Module F — Design Guide

Support Washers (DIN 988)

A support washer sits between a retaining ring and the abutting component. Its purpose is simple: by bridging the chamfer or corner radius of a rolling bearing or similar component, it reduces the effective lever arm h and directly increases the ring’s load capacity — often by a factor of two or more with no other design changes.

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The Lever Arm Problem

The load capacity of a retaining ring depends inversely on the lever arm h — the distance from the ring’s bearing surface to the groove wall edge. A larger h means the ring must dish further before transmitting load into the groove, which reduces the load it can carry.

For a sharp-cornered abutment (no chamfer), h = 0.3 + 0.002×d₁ mm — small, typically 0.35 to 0.6 mm. But rolling bearings have chamfers, and those chamfers are not small. A standard 6205 bearing (d₁ = 25 mm) has a corner radius of 1.0–1.5 mm. That gives h = 1.05–1.55 mm — three to four times the sharp-cornered value, and a corresponding reduction in ring load capacity to a third or a quarter.

Without support washer

Ring bears directly on bearing chamfer
h = 0.05 + g (typically 1.0–2.0 mm)
Load capacity often 25–50% of sharp-cornered value
May require a larger / stronger ring

With support washer

Washer bridges the chamfer; ring bears on washer
h = 0.05 + (g − s) — reduced by washer thickness
Load capacity restored toward sharp-cornered value
Same ring, significantly higher F_R

Rule of thumb: for every 1 mm reduction in h, ring load capacity increases by approximately h_old/h_new. A washer that reduces h from 1.55 mm to 0.35 mm (washer thickness 1.2 mm) increases F_R by a factor of 4.4× — with no change to the ring or groove.

How the Spring Constant is Calculated

The support washer is an annular flat spring. Its spring constant uses exactly the same equation as the retaining ring (Eq.⑤), with the washer’s own dimensions:

Washer spring constant — Eq. ⑤

K = (π × E × s³ / 6) × ln(1 + 2 × b_m / Y)

b_m = (D − d) / 2 — mean radial width of washer
Y = d — inner diameter (washer bears on shaft at inner edge)
s = washer thickness [mm] · E = 210,000 N/mm² for spring steel
Note: s³ dependence — doubling washer thickness multiplies K by eight

Axial displacement — Eq. ⑩

f = F × h² / K + V

F = axial force [N] · h = lever arm [mm] · V = 0.035 mm (initial displacement)
This gives the axial movement of the ring under load when the washer deflects. For thin washers (s = 0.1–0.3 mm) K is small and f can be significant.

Effective Lever Arm with Washer

A washer of thickness s reduces the effective gap between the ring and groove wall edge by approximately s. The effective lever arm becomes:

Effective lever arm

h_eff = max(h_sharp, 0.05 + g − s)

h_sharp = 0.3 + 0.002×d₁ mm (sharp-cornered limit — cannot go below this)
g = chamfer or corner radius of bearing / abutment [mm]
s = washer thickness [mm]
The effective h cannot fall below the sharp-cornered value regardless of washer thickness.

Choosing a Support Washer

DIN 988 specifies standard D/d combinations matched to common shaft sizes. Key selection criteria:

Inner diameter d — must clear the shaft with small clearance. Standard h11 tolerance on shaft.
Outer diameter D — should be as large as possible (larger b_m → higher K) but must fit within the housing bore or shaft shoulder.
Thickness s — determines both the h reduction and the spring constant. Thicker washers reduce h more but also deflect less (higher K). Standard DIN 988 thicknesses: 0.1, 0.2, 0.3, 0.5 mm.

Stacking washers: multiple washers in series reduce h further and increase total deflection. The spring constants add in series as 1/K_total = 1/K₁ + 1/K₂ + ... For identical washers: K_total = K/n. This is acceptable for taking up manufacturing tolerances but the total stack deflection must be checked against acceptable axial play.

Worked Example

A DIN 471 ring on a 25 mm shaft retains a 6205 bearing. The bearing has a corner radius r = 1.5 mm (g = 1.5 mm). Ring K = 45,000 N·mm, Ψ = 0.087, S = 1.5. A DIN 988 washer D=35, d=26, s=0.2 mm (spring steel) is available. Show the load capacity improvement.

Step 1 — Washer spring constant

b_m = (35 − 26) / 2 = 4.5 mm Y = 26 mm K = π × 210,000 × 0.2³ / 6 × ln(1 + 2×4.5/26) = 879.6 × ln(1.346) = 879.6 × 0.2972 = 261 N·mm

K Washer spring constant261 N·mm

Step 2 — Lever arm comparison

h_sharp = 0.3 + 0.002×25 = 0.35 mm Without washer: h_chamfer = 0.05 + 1.5 = 1.55 mm h_without = max(0.35, 1.55) = 1.55 mm With washer (s = 0.2 mm): g_eff = 1.5 − 0.2 = 1.3 mm h_chamfer_eff = 0.05 + 1.3 = 1.35 mm h_with = max(0.35, 1.35) = 1.35 mm

h without washer1.55 mm

h with washer1.35 mm

Step 3 — Load capacity improvement

F_R_without = 0.087 × 45,000 / (1.55 × 1.5) = 3,915 / 2.325 = 1,684 N F_R_with = 0.087 × 45,000 / (1.35 × 1.5) = 3,915 / 2.025 = 1,933 N Improvement = 1.55 / 1.35 = 1.15× Using a thicker washer s = 1.0 mm: h_with = max(0.35, 0.05 + 0.5) = 0.55 mm F_R_with = 3,915 / (0.55 × 1.5) = 4,745 N Improvement = 1.55 / 0.55 = 2.82×

F_R without washer1,684 N

F_R with s=0.2 mm washer1,933 N (1.15×)

F_R with s=1.0 mm washer4,745 N (2.82×)

A thicker washer gives a much larger improvement. The practical limit is the available axial space and whether a thicker washer changes the bearing setting.

Symbol Reference

Symbol	Unit	Description
D	mm	Washer outer diameter
d	mm	Washer inner diameter
s	mm	Washer thickness — standard DIN 988 values: 0.1, 0.2, 0.3, 0.5 mm
b_m	mm	Mean radial width = (D−d)/2
Y	mm	Inner diameter d (Y value for K formula)
K	N·mm	Washer spring constant
E	N/mm²	Modulus of elasticity (210,000 for spring steel)
F	N	Axial force on washer
h	mm	Lever arm at which force acts
f	mm	Axial displacement under load F at lever arm h
g	mm	Chamfer or corner distance of abutting component (bearing etc.)
h_without	mm	Lever arm without washer = max(h_sharp, 0.05+g)
h_with	mm	Lever arm with washer = max(h_sharp, 0.05+g−s)
K_ring	N·mm	Ring spring constant — from Module A detail panel

Frequently Asked Questions

Why does the washer inner diameter Y appear in the K formula rather than the outer diameter?

The washer is treated as a curved beam bending about the inner edge. The inner diameter d is the point where the washer bears on the shaft shoulder or the ring, and the deflection is measured from this point. This is the same convention as for retaining rings, where Y is the groove diameter d₂ — the inner contact diameter. The outer diameter D affects b_m and therefore the logarithmic term, but it is not the reference diameter for the curvature calculation.

Can the washer K value be ignored compared to the ring K?

Usually yes — the washer K is typically much lower than the ring K because the washer is very thin (s³ is very small). The washer contribution to axial displacement f is therefore small compared to the ring’s own dishing. However, for thin washers (s = 0.1–0.2 mm) under large forces, the washer deflection can be significant and should be checked. If the washer K is within an order of magnitude of the ring K, compute the total displacement as f = F×h²×(1/K_ring + 1/K_washer).

Does the washer thickness s reduce the available groove depth t?

No — the washer sits between the ring and the bearing face, not in the groove. It occupies axial space between the ring’s free face and the bearing’s chamfer. The groove geometry is unchanged. However, you must ensure there is sufficient axial space for the washer: the distance from the ring’s seated position to the bearing face must be at least s to accommodate the washer without preloading the bearing unintentionally.

When should I use a thicker washer vs a thinner one?

Thicker washers reduce h more and give a larger improvement in ring load capacity. The practical limit is: (1) available axial space — a 1 mm washer takes 1 mm of axial space that may affect bearing setting; (2) the effective h cannot go below the sharp-cornered limit h_sharp, so beyond a certain thickness the washer gives no further improvement; (3) very thick washers under large deflections may themselves yield, particularly if the force is applied at a large radius. In most cases a washer of 0.5–1.0 mm gives the best practical result.

The calculator asks for K_ring — where do I find this?

K_ring is shown in the detail panel of Module A when you click on a solution cell. It is the ring’s spring constant in N·mm, calculated from the ring dimensions using Eq.⑤. You can also compute it directly: K = (π×E×s³/6) × ln(1 + 2×b_m/Y) using the ring’s own s, b_m and Y values rather than the washer’s.

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