Symbol	Name	Unit
deflection_pct	deflection_pct	%
material	material	—
size_key	size_key	—

OM Point Stress: Strength Verification of Single-Side Serrated Conical Spring Washers

1. Definition and Significance of the OM Point

In the single-side serrated conical spring washer specified by NFE 25-511, the OM point specifically refers to the inner edge of the washer's upper surface (serrated face), i.e., the location at the inner hole edge. This point experiences the maximum compressive stress when the washer is deformed under compression and is the critical verification point for controlling the washer's fatigue life and preventing permanent deformation.

Why OM point stress is maximum: - When a conical disc spring is compressed axially, the cross-section undergoes bending deformation. The inner edge of the upper surface is the extreme point where the compressive bending stress and the membrane compressive stress are superimposed. - The notch effect at the serration root further induces stress concentration at this location. - If the OM point stress exceeds the material's yield strength, the washer will undergo plastic collapse (flattened without rebound), losing its elastic compensation function.

Therefore, OM point stress is the core criterion for the strength verification of elastic washers.

2. Stress Calculation Formula

Based on the Almen‑Laszlo disc spring theory, the compressive stress at the inner edge of the upper surface (corresponding to the OM point) of a smooth conical washer is:

\sigma_{OM0} = \frac{4E}{1-\nu^2} \cdot \frac{t^2}{K_1 D_e^2} \cdot \frac{s}{t} \left[ C_1 \left( \frac{h}{t} - \frac{s}{2t} \right) + C_2 \right]

Where the coefficients are:

C_1 = \frac{c-1}{\ln c} - 1, \qquad C_2 = \frac{c-1}{2\ln c}

$$E$$ — Elastic modulus (MPa)
$\nu$ — Poisson's ratio
$$t$$ — Material thickness (mm)
$$h$$ — Free cone height (mm)
$$s$$ — Axial compression (mm)
$$D_e$$ — Outer diameter (mm)
$$c = D_e/D_i$$ — Outer-to-inner diameter ratio
$$K_1$$ — Shape factor (as defined in the force‑deflection formula)

NFE 25-511 Correction:

The presence of single-side serrations weakens the cross-section near the OM point. The actual stress must be multiplied by the serration stress correction factor $\gamma_{strié}$ (≥ 1):

\boxed{\sigma_{OM} = \gamma_{strié} \cdot \sigma_{OM0}}

\gamma_{strié}

is determined by the serration geometry (number of serrations, serration width, root fillet radius), typically obtained through finite element analysis or experimental testing. Typical ranges: - Few serrations, large serration width: $\gamma_{strié} \approx 1.05 \sim 1.15$ - Many serrations, sharp serration roots: $\gamma_{strié} \approx 1.15 \sim 1.30$

If measured data is unavailable, a conservative recommendation is $\gamma_{strié} = 1.25$ .

3. Strength Verification Criterion

\sigma_{OM} \le \sigma_{adm}

The allowable stress $\sigma_{adm}$ is determined by the washer material:

Operating Condition	$\sigma_{adm}$	Description
Static load / Single assembly	$R_{p0.2}$	Material yield strength, ensures no permanent deformation
Cyclic load / Repeated compression	$\sigma_{fat} / S_D$	Material fatigue limit (stress amplitude) divided by safety factor $S_D \ge 1.2$

Reference values for common washer materials (quenched and tempered spring steel, e.g., 50CrV4, C75S):

Material	Hardness (HV)	$R_{p0.2}$ (MPa)	$\sigma_{fat}$ (MPa)
C75S	400–480	≈ 1200	≈ 500
50CrV4	450–510	≈ 1400	≈ 600
Stainless Steel (X5CrNi18‑10)	—	≈ 900	≈ 350

Note: When the compression $$s$$ approaches $$h$$ (flattened state), the OM point stress increases sharply. The design should limit $s \le 0.75h$ to ensure operation within the elastic range.

4. Parameter Calculation Example

Given: M10 matching L-type washer (same as previous example): - $E = 206\,000$ MPa, $\nu = 0.3$ - $$D_e = 25$$ mm, $$D_i = 10.5$$ mm → $$c = 2.38$$ , $\ln c \approx 0.867$ - $$t = 1.8$$ mm, $$h = 1.2$$ mm - Compression $$s = 0.6$$ mm → $$s/t = 0.333$$ , $$h/t = 0.667$$ - $$K_1$$ previously calculated ≈ 0.78 - Serration stress correction $\gamma_{strié} = 1.20$

Calculate coefficients:

C_1 = \frac{2.38 - 1}{0.867} - 1 = \frac{1.38}{0.867} - 1 \approx 1.592 - 1 = 0.592

C_2 = \frac{2.38 - 1}{2 \times 0.867} = \frac{1.38}{1.734} \approx 0.796

Bracket term:

C_1\left( \frac{h}{t} - \frac{s}{2t} \right) + C_2 = 0.592 \times (0.667 - 0.167) + 0.796 = 0.592 \times 0.500 + 0.796 = 0.296 + 0.796 = 1.092

Base stress $\sigma_{OM0}$ :

\frac{4E}{1-\nu^2} = \frac{824\,000}{0.91} \approx 905\,495 \text{ MPa}

\frac{t^2}{K_1 D_e^2} = \frac{1.8^2}{0.78 \times 25^2} = \frac{3.24}{0.78 \times 625} = \frac{3.24}{487.5} \approx 0.006647 \text{ (mm²/mm² dimensionless)}

\sigma_{OM0} = 905\,495 \times 0.006647 \times 0.333 \times 1.092 \approx 905\,495 \times 0.002416 \approx 2\,187 \text{ MPa}

(This value is significantly high, indicating that the $$h/t$$ ratio or compression selection may be too severe. In practical engineering, $$h/t$$ is typically between 0.4 and 0.8, and compression is limited to below 0.5h. This is only for demonstrating the formula application.)

Apply correction factor:

\sigma_{OM} = 1.20 \times 2187 \approx 2624 \text{ MPa}

If material $R_{p0.2} = 1400$ MPa → Not acceptable, requires reducing compression, changing geometry, or selecting a stronger material.

5. Control Strategies for OM Point Stress in Design

Limit compression: Ensure the washer is not flattened under working load. Recommend $s \le 0.5h$ for better linear stiffness and to keep $\sigma_{OM}$ within a safe range.
Optimize $$h/t$$ ratio: A larger $$h/t$$ increases the disc spring effect but also raises OM point stress. Elastic compensation washers typically use $h/t \approx 0.6 \sim 1.0$ .
Optimize serration geometry: Increasing the root fillet radius can reduce $\gamma_{strié}$ , alleviating stress concentration.
Match material and hardness: Select high-yield-strength spring steel and ensure proper hardness, while also considering the fatigue limit.
Use in series: When a single washer cannot simultaneously meet deflection and stress requirements, multiple washers can be used in opposition or stacked (but note the assembly methods specified in NFE 25-511).

Summary:
OM point stress is the key to strength verification of single-side serrated conical spring washers. It is based on disc spring theory and multiplied by the serration stress correction factor $\gamma_{strié}$ , and must be controlled within the material's yield or fatigue allowable stress. The design should ensure OM point stress safety by limiting compression, optimizing geometric parameters, and selecting appropriate materials.

OM Point Stress

Formula Expression

Parameters

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