Sizing Pneumatics for Performance and Efficiency

Authored by: Curtis Harvey Lead Mechanical Engineer Foth Production Solutions LLC Lake Elmo, Minn. Edited by Kenneth J. Korane [email protected] Key points: • Traditional techniques size pneumatic circuits based on valve flow. • To improve performance and energy efficiency, consider every component that causes flow restrictions, pressure drops, or time delays. Resources: Foth Production Solutions, www.foth.com

Too often, pneumatic circuits are sized based on the valve’s flow coefficient, C_v, without considering other system components. In the past, focusing on the valve alone often sufficed because air was considered “free” and designers tended to oversize valves. Today’s emphasis on better energy management and performance requires a more-exacting method to properly size pneumatic motion systems.

Sustainability conscious users can reduce air and energy consumption by using smaller, fewer, and less-expensive components and still ensure smooth and efficient operation.

Pneumatic systems

The C_v equation

provides a standard means to predict flow through valves and other components. But designers must consider every component that could cause flow restrictions, pressure drops, or time delays when engineering pneumatic circuits.

For instance:

Tips for optimizing air circuits • Mount valves as close to actuators as possible to keep air lines short. • Keep air lines between valve and cylinder straight with as few bends as possible. Bends greater than 10× the air-line ID do not appreciably affect performance. • Flexing air lines wear over time and can lead to restrictions. • Size cylinder bores and strokes to handle the expected load plus a reasonable safety factor. Larger and longer-than-necessary cylinders cost more, waste space and energy, and add cycle time. • Consider using frictionless air cylinders from manufacturers such as Airpot Corp. But factor in a higher leakage rate. • Valves can be oversized without appreciably wasting air. However, cycle time will increase if shift time increases. • A pair of 3/2 valves mounted directly in each cylinder port has several advantages. It should increase speed and reduce delay time. There is no exhaust-side pressure drop due to fittings, bends, air lines, and flow controls. And the design consumes less air because lines are not continuously charged and discharged. • Over-pressurizing a circuit beyond the maximum pressure drop does not increase cylinder speed, but it wastes air and increases delay time and total cycle time. • If applications call for different loads or speeds for extend and retract motions, consider using pressure regulators or flow controls. Try downsizing an air line to slow the motion and use less air. • Consider using quick-exhaust valves. Air bypasses the exhaust circuit, reducing cycle time and increasing speed. Adding regulators and lowering air consumption generates further savings. • Each application has an optimum air-line ID. Increasing air-line diameter increases Cv but also increases the volume that must be charged and discharged each cycle. • Components with the smallest Cvs and the largest pressure drops limit circuit performance. Increase these Cvs first to have the greatest impact. • Components with the largest Cvs and smallest pressure drops are probably oversized. Decreasing these Cvs could improve circuit performance and reduce costs. • Maintain good incoming-air quality. Moist air leads to rust in air lines and components and oil residue on interior surfaces causes sticking and constrictions. Poor performance results. • Plan on machine operators adjusting pressure above design spec in an attempt to boost cycle time. This is often the first knob that gets turned to compensate for wear and corrosion over time. • If cylinder speed becomes excessive, estimate a shock absorber’s effect on stroke time. Calculate the extra time a shock absorber adds to stop a load by dividing the shock’s working stroke by the cylinder speed when the rod makes initial contact. For example, adding a 1-in.-stroke shock absorber to a 3-in.-stroke cylinder with a contact speed of 40 ips would add roughly 0.025 sec to the stroke. • Standard fittings are typically rated for a higher pressure than the supply pressure. Consider modifying the fitting by increasing its ID, taking care that it withstands system pressure with a safety factor. • Challenge the design constraints. Hidden safety factors may be built in. Motion times and speeds can be too fast; masses, forces, and friction too large; and design pressures too low. These safety factors, when taken together, can often drive a design to use more air and space, and cost more than would otherwise be necessary.

• The ID of the cylinder and valve port fittings restrict airflow.• Flow characteristics through air lines depend on tubing materials and construction.• Air lines add volume that must be charged and discharged every cycle.• Fittings that are not straight increase pressure losses and delays.• Flow controls restrict airflow even in their full-open position.

Additional factors to consider:
• A programmable-logic controller (PLC) with a “scan time” typically controls the valve. Scan time is the time the processor takes to evaluate and execute a set of instructions before repeating the entire process.
• Response time for a valve to switch from fully closed to fully open once it receives a signal from the PLC.
• Loads cannot move until sufficient pressure difference develops across the cylinder piston to overcome gravity and friction caused by seals and guide bearings.

Practical considerations
To put these factors into practical terms, let’s look at an example. Consider a typical pneumatic motion system with an air cylinder pushing a 10-lb mass vertically 3 in. in 0.170 sec. Supply pressure is 79.7 psia (65 psig) and exhaust pressure is 14.7 psia.

The valve shifts from closed to open in 0.032 sec and PLC scan time is 0.010 sec. Flexible tubing 14 in. long with no angled fittings connects the valve and cylinder, and there are no flow controls or external friction.

Cylinder motion is “bang-bang.” That is, velocity increases linearly with constant acceleration and the external structure stops the load abruptly without cushions or shock absorbers. And effects of temperature changes and air leaks are negligible, as are differences between static and dynamic friction.

System sizing
These circuit calculations are iterative so a software program such as Excel or Math- CAD is recommended. Here are the key considerations.

Physics: First, calculate the required cylinder force. The maximum time air flows to the cylinder is 0.170 sec, minus the PLC scan time and half the valve-solenoid shift time. That leaves 0.144 sec for the actual move plus the delay time for enough pressure to build before the load moves. Start with an estimated move time of about two-thirds of 0.144 sec, or 0.096 sec. Average velocity v_a = 3 in./0.096 sec = 31.25 ips.

Assuming constant acceleration, peak velocity v_p = 2v_a = 62.5 ips. Acceleration = v_p/0.096 sec = 651 ips² or 1.685 g. Thus, the required lifting force is 1.685 × 10 lb (due to acceleration) + 10 lb (due to gravity) = 26.85 lbf. If there were other forces, such as guide friction, they would be added here.

Cylinder: Size the cylinder to provide an extra 33 to 100% of the calculated required force to overcome pressure losses from other components in the circuit. In this case, design for a cylinder force between 36 and 54 lb at 65 psig.

Because F = PA, bore should be between 0.84 and 1.03 in. with no rod. Start with an oversized 1.50-in.- diameter cylinder with a 0.625-in.-diameter rod and 1 /8 -in. NPT ports. From the manufacturer’s catalog, friction is 13 psi. This is the minimum pressure needed to overcome internal friction and move the piston with no load. And start with 0.25-in.-ID flexible tubing to supply air to the cylinder.

Summing losses
Sum all the pressure drops around the circuit, starting at the valve’s exhaust port (atmospheric pressure) and ending at its supply port (regulated supply pressure). These pressure drops should add up to the pressure difference between supply and atmospheric pressures. (This is similar to Kirchhoff ’s Voltage Law used to solve electrical circuits.)

Valve exhaust port: To size the valve, first calculate flow through the valve exhaust port. Calculate the volume being evacuated, divide by time, and multiply by the pressure ratio to convert to standard conditions. Air-cylinder exhaust volume = (3)(π /4)(1.5² – 0.625²) = 4.38 in.³ Airline exhaust volume = (14)(π /4)(0.25²)(79.7-14.7)/79.7 = 0.56 in.³ (Note the air line does not empty completely — one atmosphere pressure remains.) Total exhaust volume = 4.94 in.³ Divide this by 0.096 sec to get 51.5 in.³/sec, or 1.787 cfm at full pressure. Multiply by 79.7/14.7 (pressure ratio) to convert to standard conditions, and get 9.69 scfm exhaust. In the same manner, the supply flow (without the rod) through the valve supply port is 11.50 scfm.

An assumption is necessary at this point. Valve manufacturers recommend designing for a 2 to 10-psi pressure drop across the valve’s exhaust port. We’ll assume a 6-psi drop. Substituting Q = 9.69, ΔP = 6, and P = 14.7 into the C_v equation, the recommended valve C_v = 1.055. Choose a standard valve with C_v = 1.0 and ¼-in. NPT ports. Because flow requirements are unchanged, calculate pressure drop based on the smaller valve. Rearranging the C_v equation, valve exhaust-port ΔP = 6.67 psi, well within the 2 to 10-psi requirement.

Each circuit component also has a critical pressure ratio, P₂/P₁, that must be ≥0.528. If P₂/P₁ = 0.528, airflow is sonic or “choked” and is at the maximum level possible. If P₂/P₁ < 0.528, flow is impossibly high and must be reduced. For this component P₂/P₁ = 14.7/21.37 = 0.688, so it’s subsonic.

Exhaust-valve fitting: A ¼-in. NPT straight fitting has a 0.28-in. ID. The flow coefficient equation for fittings is approximately C_v =18d_f². This yields a fitting C_v = 1.411. With a downstream pressure of 21.37 psi (14.7 + 6.67) and 9.69-scfm flow, using the C_v equation gives an exhaust-valve-fitting pressure drop = 2.30 psi. P₂/P₁ = 21.37/(21.37+2.30) = 0.903, so it’s acceptable.

Exhaust-air line: Determine air line C_v using

The line-friction coefficient f_l for flexible tubing is 0.02 (use 0.03 for rigid steel pipe). This yields an exhaust-air line C_v = 1.962. Note that if the line has 90° fittings, add 48nd_f to the length of the line before calculating airline C_v. Line flow is based on the cylinder volume plus half the air-line volume or 9.14 scfm. Using 1.962 C_v, a downstream pressure of 23.68 psi (14.7 + 6.67 + 2.30) and 9.14 scfm from the C_v equation, exhaust air-line pressure drop = 0.96 psi. P₂/P₁ = 23.68/(23.68+0.96) = 0.961.

Exhaust and supply flow controls: Use the manufacturer’s C_v data, if available. Otherwise, calculate C_v for flow controls with the fitting equation but use the air-line ID. If a flow control were used here with a 0.25-in.-diameter line, C_v would be 1.125 (full open). Because flow controls typically mount in the cylinder port, calculate ΔP using flow based only on the cylinder volume or 8.59 scfm. A flow control is not in the circuit so we’ll move on to the next component.

Exhaust-cylinder fitting: A 1/8 -in. NPT straight fitting has a 0.19-in. ID. Using the fitting C_v equation, exhaust cylinder fitting C_v = 0.650. This gives a downstream pressure of 24.64 psi (23.68 + 0.96) and 8.59 scfm. From the C_v equation, exhaust-cylinder-fitting pressure drop = 7.41 psi and P₂/P₁ = 24.64/32.05 = 0.769.

Cylinder: At this point, piston exhaust-side pressure = 32.05 psia (24.64 + 7.41). Add the cylinder’s 13-psi internal friction to this to get 45.05 psia. Multiply this by the area to get a resistive force of 65.79 lb. Add the required cylinder output force of 26.85 lb to get a supply-side piston force requirement of 92.64 lb. Divide this by the area of a 1.50-in.-diameter piston with no rod to get supply side pressure = 52.42 psia.

Cylinder-supply fitting: Using C_v = 0.650 for 1 /8 -in. NPT and a downstream pressure of 52.42 psia and 10.40 scfm, cylinder supply fitting pressure drop is 5.10 psi. P₂/P₁ = 52.42/57.52 = 0.911. Supply air line: C_v = 1.962, downstream pressure = 57.52 psia, Q = 10.95 scfm, and supply air-line pressure drop = 0.57 psi. P₂/P₁ = 57.52/58.09 = 0.990.

Supply-valve fitting: C_v = 1.411, downstream pressure = 58.09 psia, Q = 11.50 scfm, and supply-valve-fitting pressure drop = 1.19 psi. P₂/P₁ = 58.09/59.28 = 0.980.

Valve-supply port: C_v = 1.0, downstream pressure = 59.28 psia, Q = 11.50 scfm, and valve-supply-port pressure drop = 2.33 psi. P₂/P₁ = 59.28/61.61 = 0.962. This adds up to a final supply pressure = 61.61 psia, with 18.09 psi to spare.

Delay time: When the valve opens, pressure in the cylinder (rod side) begins to bleed out the exhaust side while, simultaneously, pressure builds on the supply side. Because cylinder supply-side volume is small, supply pressure builds quickly. The delay before motion begins is mostly due to the time it takes exhaust pressure to fall below supply pressure and develop the necessary pressure difference across the piston to overcome gravity and friction, and initiate motion.

Calculate delay time t_d = ΔP_egV_ek_s/q_mv_s². Here, ΔP_e = 79.70 – 32.05 psia (the piston low-side pressure). Air density is approximately 0.075 lb/ft³ at 528°R. Therefore, t_d = 0.059 sec. So the initial time estimate = 0.096 shift time + 0.059 delay time + 0.032/2 valve solenoid time + 0.010 PLC scan time = 0.181 sec.

Optimizing the circuit
Besides the critical pressure ratio already discussed, experts recommend that no component in a circuit should exceed 15% of the absolute upstream pressure or 11.96 psi in this example. There was extra pressure to spare in the first iteration (79.70 – 61.61 psi) and no pressure drop exceeded 11.96 psi. This indicates we can improve the initial move-time estimate and repeat all the above calculations until the last pressure equals the supply, one component is at the maximum pressure drop, or the pressure drop across the valve exhaust port exceeds 10 psi.

Optimizing the shift time yields 0.146 sec (0.078 motion time + 0.042 delay time + 0.016 + 0.010) with a limiting pressure drop of 10 psi across the valve-exhaust port. Increasing supply pressure has little effect on speed and will increase delay time before motion begins.

As a test, we built this pneumatic-motion circuit using all the variables identified for the 1.50-in.-diameter cylinder, except without a PLC and its 0.01-sec delay. Cylinder actuation time was 0.134 sec, approximately 0.002 sec faster (0.136 calculated without a PLC) than the initial estimate. The time for the actual cylinder to lower was 0.144 sec versus a calculated time of 0.158 sec. Thus, there is good agreement between theory and actual conditions.

Assuming this cylinder operates 24/7, extending and retracting every 3 sec, operating costs will run about $182/yr based on air costing $0.50/1,000 scf. The energy to generate compressed air produces about 620 lb/yr of CO₂ (based on 1.7 lb of CO₂/1,000 scf of air.)

Reducing cylinder pressure 5.5 psi to 74.2 psia (59.5 psig) improves raise time from 0.146 to 0.138 sec and the lower time from 0.168 to 0.157 sec. It also saves about 7% in air. Reducing supply pressure further provides additional savings while staying within the 0.170-sec time frame. Further gains are possible by repeating this analysis with dual air pressures and quick exhaust valves.

Likewise, selecting smaller cylinders and reducing C_v in other components offers additional savings. For instance, adding a regulator to the 1.50-in.-bore cylinder circuit reduced costs 32%. Adding regulators with quick exhaust valves (C_v = 0.72) to the same circuit reduced costs 54%. And reducing cylinder size to 1.06-in. bore, with regulators and quick-exhaust valves, results in savings of 76%. Further reducing the cylinder bore to 0.87 in. doesn’t appear to have as many advantages, but there could be some space savings and component cost reductions. (See the “Optimized circuit” table for details.)

Benefits of an optimized circuit include lower air and electricity consumption with a corresponding drop in CO₂ production. It also lets OEMs start with smaller, fewer, and less-expensive components that consume fewer resources and generate less CO₂. If we all start to think a little greener today, we should all breath a little cleaner tomorrow.