Measuring the Dynamic Mechanical Characteristics of Japanese Food Materials against Small Impact Force

The dynamic mechanical characteristics against small impact force of konjak, one of popular Japanese foods, were measured in this study. There are many studies discussing the sensory characteristics of food materials, however few of them measure the characteristics numerically and accurately; therefore we have done the experience and show the characteristics. Konjak is flexible and slimy food material. We thought it is like rubbers and measured the response against small impact force. To measure the precise dynamic mechanical force, the levitation mass method (LMM) is used. In LMM, a pneumatic linear bearing is used to reduce friction to almost zero, and an optical interferometer is used. The acceleration, velocity, position, and inertial force of the mass are calculated from the measured time-varying frequency due to Doppler effect. LMM is used to only measure the dynamic forces of the mass before, but we utilize it to test the mechanical characteristics of food materials. Konjak has the characteristics of viscoelasticity. We reveal the numerical and logical characteristics of konjak.


Introduction
The evaluation of the mechanical properties of materials is important.There are many mechanical properties, and force is the most important among them.
However, it is difficult to measure a dynamic force that changes with time, and a suitable method for evaluating it is yet to be established (1).In previous works, Dr. Y. Fujii proposed the levitation mass method (LMM) (2-7), in which a mass is levitated using a pneumatic linear bearing, which makes the friction acting on the mass negligible.The inertial force of the mass can therefore be measured precisely.In this method, an optical interferometer is used, as shown Figure 1, and only the time-varying beat frequency   is measured; all the other quantities such as the velocity , position , acceleration , and force , are subsequently calculated.
Although the mechanical properties of traditional food materials have been discussed in many studies (8), few of them discussed the numerical and logical characteristics.Most of them focused on the sensory properties of food materials, such as appearance, smell, taste, and texture.Konjak is a traditional Japanese food that is very popular in Japan.It is flexible and slimy, and resembles rubber.In this paper, we propose numerical and logical characteristics of konjaks against small impact force.where   is the length of the laser beam wave in the air,   is the beat frequency, and   is the rest frequency.

Materials and Method
was approximately 630 nm in the test.  is the difference between the frequency of the signal beam and the reference beam.  is the beat frequency when the moving part is at rest.The inertial force can therefore be calculated from the beat frequency   with high accuracy.

Result
Figure 3 shows the data processing procedure.In this experiment, an optical interferometer was used, and only the beat frequency   and rest frequency   were therefore accurately obtained.First, the two frequencies were converted to the velocity  using equation (1).The position  was then obtained by integrating , and the acceleration  was obtained by differentiating .Further, the force  was calculated by the equation  = .The initial position  = 0 and time  = 0 were determined when the force  was 0.5% of the maximum force   .

Discussions
Figure 4 shows that the parameters do not change for different types of konjaks of the same thickness.From Figures 5 and 6, it can be observed that the thicker the material, the farther the position.The tendencies of the plotted points are almost the same in the three figures, although the points for 8 mm are not similar to those for 3 and 5 mm in Figure 5.This was due to the uncertainty of the thickness.
Figure 7 shows the maximum force   as a function of half width  ℎ for all the konjaks.The points of  ℎ are inversely proportional to the maximum force   .
Figures 4 and 5 show the force  as a function of .
The hysteresis can be clearly observed in these figures.By using  = 1 2 ⁄  2 , the energies of the moving part before collision (  0 = 1 2 ⁄  0 2 ) and after collision ( 1 = 1 2 ⁄  1 2 ) were calculated.The graph of  0 against the absorbed ratio (1 −  1  0 ⁄ ) × 100 is shown in Figure 8, which reveals that the parameters in the figure are independent of the type of konjaks.The rate of decrease (1 −  1  0 ⁄ ) × 100 is independent of the type of konjak, but dependent on the thickness.
These characteristics indicate that konjaks are viscoelastic objects.They can also absorb approximately 50% of small impact shocks.

Conclusions
Over all, the dynamic mechanical reaction of food materials such as konjaks can be accurately and numerically measured using LMM., where  1 is defined by following equation:  1 = 1 2 ⁄  1 2 ,  0 is the average of the initial velocities of 50 points, and  1 is the average of their terminal velocities.

References
(1) J.P.Hessling : "Models of dynamic measurement error variations of material testing machines," Mechanical Systems and Signal Processing, vol.23, no.

Figure 2
Figure 2 is a schematic of the experimental setup for evaluating the dynamic properties of the material.A pneumatic linear bearing (GLS08A50/25-2571; NSK Co., Ltd., Japan) was used to reduce the friction of the mass.The tested material was attached to the base by means of its viscosity.An initial force was manually applied to the

Figure 4
Figure 4 is measured impact force  as a function of