Formula Used
The calculator treats the flat spring as a rectangular beam. The second moment of area is I = b t3 / 12. With parallel leaves, b becomes total effective width.
For the selected support case, deflection is computed as Cd P L3 / (E I). Bending stress is computed as Cs P L / (b t2).
Design stress = nominal stress × stress concentration factor × service factor. Allowable stress = yield strength × allowable yield use. Safety factor = allowable stress / design stress.
Spring rate = total load / deflection. Stored energy = 0.5 × total load × deflection. The thickness suggestions solve the stress and deflection formulas backward.
How to Use This Calculator
Enter the working load and any preload. Add the spring length, width, thickness, and number of parallel leaves. Choose the support condition that matches the real mounting.
Enter material modulus and yield strength from a trusted data sheet. Add conservative factors for holes, edges, shock, uncertain loading, or rough service.
Press Calculate. Review the result section above the form. Use the CSV or PDF buttons to save the result for drawings, reports, or design notes.
Flat Spring Design Guide
A flat spring works like a controlled bending beam. It stores energy while it bends. The goal is simple. The spring must deflect enough, yet stay below the chosen stress limit. This calculator gives early values for that design step.
Key Geometry Choices
Length has a strong effect on deflection. A longer spring bends much more under the same load. Thickness has an even stronger effect because stiffness follows thickness cubed. Width and leaf count spread the load. More width reduces stress and raises stiffness. These changes help when space is fixed.
Material And Safety
Elastic modulus controls deflection. Yield strength controls the safe stress range. A spring can look strong, yet still fail if the design stress is too high. The tool applies stress concentration and service factors. These inputs make the result more conservative. Use them when edges, holes, clamps, or impact loads are present.
Practical Design Method
Start with real space limits. Enter the free length, width, thickness, and expected load. Select the support condition that best matches the mounting. Add preload when the spring already carries force before operation. Then compare deflection, stress, stiffness, and safety factor. If stress is high, raise thickness or width. If deflection is too small, reduce thickness or increase length.
Prototype Review
The calculator is best for screening designs. It cannot replace fatigue testing, tolerance checks, or material certification. Flat springs often see repeated cycles. Surface finish, heat treatment, grain direction, and sharp corners matter. Small burrs can start cracks. Clamp stiffness can also change the real deflection.
Use the output as a guide for first drawings. Keep a safety margin for manufacturing variation. Test samples under actual travel and load. Record permanent set after cycling. A good design returns to shape, avoids yielding, and fits the assembly. When results look close to the limit, choose a stronger section or a better material.
Common Warning Signs
Very high stress means the part may bend permanently. Very low safety factor means the reserve is small. Excessive deflection can cause rubbing or missed contact. Low deflection may make the spring feel rigid. Balance all four values before selecting final tooling. Document assumptions so later reviews stay clear and useful.
FAQs
What is a flat spring?
A flat spring is a thin strip that bends to store force. It is often used in clips, contacts, latches, and return mechanisms.
Which support condition should I choose?
Choose the case that matches the real load path. Use cantilever for one fixed end. Use simply supported for two supports and center loading.
Why does thickness change the result so much?
Thickness controls bending stiffness by a cubic relationship. A small thickness change can greatly change deflection and stress capacity.
What is the stress concentration factor?
It increases nominal stress for holes, notches, rough edges, sharp bends, or clamp effects. Use a higher value when geometry is uncertain.
What safety factor is acceptable?
It depends on duty, material data, fatigue risk, and failure cost. Many early static checks use a conservative reserve above one.
Does this calculator include fatigue life?
No. It gives static bending estimates. Repeated cycling needs fatigue data, surface condition review, mean stress correction, and prototype testing.
Can I use other units?
Use the shown units for reliable results. Loads are newtons, dimensions are millimeters, modulus is gigapascals, and stresses are megapascals.
What should I do if deflection is too high?
Increase thickness, reduce length, add width, add leaves, or choose a stiffer layout. Then check stress and safety again.