Belleville Spring Calculator
Estimate Belleville washer force, stack rate, working travel, and stress screening from outside diameter, inside diameter, thickness, free cone height, material modulus, stack arrangement, deflection, and target force.
⚙Named Belleville Stack Presets
Load a realistic disc spring stack, then adjust washer geometry, material modulus, deflection, and the number of nested or opposed washers.
📏Disc Geometry, Material, and Stack Arrangement
Belleville stack results
Calculation Breakdown
🧰Current Geometry Snapshot
📊Stack Arrangement Reference
| Arrangement | How It Is Built | Force Effect | Travel Effect |
|---|---|---|---|
| Single disc | One Belleville washer | Base force from one washer | Base travel equals one cone height |
| Parallel nested | Washers face the same direction | Multiplies force by nested washer count | Deflection stays near one washer travel |
| Series opposed | Washers alternate cup-to-cup or back-to-back | Force stays near one washer force | Multiplies travel by opposed group count |
| Mixed stack | Nested groups are placed in series | Force equals one group force | Travel equals one group travel times groups |
⚒Disc Spring Material Reference
| Material | Elastic Modulus | Typical Use | Design Note |
|---|---|---|---|
| Spring steel | 207 GPa / 30.0 Mpsi | General high-force stacks | Protect from corrosion and verify heat treatment. |
| 301 stainless | 193 GPa / 28.0 Mpsi | Corrosion-resistant preload | Lower modulus means lower force at same geometry. |
| 17-7PH stainless | 200 GPa / 29.0 Mpsi | Higher strength stainless stacks | Check condition and precipitation hardening data. |
| Inconel X-750 | 214 GPa / 31.0 Mpsi | Heat and relaxation resistance | Use temperature-rated catalog curves for final design. |
| Phosphor bronze | 110 GPa / 16.0 Mpsi | Electrical or nonmagnetic loads | Produces much lower force than steel geometry. |
| Beryllium copper | 131 GPa / 19.0 Mpsi | Conductive spring contacts | Confirm handling and material safety requirements. |
📐Geometry and Deflection Guide
| Check | Preferred Range | Why It Matters | Calculator Warning |
|---|---|---|---|
| OD / ID ratio | 1.5 to 2.5 | Controls force curve and stress distribution | Warns when ratio is very narrow or very wide. |
| h / t ratio | 0.25 to 1.30 | Higher cone ratio creates stronger nonlinearity | Warns when travel or cone ratio is aggressive. |
| Working deflection | 15% to 75% of h | Common working band for repeatable preload | Warns near flat or very low movement. |
| Guide clearance | Catalog fit | Disc stacks can shift, scrape, or buckle | Shown as a safety note for physical builds. |
🔢Formula and Output Reference
| Output | Method Used | Unit | Interpretation |
|---|---|---|---|
| Single washer force | DIN-style elastic disc approximation | N or lbf | Force for one disc at the calculated single-disc deflection. |
| Stack force | Single force times nested washers | N or lbf | Parallel nesting increases the stack force. |
| Stack rate | Numerical slope around working point | N/mm or lbf/in | Local tangent rate, because Belleville springs are nonlinear. |
| Target deflection | Bisection solve against target force | mm or in | Estimated stack movement needed to reach the entered force. |
| Stress screen | Force lever and section estimate | MPa or ksi | Screening value only; compare with catalog stress curves. |
💡Calculation Tips and Safety
⚠Safety Note
Belleville springs are component that create a strong push with minimal travel. Belleville springs are use in many application. In order to determine the force that a group of Belleville springs will create, a person must calculate the force that each Belleville spring will create when placed in a group.
A Belleville spring’s geometry includes the outside diameter, the inside diameter, the thickness, and the free cone height. The force that a Belleville spring is create is not created in a linear range. Additionally, the force is create differently with Belleville springs that are nested within each other in relation to the other Belleville springs in the group.
How to Calculate Force and Travel of Belleville Springs
Thus, a person makes an estimate of the force that a group of Belleville springs will create. In order to calculate the Belleville spring, there are specific parameter that must be entered into the calculation. The outside and inside diameter of the Belleville spring allow for the calculation of the lever arm that the Belleville spring will create.
The force of the Belleville spring is related to the thickness of the Belleville spring. The cone height of the Belleville spring allow for the calculation of the amount of travel that the Belleville spring will create before it becomes flat. The amount of force that the Belleville spring creates is also related to the material of the Belleville spring, spesifically the value of the modulus of that material.
The value of the modulus for materials like stainless steel are not the same as the spring steel. These two value are used directly in the calculation. Additionally, the Belleville spring can be create in different ways.
If the Belleville springs are nested within each other, the amount of force that the Belleville spring will create will be multiplied, but the amount of travel will be similar to a group of Belleville springs in series. In contrast, Belleville springs that are stacked in series will have a similar amount of force as the individual Belleville spring, but the travel will be increase in relation to the single Belleville spring. Belleville springs can be arranged in both series and parallel in a Belleville spring group.
The arrangement of Belleville springs will impact the way in which the force is distribute to the Belleville spring group. Additionally, the arrangement of the Belleville spring group will be important in the decision of whether or not to maintain the rigidity of the attached fixture or to allow for thermal expansion. When creating a Belleville spring group, both the amount of deflection and the target force with which the Belleville spring should actuate are important.
The amount of travel of the Belleville spring will be entered into the calculation as will the target load for the Belleville spring group. The designer will be provided the force that the Belleville spring will create at the targeted point of deflection. The force created by Belleville springs is not linear.
Thus, the rate of change of the force between 30% and 70% of the travel of the Belleville spring can be different. The calculation of the tangent slope of the Belleville spring will provide information on how sensitive the preload of the Belleville spring to the height of the Belleville spring group. Should the preload become sensitive to changes in the height of the Belleville spring group, the joint may become loose after thermal cycles.
Thus, understanding the tangent slope will allow the designer to avoid these potential issue. There are two reference table on the page. The first table is used to describe the trade-offs between different materials and their levels of corrosion resistance.
The other table includes information regarding the geometry of the Belleville spring. Specific ratio of the outside and inside diameter can be too narrow or too wide for the Belleville spring to distribute the forces as intended. These tables will allow the design to avoid any situation in which the Belleville spring may be stiffer or softer than expected.
A common mistake within Belleville springs is to use the cone height of the Belleville spring as the thickness of the Belleville spring. The thickness of the Belleville spring is actualy the free height of the Belleville spring. Additionally, another common mistake is to assume that placing Belleville springs in series will create an increase in the travel of the Belleville spring group with no change to the force.
Any small difference between the individual Belleville springs can drastically change the travel of the Belleville spring groups. An understanding of the position of the Belleville spring group in relation to its flat position will help to avoid mistake in Belleville spring group creation. The fatigue life of Belleville springs includes more than the stress calculation made by the calculator.
Factors like the cycles that the Belleville spring is placed under and the corrosiveness of the environment will impact the life span of the Belleville spring. The stress level that is calculated includes a service factor that can be increased for situation with shock or uncertain data. Thus, the calculator will provide an estimate to the life span of the Belleville spring.
However, the estimate is still useful in the selection of Belleville spring samples. Temperature can impact the performance of Belleville springs. Spring steel Belleville springs will lose their strength with increased temperature above a few hundred degrees.
However, materials like Inconel and certain type of stainless steel will maintain their material modulus at high temperatures. This information can be used in the material modulus field of the calculation to allow the user to avoid guesswork about derating the Belleville spring for high temperatures. Additionally, the material modulus field can also be used to compensate for low temperature at which some Belleville spring materials will become stiffer.
By performing these calculation before the Belleville spring groups are create, it is possible to determine the best way to arrange Belleville springs within the group. For example, it is possible to determine if adding Belleville springs in parallel will create too much stress within the Belleville spring. Additionally, other engineering decision can be made related to how strong the Belleville spring must be and how often it will need to be replaced.
Thus, the calculation avoids manual arithmetic calculation.
