Most pneumatic system designers are familiar with the flow coefficient Cv as a means of gauging flow through various fluid-power components. Unfortunately, there is a common misconception in the industrial community that doubling a valve's flow coefficient, or conductance, Cvv, cuts actuator stroke time in half. The reality is that this is not the case. The system's conductance, Cvs, is one of the criteria that impacts stroke time, and Cvv is only part of Cvs.
Even Cvs is not the sole yardstick for establishing piston speed. Another critical factor is the volume of compressed exhaust air that must be expelled. This includes air captured in the conductor between the valve and actuator and often represents the majority of the air. Bear in mind that stroke time is directly proportional to the entire system exhaust volume and inversely proportional to Cvs.
To better grasp the vital roles that volume and Cvs play in a circuit's performance, consider several examples of typical valves with push-to-connect fittings. The valves operate in identical circuits and have Cvv values of 0.3, 0.4, 0.5, and 0.6. Thus, only the valve impacts upon piston stroke time.
The remaining circuit components, which are common to all the valves, include: polyurethane tubing with length, L2 = 120 in., 0.197- in. diameter, and 3.66-in. 3 volume, two conductor elbows, one sandwich regulator, one silencer, one quick disconnect, and a 1.5 9-in. rodless actuator with a sweep volume of 15.90 in. 3 Note that the conductor volume in this system represents about 19% of the total volume and, if ignored, would suggest actuator performance 19% faster than actual.
The effects of the different valves can be found by first determining system capacitance. Based on manufacturer's data, the sandwich regulator capacitance, Cvr, silencer capacitance, Cvl, and quick disconnect capacitance, Cvq, have values of 0.59, 1.00, and 1.20, respectively.
The following equations are used to calculate the equivalent elbow length, L1. This will be added to the actual conductor length, L2, which is used to determine the entire conductor capacitance, Cvc, fitting capacitance, Cvf, and Cvs.
Determine a 90° elbow's equivalent length, L1, in terms of its mating conductor from:
L1 = 12nkd
= 14 in.
where n = number of identical fittings, k = curvature factor assigned to an elbow, and d = smallest diameter in the fitting. The total length Lt = L2 + L1 = 134 in. for determining Cvc.
Calculate conductor Cvc using:
Cvc = 33.22d 2 (d/fLt) 0.5
= 33.22(0.197) 2
where f = internal friction factor of the conductor.
The next step is determining fitting Cvf using:
Cvf = kfd 2
= 23(0.197) 2
where the constant kf for the fitting = 23. For comparison, a burred, drilled hole has kf = 16 and a venturi has kf = 29.
Combine all conductance values to determine Cvs:
1/Cvs 2 = 1/Cvv 2 + 1/Cvc 2 + 2/Cvf 2 +
1/Cvr 2 +
1/Cvl 2 + 1/Cvq 2
= 1/0.602 + 1/0.292 + 2/0.892
1/0.592 + 1/1.002 + 1/1.202
Cvs = 0.214.
The results for the remaining three Cvs values, calculated in similar fashion, are shown in the table.
As the table indicates, increasing Cvv 100% increases Cvs only 17.6%. Don't be fooled by hype claiming larger Cvv values produce a commensurate increase in actuator speed. Every pneumatic-circuit component has a conductance value and, thus, impacts Cvs.
In the rare case that a valve is integrated closely with the actuator, with few fittings and short conductors, the original premise of doubling the actuator speed by doubling Cvv can be approached, but never reached.
Let us briefly explore the notion of using optimum fittings and conductor diameters and replacing or, whenever possible, removing restrictive devices from a circuit. This essentially optimizes the circuit to determine how close we can approach or exceed the cylinder speed using the 0.30-Cvv valve in place of the 0.60-Cvv valve.
The elements of a pneumatic circuit can be likened to the links of a chain. The smallest component conductance dictates Cvs because the resultant Cvs is always less than the smallest component conductance, as evidenced in the above example.
In actual systems there are typically restraints on component locations, so it's often difficult to build an "optimized" system. However, designers can increase conductor diameter. For instance, changing the tubing in the previous example to 3 /8-in. with a 1 /4-in. ID raises Cvc to 0.59. Because the valve is often the most expensive component, it is wise to select the smallest valve possible while allowing an acceptable Cvs.
The valve in the fastest circuit in the example has a Cvv = 0.60 and its conductor's Cvc = 0.29. If, however, the circuit had a valve with Cvv = 0.30 and a conductor with Cvc = 0.59, stroke time would be essentially the same with a smaller capital investment.
However, a larger conductor increases total volume 11.4% from 19.56 to 21.79 in 3 . The conductor now represents 27% of the total volume as opposed to the original 19%. One possibility of eliminating the 11.4% volume increase is to shorten the conductor.
To accommodate the larger conductor it is necessary to replace push-in type insert fittings with threaded push-in fittings. The threaded fittings raise Cvf from 0.89 to 1.44 and permit a smaller valve. Another option is to replace the sandwich regulator with an external unit that will not restrict airflow.
The new circuit consists of a valve, Cvv = 0.30, conductor, Cvc = 0.59, two fittings, each with Cvf = 1.44, a silencer, Cvl, and a quick disconnect, Cvq, resulting in a Cvs of 0.245. This is 14.5% faster than the larger valve with twice the Cvv in the old circuit. With the volume change of 11.4%, net gain is 3.1%, or an equivalent Cvs of 0.221 with no volume change considerations.
The revised pneumatic circuit has a smaller valve, a larger conductor, and an external regulator instead of a sandwich regulator. The circuit generates faster cycle times with a lower capital investment than the original circuit.
Let us also consider replacing the smaller valve, Cvv = 0.30, with the larger valve, Cvv = 0.60, in the revised circuit. The new Cvs is 0.347. The net improvement over the small-valve circuit is 79.3%. The improvement resulting from the enhanced Cvs is 90.7%. Deducting the 11.4% exhaust volume increase renders a 79.3% improvement. The improvement over the original circuit with the 0.60 Cvv valve is 50.8% net.
The last comparison is between the 0.60- Cvv valve and the 0.30- Cvv valve with both used in the modified circuit. Cvs values are 0.347 and 0.245, respectively. This renders an improvement of 41.6% compared to only a 17.6% in the original circuit. This is quite an impact considering the only difference is the conductor size and the regulator relocation. It is not surprising that 32.3% of the 41.6% is credited to the conductor enhancement. The remaining 9.3% results from relocating the regulator. It is not necessary to consider volume changes because the two circuits use identical cylinders and conductors.
The lesson is that the valve is not the sole determinant in calculating for cylinder speed and the remaining pneumatic-circuit elements should not be ignored because they all impact cylinder speed.
|How valve changes impact system conductance|
|Conductance improvement (%)|
|Cvs improvement (%)|
This information supplied by Henry Fleischer, Vice President, Research and Development, Numatics Inc., Highland, Mich.