Smart Spring Calculator for Wave Spring Washers

A wave washer is a thin ring with waves formed around it. It pushes back when squeezed between two surfaces.

It supplies a moderate thrust load in very little radial space. That makes it useful in seals, bearings, motors and other rotating parts.

Common jobs include taking up end play, absorbing vibration and applying steady pressure. Demand keeps growing as parts get smaller and more compact.

Curved washers give a lighter thrust load and are often used to take up end play. Finger washers combine that flexibility with several load points like a wave washer. Each has its own calculator or design method.

The rate is close to linear between 20% and 80% of the available deflection. Design inside that band for the best load accuracy.

A ratio of D/b near 8 balances flexibility against load capacity. Here D is the mean diameter and b is the radial width of the ring.

Forming often stretches the material at each crest and trough. A washer that starts round will go out of round as it deflects. Leave radial clearance for that movement.

A washer needs at least three waves. The count is usually picked to hit the desired rate.

Rate rises with the fourth power of the wave count. A small change in waves makes a big change in stiffness.

The equations come from simple beam theory. Correction factors from experience improve the accuracy. Here K_w is the wave factor from the table below. Treat the results as engineering estimates, not exact solutions.

Published wave spring factors. The stress equation below matches the published equation.

Wave washers load mainly in bending. Stress is highest when the washer is pressed to solid.

Check the stress at the deepest deflection the washer will ever see, not only at working height.

The outside diameter grows as the washer flattens. The free outside diameter is D_o.

The wave path keeps its length as the washer flattens, so the diameter grows. The growth rises with the square of the wave height, so tall waves need real clearance.

Compare the result to the bore. There must be clearance at the largest diameter the washer reaches.

The OD grows as the washer flattens. The bore must clear the flat OD.

Allowable stress is a percent of tensile strength. It matches the values used for flat springs.

Maximum recommended operating stress in static applications, as a percent of tensile strength. Wave washers are generally supplied stress-relieved.

Cyclic limits drop quickly as the required life goes up.

For steel curved and wave washers such as AISI 1075. Assumes an ambient environment and no sharp bends, burrs or other stress raisers.

Dimensional tolerances are like those on flat springs. Tolerance only the dimensions that matter to the function.

Specify loads at a test height. Tighter tolerances are available for demanding jobs.

Fill in only the data the design needs.

• Material, with AISI 1075 as a common choice
• Hole diameter and pin diameter it works in and over
• Load and tolerance at a test height
• Required reliability
• Description of one cycle
• Maximum operating temperature and environment
• Reference data: thickness, OD, ID and free height

A wave washer must fit an 80 mm (3.15 in) bore and a 60 mm (2.362 in) shaft. It must carry about 500 to 550 N (112 to 124 lbf) at 1.8 mm (0.071 in) of deflection. The load is steady, so this is a static case. Ambient environment. Preferred material is AISI 1075.

The deflection is large for this type. Use three waves, the most flexible option.

Assume a 75 mm (2.953 in) OD and a 64 mm (2.520 in) ID. That gives a mean diameter D of 69.5 mm (2.736 in). Solve the load equation for thickness.

Steel at HRC 49 has a tensile strength near 1725 MPa (250,000 psi). Limit stress at solid to 80%, or 1380 MPa. Solve for the deflection at that stress.

The required 1.8 mm is 75% of the deflection to solid. That is acceptable.

Find the OD in the deflected position. It fits the bore with adequate clearance.

Values from the worked example above.

The worked example with its final dimensions, in millimeters.

Belleville washers, wave washers, curved washers, finger spring washers, and stacked wave springs are all doing the same basic thing: a thin annular ring, formed out of flat, pushes back axially when compressed. What changes between them is how much force they give you, how much stroke they give you, and how much axial height that stroke costs. Picking the right one is mostly a matter of where your application sits on that trade-off, plus a couple of jobs (electrical contact, coil-spring-like travel) that only one shape really covers.

The Belleville washer (see the Belleville washer calculator) sits at one extreme: for a given radial envelope and axial height, it delivers the most force of the five, at the smallest deflection per washer. Stacking trades some of that force back for more stroke, but a single disc is still the highest-force-density option here.

The curved washer (see the curved washer calculator) sits at the other extreme. It's a single gentle curve rather than a true cone or wave, the simplest and cheapest of the five to produce, and by far the lowest-force option. It exists almost entirely to take up assembly slack: light bearing preload, anti-rattle, a small constant push against a race, nothing that needs real clamping force.

The wave washer, the subject of this calculator (typically three waves around the circumference, single turn), is a step up from the curved washer: more force for the same material, at a moderate deflection, still a fraction of a Belleville's force density. It's the common drop-in for light-duty bearing preload where a Belleville would be overkill.

Nest wave washers crest-to-crest and you get a stacked wave spring: a compact substitute for a coil spring, with more total deflection and a more linear rate than any single washer in this family, in a much smaller radial envelope than a coil spring would need for the same force (though it does need more axial height than a single washer or a short Belleville stack).

The finger spring washer replaces the continuous wave or cone with cantilevered fingers. Force output is comparatively low, and the fingers are shaped to hold that force nearly constant across the working travel, which is exactly what steady electrical contact pressure needs through vibration and thermal cycling. If the joint also has to carry current or hold an EMI/RF shield path, this is usually the only one of the five actually built for that job.

A wave washer is a closed ring. A single-turn wave spring is split. The split gives it a different fit.

A gap type leaves a small gap at the ends. An overlap type lets the ends overlap.

The split lets the spring sit in a tighter cavity. The ends can touch the housing without binding.

Most single-turn springs use three to six waves.

A static spring is loaded once and held. Wave spring makers allow stress up to the full tensile strength here. The handbook is more cautious for stress-relieved parts.

A dynamic spring cycles. Keep operating stress at or below 80% of tensile. Go lower for long life.

Use the cyclic table in the design guide for a life target. Stress range matters more than the peak alone.

The calculator uses the handbook static values (80% or 75%). That is the cautious choice.

The calculated rate is linear through the first 80% of the available deflection. Past 80% the real load runs well above the calculated load.

Some makers suggest 30% to 70% for a single-turn wave spring. Multi-turn springs use 20% to 80%. This calculator flags anything outside 20% to 80%.

Free height is the height with no load. Work height is the height at the specified load. Give the load at the work height on the drawing.

Tolerance the load at that height. Height alone is a poor way to hold load.

Rubbing between the crests and the mating parts uses energy. The load while pressing is higher than the load while releasing.

That gap is hysteresis. It shows up as a loop on a load-deflection plot.

Good lubrication shrinks the loop. Dry parts show more of it.

Some designs want the loss. It damps vibration.

State on the drawing which way the load is measured.

Presetting compresses the part past its yield point once. The part keeps a small permanent set. It also keeps a helpful residual stress.

That stress opposes the working stress. The part carries more load and lasts longer in fatigue.

The handbook lists 100% of tensile for steel with favorable residual stress. It lists 80% without. Parts that are only stress-relieved get the lower value.

Presetting is a maker process. Ask for it on the drawing. Say how far and how many times.

Life falls as the stress range rises. Cut the range and life goes up fast.

Wave spring makers estimate life from the stress at two work heights. S1 is the stress at the lower work height. That is the more compressed one. S2 is the stress at the upper work height.

Here σ is the tensile strength. A higher X means a longer life. Higher tensile material raises X.

Published for hardened wave spring material. The calculator shows this band when you enter a working point. Leave the minimum load blank if the spring returns to free height.

Raise the minimum load. That narrows the swing. It works for both wave and curved parts.

Burrs, sharp edges and surface flaws start cracks. Ask for clean edges.

The handbook gives a modified Goodman diagram for steel at HRC 47 to 49. The lines are for 10⁶ cycles.

Reduce the values 10% for 10⁷ cycles. Increase them 20% for 10⁵ cycles.

Thin strip does better in fatigue. Plot the higher stress against the lower stress. A point under the line lasts longer than the line's life.

Heat lowers strength and modulus. The rate drops. The part can also relax and lose load over time.

Hard-temper wave springs are quoted to about 700 °F. Check the material you pick. Some alloys go much higher.

Load and travel needs often force a design to accept a little set. Plan for some load loss over life. Test at the real temperature.

Stack several turns crest to crest. The turns act in series. Travel adds up. The rate drops.

The load stays the same as one turn. Total travel is Z times larger.

Nest springs inside each other. They act in parallel. The loads add. The travel stays the same.

A crest-to-crest wave spring can match a coil spring's load. It needs about half the operating height.

It also needs less radial room than a coil spring of the same force.

Crest to crest acts in series. Nested acts in parallel.

Same load, same scale. The wave spring needs about half the height.

Carbon steel and 17-7 stainless are the usual starting points. They are stocked and cost less.

Makers also offer many other alloys. Examples are Inconel X-750 and Elgiloy for harsh service.

Start with the environment. Then the life target. Then the budget.

• Corrosion or wet service: stainless or a nickel alloy
• Heat: a nickel alloy or 17-7 stainless
• Electrical or nonmagnetic parts: beryllium copper or phosphor bronze
• Low weight: titanium

Values from the calculator's material list. Modulus sets the rate. Density sets the weight.