A bump stop cushions the end of a moving assembly’s travel. This calculator explores a specified progressive spring law and shows an illustrative fluted elastomer bumper compressing between two plates. It does not select a suspension component or establish a safe load.
Bump Stop Interactive Calculator
Set compression, initial and final stiffness, and the compression where stiffness reaches its final value. The drawing cycles through the entered travel; result cards show the target state.
Equation Used
- Force is zero at first contact. Stiffness rises linearly with compression to L and stays constant thereafter.
- The animation uses an illustrative 60 mm free height. Shape and bulging are not calculated from a material model.
- Loading work is the area under the loading curve. Dissipated energy requires an unloading curve; no hysteresis, strain-rate, temperature, ageing or hard-bottoming model is included.
A specified progressive force law; no certified bumper rating or impact model.
How a bump stop compresses
An elastomer bumper is placed between a moving part and its support. After contact, axial compression changes its shape and raises the resisting force. A fluted profile provides room for deformation; a surrounding cup can restrict bulging. Shaft-mounted designs may have a central bore. The drawing shows a generic free-standing arrangement.
The geometry is illustrative. The calculator uses your specified stiffness curve rather than predicting a material response from shape. Real force–displacement behaviour must come from tests or component data.
Where bump stops are used
Suspension jounce bumpers and machinery end stops are examples. Each installation needs its own contact geometry, stroke, force and duty-cycle checks. This model does not establish suitability for a vehicle, lift, crane or safety stop.
The progressive force law
The input stiffness rises linearly from k₀ at zero compression to k₁ at compression L. Integrating stiffness gives force; integrating force gives loading work. For x ≤ L:
F(x) = k₀x + (k₁ − k₀)x²/(2L)
W(x) = [k₀x²/2 + (k₁ − k₀)x³/(6L)]/1000 J
For x > L, stiffness stays at k₁. The force and work continue continuously from their values at L. L is not a physical height or bottoming point.
The area under a loading curve is work supplied during compression. Energy dissipated per cycle is the area between loading and unloading curves. This calculator has no unloading model and cannot calculate that loss.
Worked example using the default inputs
At x = L = 5 mm, k₀ = 50 N/mm and k₁ = 2000 N/mm, tangent stiffness is 2000 N/mm. Force is 50 × 5 + 1950 × 25 / 10 = 5125 N. Loading work is [50 × 25 / 2 + 1950 × 125 / 30] / 1000 = 8.75 J.
These values describe the entered law. They do not demonstrate that a particular bumper, strut tower or vehicle can withstand that load. No vehicle-specific capacity is assumed.
What this model can and cannot compare
You can compare the effect of changing initial stiffness, final stiffness or transition compression on force and work. A longer transition gives a more gradual stiffness increase. Higher rates produce higher force at the same compression.
Choosing between an elastomer, spring and hydraulic buffer requires measured dynamic response, available stroke, allowable load and duty cycle. The present quasi-static model does not provide those comparisons or universal speed limits.
Questions about this calculator
Is loading work the energy permanently absorbed?
No. Part can be returned during unloading. A measured hysteresis loop is needed to estimate dissipated energy.
Does L represent bumper height?
No. It is the compression where the assumed stiffness reaches k₁. The illustrated free height is 60 mm only to make the motion readable.
What happens above L?
The calculation continues at constant stiffness k₁. It does not predict hard bottoming or a failure load.
Why do the output cards stay fixed while the bumper moves?
The cards describe the compression you entered. The live force and shaded work area follow the animated position between zero and that target.
References and model scope
US20060001205A1, Jounce bumper: physical form and compression arrangements. The illustration is a generic bumper, not a reproduction of the patent’s insert design.
The force and work equations are integrations of the specified stiffness law. They are not manufacturer test curves.
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