Nagasawa, Kaneko and Adachi, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.13, No.1 (2019)
longer than 2s. Comparing this tendency with the variance of M 90,1 ( t 1ep ), it is revealed that the pre-stage and the early stage of the hold time (e.g., t 1ep < 1 or 2s) are extremely sensitive to the relaxation or dissipation of accumulated bending moment energy. From the results of Fig.13, 14, and also seeing Fig.12 (b), the quasi-stationary relaxation of holding motion is performed for t 1ep >5s. 4. Conclusions One-loop bending characteristics of creased white-paperboard of 0.3mm thickness were investigated by varying the folding rotational velocity Z and the unfolding (returning back) rotational velocity Z ’ when the hold time t 1ep = 0~20s was considered at the tracking position of 4 =90°, using a digital microscope camera. Through this work, the followings were found. 1) The release angle T 2,1 ( t 2ep ) was characterized with a logarithmic function of the elapsed release time t 2ep for the measured range of t 2 ep = 0~10s, when keeping the folding and unfolding rotational velocities in a constant. The release angle T 2,1 ( t 2ep ) appears to be decomposed into the intercept part b 0 which is determined by the hold time t 1ep at the tracking position and the gradient part p 2 which is independently related to the release time t 2ep . 2) In the case of Z = Z ’=0.2 rps (1.26 rad ή s ), the exponential coefficient p 2 = b 1 / b 0 of Eq.(4) was stably 0.050~0.053 for t 1ep = 0~20s, whereas the coefficients b 0 , b 1 of E.(3) were limitedly saturated for t 1ep >5s. 3) When varying the folding and unfolding (released) rotational velocities under the synchronized condition: Z = Z ’ for 0.1 Z /0.2 3, the initial release angle θ 2,1 (0) was characterized with a logarithmic term ln( Z /0.2) using the gradient coefficient E 1 = μ ߠ ଶǡଵ ሺͲሻȀ μሺሺ߱ ȀͲǤʹሻሻ and the intercept E 0 = T 2,1 (0)| Z =0.2rps . 4) When t 1ep <2s, the coefficients E 1 and E 0 were remarkably varied. A change in the sign of E 1 occurred at this duration. When t 1ep >5s, E 1 and the ratio E 1 / E 0 were asymptotically and slightly increased with t 1ep . 5) Regarding the response of bending moment, a drop rate of the bending moment in the early stage ( t 1ep = 0~1s) of holding process remarkably increased with the term ln( Z /0.2) for 0.1 Z /0.2 3, whereas the relaxation behavior settled down with the exponential coefficient p 1 = a 1 / a 0 of Eq.(2) for t 1ep >1s. Comparing this early stage of bending moment with the item 4), it was revealed that the gradient coefficient E 1 was under a transient state of the relaxation for t 1ep <2s, while that was under a quasi-stationary state for t 1ep >5s. 6) When varying the folding velocity Z under keeping the unfolding velocity Z ’=0.2 rps (1.26 rad ή s ) (asynchronous condition), the gradient coefficient E 1 and the ratio E 1 / E 0 were relatively smaller than that of synchronized condition. Also, the value of E 1 / E 0 was stably invariant for t 1ep >10s. 7) Seeing 3), 4) and 6), the hold time at the tracking position makes the folded part in relaxed state and then the holding posture isolates the second half unfolding released behavior from the first half folding rotational velocity effect when the hold time is longer than 5s.
Nomenclature d : indentation depth of creaser knife t : thickness of work sheet (paperboard) B : width of groove on counter face plate J = 2 d ڄ B : normalized indentation depth, ( J = 0.6 was chosen in this work) M : bending moment for the unit width against folding (Nm ή m ) T : folding angle of fixture (°) 4 : tracking (maximum) angle (°) ( 4 = 90° was chosen in this work) n : number of folding repetitions ( n =1 was considered in this work) M 4 (, n) : the n -th round bending moment at a tracking position T 1, n , T 2, n : the n -th round starting, release (angle) position ( T 1,1 was zero in this work)
t 1ep : the n-th round hold time before returning back ( t 1ep was varied from 0 up to 20s, in this work) t 2ep : the n-th round elapsed release time until the next folding ( t 2ep was measured up to 10s in this work) Z : rotational velocity of fixture for folding (rps, revolution per second) (= 2 S Z rad ή s 1 ) Z : rotational velocity of fixture for unfolding (released, returning back process) (rps) (= 2 S Z rad ή s 1 ) a 1 , a 0 : relaxation coefficients derived from Eq. (1) Here, a 0 is M 4 at t 1ep =1s. p 1 = a 1 ή a 0 : an exponential coefficient derived from Eq. (1), Eq.(2) b 1 , b 0 : release coefficients derived from Eq.(3) Here, b 0 is the intercept as T 2,1 at t 2ep =1s.
© 2019 The Japan Society of Mechanical Engineers
[DOI: 10.1299/jamdsm.2019jamdsm0004]
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