BIZOMAT MAKEOS · Springs
Springs in Series or Parallel
What is the combined rate of these springs, and how is the load shared?
Equivalent rate of up to four springs in series or parallel, with the deflection and load of each spring under a given total load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Arrangement | choice | Parallel when springs act side by side or nested; series when one pushes on the next. |
| Rate of spring 1 | N/mm | Rate of spring 1 from its data sheet or a test. |
| Rate of spring 2 | N/mm | Rate of spring 2. |
| Rate of spring 3 (0 = not used) | N/mm | Rate of spring 3, or 0. |
| Rate of spring 4 (0 = not used) | N/mm | Rate of spring 4, or 0. |
| Total load | N | Total load on the combination. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Arrangement
- What it is
- How the springs are connected: in parallel they sit side by side and share the load with the same deflection; in series one pushes on the next, so each carries the full load and the deflections add.
- Units and format
- Choose one of 2 options from the list: Parallel (share the load, same deflection); Series (same load, deflections add).
- Example
- The form opens with “Parallel (share the load, same deflection)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Nested springs on the same seat act in parallel.
What this means: Rate of spring 1
- What it is
- The rate of the first spring: the force needed to deflect it by one millimetre, from its data sheet or a load test.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0.000001 N/mm or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter N/mm; a rate quoted in N/m must be divided by 1000.
What this means: Rate of spring 2
- What it is
- The rate of the second spring: the force needed to deflect it by one millimetre, from its data sheet or a load test.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0 N/mm or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter N/mm; a rate quoted in N/m must be divided by 1000.
What this means: Rate of spring 3 (0 = not used)
- What it is
- The rate of an optional third spring in the combination, from its data sheet or a load test. Zero leaves it out.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0 N/mm or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 if there are only two springs.
What this means: Rate of spring 4 (0 = not used)
- What it is
- The rate of an optional fourth spring in the combination, from its data sheet or a load test. Zero leaves it out.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0 N/mm or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave it at 0 if there are fewer than four springs.
What this means: Total load
- What it is
- The total load applied to the whole spring combination.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Total deflection rises in proportion to the load.
- Get it right
- Check each spring’s share of load and deflection against its own rating afterwards.
Method and formulas
- Parallel: k = Σkᵢ; every spring deflects F ÷ k and carries kᵢ × deflection.
- Series: 1/k = Σ(1/kᵢ); every spring carries F and deflects F ÷ kᵢ.
- Example: 20 and 30 N/mm in parallel give 50 N/mm and 10 mm under 500 N.
Limitations
- Linear springs within their working range; parallel springs must start loading together (no preload differences).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Combine springs for a target rate
- Find load sharing in nested or stacked springs
- Model mounts and supports
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Equivalent rate
- Total deflection
- Load and deflection of each spring
Interpreting the result
- Check that no individual spring exceeds its own maximum load or deflection.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 304–320. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Spring rate, stored energy and springs that work together
What it covers: What a spring's rate is, how much energy it stores, and how springs and their supports combine in series and in parallel, with the VM-8's spring register.
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