MethodWhat is calculated?
In a pressure-loaded, edge-clamped circular diaphragm the radial and tangential directions are principal. At the centre both strains are equal and positive; at the edge the radial strain is negative and twice as large. Diaphragm rosettes exploit this: two tangential grids in the centre and two radial grids at the edge form a full bridge with opposite-sign strains in adjacent arms. The relation stays linear as long as the centre deflection is below a quarter of the thickness.
Equations
σ_z = 3p·R²(1+ν)/(8s²) (Keil Gl. 10.89)
ε_z = 3p·R²(1−ν²)/(8Es²) (Gl. 10.93)
ε_R = −3p·R²(1−ν²)/(4Es²) (Gl. 10.94)
f_z = 3R⁴p(1−ν²)/(16Es³) < s/4 (Gl. 10.95)
U_M/U_B = k/4·(2ε_z + 2|ε_R|) = 1,5·k·ε_z (ideal)
ProcedureStep by step
- Enter rated pressure, radius and thickness.
- Check f_z/s; at ≥ 0.25 stiffen the diaphragm.
- Compare the signal with the actual rosette layout – real grids sense averages, not the extremes.
Typical mistake
Using bar as N/mm² without conversion (1 bar = 0.1 N/mm²) or entering the diameter instead of the radius.
PracticeApplication and limits
Designing pressure transducers with diaphragm rosettes, estimating strains on vessel ends and covers, choosing diaphragm thickness and rosette diameter.
Thin plate (Kirchhoff), ideally rigid clamping, small deflection; the signal is the ideal value for grids exactly at centre and edge – real rosettes yield markedly less per Keil.
SourceTechnical basis
Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 10.5.1 diaphragm rosettes, eqs. (10.87)–(10.95), figs. 10.43–10.45.
The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.
FAQFrequently asked questions
Why is ε_R twice ε_z?
From eq. 10.92 with r = R, ε_r = −2·ε_z; the edge fibre is bent most.
What does the limit f_z < s/4 mean?
Up to there bending dominates; beyond it the diaphragm stretches and the characteristic turns non-linear (> 0.3 %).
Which rosette diameter is optimal?
Per Keil it should equal the diaphragm diameter so the edge radial grids capture the negative strains.
In the same cluster
All strain-gauge calculators