Module D — Design Guide
Radially Assembled
Retaining Rings
Radially assembled rings — ST rings, DIN 6799 E-rings and crescent rings —
are pressed into the groove from the side rather than slid over the shaft end.
This makes them uniquely useful on long shafts, shafts with shoulders, or wherever
axial ring assembly is not practical. The trade-off is lower and empirically
determined load capacity, and a unique assembly geometry for crescent rings where
the gap must open significantly during installation.
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When to Use a Radially Assembled Ring
The primary advantage of radial assembly is that the ring does not need to travel
axially along the shaft. This removes the clearance constraint that often limits
groove placement for axial rings:
- Grooves positioned adjacent to shoulders, bearing seats or gear faces that a ring cannot pass over
- Very long shafts where sliding the ring from the end is impractical
- Shafts with splines, threads or other features that prevent axial ring travel
- Applications requiring quick ring replacement without full shaft disassembly
- Thin-section rings (ST rings) where bending stress during axial assembly would be excessive
Lower load capacity: radially assembled rings cannot make full circumferential
contact with the groove in the same way as axial rings. The load capacity depends on the
specific ring design and is determined experimentally. No design formula exists —
always check the manufacturer’s catalogue for the specific ring type and size.
For the highest load capacity, use a
grooved axial ring (Module A).
Ring Types
ST Rings
Data charts 31/32
- Standard radial ring — concentric contour
- Pressed in from side via slot in housing or gap in shaft
- Same groove dimensions as axial rings
- Lower load capacity than equivalent axial ring
- Bending stress: Eq.⑬ with z/b = 0.25
DIN 6799 (E-rings)
DIN 6799 / data charts 32
- Concentric outer contour — retained in groove by own tension
- Groove diameter = nominal d₁ (different convention!)
- Snap into groove radially — no separate groove base
- Very low load capacity
- Common in light engineering, 1–50 mm
Crescent Rings
Data charts 33
- Eccentric outer contour — z/b = 0.35
- Gap must enlarge significantly during assembly (Δe)
- Gap change calculated from Fig.71 chart data
- Concentric outer contour enables radial retention
- Unique — no other ring type has the gap calculation
Assembly Bending Stress
During radial insertion, the ring deforms as it is pressed over the shaft
and into the groove. The bending stress equation is the same as for axial rings
(Eq.⑬) — the geometry of curvature change governs in both cases:
Assembly bending stress — ST & DIN 6799 (Eq. ⑫)
σ_b = (d₁ − d₃) × E × b / [(d₁ + 0.75b)(d₃ + 0.75b)]
z/b = 0.25 for ST rings and DIN 6799 rings
d₁ = shaft diameter · d₃ = ring unstressed inner diameter
For DIN 6799: groove diameter = d₁ (nominal), d₃ is the ring’s own free-state inner diameter
Assembly bending stress — Crescent ring (Eq. ③ variant)
σ_b = ΔD × E × b / [(d₃ + 0.65b)(d₃ + ΔD + 0.65b)]
z/b = 0.35 for crescent rings (different from standard 0.25)
Neutral diameter D₃ = d₃ + 0.65b
ΔD = diameter change during assembly (= d₁ − d₃ approximately)
Higher stresses are accepted for crescent rings — see note below
Crescent rings tolerate higher stress: the handbook explicitly states
that considerably higher calculated bending stresses are permissible for crescent rings
because some permanent deformation of the ring during initial assembly is accepted —
the ring must deform enough that it still retains itself in the groove by its own tension
after installation. This is fundamentally different from axial rings where the stress limit
is an elastic design requirement.
The Crescent Ring Gap Calculation
The distinctive feature of crescent ring assembly is the gap enlargement. The ring
starts with a free-state gap e. During assembly, as ΔD is forced in, the gap
must open by an additional amount Δe. A slot or recess in the housing must be
large enough to accommodate the maximum gap at assembly (e + Δe).
The ratio Δe/ΔD depends on the ring geometry and is read from a chart
(Fig.71 in the handbook, digitised for this calculator). The ratio is high (≈3.0)
for small gaps relative to ring diameter, dropping toward 1.0 as the gap becomes
comparable to the ring diameter:
Crescent ring gap enlargement
Δe = (Δe / ΔD) × ΔD
Δe/ΔD from Fig.71 as function of e/D₃ (e = free gap, D₃ = d₃ + 0.65b)
Δe/ΔD ≈ 3.0 for e/D₃ < 0.15 (small gap rings — gap opens three times more than diameter changes)
Δe/ΔD → 1.0 for e/D₃ → 1.0 (large gap rings — approximately proportional)
e_assy = e + Δe — this is the required clearance slot width in the housing
Worked Example — Crescent Ring
A crescent ring for a 15 mm shaft: d₃ = 13.5 mm, b = 2.5 mm, e = 2.0 mm (free gap).
Spring steel, E = 210,000 N/mm². What is the assembly stress and required housing slot width?
Assembly stress and gap enlargement
d₁ = 15 mm, d₃ = 13.5 mm, b = 2.5 mm, e = 2.0 mm
z/b = 0.35 → z = 0.875 mm
D₃ = d₃ + 0.65b = 13.5 + 1.625 = 15.125 mm
ΔD = d₁ − d₃ = 15.0 − 13.5 = 1.5 mm
σ_b = 1.5 × 210,000 × 2.5 / [(13.5 + 1.625)(13.5 + 1.5 + 1.625)]
= 787,500 / [15.125 × 16.625]
= 787,500 / 251.4
= 3,132 N/mm² (above standard limit — accepted for crescent rings)
Gap enlargement:
e/D₃ = 2.0 / 15.125 = 0.132
Δe/ΔD from Fig.71 at 0.132 → 3.00 (flat region)
Δe = 3.00 × 1.5 = 4.5 mm
e_assy = 2.0 + 4.5 = 6.5 mm ← required housing slot width
σ_b3,132 N/mm² (accepted for crescent rings)
Δe Gap opens by4.5 mm during assembly
e_assy Required slot width6.5 mm
The housing slot or recess must be at least 6.5 mm wide to allow the crescent ring
to be pressed in. If only 2 mm was provided (the free-state gap), the ring could
not be installed.
Symbol Reference
| Symbol | Unit | Description |
|---|
| d₁ | mm | Shaft nominal diameter. For DIN 6799: groove diameter = d₁. |
| d₃ | mm | Ring unstressed inner diameter in free state (always < d₁) |
| b | mm | Ring radial width |
| s | mm | Ring thickness (axial) |
| z | mm | Eccentricity: 0.25b (ST, DIN 6799) or 0.35b (crescent) |
| D₃ | mm | Neutral diameter = d₃ + (b−z) = d₃+0.75b (ST) or d₃+0.65b (crescent) |
| ΔD | mm | Diameter change during assembly ≈ d₁ − d₃ |
| σ_b | N/mm² | Assembly bending stress |
| e | mm | Gap size in free (unstressed) state — crescent rings only |
| Δe | mm | Gap enlargement during assembly — crescent rings only |
| e_assy | mm | Gap at assembly state = e + Δe — minimum slot width required |
| Δe/ΔD | — | Gap amplification ratio from Fig.71 (function of e/D₃) |
Frequently Asked Questions
Why can’t the load capacity of radial rings be calculated?
For axial rings, the full circumference bears against the groove wall, and the dishing mechanism is well-defined. For radial rings, the contact geometry depends on the specific ring design — how many points it contacts, how the gap distorts the load path, and how the ring seats under load. These effects are not captured by the simple beam-on-curve model. The manufacturer determines load capacity experimentally for each ring type and size, and the values are given in data chart tables in the catalogue.
What is the DIN 6799 groove dimension convention?
For DIN 6799 E-rings, the groove diameter equals the nominal shaft diameter d₁. The ring sits directly on the shaft surface with the groove at nominal diameter — there is no undercut below d₁ as with DIN 471 axial rings. This is why DIN 6799 rings are so easy to retrofit: you can groove an existing shaft at its nominal diameter without reducing the effective shaft cross-section significantly. The ring’s own spring tension holds it in the groove. The groove depth is typically only 0.2–0.5 mm.
Why is the crescent ring assembly stress so high?
Crescent rings must deform significantly during installation — the gap opens by 3× or more the diameter change — which produces bending stresses well above the values considered acceptable for axial rings. The handbook accepts this because: (1) the permanent deformation is small and the ring still functions after seating; (2) the crescent ring’s concentric outer contour provides positive radial retention in the groove, unlike narrow axial rings which can lift out under radial forces; (3) the material is specifically chosen and hardened for this application. Always verify the specific ring’s permissible stress with the manufacturer.
The crescent ring has a very small gap — does the Δe/ΔD ratio stay at 3.0?
Yes — for e/D₃ ratios below about 0.15, the Fig.71 chart is flat at approximately 3.0. This means that for small-gap crescent rings, the gap opens at three times the rate of the diameter change. A ring with a 1 mm free gap being forced 0.5 mm over a shaft will open its gap by approximately 1.5 mm. This is the worst case — the housing slot must accommodate the full e + Δe.
Can I use a radial ring where I currently have an axial ring?
Possibly — but only if the groove can be modified or the application suits a lower load capacity. ST rings and DIN 6799 rings have significantly lower load capacity than equivalent axial rings. If the existing axial ring was correctly sized for the load (using
Module A), a simple substitution is unlikely to work. The more common use case is the reverse: designing with a radial ring where an axial ring cannot be fitted due to assembly geometry, then checking whether the catalogue-listed load capacity is sufficient for the application.
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