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THE DIFFERENCE BETWEEN ISOTHERMAL AND ADIABATIC CONDITIONS

Hydraulic accumulators use weights, springs, or gas pressure to generate the precharge force against the fluid that is stored for use in the system. Gas-charged accumulators use pistons, bladders, or diaphragms to separate the hydraulic fluid from the gas charge. Bladder type accumulators are available in sizes ranging from 115 cc (7 in3) to 300 liters (80 gallons), generally in pressure ranges of 21 MPa and 35 MPa (3,000 and 5,000 psi).

Gas-charged accumulators operate by placing the compressible gas over the nearly incompressible hydraulic fluid in a constant volume pressure vessel. The hydraulic pressure and volume of fluid available to the system are dependent on the precharge pressure and the expansion characteristics of the gas. Dry nitrogen is typically used to precharge accumulators.

SAFETY TIP: Because of the risk of combustion, never use oxygen or air to precharge an accumulator.

The terms "isothermal" and "adiabatic" are used to describe the expansion characteristics of the gas. Compressing and decom- Bladder-type accumulator pressing gas causes it to heat and cool respectively. If the volume of the gas is changed slowly, the changes in temperature are dissipated through the solid materials of the accumulator and so the temperature of the gas is kept constant. This is called isothermal (same temperature) contraction and expansion.

When a gas is compressed and expanded quickly, heating and cooling cause pressure changes in addition to those occurring strictly as the result of volume changes. If the gas is insulated so that very little heat can escape, the pressure of the gas will increase and decrease more than inversely to the change in volume. Under compression, heat added to the gas as it is compressed will raise the pressure above the pressure increase caused by reducing the volume. Under expansion, the pressure will decrease more than would be expected just by decreasing the volume. This is called adiabatic (cannot pass) contraction and expansion.

To accommodate changes in both pressure and temperature of the precharge gas, the general gas law can be used to compute the volume available from an accumulator. Absolute values are used for temperature and pressure when making computations. Rankine is the absolute scale for Fahrenheit and Kelvin is the absolute scale for Celsius. Formulas for converting from Fahrenheit to Rankine and Celsius to Kelvin are as follows: °F to °R: °R = °F + 459.7 °C to K: K = °C + 273.15

The ideal gas law:

p1 i V 1 i t2 = p2 i V 2 i t 1

p1 = Initial pressure (psia)absolute V1 = Initial volume t1 = Initial temperature Rankine p2 = Final pressure (psia)absolute V2 = Final volume t2 = Final temperature Rankine p1 = Initial pressure (MPa)absolute V1 = Initial volume t1 = Initial temperature Kelvin p2 = Final pressure (MPa)absolute V2 = Final volume t2 = Final temperature Kelvin Gas laws with temperature and pressure.

For isothermal conditions, the equation is:

p1 = Absolute precharge pressure V1 = Accumulator gas volume at precharge p2 = Absolute minimum pressure V2 = Accumulator gas volume at minimum pressure p3 = Absolute maximum pressure V3 = Accumulator gas volume at maximum pressure Gas laws with pressure.

p1 i V 1 = p2 i V 2 = p3 i V 3

Note: Accumulators should be mounted vertically.

Temperature has an effect in the application of accumulators. The ideal gas laws tell us that for a given change in temperature, there will be a corresponding change in the pressure within an accumulator. This makes temperature a necessary consideration when sizing an accumulator. If the ambient temperature changes, the gas temperature in the accumulator will also change and will affect the pressure. For example, an accumulator on a piece of equipment that is outdoors may have a much different ambient condition in the early morning than it will have in the heat of the day. The designer must be sure that the accumulator will be adequately sized to address these conditions.

In general, charging the accumulator can be considered an isothermal process and the normal operation of the accumulator considered an adiabatic operation.

The following equations are for adiabatic conditions when solving for accumulator sizing or available volume:

VI = V U ⎛ ⎜ ⎜ ⎝

p1 p2 1 n p1 p3 1 n VI = Initial accumulator volume VU = Available liquid volume Sizing an P1 = Absolute precharge pressure accumuP2 = Minimum system pressure lator with P3 = Absolute maximum pressure adiabatic = Polytropic exponent 1 conditions. (n=1.4 for nitrogen gas,1/n=0.714) n

VU = V I i

p1 p2 1 n p1 p3 1 n VI = Initial accumulator volume Finding the VU = Available liquid volume available P1 = Absolute precharge pressure P2 = Absolute minimum pressure volume from an accumulator P3 = Absolute maximum pressure with = Polytropic exponent 1 adiabatic (n=1.4 for nitrogen gas,1/n=0.714) n conditions.

a

P

T a

P A T B

b

Accumulator circuit

The closed-center accumulator circuit shown above helps to maintain system pressure. It could also supplement pump flow to operate the cylinder. Maintaining system pressure with the accumulator and closed-center valve makes the circuit more responsive. The accumulator will also supplement pump flow to supply more fluid than the pump alone could during brief periods of high usage. When the cylinder deadheads and the directional valve is actuated, the pump refills the accumulator. Pressure will pilot open the unloading valve, unloading the pump, while the accumulator makes up fluid lost due to system leakage. When the fluid in the accumulator has been depleted and pressure falls below the setting of the unloading valve, the unloading valve will close, directing pump flow into the circuit and also refilling the accumulator. Theoretically, very little flow will ever pass over the relief valve. The line to the accumulator is equipped with a free-flow check valve allowing unrestricted flow into the accumulator and an adjustable orifice in parallel with the check valve to control flow from the accumulator to the circuit. Without the needle valve, the cylinder speed would SAFETY TIP: A charged accumulator has stored energy. The uncontrolled release of that energy can cause serious injury, either by direct contact with pressurized fluid or the unexpected and uncontrolled movement of a machine. It is absolutely essential that the energy be drained or isolated before any work is performed on or around the accumulator. This means that the pressure of the hydraulic fluid must be isolated or brought to zero gauge or be isolated from possible unexpected release. A gas-charged accumulator must also have the gas pressure brought to zero gauge or isolated from unexpected release.

SAFETY TIP: Releasing the gas charge will displace the air around the accumulator. If this is done in a small area, there is the danger of asphyxiation. Be sure the area is well ventilated or that the gas is vented to the outside.

be dependent on the discharge rate of the accumulator, which can be much greater than the flow rate required by the application.

The fixed displacement pump fills the accumulator while the directional control valve is in the center position or when the cylinder is bottomed out when the valve is still shifted. Once the set point of the unloading valve has been reached, the unloading valve directs unneeded flow from the pump to the reservoir. Shifting the directional control valve releases the fluid in the accumulator and routes it to the cylinder. The pump remains unloaded as long as the accumulator can supply fluid to the cylinder at a pressure above the setting of the unloading valve. As the pressure drops, the unloading valve closes and the pump powers the cylinder, and given time, refills the accumulator. Maximum system pressure is controlled by the setting of the unloading/relief valve. The internal pilot would operate the relief valve should the external pilot become inoperative. As a safety measure, the 2/2 normally open solenoid valve releases pressurized fluid, through a small orifice, when the system is turned off. The check valve prevents downstream fluid from passing to tank when the unloading valve is piloted open. 

1A 4-liter capacity accumulator supplies fluid to a hydraulic system between 12 MPa and its precharge pressure of 6.9 MPa. Using the ideal gas law, how many liters of hydraulic fluid are available from the accumulator if the temperature changes from 27 °C to 65 °C as the accumulator fills? Assume adiabatic compression and expansion of the gas.

a. 0.4 liters. b. 1.4 liters. c. 2.1 liters. d. 4 liters. e. 5.5 liters.

2A 2-gallon accumulator supplies fluid to a hydraulic system between 3,000 psi and 2,000 psi. If the precharge pressure is 1,000 psi, how many cubic inches of hydraulic fluid are available from the accumulator if the process is isothermal as the accumulator fills?

a. 77.2 in3 b. 81.4 in3 c. 155.5 in3 d. 180.6 in3 e. 232.7 in3

See solution on page 31.

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Robert Sheaf has more than 45 years troubleshooting, training, and consulting in the fluid power field. Email rjsheaf@cfc-solar.com or visit his website at www. cfcindustrialtraining.com.

New Problem

Pusher Cylinders Stop Midway

By Robert Sheaf, CFPAI/AJPP, CFPE, CFPS, CFPECS, CFPMT, CFPMIP, CFPMMH, CFPMIH, CFPMM, CFC Industrial Training

»THE MAINTENANCE department of a large recycling company had us look at a metal shredder that had problems with two “pusher cylinders” stopping midway in their stroke.

The shredder had a 6-foot diameter shredding drum approximately 12 feet long driven by a hydrostatic system using an 800-hp electric motor driving two large pumps and four hydraulic motors. Two separate open loop hydraulic systems ran the auxiliary cylinders and motors that fed the raw material and then removed the shredded metal. The two cylinders would push the metal down a chute until it engaged the shredding drum. They were controlled by one directional valve stack on a manifold. There were multiple hydraulic feedback devices sending signals to the unit’s computer.

The above control circuit for the push cylinders (only one cylinder is shown) includes a counterbalance valve that was recently added with the thinking that they would keep the cylinders from stopping every few hours in midstroke. They were sure the computer was not the problem.

They had to stop the machine, remove, and reinstall the counterbalance valve, and then the system would start up again. They replaced the directional valve and pilot-operated checks, but it did not help. The valve’s coil indicator light was on, and they would manually shift the directional valve, but it made no difference. I then asked what the pressure on the HPU read, and they said it was on the other side of the machine where the HPU was located, and the gauge was broke. The unit was running when I arrived and could not do much.

What would you tell them to check the next time it failed?

Solution to January 2021 problem:

Intensifier Drops from Required Pressure after Several Hours

The filter press circuit that started at 8,500 psi and dropped to 5,000 psi had two problems. The first was that the pilot-operated check was leaking; the second was that the four-way directional valve spool was scarred and leaking high-pressure fluid back to the tank. The air-over-oil intensifier could have been replaced with a larger output unit to fix the problem, but it was the leaking valves that caused the problem.

The directional valve leakage increased as the oil heated up, and the 5,000-psi pressure drop would leak the entire intensifier output back to the tank. Increasing the oil viscosity could have been a possible fix, but the actual problem would still exist. Changing the directional valve and pilot-operated check valve stack solved the problem.

We also pushed them to install a return line filter. There was no filter anywhere on the oil circuit. Visit www.fluidpowerjournal.com/figure-it-out to view previous problems.

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