning power that began in the engine to the back of the vehicle at the differential.

While driveshaft designs are two types :

1. Torque tube 
2. Hotchkiss 

Torque tube driveshafts were used on older vehicles and trucks and SUVs used nowadays. Torque tubes connect the transmission and differential via a single universal joint is called U-joints.

Hotchkiss drive shafts are the common drive shaft design. Instead of just using one U-joint to connect the transmission and the differential, Hotchkiss drive shafts use two U-joints.

Then differential that sits between the two rear wheels. It is the last stop along the drive train before torque is transferred to the rear wheels.

If you want to know how the differential works check out the awesome video below :

Front wheel drive

What is a front-wheel-drive?

• A transmission system that provides power to the front wheels of a motor vehicle. 

In a front-wheel-drive vehicle power produced by engine directly transferred to both the front wheel of the vehicle.

In this layout, the engine drives the front wheels only and front-wheel can drive the real wheel of the vehicle.

Though the front-wheel-drive can be found is around 1929 where the engine is fitted in the front of the wheel, powering the front axle. it was the first front-wheel-drive automobile vehicle.

Many cars today use front-wheel drive. In front-wheel drive all the components of the drive train name transmission, differential and driveshaft are in front of the car. To fit all of this components in the front the engine is placed sideways in the car this is called transverse engine placement. 

Because all the parts of a front-wheel drive train are positioned at the front of a vehicle, you can make cars smaller and lighter or make the bigger cars but just have more room for passengers. 

Because of this more weight and traction are available at the front it provides more traction on slippery surfaces, like snow.

What really happens when you press down on the accelerator? To understand this you should know the drive-train assembly of front-wheel drive 

Assembly of front-wheel drive train :

In most of the front wheel, the drive train has a transaxle. A transaxle combines the transmission and differential into one single unit.  
Because all components are in front of the car front-wheel-drive vehicle don't need long drive shafts to transfer torque to the wheels. Instead of this half-shafts is used. Half-shaft is connected with the trans-axle to the wheel assembly.
Half-shaft connect with the trans-axle to the wheel assembly with the use of constant velocity joints or CV-joints instead of U-joints. 
CV-joints use a ball bearing mechanism to reduce the friction and to allow more complex wheel movement.

Nowadays a car buyer will also one thing keep in mind and make a comparison between Front-wheel drive (FWD) Vs Rear-wheel drive (RWD) cars and Front-wheel drive (FWD) vs All wheel drive (AWD) cars.

Castigliano's theorem

Italian engineer Alberto Castigliano developed a method of determining the deflection of structures by strain energy method.

He is known for his two theorems :

1. Castigliano's first theorem - for forces in an elastic structure
2. Castigliano's second theorem - for displacements in a linearly elastic structure.

We can discuss the second theorem below :

Castigliano's theorem statement : 

It is mainly used in machine design while designing shafts, keys and coupling.

• When a body is elastically deflected by any combination of forces or moments, the deflection at any point and any direction are equal to the partial derivative of total strain energy of the body with respect to the force located at that point and acting in that direction.

Castigliano's theorem is one of the important techniques for determining the deflection of a complex structure.

Castigliano's theorem is applicable only in the elastic range of the materials.

Procedure :

Steps :

1. Write an expression for each of the internal actions (axial force, bending moment, shear force, and torque) in each member of the structure in terms of external loads. 
2. Take derivatives of strain energy to get deflections and/or rotations.

For example :

Consider an elastic body subjected to a system of forces P₁, P₂, P₃ etc and U is total strain energy of the body. ∂1,∂2,∂3 are deflection at point of application and in direction of P₁, P₂, P₃ etc. then according to the theorem,

∂₁ = ∂U / ∂P₁

∂₂ = ∂U / ∂P₂

∂₃ = ∂U / ∂P₃

∂_I = ∂U / ∂P_i

Advantage and disadvantage of rigid flange coupling

Rigid flange couplings are commonly used in large, straight shafts where tight alignment tolerances must be maintained. In the power transmission industry, these couplings are very common and consist of two separate flanged halves that are bolted together. To ensure proper alignment and tight fit, the halves are keyed to the shaft with tapered keys. In situations where a strong coupling is required, a rigid flange coupling is often used, but there is little axial distance available. Let us have a deep insight into the pros and cons provided by this type of coupling. 

Advantages of rigid flange coupling :

• High torque transmitting capacity.
• Easy to assemble and dismantle.
• Simple in construction.
• Easy to design and manufacture.

Disadvantages of rigid flange coupling :

• It can't tolerate misalignment between the axes of two shafts.
• It is used only where the motion is free from shock and vibrations.
• It requires more radial space.

Hollow shaft vs Solid shaft

The hollow shaft contains the same amount of material all at the ends if hollow and a solid shaft are of the same weight whereas in the solid shaft distributed the material is uniformly throughout the shaft leaves little material at the ends. Difference between both of them is resistance to bending, resistance to torsion. Let us have a deep insight into the difference between the hollow and solid shaft.

Difference between the hollow shaft and solid shaft : 

• The material at the centre is removed in the hollow shaft and spread at large radius therefore, hollow shafts are stronger than solid shafts with the same weight.
• The stiffness of the hollow shaft is more than the same weight solid shaft.
• The strength of the hollow shaft is more than the same weight solid shaft.
• The natural frequency of the hollow shaft is higher than the solid shaft with the same weight.
• Hollow shaft is costlier than the solid shaft.
• The diameter of the hollow shaft is more than a solid shaft and require more space.
• Hollow shafts have a more polar moment of inertia, which enables them to transmit more torque than solid shafts.
• Hollow shafts do not transfer more power but the power to weight ratio of hollow shafts is more as compared to the solid shaft.
• Solid shafts, when subjected to bending, are stronger than that of the hollow shaft.

Depends on the application of the shaft :

Hollow shaft better for structural applications because it can beat the same loads as a solid shaft for lesser weight. Example: Rollcage of offroad vehicles.

The solid shaft is better for power transmission when compared to the hollow shaft. Example: Driveshaft

For the load-bearing type of shaft, it is always better to choose hollow shaft because it has higher stiffness and rigidity and can resist slightly higher bending moments. 

A shaft for transmission of torque like crankshafts, driveshafts, choosing a solid shaft is always better because it has higher torsional stiffness. 

Advantages and disadvantages of riveted joints

A rivet is a cylindrical mechanical joint that has a head. It is used as a member of the joint structure. It is a permanent joint which means that without failure of the machine component it can not be disassembled. This joint interference form fits the parts together. On the two plates, rivets apply a mechanical force that permanently joins the plates. Let us have a deep insight into the pros and cons of riveted joints in this article. 

Advantages of riveted joints :

• A riveted joint is more reliable than welded joints in applications which are subjected to vibrations and impact forces.
• Riveted joints can be used for non-ferrous metals like aluminium alloy, copper, brass or even non-metal like plastic and asbestos.
• Riveted joints are free from thermal after-effect because no heat required in this joint.
• Quality inspection is easy in a riveted joint.
• When the riveted joint is dismantled, the connected components are less damaged as compare to a welded joint.

Disadvantages of riveted joints :

• The material cost of a riveted joint is more.
• The labour cost of riveted joints is also more than that of the welded joint.
• Overall cost if the riveted joint is also high.
• The riveted assembly has more weight than the welded assembly.
• The riveting process creates more noise because of hammer blows.
• Holes required to insert rivets cause stress concentration.
• Production time is more for assembly.
• Riveted assemblies are not tight and leak proof.
• The projection of the riveted head adversely affects the appearance of the riveted structure.