Nagasawa, Kaneko and Adachi, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.13, No.1 (2019)
was expressed with Z /0.2 for 0.2< Z /0.2<3, the relaxed bending moment at t 1ep =20s was estimated using Eq.(8). Here, a 0 was calculated from Eq.(7), and p 1 was estimated as 0.046 for Z /0.2<0.5 and 0.055~0.057 for 0.5< Z /0.2<3 from the preliminary experiment. The result of Eq.(8) was well similar to the current experiment as shown in Fig.11. M 90,1 ( t 1ep ) = a 0 (1 p 1 ln( t 1ep )) (8) So far, it was revealed that the bending moment at the pre-stage of tracking position ( 4 =90°) was sufficiently accumulated as an elastic strain energy, namely the measured quantities M p1 and M 90,1 (0) increased with the folding velocity Z , whereas the quasi-stationary relaxation of the bending moment was performed when the hold time was kept in a certain duration. In such the relaxation state based on the hold time ( t 1ep > 1s), the bending moment decreased slightly with Z . Also, a drop rate of the bending moment in the early stage of holding process increased with Z , owing that the difference of Eq.(6) and Eq.(7) derived the drop rate M 90,1 (0) M 90,1 (1)= 0.01 ln( Z /0.2) + 0.04. 3.2 Dependency of release angle on hold time Figure 12 (a) shows a relationship between the first round’s release angle T 2,1 and the elapsed release time t 2ep when choosing the hold time t 1ep as 0, 5, 10 and 20s under the synchronized condition Z = Z ’=0.2 rps (1.26 rad ή s ). Here, the value of T 2,1 was plotted as the average of 5 samples. Seeing Figure 12 (a), it is found that the variation of T 2,1 is decreased as a logarithmic form with t 2ep , and the intercept of T 2,1 (1) tends to be increased with t 1ep . Hence, the release angle T 2,1 was approximated with the term ln( t 2ep ) using Eq.(3), (4).
62
t 1ep = 20s
0 10 20 30 40 50 60
3
54
t 1ep = 10s
2
46
t 1ep = 5s
1
38
b 0 b 1
4 =90 㼻 , J =0.6 Z = Z 䇻 =0.2 rps
4 =90°, J =0.6 Z = Z ’=0.2 rps
t 1ep = 0s
0
30
0 20 Elapsed time for relaxation at tracking angle t 1ep /s 5 10 15
0.1
1 10 Elapsed time for release of folding t 2ep /s
(a) Relationship between release angle (average) and elapsed release time when varying hold time crease with respect to hold time Figure 12 Response of release angle (average) with respect to elapsed release time when keeping rotational velocity Z = Z ’=0.2 rps (1.26 rad ή s ). The standard deviation of measured release angle was about 0.7°. (b) Approximation coefficients of folding angle of Figure 12 (b) arranges the dependency of those two coefficients b 1 , b 0 on the hold time t 1ep . It is found that the intercept b 0 is remarkably varied in a short time less than 5s, while it tends to be saturated or asymptotically increased for t 1ep >5s. Since the exponent coefficient p 2 was about 0.050~0.053 in stable, the time-delay characteristic (creep- recovery) of release angle appears to be independent to the hold time, when keeping Z = Z ’=0.2 rps (1.26 rad ή s ). 3.3 Dependency of initial release angle on rotational velocity According to the preliminary experiment (Nagasawa et al., (2016), Fig.15), when Z > 0.1 rps (0.63 rad ή s ) and t 1 ep = 0s, the exponential coefficient p 2 was about 0.05 for t 2ep =0.2~10s, namely p 2 appeared to be insensitive for Z >0.1 rps (0.63 rad ή s ). Since the expression of Eq.(4) is composed of two factors p 2 and b 0 , in order to discuss the effect of hold time on the release angle, the behavior of the intercept b 0 = T 2,1 (1) seems to be necessary. In this work, the initial release angle T 2,1 (0) was measured and analyzed instead of T 2,1 (1). Figure 13 shows the initial release angle T 2,1 (0) when varying the hold time t 1ep = 0~20s at the tracking angle 4 =90°. Here, the synchronized condition was considered: Z = Z ’ = 0.02~0.4rps (0.13~2.51rad ή s ). The value T 2,1 (0) was the average of 5 samples and the error bar shows the maximum and minimum value in the 5 samples for each rotational velocity. It is found that T 2,1 (0) tends to be linearly varied with a logarithmic function of rotational velocity. Therefore, Eq.(9) was introduced and the gradient coefficient E 1 and the intercept E 0 = T 2,1 (0)| Z =0.2rps were investigated
© 2019 The Japan Society of Mechanical Engineers
[DOI: 10.1299/jamdsm.2019jamdsm0004]
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