Nagasawa, Kaneko and Adachi, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.13, No.1 (2019)
(Nagasawa et al., 2014, 2015). The first round’s starting angle T 1,1 was zero (in a flat attitude). In this work, only the first round was considered (the number of folding repetition was suffixed as “,1”). The early stage in which T was less than 20° was mainly characterized by the elastic bending stiffness without detaching and bulging of inside layers. Since the middle stage (20° < T < 90°) had a certain stationary resistance (almost constant) under the specified rotation velocity Z , the behavior of resistance appeared to be a sort of the creep response of Maxwell type two-element model (Betten, 2002). This bending moment diagram was used here for confirming the hold time t 1ep =0~20s and detecting the initial unfolded state t 2ep =0s. Here, t 2ep is the elapsed release time for observing the release angle T 2,1 . The quantity T 2,1 (0) is the initial release angle.
Load cell
Load cell
Load cell
T 2,1 ( t 2ep ) Released angle
Center of rotation
. Z = T Z ’ T 䞉
10 mm
. Z = T
T = T 2,1 (0)
Z ’ = T 䞉
T
T
T = 4 =90 㼻
10 mm
10 mm Center of rotation
Center of rotation
Angle of fixture
(a)
(b)
(c)
Figure 9 Schematics of unfolding and relationship between release angle and fixture angle (a) State of tracking angle of 90°; (b) State of initial release angle ( t 2ep =0) when reaction force of load cell becomes zero; (c) In case of unfolded state when detaching the load cell (for t 2ep >0).
t 2ep =0.0s
t 2ep =0.42s
1mm
(a) T =34.0 㼻
(b) T =89.9 㼻
(c) T = T
2,1 =46.0 㼻
(d) T 2,1 =42.7 㼻
Figure 10 CCD camera photographs of side views of creased part during folding test ( J =0.6, Z =0.2 rps). (Ref. Nagasawa, S. et al., 2016) Figure 9 illustrates three states of unfolding process: (a) the state of tracking angle of 4 = 90 ° , (b) the initial released state when defining t 2ep =0, and (c) the released state after detaching the load cell. Generally, T 2,1 is not equal to the rotation angle of fixture T for t 2ep >0, while T 2,1 is equal to T at t 2ep =0 or before detaching the load cell. Figure 10 showed representative side views of real creased part during a folding test. In the folding process (a),(b), the bulged inside layers were compressed in the in-plane direction, while the height of bulged zone decreased with the released angle T 2,1 in the unfolding process (c),(d). Namely, the released behavior of folded attitude appeared to be mainly caused by the released energy of compressed and bulged layers. According to the preliminary experiments (Nagasawa, et al., 2014, 2015), the relationship between the bending moment at the tracking position M 4 (=90°),1 and the hold time t 1ep was linearly approximated with the logarithmic term ln( t 1ep ) using Eq.(1),(2). Here, the intercept a 0 was defined as M 90,1 (1) (at t 1ep =1s), a 1 was the gradient coefficient of Eq.(1), and the exponential coefficient p 1 of relaxation was defined as the ratio of a 1 / a 0 . They describe the relaxation characteristics of bending moment accumulated at the tracking angle of 90°. M 90,1 = a 1 ln( t 1ep ) + a 0 (1) M 90,1 / a 0 = ܯ ഥ ଽǡଵ = 1 – p 1 ln( t 1ep ) , p 1 = a 1 / a 0 (2) The logarithmic relaxation of bending moment at the holding of T =90° was similar to the stress relaxation of the white-coated paperboard subjected to an uni-axial tensile displacement (Nagasawa et al., 2017). Namely, the value of
© 2019 The Japan Society of Mechanical Engineers
[DOI: 10.1299/jamdsm.2019jamdsm0004]
2 5
Made with FlippingBook - Online catalogs