Design studies of a square ring shaped force sensor - Integrated ...

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL
Volume 1, No 4, 2011
© Copyright 2010 All rights reserved Integrated Publishing Association
RESEARCH ARTICLE ISSN ­ 0976­4259
etc (Chen.B et.al,2007). Various expressions have been developed for stress / strain and axial
deflection for the modified shapes suggested so far. But, other modifications have not been
suggested and studied so far like hexagonal ring shape or square ring shape. Besides it, no
past observations are found about the studies related to square ring shaped force sensors.
Hence, the present paper attempts to study a square ring shaped force sensor as a
modifications of the ring shaped force sensors analytically and suggests suitable
modifications in the analytically derived expressions for stress / strain and deflection under
action of external forces subjected to a ring shaped force sensor with the help of finite
element analysis. The software used for finite element analysis is ABAQUS 7.2 standard
student edition.
2. Analytical Study
Ring shaped force sensors have been studied by various researchers and the analytically
derived expressions for stress / strain and deflection of the force sensor are well know, though
few deviations has been observed by experimental studies. The ring shaped force sensors and
the expressions used for stress / strain and deflection have been discussed else where
(Harishkumar Et.al, 2011). The ring shaped force sensor has been analyzed under action of
axial forces (Figure 1) and has been modeled as a ring. Taking the advantage of symmetry, a
quarter may be selected for the analytical study. The free body diagram suggests that the
moment M is statistically indeterminate, the strain energy U for this quadrant of the ring is
due only to the bending moment M in the ring. According the castigliano’s theorem
(Kumar,2010)
F
R i
R 0
F/2
θ
F
Figure 1: Ring Shaped Force Transducer – Idealizing as a Ring
U
M
= 0
(1)
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