Abstract
Design data for a family of ring-shaped elastic elements are derived using analytical, numerical and experimental methods. The development of a family of elastic elements for load cells operating at medium to low load level is considered in detail, using several approaches. Snapes analyzed were circular ring with integral bosses and ‘square’ ring. The effects of thickness, boss size and fillet radius (reduced to nondimensional form) on strain/load and defiection/load relationships are evaluated within a given sample space, considering a two-dimensional problem.
Thin-ring and curved-beam theory support the analytical approach, with correction terms covering some departures from theoretical shape. Numerical analysis with the finite-element method was mainly used to evaluate the effects of boss size and shape.
Accordingly, the required grid patterns were developed using a mesh-generating method capable of covering the range of parameters considered. A set of configurations was selected, enabling single and combined effects to be analyzed with little entanglement between estimates. For the square ring, frame theory and a limit solution for the case of the plate with central hole are resorted to.
Photoelastic tests were performed, covering a range of shapes by sequential remachining of the model, and equal contigurations were analyzed with the finite-element method. Strain-gage tests on actual elastic elements were made, considering also the results of a series of tests carried out at the Metrology Institute some time ago. Results obtained yield comprehensive information on the effect of several parameters on the load-output transfer function of ring-shaped elastic elements.
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Abbreviations
- A :
-
area of the diametral cross section of ring, mm2
- BH :
-
boss height, mm
- BR :
-
boss-fillet radius, mm
- BW :
-
half width of boss, mm
- b o :
-
zero-order coefficient in eq (1)
- b 1 :
-
first-order coefficient in eq(1)
- b 2 :
-
second-order coefficient in eq(1)
- E :
-
Young's modulus
- ER :
-
outer radius, mm
- F :
-
axial load,N
- FC :
-
axial load on ring withx 1=x 2=x 3=x 4=0.2,N
- f iv :
-
vertical deflection
- IR :
-
inner radius, mm
- R :
-
radius of center line of ring, mm; for square ring,R=IR+s o/2
- s :
-
thickness of cross section of ring, mm
- s o :
-
thickness of square ring on horizontal diameter
- W :
-
width of ring, mm
- x :
-
s/R; for square ring,x=s o/R
- x 1 :
-
BH/ER
- x 2 :
-
BW/ER
- x 3 :
-
BR/ER
- x 4 :
-
s/ER
- ∈ eo :
-
strain at outer surface, horizontal diameter
- ∈ iM :
-
maximum strain at inner surface
- ∈ io :
-
strain at inner surface, horizontal diameter
- ∈ iv :
-
strain at inner surface, vertical diameter
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Barbato, G., Desogus, S., Zompi, A. et al. Load-cell-design developments by numerical and experimental methods. Experimental Mechanics 21, 341–348 (1981). https://doi.org/10.1007/BF02326234
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DOI: https://doi.org/10.1007/BF02326234