Shock Absorber and End-of-Stroke Damping Calculator
Size an industrial shock absorber for end-of-stroke damping: from moving mass, impact velocity, additional propelling force and damper stroke the calculator returns the energy to absorb per stroke W3, the thermally decisive energy per hour W4 and the effective mass m_e. The basis are the ACE calculation fundamentals W1 = ½·m·v², W2 = F_drive·s, W3 = W1 + W2, W4 = W3·x and m_e = 2·W3/v² - live with every input and with a traffic-light check against the limits of the selected damper type.
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Formulas and fundamentals
Kinetic energy and propelling energy
An end-of-stroke damper decelerates a moving mass smoothly at the end of its travel and converts the kinetic energy into heat. The starting quantity is the kinetic energy of the mass m at the impact velocity v. If the drive keeps pushing with a force F_drive during the damper stroke s (for example a cylinder or feed force), the propelling energy is added:
Energy per stroke and per hour
The total energy to be absorbed per stroke and the energy per hour that governs the thermal sizing (with x the number of strokes per hour) are:
W4 must stay below the damper's permissible energy absorption per hour so it does not overheat. Both checks - energy per stroke and energy per hour - are independent.
Effective mass and selection criterion
For selecting the type the effective mass is used in addition:
It combines kinetic and propelling energy into an equivalent, purely kinetically damping mass at the velocity v and must lie within the permissible mass range of the damper type. The selection is satisfied when the following hold at the same time:
and m_e is within range.
Worked example
A mass of m = 100 kg impacts the damper at v = 1 m/s. The drive keeps pushing with F_drive = 200 N over the damper stroke s = 50 mm. The kinetic energy is W1 = ½·100·1² = 50 Nm, the propelling energy W2 = 200·0.05 = 10 Nm.
The energy per stroke is thus W3 = 50 + 10 = 60 Nm. The effective mass is m_e = 2·60/1² = 120 kg - clearly more than the bare mass of 100 kg, because the propelling force raises the load.
At x = 600 strokes per hour the energy per hour is W4 = 60·600 = 36,000 Nm/h. A damper is needed whose energy absorption exceeds 60 Nm per stroke and 36,000 Nm/h, and whose permissible mass range includes m_e = 120 kg.
Frequently asked questions
What is the difference between W3 and W4?
W3 is the energy to absorb per single stroke (W3 = ½·m·v² + F_drive·s) and must not exceed the damper's permissible energy absorption per stroke. W4 = W3·x is the energy per hour at x strokes and governs the thermal continuous load; it must stay below the permissible energy absorption per hour. Both checks are independent.
Why is the propelling force F_drive taken into account?
If the drive (e.g. a pneumatic cylinder or feed) keeps pushing during the damper stroke, it adds the work W2 = F_drive·s on top of the kinetic energy. The damper must absorb this energy as well. Neglecting F_drive leads to an undersized damper.
What does the effective mass m_e mean?
m_e = 2·W3/v² is the equivalent mass that at velocity v would introduce the same energy W3 through its kinetic energy alone. It combines kinetic and propelling energy and is compared with the permissible mass range of the damper type. Because of the propelling force m_e is usually larger than the actual moving mass.
Which velocity should I use?
What matters is the impact velocity v at the moment of first contact with the damper, not the average travel speed. Since the energy grows quadratically with v, this is the most sensitive parameter of the sizing - an underestimated velocity quickly leads to overload.
Does the calculator select the specific damper?
No. The calculator provides the sizing quantities energy per stroke, energy per hour and effective mass. The specific damper selection is made from the manufacturer's catalogue values (permissible energy per stroke and per hour, permissible mass range, maximum impact velocity).
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