Calculation
Rtotal = R₁ + R₂
Both springs have the same travel; their forces and rates add.
Roloff/Matek Gl. (10.2)
Springs in parallel
Both springs have the same travel; their forces and rates add.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Combined spring rate Rtotal — Stiffness of the complete parallel-loaded spring set.
- Spring rate R₁ — Rate of the first spring.
- Spring rate R₂ — Rate of the second spring.
- Additional spring R₃ — Optional third parallel spring; 0 means absent.
Example
10 N/mm and 20 N/mm give 30 N/mm.
Assumptions and limits
Linear characteristics, equal travel and concentric loading.
Understand Springs in parallel
Parallel spring combination is a focused preliminary calculation based on Roloff/Matek. The calculator rearranges the closed-form relationship for every included quantity and deliberately separates this result from a complete component verification.
What does this quantity describe?
For linear springs in parallel, deflection is equal while the component forces add. Therefore Rtotal = R1 + R2 (+ R3).
Formula and variables
Rtotal = R₁ + R₂
Rges = R1 + R2 (+ R3)
| Symbol / input | Meaning |
|---|---|
| Combined spring rate Rtotal | Stiffness of the complete parallel-loaded spring set. |
| Spring rate R₁ | Rate of the first spring. |
| Spring rate R₂ | Rate of the second spring. |
| Additional spring R₃ | Optional third parallel spring; 0 means absent. |
Choose the inputs correctly
R1 to R3 are the slopes of the individual force-deflection curves. R3 may remain zero for two springs; Rtotal describes the complete set.
How to use the calculator
Select the target, enter all remaining quantities for the actual component, and verify the units. Then compare the result with the stated model limits and with the required strength, safety and operating checks.
Worked example
10 and 20 N/mm combine to 30 N/mm.
Understand the result and units
Rtotal must be at least as large as either individual rate; a smaller result indicates the wrong connection model.
The calculator converts internally to coherent SI units. Length, force, torque, stress and angle may therefore use the offered units; dimensionless factors are entered as decimals.
What is taken from Roloff/Matek
Only the closed-form relationship from Kapitel 10.1.1, Gleichung (10.2) is used. Tabulated data, material limits and detailed design checks are not silently added; they remain explicit inputs or are expressly outside the model.
Typical applications
Parallel spring combination supports option comparison, plausibility checks and early sizing within its machine-element cluster. Releasing a design requires the additional checks described in the cited chapter.
Assumptions, limits and common mistakes
Valid for linear characteristics, equal travel and concentric loading under the conditions stated for equation 10.2.
Common mistake: Typical errors are misreading the effective length or force, entering percentages instead of decimals, and treating a preliminary result as a complete verification. In particular: Valid for linear characteristics, equal travel and concentric loading under the conditions stated for equation 10.2.
Frequently asked questions
Is Parallel spring combination a complete strength verification?
No. Valid for linear characteristics, equal travel and concentric loading under the conditions stated for equation 10.2.
Where do the equation and validity limits come from?
Roloff/Matek, Machine Elements, Kapitel 10.1.1, Gleichung (10.2); the local 21st edition was cross-checked against the available 24th edition.
Can I order the calculated value directly as a nominal size?
Only after matching it to available standard or manufacturer series and completing the additional safety, material and operating checks.