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One method the analyzer may use, is to make the measurement at each degree pair of the crankshaft revolution. A degree pair, for example, is the distance between 270 and 271 degrees in the rotation of the crankshaft, so there are a total of 360 degree pairs in the full rotation. IHP is the Force in pounds X the Distance in feet / the Time in minutes.
Work = Force X Distance
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Force in pounds is the area of the piston X the average pressure of each degree pair.
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Distance in feet is how far the piston moved between the degree pair.
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Time is how long it took for the piston to travel from one degree to the next in the pair.
To further explain:
Horsepower = PLAN/33000
P is the Mean Effective Pressure (MEP). Indicated Mean Effective Pressure (IMEP) is used for IHP calculations while Brake Mean Effective Pressure (BMEP) is used for BHP calculations.
L is the distance that the piston traveled in feet.
A is the area of the piston.
N is the number of functional cycles per minute, or RPM in a compressor.
33000 is a constant that represents the number of ft/lbs per minute for 1 horsepower.
IHP can also be referred to as Gas Horsepower (GHP).
One method the analyzer may use is to solve the PLAN/33000 formulae one degree at a time for one complete revolution of the crankshaft.
Beginning at degree 0, P is the average pressure of degree 0 and 1.
L is the distance the piston traveled from degree 0 to degree 1 divided by 12.
A is the surface area of the piston less the area of the piston rod if present.
Now we make the same calculations for the next degree pair (2 and 3) and so on and so forth.
The total cylinder end IHP is the summation of the 360 measurements and calculations.
Another method is to measure the area of the indicator card (figure 1) and calculate the work and relate that to time to get IHP. The two methods return virtually the same result.
So, how accurate is the analyzer measurement of IHP? The answer is very accurate if the following conditions are met:
- An accurate bore, stroke, connecting rod length, and compressor and/or tail rod diameter are used in the setup of the analyzer.
- The analyzer is accurately phased to the TDC position of the cylinder being measured.
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The pressure indicator passage has no leakage, restrictions or trapped volumes. Indicator passage acoustical resonance does not affect the accuracy of the IHP measurement.
- The pressure transducer is linear and sized to indicate the minimum and maximum pressures encountered in the cylinder. Pressure transducer zero offset error does not affect IHP measurement.
The following things that are needed for a theoretical prediction of IHP are not needed when IHP is measured with an analyzer:
- Gas composition, including specific gravity, ratio of specific heats, and compressibility factors.
- Cylinder end clearance volumes (load step information).
- Pulsation effects and valve and cavity losses.
- Suction and discharge temperatures.
- Reference suction and discharge pressures and their relationship to the internal cylinder pressures.
The above items affect the measured IHP but are not needed for measurement accuracy. In addition, the mechanical condition (valve and ring condition) of the compressor does not affect the accuracy of the IHP measurement but may have a significant effect on the accuracy of a theoretically predicted IHP. Differences exist between using a portable analyzer or an on-line monitoring system for measurement.
The on-line monitoring system will use a pressure sensor for each cylinder end on the compressor unit (8 sensors for a 4-throw machine). This requires periodic calibration of the sensors for consistent accuracy, however, the IHP measurement occurs almost real-time on all cylinder ends.
The portable analyzer may use only one pressure transducer to measure all the cylinder ends. If the analyst properly calibrates the sensor between cylinders, the accuracy of the measurements should be the same for all cylinders, however, the load conditions must remain stable for the duration of the testing.
Compressor packages are generally rated to the HP capacity of the driver. This is referred to as Brake Horsepower (BHP) or horsepower available at the output of the driver. Since we are only measuring the IHP or GHP, we need some method to add the horsepower requirement for internal friction, bearing and internal drive losses of the compressor frame and components. To get from IHP to BHP, we must divide IHP by the compressor mechanical efficiency. BHP = IHP / me. A mechanical efficiency of 95% has been the industry standard for slow-speed compressors for many years; however, it may vary from manufacturer to manufacturer, unit model to unit model, and/or rated speed. Please consult the OEM for the proper conversion for your specific compressor.
Now that you know,
Happy monitoring.
Regards,
Warren
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