Air bellows are critical components in many industrial systems. Understanding how to calculate their stiffness is key to performance. Whether we’re dealing with vibration isolation, actuation, or load support, stiffness defines how the air bellow responds under force. At a nominal pressure of 7 bar, a single convolution air bellow with a 215 mm diameter can generate over 18 kN of force at standard design height. This output confirms the nonlinear nature of stiffness in air systems. The corrugated flexible body changes shape during compression, affecting stiffness. Stiffness is not fixed but varies as pressure and height change. The behavior must be predicted carefully, especially when accuracy is crucial. Calculations must align with real-world measurements. Force is not constant per mm of movement, which makes assumptions risky. Therefore, combining theory with empirical data ensures reliability. Accurate stiffness calculation improves the longevity and safety of machinery where air bellows are essential.
Understanding air spring force behavior
When pressurized, air bellows behave like nonlinear springs. Their load capacity changes with internal pressure and effective area. To determine stiffness, we begin with the fundamental force formula:
F = P x A
Where:
F = Force (N)
P = Internal Pressure (Pa)
A = Effective Area (m²)
This effective area is not constant. It varies with bellows height due to geometry and pressure interaction. A double convolution bellow with a 260 mm diameter may generate 27.1 kN at 7 bar and 220 mm design height. At a lower height, the same bellow may exert significantly higher pressure on the system. This change confirms that effective area decreases under compression. Relying on a fixed value leads to inaccurate force estimates. The area must be recalculated at each height stage. Manufacturer-provided load charts support this. They give a close approximation of effective surface area at given pressures and heights. Always validate with these charts when modeling real systems. Engineers must account for variable geometry when building stiffness models. Accurate predictions require dynamic values—not assumptions. Using these formulas without updated geometry leads to large errors in system design.
What stiffness really means in air bellows
We define stiffness (k) as the change in force over the change in height:
k = ΔF / Δh
Where:
ΔF = Change in force (N)
Δh = Change in height (m)
Stiffness is not linear in air bellows due to their compressible nature. It depends on pressure, geometry, and structural design. For instance, a triple convolution air bellow with 310 mm diameter shows force values ranging from 44.4 kN to 70.4 kN across its stroke. If the vertical movement is 50 mm, the stiffness becomes roughly 520 N/mm. That number is valid only for that movement range. Outside this range, stiffness may increase sharply. This sensitivity makes it crucial to use multiple data points. Calculating a single stiffness number may give misleading results. Stiffness profiles help capture this variation across the entire stroke. They are especially useful for precision applications. Always confirm that Δh is taken from the actual working range. A nominal design height is not always the actual installed height. Even 10 mm deviation can affect stiffness by 10–15 percent depending on bellow type.
Estimating initial stiffness at nominal pressure
To get a starting point, we estimate stiffness near the design height. Here’s a simplified version that assumes the effective area remains relatively constant over small displacement:
k ≈ P × (dA/dh) + A × (dP/dh)
In most standard applications, dA/dh is minimal. Because pressure is often externally regulated, the second term dominates. Simplified further:
k ≈ A × (dP/dh)
Assume a bellow with a 310 mm diameter, delivering 43 kN at 7 bar. If compressed by 10 mm, and force increases to 48.8 kN, stiffness is 580 N/mm. These numbers apply only within this range. Beyond that, nonlinear behavior must be considered. Always model stiffness with safety margins. Many systems operate near 70% of maximum load to maintain predictable stiffness. Include external regulators or sensors when precision is required. Basic formulas are best used for early-stage design or comparative analysis. Actual stiffness should be confirmed via physical testing or validated simulation. This ensures load-bearing safety and long-term performance reliability.
Using charts for stiffness estimation
We recommend using load charts alongside formulas. For example, at 7 bar, a double convolution bellow with 215 mm diameter yields 19.5 kN at 210 mm design height. If the same bellow, compressed by 15 mm, generates 22.0 kN, stiffness is:
k = (22.0 – 19.5) / 0.015 = 1667 N/mm
These values depend on the bellow design and number of plies. Load charts often provide design height, force output, and frequency data. These allow stiffness modeling with confidence. Without charts, stiffness predictions are risky, especially for dynamic loads. Charts also show how much the force changes with small height adjustments. That data helps determine sensitivity. For applications requiring vibration damping, knowing the rate of change in force is essential. Always align chart readings with actual installation dimensions. If a system compresses the bellow beyond its standard height, stiffness increases rapidly. This affects shock absorption and stability. Avoid overestimating stroke capability when using simplified stiffness estimates. Engineers must ensure compatibility between stiffness values and end-use requirements.
Impact of convolution type on stiffness
Tevema air bellows are available in single, double, and triple convolutions. Each affects vertical stiffness and lateral movement differently. A single convolution design with 215 mm diameter and 7 bar pressure may produce 18 kN force. Triple convolution bellows of the same diameter can deliver similar force but allow larger stroke and better lateral compliance. In terms of stiffness, single convolutions are higher and better suited for vertical actuation. Triple convolutions offer lower stiffness and longer travel distance. Double convolution bellows balance both characteristics. Engineers must evaluate application needs before choosing. If compact height and high vertical load are key, single convolution models work well. Where more flexibility is needed, double or triple designs are better. Stiffness varies accordingly. A triple convolution unit may have 200 N/mm stiffness, while a single type may reach 400 N/mm. Always reference load charts for exact values. Choose convolution type based on movement, load, and mounting requirements.
Pressure influence on air spring stiffness
As pressure increases, force output increases, but stiffness rises non-linearly. For instance, at 6 bar, a triple convolution bellow may produce 60 kN force. At 7 bar, that same unit may deliver 70.4 kN. Over 10 mm compression, the increased stiffness is visible. More pressure compresses the air volume faster, making height adjustments more force-sensitive. Stiffness becomes harder to predict unless monitored in real-time. Higher pressure doesn’t linearly translate to higher force. Instead, internal resistance to compression grows. Air compressibility means less movement per unit of added force. This behavior is essential in systems needing stability at varying loads. Always consider using regulators to manage pressure fluctuation. Without them, inconsistent pressure can create safety concerns. Load charts often include force ranges at multiple pressures, helping with accurate stiffness calculations. Maintain operating pressure as constant as possible. Variable pressure introduces nonlinear stiffness response, complicating system behavior. Stable pressure equals predictable stiffness, which improves control and safety.
Air spring stiffness in dynamic systems
Air bellows used in dynamic environments experience more than static forces. We calculate dynamic stiffness using:
k_dyn = k_static + c × ω
Where:
- c = damping coefficient
- ω = angular frequency (rad/s)
Dynamic stiffness reflects resistance to motion during oscillations. For example, if a system vibrates at 20 Hz, the angular frequency is 125.7 rad/s. Assuming static stiffness of 300 N/mm and damping of 0.8 Ns/mm, dynamic stiffness becomes 401 N/mm. This model helps size air bellows for machinery mounts and equipment bases. Dynamic stiffness differs from static values and increases with frequency. For vibration isolation, low stiffness is preferred. Therefore, choose air bellows with broad stroke and low-frequency response. Always verify frequency range with the manufacturer’s chart. Systems operating above 30 Hz require bellows with advanced damping properties. Inadequate sizing leads to resonance and system instability. Engineers should combine static and dynamic stiffness models for full evaluation. Testing in real conditions helps confirm values. Where exact vibration performance is required, simulation software is recommended. Include all motion axes for best results.
Selecting the right material and design
Tevema air bellows are made with various rubber compounds and closures, which affect stiffness indirectly. Standard NR/SBR materials offer wide usability from -40°C to +70°C. For high-temperature areas, EPDM or CIIR compounds extend usable range up to 115°C. Material affects durability and response curve. Use CIIR where chemical resistance is needed. NBR is better suited for oil-heavy environments. Closure types include dismountable, bead ring, and crimped designs. Dismountable closures allow easy replacement but add mechanical slack. Crimped closures provide rigidity, enhancing vertical stiffness. For instance, a crimped design may deliver 10–15% more stiffness compared to dismountable types. Choose closure based on mounting surface, space, and expected forces. Stainless steel end plates are used for corrosive environments. They may slightly reduce stiffness due to added weight and flexibility. Always match material and design to the environmental and mechanical requirements. This ensures long-term performance and safety under operational load conditions.
Importance of preload and mounting height
Correct installation height ensures consistent performance. Every air bellow has a recommended design height. Mounting it too high or low changes stiffness drastically. For example, a 310 mm triple convolution bellow shows 70.4 kN at 140 mm height. If compressed to 120 mm, the same bellow exerts over 75 kN. This implies higher stiffness and lower stroke flexibility. Always install close to design height. A preload—force applied before pressure—is sometimes added. This raises initial stiffness and alters force response. For static loads, this improves position stability. However, in dynamic setups, preload may shift resonance. Check if preload is needed before installation. Systems with high accuracy demand should consider this. Misalignment or incorrect height causes uneven wear and unpredictable stiffness. Use proper leveling tools during installation. Measure force after inflation to validate initial stiffness. For critical applications, monitor height with sensors. This helps ensure long-term stability and safety.
When to use high-pressure constructions
Tevema offers four-ply constructions for demanding applications. These support pressures up to 12 bar, compared to 8 bar in standard types. Use these when compact installation, high force, or harsh environments are expected. For example, a 410 mm bellow at 12 bar can exceed 120 kN force output. This enables load-bearing systems with tight space constraints. Four-ply designs resist deformation better, preserving stiffness over many cycles. In environments with temperature swings or chemical exposure, thicker construction helps maintain shape. Always verify compatibility with system pressure. Overloading a two-ply bellow beyond 8 bar reduces lifespan and changes stiffness response. Four-ply versions offer consistent behavior across longer durations. Choose these for systems requiring uptime and reliability. They also reduce the need for external damping. The added thickness improves stiffness stability under dynamic motion. Installation requirements remain the same, though handling may need adjustment due to added weight and rigidity.
Final insights on stiffness formulas
While the fundamental formulas help estimate stiffness, combining them with data ensures reliability. A triple convolution bellow, for instance, with 410 mm diameter at 7 bar may deliver 75 kN over a 125 mm height. If force increases 5 kN over 10 mm, stiffness is 500 N/mm. This number reflects dynamic range, not the entire stroke. Always confirm if this range matches your system. Tevema’s catalog includes height, force, and pressure relationships. Use these alongside formulas for complete modeling. Proper stiffness estimation avoids undersizing or overspecifying components. Safety margins should be built-in. Avoid using static values for dynamic systems. Instead, calculate per operating point. Include mounting height, material, and pressure range in every model. Empirical measurements validate calculations. Predictive models only guide early design stages. For final validation, use testing. Stiffness directly affects system safety and performance. Calculating it accurately ensures stability, longevity, and cost efficiency. Select the right air bellow by understanding stiffness thoroughly.