Nagasawa, Kaneko and Adachi, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.13, No.1 (2019)
tensile
Center of rotation
tensile
Comp. Comp. Bulging by in-plane compression
Damaged area
(a) Concave shape after scoring (b) Behavior of crease in folding process Figure 4 Model of crease mechanism. (a) Scoring by creaser knife makes damaged area in a laminated paperboard, and causes an offset with the center position of rotation. (b) Lateral in-plane compression on the inside layer buckles and makes the inside layer bulged. This moves the neutral plane of bending upwards and reduces the tensile stress in the outside layer. (Ref. Nagasawa, S. et al., 2004)
CCD Camera
Load cell
Load cell
. Z = T
1.0 mm
Load cell
. Z = T
Test piece
Coated side
T =0 㼻
10 mm
10 mm
T
Center of rotation
10 /mm
Paperboard
Center of rotation
Figure 5 General view of bending test apparatus Figure 6 Conception of bending test (folding process)
In the folding process, the folding angle T was recorded by a CCD camera of digital microscope, while the bending moment M was measured by a load cell of the bending test apparatus. A scored paperboard was set up in the test apparatus and clamped by the fixture which rotated with the rotational velocity Z . The clamping position was shown in Fig.6. The scored paperboard was bent from the original position T = 0° up to the folding angle of T = 90°. The folding process was completed at 90° (named as the tracking angle 4 = 90°) and its angle of fold state was paused for a specified duration defined as the elapsed hold (stopping) time t 1ep . This pause of 4 =90° was used for observing the relaxation of bending moment. After completing this relaxation process with the hold time t 1ep , the folded paperboard is sequentially released under returning back with the unfolding rotational velocity Z ’ until the reaction force of the load cell becomes zero. This returning back duration was named as the unfolding or release process.
Stopping (hold) time t 1ep T = 4 M 4 ( t 1ep )
γ =0.6 䠈 ω =0.2rps J =0.6, Z = Z 䇻 =0.2rps (1.26rad ȉ s 1 ) Loading, Z
Tracking angle
M 4 (0)
4 =90 / 㼻
1s
M p1
θ 1 T 1,1
M 4 (0) Stopping for t 1ep (0)
Unloading (released) Velocity Z ’ t 2ep Elapsed release time
M 4 (1)
M p1
M 4 ( t ep ) M 4 (t 1ep )
Loading Velocity Z
θ 2 T 2,1 (0)
C 1
1,1
Unloading, Z 䇻
Elapsed time t 1ep , t 2ep /s
Folding angle T / 㼻
Rotation angle T / 㼻
Figure 7 Conceptual bending moment response with
Figure 8 Analysis parameters on folding resistance
elapsed time and measured parameters.
diagram.
The conceptual relationship between the bending moment resistance (for the unit width) M and the elapsed time was illustrated in Fig.7. Figure 8 is an example of the first round’s folding load response described as the relationship between the folding rotation angle T and bending moment resistance M . The first term maximum peak bending moment M p1 and the bending moment at the first round’s tracking angle M 4 (=90°) , 1 ( t 1ep ) were explained in the previous report
© 2019 The Japan Society of Mechanical Engineers
[DOI: 10.1299/jamdsm.2019jamdsm0004]
2 4
Made with FlippingBook - Online catalogs