FEA OF A LOAD CELL

FEA OF A Load Cell

FEA OF A Load Cell

Introduction

LOAD cells are commonly used force transducers that convert an applied mechanical load into a voltage. Load cells typically comprise spring elements that are designed to deform with load, strain gages that vary their resistance with deformation (strain) of the spring element, and a Wheatstone bridge circuit that produces voltage proportional to strain. One popular spring element design is the binocular configuration, which is a beam with two holes and a web of beam material removed, as shown in Figure 1. The complexity of the binocular section of this beam prevents prediction of strain via simple hand calculation; hence, a COMSOL model was used to guide load cell design (Katona 2000, 554-9).

Modeling the load cell requires three equations: an equilibrium balance, a constitutive relation relating stress and strain, and a kinematic relation relating displacement to strain. Newton's second law serves as the equilibrium equation, which in tensor form is:

where is stress, Fv is body force per volume, is density, and is acceleration. For static analysis, the right-hand side of this equation goes to zero. The constitutive equation relating the stress tensor to strain is the generalized Hooke's law (Paydar 1996, 1477-83).

where C is the fourth-order elasticity tensor and : denotes the double dot tensor product. In COMSOL, this relation is expanded to

Extent of model

Multiphysics was used to design a binocular load cell. A three-dimensional linear solid model of the load cell spring element was studied to quantify the high-strain regions under loading conditions. The load cell was fabricated from 6061 aluminum, and general purpose Constantin alloy strain gages were installed at the four high-strain regions of the spring element. The four gages were wired as a full Wheatstone bridge configuration and total strain was measured for applied loads ranging from 0-2.5 kg in 100 g increments. Model total strain was measured using point probes at each of the four strain locations, and with a load parametric analysis. Absolute mean model-predicted strain was 1.41% of measured strain. The load cell was highly linear. (Davidson 2002, 295-303).

For this application, initial stress , initial strain, and inelastic strain are all zero. For isotropic material, the elasticity tensor reduces to the 6X6 elasticity matrix:

where and µ are the Lam´e constants

E is elastic modulus and is Poisson's ratio, with material properties. The final required equation is the kinematic relation between displacements and strains . In tensor form

Where T denotes the tensor transpose. For rectangular Cartesian coordinates the strain tensor may be written in indicial notation (Ausiello 2001, 1269-77).

where =1,2,3,. . . . For small deformations the higher order terms are negligible and reduces to Cauchy's infinitesimal strain tensor

Type of symmetry

Figure 1 shows the plain weave fabric composites RVE. The first three assumptions are the same as the Vandeurzen's “double-convex model”:

The track-lines of the warp and wefts are the sine curves;

The cross-section of the yarns are not changing along the track-line;

The warps and wefts are close enough to prevent ...