Page 294 - Carbon Nanotube Fibres and Yarns

Carbon nanotube yarn-based actuators 283

11.5.2 Output stress (σ)
Definition: the maximum generated force upon excitation normalized to
the initial cross-sectional area of the actuator (engineering stress, σ E ) or the
cross-sectional area at the excited state (true stress, σ T ).
F
σ = (11.7)
E
S
2
where F (N) is the maximum generated force upon excitation and S (m )
is the initial cross-sectional area of the actuator. For coiled yarn actuators,
the cross-sectional area of the coil cylinder (diameter D+2r in Fig. 11.6)
should be used, rather than the cross-sectional area of the yarn (diameter 2r
in Fig. 11.6).
For a coil actuator, if we increase the yarn strain (ε y ), for example, by hang-
ing a heavier weight, the yarn torque Q will also increase according to Eq.
(11.3). Consequently, the lifting force F will increase according to Eq. (11.4).
This means that the maximum contractile stress achieved in these coils is de-
pendent on the initial conditions, in particular the pre-strain or load applied to
the coil at the start of the experiment. Shang et al. [55] carried out a systematic
study on the electromechanical actuation in helical yarns stretched to a wide
range of tensile strains. They found that the stress increased with increasing pre-
strain up to 50%, and then decreased at larger strains (50%–130%).

11.5.3 Energy density or work density (E)
Definition: the output work generated by the actuator upon excitation nor-
malized to the mass or volume of the actuator. The output work density (E)
can be calculated using Eq. (11.8)

E ( J / g) = W or E ( J m ) == W (11.8)
3
/
m
v
m
v
2
2
3
where W ( J), m 2 (kg), and v 2 (m ) correspond to the output work generated
by the actuator upon excitation, the mass of actuator, and the volume of
actuator, respectively.
The easiest way to test the output work of a linear contractile actuator
is hanging a weight and measure how high it can be lifted upon excitation.
The contractile output work (W C ) can then be calculated using Eq. (11.9)
W () = mgh (11.9)
J
1
C
2
where m 1 (kg), g (m/s ), and h (m) correspond to the mass of the object that
is lifted by the actuator, the gravitational acceleration, and the contractive
length of the actuator, respectively.