Technical Analysis: Why Use E/(1-μ²) Instead of E in the Calculation Formula for Disc Spring Force?

In the theoretical calculations and engineering design of disc springs, the accuracy of force calculation formulas is critical. A frequently discussed core issue is why the material constant in standard formulas is E/(1-μ²) rather than the material's inherent elastic modulus E. Jiangsu Sunzo Spring will combine disc spring technology theory with measured data to reveal the engineering wisdom behind this correction.

1、The Difference between Theoretical Hypothesis and Engineering Reality

1. Hypothesis of classical theory:

The early theoretical derivations (e.g. Alman-Lazaro formula) were based on a simplified assumption that the cross-section of the disc spring would not deform radially under a load. In this idealized model, the derivation process did not involve the Poisson effect of the material, and therefore the use of the elastic modulus E was theoretically self-consistent.

2. Actual physical behavior:

However, the real disc spring will inevitably produce radial deformation in its cross section when bearing load, which is a physical phenomenon determined by the Poisson's ratio (μ) of the material. Therefore, from the perspective of mechanics, a more accurate model should directly use the elastic modulus E to account for the complete constitutive relationship of the material.

2、Engineering Correction Driven by Field Data

The comparison between theory and experiment reveals the key point:

Calculation discrepancy: When the elastic modulus E is directly applied in calculations, the theoretical force value obtained will differ by approximately 9% compared to the result derived from E/(1-μ²).

Data coincidence: A large number of experimental data show that the actual force value of disc spring is more consistent with the calculated result of E/(1-μ2).

Therefore, in GB/T 1972 and the international standard, E/(1-μ2) is used as a constant, which is not derived from pure theory, but is a successful engineering correction based on the measured data. It cleverly compensates the difference between the classical theory and the complex reality.

3、The Practice of Three-Group Elasticity:Connecting Theory and Reliable Product

At Jiangsu Sunzo Spring, our disc spring design and services go beyond standard formulas. We have a deep understanding of the complete process from theoretical models and material behavior to final product performance. We achieve this through:

Accurate calculation: Use proven standard formulas to ensure the accuracy of design and selection.

The experimental verification: the calculation result is compared with the actual measurement by the modern testing center, and the closed-loop verification is carried out.

We are dedicated to transforming profound theoretical knowledge into reliable disc spring products with precise performance and accurate data, providing solid technical support for your engineering design.