Pneumatic Cylinder Sizing and Motion Control

1. Engineering answer: size the complete motion, not just the piston

Pneumatic cylinder sizing connects a mechanical task to an actuator and its complete air circuit. Begin with the required force, stroke, orientation, moving mass and travel time. Calculate extension and retraction separately using the effective areas and realistic chamber pressures. Then check mounting, guidance, rod stability, valve and tubing flow, speed control, cushioning, sensing and behaviour after loss of energy. A bore that passes a static force calculation is only a candidate until those other requirements are satisfied.

The pressure that matters is the pressure available at the working chamber during the relevant part of the cycle. The opposing chamber can retain backpressure, particularly when exhaust flow is restricted. The regulator setting and the compressor-room gauge are not substitutes for those two values. Likewise, average air consumption describes utility demand over time; it does not demonstrate that a valve can fill and exhaust the cylinder quickly enough.

A successful selection delivers the required outcome without excessive impact, unstable low-speed motion, unacceptable force variation or unnecessary air use. The useful engineering output is therefore a cylinder-duty record with a supported component configuration and a verification plan. It is not simply a recommendation to increase pressure or choose the next larger cylinder.

This page supplies that decision method and worked examples. Its calculations are transparent screening models, not a product configurator, a completed machine design or a safety-function approval. Values in the examples are fictional, and no supplier availability or catalogue suitability is implied.

2. What owns within the pneumatic application series

Keeping these responsibilities distinct prevents a consumption calculation from becoming an unsupported motion guarantee.

Use this page for clamping, pushing, indexing, transferring, ejecting and other linear pneumatic tasks where a suitable cylinder architecture is under consideration. Record whether the actuator drives the load directly or through a lever, toggle, linkage or guided carriage. Force at the piston, force at the workpiece and force carried by a guide may be different quantities.

The examples use conventional double-acting, single-rod geometry. Single-acting, double-rod, rodless, tandem, guided and locking arrangements need their own geometry and manufacturer information. The calculation must not silently apply a single-rod equation to another architecture. Nor does this page assign a lifting capacity, prescribe a protective circuit or approve a pressure-containing component.

The final decision may remain “candidate suitable for detailed review” while a rod-load chart, valve curve, cushion limit or actual pressure trace is still missing. That is a useful, honest result. Completing the numerical fields cannot manufacture the missing engineering evidence.

3. Write a cylinder-duty brief before opening a catalogue

Define the process outcome in measurable terms. “Push the product” leaves unanswered how far it moves, how much resistance occurs, when contact happens and what must be true before the next machine step starts. A useful brief identifies the load path throughout travel, not only the most visible final position.

Keep measured, supplier-declared and assumed inputs distinguishable. An operator estimate of cycle time can support an initial enquiry, but should not be labelled a witnessed acceptance value. A future production rate should remain a scenario until the machine owner confirms it.

Include maintenance access, replacement constraints and the consequences of unexpected movement. A compact arrangement that cannot be aligned or serviced without disturbing the process can create a larger lifecycle problem than its initial space saving.

4. Resolve the mechanical load and its direction

Draw the load path and choose a positive direction before calculating. For a direct linear movement, the required pneumatic contribution must account for process resistance, gravity projected along the axis, friction and acceleration. During deceleration, the acceleration term reverses direction. During a dwell, the moving mass may still create a gravity load even though acceleration is zero. [N2]

For a deliberately simplified horizontal load case, the resisting demand can be written as F_required = F_process + F_external-friction + m × a. Identify whether cylinder seal resistance is already included; do not add it twice. For an inclined upward movement, a gravity contribution m × g × sin(θ) can be added when θ is measured above horizontal. For downward travel, gravity can assist movement and increase the stopping burden rather than merely reduce the required bore.

Use newtons for force and kilograms for mass. Multiplying mass by gravitational acceleration converts weight to force; a statement such as “the load is 100 kg” does not say whether the cylinder is lifting it, moving it along a low-friction guide or pressing it through a process. Those duties cannot share one unexplained force assumption.

A lever or linkage requires the relationship between cylinder position and mechanical advantage. The worst cylinder load may occur before the final workpiece position, or close to a geometry in which a small movement produces a large change in force. Include transmission losses and load reversals where supported. Do not substitute the most favourable leverage ratio for the complete travel.

Resolve startup friction separately when necessary. A seal or guide can require more force to break away than to keep moving, and a process can become tighter after contamination or temperature change. Use measurements or applicable supplier guidance rather than a universal friction percentage. Record uncertainty in an assumption as a scenario to investigate, not as an invisible multiplier.

5. Calculate piston and annular areas correctly

For a circular single-rod cylinder with bore D and rod diameter d, the full piston area is A_p = πD²/4. The rod area is A_r = πd²/4, and the annular area is A_a = A_p − A_r. The cap-end chamber acts over A_p; the rod-end chamber acts over A_a. Extension and retraction therefore have different theoretical force and volume relationships.

One bar equals 0.1 N/mm². This relation is convenient when dimensions are supplied in millimetres, but the worksheet should preserve the original pressure reference as well as the conversion. Unit conversion does not change gauge pressure into absolute pressure.

For equal chamber pressure and negligible opposing pressure, the retraction-to-extension force ratio is A_a/A_p. That ratio is not a universal stroke-speed ratio because filling, exhausting and loading can differ. A larger rod improves some structural characteristics while reducing annular area; both consequences need review.

Geometry is also architecture-specific. A double-rod cylinder has a different effective-area arrangement, while a rodless cylinder transfers load through its own carriage and guidance. Retain the exact architecture in the record before using any formula.

6. Use both chamber pressures in the force balance

For extension, the available axial force after a separately defined internal resistance is F_available,e = p_cap,g × A_p − p_rod,g × A_a − F_internal,e. For retraction, using retraction as the positive direction, F_available,r = p_rod,g × A_a − p_cap,g × A_p − F_internal,r. Both gauge pressures must refer to the same surrounding atmospheric pressure. [S1, S2; N2]

The internal-resistance term here means cylinder resistance only. Compare the resulting available force with the external process, guide-friction, gravity and acceleration demand. Another calculation may include all resistance on one side of the equation, but its definitions must make double counting impossible. Preserve the chosen convention beside the result.

These expressions describe the instantaneous pressure-force relationship under the stated geometry; they do not predict the chamber pressures. Those pressures depend on valve behaviour, line restriction, piston movement, exhaust conditions and gas storage. A static example using fixed pressures must not be represented as a complete dynamic simulation.

The same atmospheric reference matters because the exposed rod also experiences the surrounding pressure. Using gauge chamber pressures in the expressions above already accounts for that common reference. Inserting absolute pressures into the same simplified expression without the corresponding external rod-force term would create a spurious atmospheric contribution.

An important consequence follows when both chambers have the same positive gauge pressure p: the net pressure force toward extension is p × A_r, before resistance and external load. Supplying both sides of a single-rod cylinder therefore does not automatically balance it. That observation must not be turned into a regenerative-circuit design without reviewing flow paths, controls and the actual application.

Negative calculated available force is meaningful: it indicates that the assumed pressures and resistance do not support the requested direction. The tool should report that result rather than clamp it to zero and suggest that a larger compressor has been selected.

7. Establish a minimum and maximum pressure envelope

The minimum useful pressure belongs to the operating event. Record pressure at the machine inlet, directional-valve supply and relevant chambers where available. Filters, regulators, isolation devices, valve passages and tubing can all separate these values. A no-flow regulator adjustment is not a measurement of chamber pressure during acceleration.

Evaluate the credible low-supply, high-demand condition without pairing it with an unrealistically favourable zero exhaust pressure. Where opposing pressure is not measured, define an explicit screening assumption and identify the evidence needed to replace it. Use time-aligned observations when the event changes rapidly.

The maximum pressure case answers a different question. It may govern peak contact force, fixture loading, cylinder stress or trapped-chamber behaviour. Do not credit uncertain friction as a dependable protective limit. A cylinder sized at the lowest available pressure may exert a substantially greater force when supply rises or the exhaust path opens.

Separate functional minimum, intended operating target and maximum permitted component pressure. A catalogue maximum is not a recommended process setting. Reducing an ordinary regulator setting is not, by itself, a complete safety-rated force-limiting measure.

In a restricted or trapped chamber, unequal areas, external loading and deceleration can produce pressure behaviour not explained by the upstream setting alone. Identify any requirement for pressure monitoring, pressure protection or a different circuit architecture through competent design. The workbook does not presume that every downstream chamber is always bounded by a visible supply gauge. [N1]

8. Select candidate bores without hiding the margin

Start with the governing extension and retraction cases, then evaluate actual candidate bore-and-rod combinations. A rod diameter may change with bore or product series, so selecting a continuous mathematical bore and independently retaining an unrelated rod is not a completed catalogue selection. Show each candidate's geometry, assumptions, available force, required force and unresolved checks.

For the extension model with a fixed rod diameter, constant chamber pressures and p_cap,g greater than p_rod,g, the force inequality can be rearranged. The minimum full piston area is A_p,min = [F_required + F_internal − p_rod,g × A_r] / [p_cap,g − p_rod,g]. This expression is only a preliminary geometric screen. If its prerequisites are not met, return to the complete force balance rather than forcing a square-root answer. [N2]

Report nominal force surplus as F_available − F_required. Where F_required is positive, a relative surplus can be shown as 100 × (F_available/F_required − 1). That percentage is descriptive; it is not a universal acceptable margin, load factor or safety factor.

SMC's selection guide distinguishes operating purpose, direction, cushioning, lateral loading, buckling and air demand. Its numerical load-factor guidance is tied to the stated selection method. Use the chosen supplier's method and disclose how it relates to explicit friction, backpressure and dynamic-load assumptions. [R1]

Avoid stacking unexplained allowances. Applying a supplier load factor, a separate friction deduction and another broad multiplier can double count the same provision. Conversely, omitting all reserve because the theoretical force barely exceeds the load can leave no allowance for real variability. The decision needs a documented basis, not an attractive percentage.

9. Choose stroke, end positions and the physical arrangement

The required working travel, the cylinder's nominal stroke and the available installation length are different dimensions. Identify the actuator positions at the mechanical limits, the useful process travel, adjustment range and clearance for mounting. A cylinder must not bottom against its internal end before the intended external process position is reached unless that is part of the supported design.

Define where deceleration begins and where the load finally stops. An external stop can determine workpiece position while the cylinder still applies force; that continuing force must be included in the stop and fixture assessment. A contact sensor can confirm a position without proving acceptable impact energy or clamping force. [S1; N1]

Check installed length with the rod retracted and extended, access for fasteners, orientation of ports and sensors, and hose movement throughout travel. A swivel or clevis arrangement needs suitable freedom without imposing bending through a misaligned pin. A rigid mounting needs alignment with the guide and load path.

Do not lengthen a stroke simply to create an informal cushion or adjustment zone. Additional travel can change rod stability, cycle time, stored air and collision risk. Likewise, shortening a cycle by stopping the piston before the intended cushion engages can invalidate the existing stopping assessment.

Record the exact mechanical reference for acceptance: cylinder end position, carriage datum, workpiece contact or another defined point. A replacement with the same nominal bore and stroke can still change the installed dimensions, sensor location, cushioning length and connection geometry. Preserve those requirements in procurement and maintenance records.

10. Check guidance, side loads and rod stability

The piston rod should not be treated as an unlimited structural guide. Identify transverse forces, overturning moments and misalignment from the load or mechanism. A separately guided carriage can isolate the cylinder from loads that belong to bearings and structure, but the coupling must still transmit axial force without creating an unintended constraint.

For a compression-loaded extended rod, evaluate buckling using the manufacturer's permitted-load and mounting information. The effective unsupported length depends on the complete support arrangement, not simply the nominal stroke. Rod-end threads, fixtures, bushings, mounting flexibility and off-axis loads can govern before a simple column estimate does. [R1]

As an explanatory mechanics relationship, the ideal Euler load for a slender elastic column is F_cr = π²EI/(K L)². For a uniform solid circular rod, I = πd⁴/64. E is elastic modulus, L is the defined unsupported length and K represents the idealised end conditions. The fourth-power diameter and inverse-square effective-length dependence explain why long-stroke compression deserves attention. They do not constitute a manufacturer's allowable rod load. [N2]

This ideal relationship excludes eccentricity, material yielding, imperfect alignment and actual cylinder construction. A structural check needs the applicable component data and engineering interpretation.

Guided cylinders and rodless actuators require their own allowable force-and-moment review. A guide rated for one load direction may not accept the same magnitude at a different offset. Record the centre of mass, load offset and changing moment through the stroke; a mass value without geometry cannot close this assessment.

11. Turn the timing target into a motion requirement

Separate command-to-motion delay, acceleration, useful travel, deceleration, settling and feedback confirmation. The actuator's nominal stroke divided by the full PLC step time can understate actual travelling speed when the step also includes waiting or dwell. Conversely, a stopwatch reading that begins after movement starts omits pressure buildup and command delay.

For travel s completed in travel time t, average velocity is s/t. Peak velocity generally requires a motion profile or measurement. For a teaching trapezoidal profile starting and ending at rest, with acceleration time t_a and deceleration time t_d, the peak velocity is v_peak = s/[t − (t_a + t_d)/2], provided t ≥ t_a + t_d. Constant-acceleration magnitudes are v_peak/t_a and v_peak/t_d. These are kinematic requirements, not a prediction that an ordinary pneumatic circuit will produce that profile. [N2]

The force calculation must then include the corresponding acceleration load. A bore that had comfortable surplus under a slow approach can have less surplus when travel time is shortened. Review return movement separately because its effective area, load and permitted timing can differ.

A pneumatic cylinder with ordinary flow controls may not follow a linear ramp or hold a constant speed through changing resistance. Compressibility, friction, pressure development and end cushioning affect the actual trajectory. Use the teaching profile to expose what a requested cycle implies, then use supported sizing tools, dynamic analysis or measured trials to establish the achievable behaviour.

Specify which timing limit is mandatory and which is preferred. “No slower than this process limit” and “no faster than this impact limit” can both apply. A supplier enquiry should include both, rather than asking for the fastest possible cylinder.

12. Separate swept-volume flow from pressure-building flow

At approximately constant chamber pressure and temperature, the geometric rate at which a chamber grows is Q_chamber ≈ A × v. Convert that actual chamber-volume rate to the declared reference state before comparing it with a valve's reference-flow figure. A reference litre and a litre inside a pressurised chamber represent different gas quantities.

Under an ideal, isothermal chamber model with constant gas temperature T, the net reference-volume inflow is Q_ref,net = [T_ref/(p_ref T)] × [p_abs × dV/dt + V × dp_abs/dt]. Use coherent pressure, temperature, volume and time units. This follows by differentiating the chamber gas inventory pV/(RT); it is an original explanatory derivation, not an implemented dynamic solver. [N2]

The first term supplies increasing chamber volume. The second changes the gas inventory by increasing pressure. A stationary piston can therefore consume air while its chamber pressurises. Leakage or simultaneous outflow requires additional mass balance. Temperature changes and non-ideal gas effects require a more complete model.

This explains why a value obtained by dividing stroke consumption by stroke time is an average filling screen, not a guaranteed maximum valve-flow requirement. The pressures across a valve change during filling, and its rated flow must be interpreted at the manufacturer's stated conditions. Do not equate a connection thread size with conductance.

Record valve model, relevant flow characteristic, upstream/downstream pressure, pilot conditions, tubing internal diameter, length, fittings, manifolds and exhaust routing. Include the exhaust path in the response model.

13. Choose speed control by the load and exhaust behaviour

Meter-in controls the entering air; meter-out restricts the exiting air. For many conventional double-acting cylinder applications, meter-out provides a useful speed-control arrangement, but it also creates opposing chamber pressure. The resulting force and pressure envelope must be considered together with motion. SMC's C96 manual describes the distinction and generally uses exhaust-side control for the documented product. That is product guidance, not a universal circuit prescription. [R2]

A load that assists motion can cause different behaviour from a load that resists it. Gravity, spring release or a changing mechanism can drive the piston faster than an inlet restriction alone is intended to permit. A direction that behaves acceptably on an unloaded bench may not represent the real working load.

Do not fully close a flow control and assume that it has become a dependable load-holding or isolation device. Internal leakage, trapped pressure and external forces remain separate questions. Quick-exhaust arrangements also change the pressure-force relationship, noise, acceleration and stopping burden; they need a new motion assessment rather than being installed as a universal cure for slow travel.

Specify controlled extension and retraction settings, the applicable adjustment procedure and access restrictions. Commissioning adjustments should follow the selected equipment's instructions and the site's controlled method. The website worksheet is not permission to adjust devices while a person is exposed to movement.

Where repeatable speed over a broad load range is important, consider whether a supported proportional, servo-pneumatic, hydraulic or electric motion architecture is more appropriate. An ordinary throttle cannot be assumed to provide programmable trajectory control or precise intermediate positioning.

14. Size stopping capacity as carefully as driving capacity

Kinetic energy at cushion entry is E_k = ½ m_eff v_entry². Use the effective moving mass and the speed when cushioning actually begins, not a convenient average speed over the entire stroke. A speed increase can raise kinetic energy disproportionately because velocity is squared. [N2]

The absorber may also need to oppose continuing work by pneumatic force, gravity or another driving load during its stopping travel. For a stated simplified case, E_absorb = ½ m_eff v_entry² + ∫F_assist(x) dx, less any separately justified dissipative contribution. For constant net assisting force over distance s_stop, this becomes E_absorb = ½ m_eff v_entry² + F_assist × s_stop. Avoid deducting uncertain friction as dependable energy absorption.

Festo's cushioning selection aid includes impact velocity, equivalent mass, continuing force, energy per stroke and energy per hour.

Check the manufacturer's mass-speed or energy limit for the exact bore, cushion type, operating condition and mounting. Elastic bumpers, adjustable air cushions and external absorbers serve different duties. A cushion adjustment changes deceleration; it does not increase the manufacturer's allowable structural load.

Average stopping force E_absorb/s_stop can help explain a load path, but peak force can be higher. Review the absorber, cylinder, brackets, stop, guide, workpiece and supporting structure together. Repeated operation also creates a thermal and fatigue duty. A per-impact check alone cannot establish acceptable continuous cycling.

15. Address low-speed motion, dwell and intermediate stopping

At very low speed, friction and compressible-air storage can dominate response. Pressure can build while the piston remains stationary, followed by breakaway movement when the resisting force is exceeded. A system that runs smoothly at one speed may become intermittent at another. Check the product's supported speed range and application conditions rather than assuming arbitrarily slow motion is available.

Distinguish three requirements: staying at an end stop, holding a process force during dwell, and stopping accurately at an intermediate position. They require different evidence. A cylinder seated against a mechanical stop can have a well-defined position while its applied force changes with pressure. An end-position sensor does not measure that force.

An ordinary closed-centre directional valve does not create a rigid mechanical lock. Gas compressibility and leakage can permit movement or pressure decay. The existing circuit material specifically retains this distinction between stopping, blocked chambers, isolation and retention.

Specify the permitted position error, force variation, dwell duration, settling time and response to pressure loss. Precision intermediate positioning may require dedicated feedback and a supported control architecture. Load retention may require separately engineered mechanical or protective measures. Neither is established by the static bore calculation.

For a clamp, review the maximum force as well as the minimum. More bore can damage a product or overload a fixture even while improving minimum-pressure operation. The practical selection should preserve both ends of the accepted force envelope.

16. Select the actuator architecture deliberately

A single-acting cylinder uses air for the powered direction and relies on a spring, gravity or another return arrangement. The return force can vary with position, and the powered stroke must overcome any opposing spring force. A double-acting cylinder powers both directions but introduces two chamber pressure histories and two controlled flow paths.

A guided cylinder combines motion with a specified load-guidance capability; its moment limits still matter. A rodless arrangement can reduce installation length for a long stroke but needs product-specific carriage, sealing and guidance assessment. A double-rod arrangement changes effective areas and dimensions. Tandem or other special arrangements must use their actual manufacturer force and consumption definitions.

A rod lock or brake is not automatically designed to arrest a moving load. Establish whether the selected device is intended for static holding, dynamic braking or another stated function, and under what conditions it may engage. The part name cannot supply a missing rating or safety assessment. [N1]

Compare the complete arrangement rather than choosing a special cylinder solely to avoid correcting a guide or valve problem. The best candidate can be an ordinary cylinder with an improved mechanical interface; another task may genuinely need a different technology. Record the reason for the architecture choice so later replacement does not undo it.

17. Preserve environmental and air-quality requirements

Record the working medium, pressure range, temperature range, contamination exposure and installation environment for the exact component. Cylinder seals, lubrication, tubing and sensing may have different limitations. A device suitable for a dry indoor machine should not be assumed suitable for washdown, abrasive dust, corrosive exposure or a hot process zone without supporting data.

Define filtration, moisture and lubrication requirements from the selected equipment and the process. Adding a lubricator by habit can be inappropriate where downstream air affects the product; removing an established lubrication requirement can also be inappropriate.

Account for the pressure loss of the required preparation train in the dynamic supply case. A filter that is adequate for average consumption may impose an important restriction during a fast stroke. The design must satisfy air quality and response at the same time; bypassing treatment to gain speed is not an acceptable undocumented substitution.

Maintenance access should allow inspection of rod condition, mounting, tubing, leakage and sensor alignment without uncontrolled movement. Define the preserved replacement attributes: geometry, mounting, seals, sensing, cushioning, port configuration and applicable flow-control settings. Physical interchangeability is not proof of equal performance.

18. Calculate air use without confusing consumption and speed

For the simplified swept-volume model, convert each powered chamber's swept volume to the specified reference state using V_ref = V_swept × (p_chamber,abs/p_ref,abs) × (T_ref/T_chamber) × (Z_ref/Z_chamber). Sum the actual powered strokes. For one extension and one retraction per cycle, the baseline cycle quantity is the sum of their two converted volumes. Multiplying by complete cycles per minute gives average reference flow.

This is a declared screening model. It assumes the swept chamber volume reaches the stated condition and excludes leakage, valve losses, extra dead volumes and detailed pressure evolution unless explicitly added. Do not interpret it as a measurement of the selected machine or apply a second diversity factor to an already averaged cycle rate.

Fixed dead volume needs careful treatment. When a known tube or cavity is retained at an initial pressure and then repressurised, only its gas-inventory increase is newly supplied. Under equal temperature and ideal-gas assumptions, the additional reference volume is V_dead × (p_final,abs − p_initial,abs)/p_ref,abs. Counting the entire final inventory each cycle would count the gas already present at the initial state. [N2]

For a general fixed-volume inventory change, use V_ref,added = V_dead × (Z_ref T_ref/p_ref) × [p_final/(Z_final T_final) − p_initial/(Z_initial T_initial)]. This applies to the identified volume and states; it must not be used to subtract the initial pressure from the entire swept-volume formula indiscriminately. The swept and fixed-volume boundaries are different.

State whether tubing is repeatedly pressurised and exhausted, remains supplied or is served through a different topology. Include measured leakage separately when it belongs to the reporting boundary. Annual air volume follows actual operating time and cycle count, not calendar hours by default. Converting air volume to electricity requires separate system-energy evidence; the cylinder model does not provide a universal kWh-per-cycle value.

19. Verify motion with pressure, position and timing evidence

Plan the evidence before a trial. Record the cylinder and valve configuration, load, orientation, regulator setting, tube lengths, exhaust arrangement and temperature conditions. Align position or motion observations with pressure measurements and command/feedback timestamps where the conclusion depends on their relationship.

Check extension and retraction under the relevant normal and demanding conditions. Record travel time, delay before motion, arrival behaviour, settling and repeatability against the approved requirement. A completed stroke is not proof that the impact or force remained acceptable. A controller signal is not proof that the mechanical event occurred at the same instant.

Select measurement resolution appropriate to the event. A slow gauge can miss a short pressure drop or cushioning peak. An end switch alone cannot establish the full velocity profile. Where the available instruments cannot resolve the question, disclose the limitation rather than deriving a precise acceleration from two poorly timed observations.

Keep operational acceptance separate from safety verification. Controlled movement and product quality can pass their checks while a separate retention or restart requirement remains unresolved. Trials involving faults, pressure loss or restart must follow the machine's approved method and responsible authority, not an improvised experiment suggested by a worksheet.

After a repair or substitution, repeat the affected tests under comparable duty. Preserve the previous record, the change, the new configuration and the results. A new baseline should not erase why the earlier configuration was rejected.

20. Diagnose the motion failure before enlarging the cylinder

The table identifies investigation directions, not proven causes. A larger cylinder increases swept volume and may worsen a flow-limited stroke. More supply pressure can increase impact or product force while concealing a local restriction. Verify the failed outcome, localise the cause and reassess the complete duty before modifying equipment. [S1, S2; N1]

21. Worked example 1: a static-looking bore choice changes with backpressure

All values in this example are invented. A horizontal cylinder must provide 1,800 N of external process resistance and accelerate a 40 kg moving assembly at 3.0 m/s². External guide resistance is assumed already included in the 1,800 N. Cylinder internal resistance is separately assumed to be 180 N. The required external force is therefore 1,800 + 40 × 3.0 = 1,920 N.

During the governing event, cap-end pressure is assumed to be 5.2 bar gauge and rod-end pressure 0.8 bar gauge. Evaluate three fictional geometry candidates. No supplier product is being selected.

For the 80 mm candidate, F_available = 0.52 × 5,026.548246 − 0.08 × 4,535.674394 − 180 = 2,070.951136 N. The nominal surplus is 150.951136 N, approximately 7.86% of the stated external demand. This is not an approved margin; it is the result of the stated assumptions.

With a fixed 25 mm rod, rearranging the force inequality gives a mathematical minimum bore of approximately 77.22 mm. The 80 mm geometry therefore remains a candidate for the subsequent motion, mounting, cushion and supplier checks. It is not automatically accepted because its diameter exceeds the calculated minimum.

Now compare the misleading shortcut. At 6 bar gauge with the rod chamber assumed exhausted to atmosphere, the same candidate appears to provide 2,835.93 N after the same internal resistance. That is 764.98 N more than the governing case, created by changed pressure assumptions rather than a better cylinder. The example shows why a static supply number can conceal inadequate real margin.

At a separate 6.5 bar gauge cap-end condition with negligible rod-end pressure, the theoretical pressure force before resistance is about 3,267.26 N. The fixture's maximum-force assessment must consider the applicable upper case independently; uncertain friction should not be relied on as protection.

22. Worked example 2: average consumption does not prove travel time

Use the fictional 80 mm bore and 25 mm rod geometry with a 400 mm stroke. The intended extension travel time is 0.80 s, excluding command delay and settling. A teaching trapezoidal requirement allocates 0.15 s to acceleration, 0.50 s to constant speed and 0.15 s to deceleration. This is an intended motion profile, not simulated performance.

The average travel speed is 0.400/0.80 = 0.500 m/s. The required peak is 0.400/[0.80 − (0.15 + 0.15)/2] = 0.615384615 m/s. The acceleration magnitude is 0.615384615/0.15 = 4.102564103 m/s². For the 40 kg assembly, the acceleration force is 164.102564 N.

This is greater than the 120 N acceleration contribution used in example 1. Under its unchanged 1,800 N external resistance, the revised force demand becomes 1,964.102564 N. Comparing with 2,070.951136 N available leaves 106.848572 N. The pressure and motion calculations must therefore be iterated together; a shorter travel requirement can consume the apparent force surplus.

For the constant-speed part of travel, actual cap-chamber volume growth is A_p × v_peak = 0.003093260459 m³/s, or 185.595628 L/min at that chamber condition. Assume 5.2 bar gauge, a stated atmosphere of 1.0 bar absolute and a reference pressure of 1.0 bar absolute, with equal temperatures and ideal gas. The pressure ratio is 6.2, giving a reference-volume growth requirement of approximately 1,150.692891 L/min. This excludes pressure-building transients and is not a final valve rating.

The average cycle demand is far below the short-period flow screen, and neither establishes pressure buildup or exhaustion. The selected valve, tubing, preparation and supply must be evaluated dynamically at their actual pressure conditions. A nominal “1,200 L/min” valve cannot be accepted without understanding its rating basis and the rest of the flow path.

23. Worked example 3: a descending load needs more than kinetic-energy absorption

This is an energy-accounting illustration, not a lifting-system design. Assume a separately supported and safeguarded 40 kg moving assembly is travelling downward at 0.60 m/s when an external absorber engages. Available stopping travel is 25 mm. A net pneumatic driving contribution of 300 N is assumed to continue in the downward direction through that distance; gravity is excluded from that 300 N and added separately. No additional friction credit is taken.

Initial kinetic energy is ½ × 40 × 0.60² = 7.20 J. Gravity contributes 40 × 9.81 × 0.025 = 9.81 J during descent through the stop. The continuing pneumatic contribution is 300 × 0.025 = 7.50 J. The stated absorber demand is therefore 7.20 + 9.81 + 7.50 = 24.51 J per event.

Considering kinetic energy alone would omit 17.31 J. The average resisting force over the 25 mm stop is 24.51/0.025 = 980.4 N. This average is not the peak force, the shock absorber's rating or the force to use automatically for every bracket. The actual deceleration characteristic and load path must be checked.

At 1,200 such impacts per hour, the absorbed energy is 29,412 J/h, equivalent to an average dissipation of 8.17 W. This is local mechanical-energy dissipation under the example assumptions, not electrical input or a compressor-energy saving. Another absorber at the opposite end needs its own event count and energy case.

If the actual entry speed were 0.80 m/s, kinetic energy would rise to 12.80 J and the same assumed continuing-work terms would make the event total 30.11 J. The changed demand illustrates why average travel speed is not an acceptable substitute for cushion-entry speed.

A real selection must satisfy the exact absorber's supported impact, cycle, force, stroke and mounting conditions and the machine's separate safety requirements. Passing this arithmetic does not authorise a suspended-load test, a brake arrangement or operation without an approved protective system.

24. Worked example 4: dead-volume pressurisation changes cycle consumption

Return to the 80/25 mm cylinder and 400 mm stroke. Assume both powered strokes reach 5.2 bar gauge, the local atmosphere and reference are each 1.0 bar absolute, and all relevant temperatures and compressibility factors are equal. The extension swept volume is 2.010619298 L and the retraction swept volume 1.814269757 L.

Their combined swept-volume reference quantity is (2.010619298 + 1.814269757) × 6.2 = 23.714312146 L per complete cycle. This is the same baseline model used in the supplied cylinder-consumption worksheet, now applied to a new fictional geometry. [S3; N2]

Suppose a documented 0.12 L cap-side fixed volume and 0.18 L rod-side fixed volume are each vented to 1.0 bar absolute and then raised to 6.2 bar absolute once per cycle. The additional reference quantity is (0.12 + 0.18) × (6.2 − 1.0)/1.0 = 1.56 L per cycle. Total screened demand is therefore 25.274312146 L per cycle before other explicitly excluded losses.

Counting the entire final fixed-volume inventory would give 0.30 × 6.2 = 1.86 L instead of the 1.56 L increment. The difference, 0.30 L per cycle on this reference basis, is gas already present in those fixed volumes at the initial condition. Conversely, subtracting one atmosphere from the whole swept quantity would incorrectly treat a growing chamber as if all of its swept volume already existed at the beginning.

The correction depends on the actual circuit. A volume that remains pressurised or retains another pressure has a different inventory change. Leakage, pilot consumption, valve overlap and pressure-building details remain outside this teaching total unless separately supported. Measure accepted production-cycle consumption when the final objective is machine acceptance rather than an initial utility estimate.

25. Three editable cylinder-duty and verification records

The tables below are manually editable Word records. Duplicate them for each cylinder and governing case. Use explicit “unknown,” “not applicable” and “pending evidence” entries rather than leaving blanks that can be mistaken for zero. Keep the source of a requirement separate from the person entering it.

Worksheet A — Duty, geometry and pressure envelope

Worksheet B — Candidate calculation and unresolved selection checks

Worksheet C — Trial, acceptance and change record

A calculation result and an acceptance decision should remain separate fields. “Positive force surplus” can coexist with “cushion limit unresolved.” “Travel time achieved” can coexist with “maximum contact force not demonstrated.” The record must show those combinations rather than replace them with one overall green badge.

The structured companion templates preserve these same fields without customer values. They are not connected to equipment, email or a public upload service. A developer can use them as a starting data contract while retaining the original Word tables for manual review.

26. Engineering questions and answers

How do I choose the bore of a pneumatic cylinder?

Define the external load and movement first. Evaluate both chamber pressures, the relevant piston area and resistance for extension and retraction. Select candidate geometries, then verify motion, mounting, rod stability, cushioning and component conditions. A bore derived from force alone is not a complete selection.

Why is retraction force usually lower than extension force?

For a conventional single-rod cylinder, the rod reduces the rod-end working area. At equal supplied gauge pressure with negligible opposing pressure, retraction force follows the smaller annular area. Actual force still depends on both chamber pressures, resistance and load.

Should I use gauge or absolute pressure in the calculation?

The force equations on this page use chamber gauge pressures referenced to the same atmosphere. Gas-inventory and reference-air calculations use absolute pressure. The two calculations must not share an unqualified pressure field; the worksheet records the reference explicitly.

Will a larger cylinder make a slow machine faster?

Not necessarily. A larger area increases the volume that must be filled and exhausted. If valves, tubing or exhaust are restricting flow, the larger cylinder can increase air demand without resolving travel time. Diagnose whether force, flow, friction, sequence or cushioning is limiting the outcome.

Is stroke divided by travel time the correct cushioning speed?

It gives average travel speed. Cushion selection needs the relevant speed at cushion entry or impact. A cylinder can accelerate above its average before slowing, so use a supported dynamic model or suitable measurement. The examples distinguish the two quantities.

Can a closed-centre valve hold a cylinder indefinitely?

That should not be assumed. Trapped air is compressible and real components may leak. Position retention, safe access and behaviour after energy loss are separate machine-design requirements. A valve-centre label does not prove an approved holding function.

What is the difference between meter-in and meter-out control?

Meter-in restricts supply to the working chamber; meter-out restricts the exhausting chamber. The load and circuit determine which arrangement is appropriate. Meter-out backpressure affects available force and stopping behaviour, so speed adjustment must not be evaluated independently from pressure.

Is kinetic energy alone enough to select an external shock absorber?

Not when pneumatic force, gravity or another load continues to drive the movement during stopping. Include the applicable continuing work and the repetition duty, then use the exact absorber's force, stroke, energy and mounting criteria. Average stopping force is not peak force.

Does calculated air use include hoses and leakage?

Only when those quantities are explicitly included. The basic swept-volume calculation excludes fixed-volume recharge, leakage and other circuit consumption. Record the initial and final pressure of any additional fixed volume and avoid counting its retained gas twice. [S3; N2]

What should be sent for a cylinder-sizing review?

Provide the required process outcome, load/orientation, stroke and timing, candidate or existing cylinder, dynamic pressure evidence, valve and tubing details, mounting drawing, cushion arrangement and the failure or acceptance criterion.