Cross-Category Force Comparison
Cross-Category Force Comparison
Parameters
| Symbol | Name | Unit |
|---|---|---|
| De | De | mm |
| Di | Di | mm |
| h0 | h0 | mm |
| material | material | — |
| s | s | mm |
| t | t | mm |
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Contact Engineering TeamDetailed Calculation Guide
Cross-Category Force Comparison: Methods for Comparing Mechanical Properties of Different Locking Washers
1. Purpose of Comparison
In bolted joint design, selection often needs to be made among various standard washers such as DIN 6796 (disc spring washers), DIN 9250 (tooth lock washers), NFE 25‑511 (single-sided toothed conical spring washers), and DIN 25201 (wedge lock washers). Cross-category force comparison aims to:
- Quantify differences among washer types in terms of elastic compensation capacity, locking torque, and load-bearing capacity.
- Select the most suitable washer type based on connection requirements (preload level, vibration intensity, temperature range, space constraints).
- Provide data support for combined use (e.g., spring washer + locking washer).
2. Key Force Comparison Indicators
| Indicator | Symbol | Definition | Main Relevant Washer Types |
|---|---|---|---|
| Flat load | $F_{flat}$ | Load when the washer is fully flattened, determining its load limit | DIN 6796, NFE 25‑511, DIN 9250 (disc types) |
| Working stiffness | $k$ | Tangent slope of the force‑deflection curve at the working point | Same as above |
| Elastic stored energy | $U$ | Energy absorbed when compressing from free state to a certain displacement | Same as above |
| Locking torque | $M_{lock}$ | Maximum static friction torque resisting bolt loosening rotation | DIN 25201, DIN 9250 (wedge/tooth types) |
| Unlocking torque | $M_{unlock}$ | Minimum sustained torque required to maintain washer sliding | Same as above |
| Anti-slip safety factor | $S_{lock}$ | Ratio of locking torque to thread back-off torque | All types |
| Compensation capacity | $\Delta s$ | Allowable axial settlement without losing preload | Elastic washers |
3. Quick Overview of Force Calculation Methods for Each Washer Type
3.1 Disc Spring Washers (DIN 6796, NFE 25‑511 disc portion)
Flat load (Almen‑Laszlo):
- DIN 6796: Smooth, no teeth, directly uses this formula.
- NFE 25‑511: Toothed, flat load multiplied by tooth cross-section reduction factor $\beta_{strié} \approx 0.7\sim0.9$.
Working stiffness: Obtained by derivation or secant slope of the force‑deflection curve at working preload $F_M$. DIN 6796 has near-linear stiffness due to low $h_0/t$; NFE 25‑511 has reduced stiffness due to tooth pattern.
Elastic stored energy (flattening process):
Compensation travel: Usable compression travel $s_{max} \le 0.75h_0$, used to compensate for settlement.
3.2 Wedge Lock Washers (DIN 25201)
Locking torque:
- $\alpha$ — Wedge angle (typically 6°~8°)
- $\rho = \arctan(\mu_{cam})$ — Wedge friction angle
Unlocking torque:
Characteristics: Almost no elastic compensation capacity, but extremely high locking torque unaffected by vibration friction decay.
3.3 Tooth Lock Washers (DIN 9250)
Combines both disc spring elasticity (flat load) and tooth locking (locking torque) characteristics.
Flat load:
.
Locking torque (based on tooth bite + flat friction):
- $\mu_{bite}$ Equivalent friction coefficient at tooth tip (0.5~1.0)
- $\mu_{flat}$ Flat friction coefficient (0.1~0.2)
Compensation capacity: Due to tooth cross-section weakening, stiffness and stored energy are lower than smooth disc washers of the same size, but still elastic.
4. Cross-Category Force Comparison Methods
4.1 Parallel Comparison Under Same Bolt Specification
Select the same bolt (e.g., M10), look up or calculate the standard dimensions of each washer type for that bolt specification, then compute the above force values and list them in a comparison table.
| Washer Type | Flat Load $F_{flat}$ (kN) | Working Stiffness $k$ (kN/mm) | Locking Torque $M_{lock}$ (N·m) | Elastic Compensation Travel (mm) | Applicable Vibration Level |
|---|---|---|---|---|---|
| DIN 6796 (smooth disc) | ~11 | ~12 | Friction only, ≈0.5 | 0.75 | Weak |
| NFE 25‑511 (toothed disc) | ~8 | ~9 | ~8 | 0.6 | Medium |
| DIN 9250 (toothed disc) | ~9 | ~10 | ~20 | 0.5 | Strong |
| DIN 25201 (wedge) | Not applicable (rigid) | Very high | ~40 | ≈0 | Very strong |
Note: Values are examples; actual values must be calculated based on standard dimensions and materials.
4.2 Key Ratio Comparison Method
Define a series of dimensionless ratios to intuitively compare the mechanical characteristics of different washers:
- Elastic utilization: $\eta_{ela} = \frac{F_{Mmax}}{F_{flat}}$; smaller value under the same preload indicates greater margin.
- Locking efficiency: $\eta_{lock} = \frac{M_{lock}}{M_A}$ (ratio of locking torque to tightening torque); wedge washers have very high values.
- Compensation efficiency: $\eta_{comp} = \frac{\Delta s_{allowable}}{\Delta s_{predicted}}$; ratio of compensation capacity to expected settlement.
Visualize these ratios using radar charts or bar charts to quickly identify the strengths and weaknesses of each washer type.
4.3 Decision Matrix Based on Connection Requirements
| Connection Requirement | Preferred Washer | Reason |
|---|---|---|
| Large settlement compensation + moderate locking | NFE 25‑511 or DIN 9250 | Combines elasticity and tooth locking |
| Strong vibration, high locking requirement | DIN 25201 or DIN 9250 | Wedge or tooth provides high locking torque |
| Pure elastic compensation, slight vibration | DIN 6796 | Low cost, good linear stiffness |
| High temperature + compensation + locking | DIN 9250 + spring washer combination | Tooth locking withstands temperature, elastic element compensates |
| Very tight space | DIN 6796 or small tooth washer | Disc washers have small axial dimensions |
5. Force Superposition Principle for Combined Use
Sometimes a single washer cannot simultaneously meet force and compensation requirements, requiring combination of different types. Superposition rules:
- Parallel combination (stacked in same direction): Total flat load $n$ times, stiffness $n$ times, travel unchanged.
- Series combination (opposing placement): Total travel adds, force unchanged, stiffness reduced to $1/i$.
- Mixed combination: e.g., DIN 25201 (locking) + DIN 6796 (compensation) in series; total stiffness determined by the softer element, locking torque provided by the wedge washer.
The combined characteristics must be determined through separate modeling or testing.
6. Precautions for Force Comparison
- Data source: Prioritize manufacturer-measured force‑deflection curves and friction coefficients; theoretical formulas serve as initial selection basis.
- Temperature derating: At high temperatures, elastic modulus decreases and material yield reduces; comparisons should be uniformly corrected to working temperature.
- Reuse: After repeated use, $M_{lock}$ and $F_{flat}$ of tooth washers decrease; wedge washers also require replacement; comparisons should be based on first-use performance.
- Surface pressure: High force values often accompany high surface pressure; simultaneously verify that the connected parts are not crushed.
- Cost and lead time: Final selection must also consider procurement cost, delivery lead time, and assembly process complexity.
Summary: Cross-category force comparison, by calculating the flat load, stiffness, and locking torque of each washer type, combined with dimensionless indicators such as elastic utilization and locking efficiency, helps designers select the best among different standard washers. For complex operating conditions, a combined solution is recommended and should be validated through testing.