CYLINDER BUCKLING CALCULATIONS

hydraulic cylinders selection mostly depend on the critical buckling strength and bending strength of the cylinder apart from the other criteria like bore diameter,rod diameter and stroke length.

Buckling is a kind of failure where the cylinder fails under axial compressive load. In science, buckling is a mathematical instability, leading to a failure mode. Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium. At a certain stage under an increasing load, further load is able to be sustained in one of two states of equilibrium: an undeformed state or a laterally-deformed state.

 In practice, buckling is characterized by a sudden failure of a structural member subjected to high compressive stress, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding.

while calculating buckling we normally use the most conventional formula of mathematician Leonhard Euler.He derived a formula that gives the maximum axial load that a long, slender, ideal column can carry without buckling. 

An ideal column is one that is perfectly straight, homogeneous, and free from initial stress. The maximum load, sometimes called the critical load, causes the column to be in a state of unstable equilibrium; that is, the introduction of the slightest lateral force will cause the column to fail by buckling. The formula derived by Euler for columns with no consideration for lateral forces is given below. However, if lateral forces are taken into consideration the value of critical load remains approximately the same.

EULER'S FORMULA :- 

where

= maximum or critical force (vertical load on column),

= modulus of elasticity,

  = area moment of inertia,

= unsupported length of column,

= column effective length factor, whose value depends on the conditions of end support of the column, as follows.

For both ends pinned (hinged, free to rotate), = 1.0.

For both ends fixed, = 0.50.

For one end fixed and the other end pinned, = 0.699....

For one end fixed and the other end free to move laterally, = 2.0.

is the effective length of the column.

 Examination of this formula reveals the following interesting facts with regard to the load-bearing ability of slender columns.

1. Elasticity and not compressive strength of the materials of the column determines the critical load.
2. The critical load is directly proportional to the second moment of area of the cross section.
3. The boundary conditions have a considerable effect on the critical load of slender columns. The boundary conditions determine the mode of bending and the distance between inflection points on the deflected column. The closer together the inflection points are, the higher the resulting capacity of the column.

 The strength of a column may therefore be increased by distributing the material so as to increase the moment of inertia. This can be done without increasing the weight of the column by distributing the material as far from the principal axis of the cross section as possible, while keeping the material thick enough to prevent local buckling. This bears out the well-known fact that a tubular section is much more efficient than a solid section for column service.
Another bit of information that may be gleaned from this equation is the effect of length on critical load. For a given size column, doubling the unsupported length quarters the allowable load. The restraint offered by the end connections of a column also affects the critical load. If the connections are perfectly rigid, the critical load will be four times that for a similar column where there is no resistance to rotation (hinged at the ends).
Since the moment of inertia of a surface is its area multiplied by the square of a length called the radius of gyration, the above formula may be rearranged as follows. Using the Euler formula for hinged ends, and substituting A·r² for I, the following formula results.

where is the allowable stress of the column, and is the slenderness ratio.

Since structural columns are commonly of intermediate length, and it is impossible to obtain an ideal column, the Euler formula on its own has little practical application for ordinary design. Issues that cause deviation from the pure Euler strut behaviour include imperfections in geometry in combination with plasticity/non-linear stress strain behaviour of the column's material. Consequently, a number of empirical column formulae have been developed to agree with test data, all of which embody the slenderness ratio. For design, appropriate safety factors are introduced into these formulae. One such formula is the Perry Robertson formula which estimates of the critical buckling load based on an initial (small) curvature. The Rankine Gordon formula is also based on experimental results and suggests that a strut will buckle at a load Fmax given by:

where Fe is the Euler maximum load and Fc is the maximum compressive load. This formula typically produces a conservative estimate of Fmax.

Normally for factor of safety for linear buckling is taken more than 3.5.


hope this helps the needful..
If any query about this topic please comment..

HYDRAULIC CYLINDER BASICS

The most important linear actuator in a hydraulic system is a Hydraulic cylinder.It converts the hydraulic energy in to mechanical energy.Hydraulic cylinder can be of any size depending on the purpose for which it is built.The type of work to be done and power requirements determine the size of the hydraulic cylinder.

Types of hydraulic cylinders:-

1. Single acting cylinder.

Single acting cylinders are pressurized at one end only and the other end is vented to the reservoir.

2. Double acting cylinder.

Double acting cylinders can be pressurized from both ends resulting in two way motion of the actuator i.e it can extend and retract.

Basic double acting cylinder.

spring return single acting cylinder

single acting cylinder(ram cylinder)

telescopic cylinder

Operation:-

Hydraulic cylinders get their power from pressurized hydraulic fluid, which is typically oil. The hydraulic cylinder consists of a cylinder barrel, in which a piston connected to a piston rod moves back and forth. The barrel is closed on each end by the cylinder bottom (also called the cap end) and by the cylinder head where the piston rod comes out of the cylinder. The piston has sliding rings and seals. The piston divides the inside of the cylinder in two chambers, the bottom chamber (cap end) and the piston rod side chamber (rod end). The hydraulic pressure acts on the piston to do linear work and motion.
Flanges, trunnions, and/or clevises are mounted to the cylinder body. The piston rod also has mounting attachments to connect the cylinder to the object or machine component that it is pushing.
A hydraulic cylinder is the actuator or "motor" side of this system. The "generator" side of the hydraulic system is the hydraulic pump which brings in a fixed or regulated flow of oil to the bottom side of the hydraulic cylinder, to move the piston rod upwards. The piston pushes the oil in the other chamber back to the reservoir. If we assume that the oil pressure in the piston rod chamber is approximately zero, the force F on the piston rod equals the pressure P in the cylinder times the piston area A:

The piston moves instead downwards if oil is pumped into the piston rod side chamber and the oil from the piston area flows back to the reservoir without pressure. The fluid pressure in the piston rod area chamber is (Pull Force) / (piston area - piston rod area):

where P is the fluid pressure, F_p is the pulling force, A_p is the piston face area and A_r is the rod cross-section area.

TYPICAL CYLINDER CONSTRUCTION

Parts of a hydraulic cylinder:-

A hydraulic cylinder consists of the following parts

Cylinder barrel

The cylinder barrel is mostly a seamless thick walled forged pipe that must be machined internally. The cylinder barrel is ground and/or honed internally

Cylinder base or cap

In most hydraulic cylinders, the barrel and the bottom portion are welded together. This can damage the inside of the barrel if done poorly. Therefore, some cylinder designs have a screwed or flanged connection from the cylinder end cap to the barrel. (See "Tie rod cylinder", below) In this type the barrel can be disassembled and repaired.

Cylinder head

The cylinder head is sometimes connected to the barrel with a sort of a simple lock (for simple cylinders). In general, however, the connection is screwed or flanged. Flange connections are the best, but also the most expensive. A flange has to be welded to the pipe before machining. The advantage is that the connection is bolted and always simple to remove. For larger cylinder sizes, the disconnection of a screw with a diameter of 300 to 600 mm is a huge problem as well as the alignment during mounting.

Piston

The piston is a short, cylindrical metal component that separates the two parts of the cylinder barrel internally. The piston is usually machined with grooves to fit elastomeric or metal seals. These seals are often O-rings, U-cups or cast iron rings. They prevent the pressurized hydraulic oil from passing by the piston to the chamber on the opposite side. This difference in pressure between the two sides of the piston causes the cylinder to extend and retract. Piston seals vary in design and material according to the pressure and temperature requirements that the cylinder will see in service. Generally speaking, elastomeric seals made from nitrile rubber or other materials are best in lower temperature environments, while seals made of Viton are better for higher temperatures. The best seals for high temperature are cast iron piston rings.

Piston rod

The piston rod is typically a hard chrome-plated piece of cold-rolled steel which attaches to the piston and extends from the cylinder through the rod-end head. In double rod-end cylinders, the actuator has a rod extending from both sides of the piston and out both ends of the barrel. The piston rod connects the hydraulic actuator to the machine component doing the work. This connection can be in the form of a machine thread or a mounting attachment, such as a rod-clevis or rod-eye. These mounting attachments can be threaded or welded to the piston rod or, in some cases, they are a machined part of the rod-end.

Rod gland

The cylinder head is fitted with seals to prevent the pressurized oil from leaking past the interface between the rod and the head. This area is called the rod gland. It often has another seal called a rod wiper which prevents contaminants from entering the cylinder when the extended rod retracts back into the cylinder. The rod gland also has a rod wear ring. This wear ring acts as a linear bearing to support the weight of the piston rod and guides it as it passes back and forth through the rod gland. In some cases, especially in small hydraulic cylinders, the rod gland and the rod wear ring are made from a single integral machined part.

Other parts

• Cylinder base connection
• Seals
• Cushions 

CYLINDER RATINGS:- 


 The rating of a cylinder is designated by the size and pressure capability of the cylinder. 
 The principal size features are
1.piston diameter.(bore diameter of cylinder)
2.piston rod diameter.
3.stroke length. 
The pressure capability is mentioned on the cylinder nameplate by the manufacturer .

to be continued......

HYDRAULIC RESERVOIR DESIGN

figure-1(a typical reservoir cut away view)

Introduction:- 

The main function of hydraulic reservoir in hydraulic system is to store and supply the hydraulic fluid to be used in the system.Hydraulic systems need a finite amount of liquid fluid that must be stored and reused continually as the circuit works, therefore, part of any hydraulic circuit is a storage reservoir or tank.

Reservoir design and implementation is very important, the efficiency of a well-designed hydraulic circuit can be greatly reduced by poor tank design.

Functions of Hydraulic reservoir:- 

1. Storage of hydraulic fluid.

2. Acts as a heat exchanger.

3. Acts as a De-aeration system.

4. Can be used to support the hydraulic components to save  floor space.

5. Acts As a fluid conditioner.

Components of Hydraulic reservoir:- 

A typical industrial reservoir is made up of steel sheet metal fabricated to a definite shape according to requirement.In case the reservoir is used in any mobile equipment like mobile cranes or material handling equipments the the reservoir sizing and weight is very critical.

A reservoir has different components and accessories(see above picture).

1. Reservoir(sheet metal fabricated structure to suit particular requirement)

2. Strainer

3. Drain plug

4. Baffle plates 

5. Suction pipes (towards the pump)

6. Return line pipe.(from all the return line manifolds)

7. Return line filter

8. Breather

9. Riser.

10.Man hole or clean out plates(for cleaning the reservoir) 

11.Filler cap.

12.Oil level gauge.

13.Temperature gauge.

14.Hydraulic oil cooler (it is not an integral part of reservoir)

15.Oil heater (in case of cold countries)

All the above components are very essential for a good hydraulic tank design as every component has its specific function.

Strainer:-

It is fitted to the suction line inlet.It provides the filtered fluid to the pump.It normally contains some filtering screens (for particular size particulates) which filters the contaminants before it goes to the pump.It is replaced time to time to ensure blockage and reduced flow.

Drain plug:-
It is normally fitted at the bottom of the tank to drain away the fluid while overhauling or

cleaning.The drain plug size should not be so large or so small.one or more drain plugs can be provided depending on requirement.Normally drain plugs are fitted to the welded flanges.Most important factor is to choose proper fittings for the drain plug to avoid leakage issues.

Baffle plates:-

baffle plates are normally the steel plates which are incorporated in the reservoir to divide the fluid in to different chambers so that the fluid has to travel through other ways to get to the suction chamber.Baffle plates divide the reservoir into to chambers return flow chamber and suction chamber.From the suction chamber pump suction lines start. The return line flows are  put into the return chamber so that the return flow has to flow certain distance before it reaches the suction line and in the way get cooled and contaminants get to the bottom of reservoir.No through holes are to be in the baffle, we want the oil flow to go over the top of the baffle.  A small ¼” gap at each end of the baffle allows oil levels to remain equal on each side of the baffle, (majorly of flow goes over the top).

Suction pipe:-

Suction pipes generally have larger diameter as compared to return lines.Suction pipes have smaller length so as to facilitate lesser loss and cavitation.

Return pipe:-

Return pipe comes directly from the return line manifold or the return line filter if provided.The return line end should not be too high from the bottom of the reservoir as too high outlet will cause turbulence to the output flow.Normally the return line ends are taper cut to facilitate the flow direction towards the wall side.This will help the fluid to travel larger distance so that it gets more time to cool,purify and de-aeration.

Breather:-

 The breather cap of the correct size should include a filter media to block contaminants as the fluid level lowers and rises during a cycle. It is important to understand that too small a breather cap will cause a vacuum in the oil tank and cause cavitations in the pumps.  You should never use a filler-breather type cap, as any opening where someone can pour contaminated fluid into the tank should be avoided.  Always provide a quick disconnect just before the return filter used for adding or filling the reservoir, that way all fluid going into the tank is filtered.

 Filler cap:-

 The filler opening is often a part of breather assembly.The opening has removable screen that keeps  contaminants out of the tank while fluid is being added to the reservoir.A cap that would provide tight seal should be chained to the reservoir.
 Oil level gauge:-
 To check the fluid level of the reservoir without opening it and preventing it from contaminants oil level gauge is used.
 

These notes are just basic simple suggestions and are not intended to be detailed design notes in designing reservoirs.  There are many other factors and design notes required to make a good reservoir, and are too many to outline is the forum.  A good reservoir design is the least expensive to build, but the most critical component of any hydraulic system.

Heat dissipation by the wall surface of reservoir:-

 A baffle separates the return line from the pump inlet line, forcing the fluid to take the longest possible path through the reservoir before returning to the pump inlet. This arrangement also mixes the fluid well and provides more time to drop contaminates and de-aerate. In addition, the fluid spends more time in contact with the outer walls of the reservoir to dissipate heat.
A formula for estimating how much heat a reservoir can dissipate is as follows:

HP = 0.001 x (Tf – Ta) x A
HP = maximum HP tank can dissipate.
Tf = maximum fluid temperature as °F.
Ta = maximum ambient air temperature as °F.
A = tank area as sq. ft. in contact with fluid.

Reservoir sizing :-
The main reason the reservoir exists is to store fluid.The accepted general rule for sizing a tank is; the tank volume should be two to four times the pump flow in gpm. This is only a general rule, and some circuits may require more volume, while less fluid may be adequate for other circuits.

With this general rule, the returned fluid theoretically will have two to three minutes in the tank before it circulates again.  The application really determines the reservoir size, for example, in very high ambient temperatures the reservoir should be oversized if possible even with an oil cooler.  It requires time to dissipate heat, allow contamination and air to escape the fluid, and the longer you can give the fluid time to rest before it circulates again the better.

On mobile equipment where space and weight are a premium, the reservoir still must provide all the basic functions, just at a lower level.  More external cooling and filtration is required in most mobile applications to make up what the oil tank could do if sized larger.

The reservoir level during operation should raise and lower no more than is necessary, about 6”-8”.  The more the fluid level changes, the more air is required to enter and leave the reservoir.  Along with this air exchange, comes moisture which produces condensation (water) in the fluid. There also should be about a 4”-6” air pocket above the oil level at all times and sufficient level above the pump from falling below the inlet and to prevent a vortex from developing above the pump inlet allowing air to enter the system.

Another situation where a tank may need to be larger is if the circuit has accumulators. Accumulators need fluid to fill them at start up and space into which to discharge this fluid at shut down. An undersized reservoir may not have enough fluid to keep the pump inlet covered at all times.