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Sliding and plowing are discriminated based on Hertz contact, and the grain number statistics model is established considering that grain size and abrasive protrusion height fit normal distribution.
Therefore, statistics on the number of the rubbing, plowing and cutting grains will play a crucial role in forecasting the grinding force and grinding heat.
The number of grains per unit area, Ns The grain diameters follow normal distribution in a grain size number.
The density of the grains in the volume of Δ3 is: (4) Therefore the average grain spacing Δ can be derived as, then the number of grains per unit area can be obtained as Ns= (1/Δ)2.
The analysis shows that the possibilities of contacting, sliding, plowing and cutting grains also increase along with grain size number, less than 5% of grains are contacting with workpiece in the grinding arc, about 96% of contacting grains occur plowing and about 4% occur cutting.

Permeability Number for Various Grain Size of Tin Mine Tailing Sand for Greensand Casting Mould.
This research is to determine the effect of grain size by the increasing of water content on the permeability number.
Grain sand size of 297 µm was discovered has appropriate permeability number with the water content of 4% which is within the requirement as moulding sand.
Figure 4 shows the comparison on the permeability number for grain size of 149 µm, 297 µm and 425 µm.
Sample with grain size of 425 µm has superiority in permeability number where its curve is above the curve of other samples.

The average intercept length and related corrective method are proposed to calculate the average grain boundary number.
The average grain size is used to obtain the number of grain boundaries in series in the height of a ZnO varistor, and the breakdown voltage, VB, is often described in volts per grain boundary, which is derived from the global breakdown voltage and the grain-boundary number.
The average grain size is expressed as ( )[ ] D L D Dm = −178 0156 2 . exp . ln / (3) If using the average intercept length L to calculate the average grain boundary number, then the number should be corrected.
We think their statistical results from a large number of grains can correctly describe the geometrical property of the nonuniform structure.
In other hand, the grain boundary size does not increase linearly with the volume of grain, ordinary the side number of grain increases with the increase of grain volume, so the relative standard deviation of grain boundary length is not as large as grain area.

Grain Emergency Transport Model on Unascertained Number GAO Youjian1, a , LIU Guangli1,b and LI Di1,c 1 China Agricultural University, Beijing, China a 317882655@qq.com, b liugl@cau.edu.cn, clgl7109@163.com Keywords: Unascertained Number, Emergency Transport, Algorithm Abstract.
The question to choose a grain supplement emergency path is uncertain.
Between this place and the grain bins around, there are still some roads to choose.
The expectation is a real number which cannot operate with interval number, so we can consider that put these two kinds of numbers into a wider range which called grey number.
Research on Grain Logistic Distribution in Times of Emergency.

Fig. 1(a) presents histograms of number of faces of a grain(abbreviated hereafter to number of faces).
Effect of number of faces on growth of grains in a short period.
The number of faces of a single cell grain is in the present program counted as zero.
Those grains whose number of faces was were left out of the statistics(Fig. 1).
Increasing/decreasing tendency of number of surfaces of the embedded grains between adjacent observations.

We found that the Betti number (b1) is strongly correlated to the number of grains.
In this study, we used ChomP programs [13, 14] in order to calculate the Betti numbers of the grain structures.
In order to investigate the effect of the number of grains on the Betti numbers (b0 and b1), we prepared photographs in three sizes.
The Betti numbers of their prior austenite grains were observed by a numerical Homology method.
We concluded that the Betti number (b1) per unit area is strongly correlated to number of grains.

This requires that there are at least a few large grains with a sufficient number of faces, N >>13, such that -H >Z.
Figure 1 - Increase in the number of faces, NA, of an abnormal grain as a function of dimensionless time for abnormal grains with different initial number of faces, N0=41 and 100.
Fig. 1 shows the increase in the number of faces, NA, of an abnormal grain as a function of dimensionless time for different initial values of the number of faces.
The number of faces of the abnormal grain increases in time and so does its corresponding volume.
Therefore, as this large grain shrinks in relative size to the average it must also decrease its number of faces.

In this investigation, various parameters of the process including the number of abrasive grains in actual contact, the number of actual cutting grains per unit area for a given depth of wheel indentation, the minimum diameter of the contacting and cutting grains, the probability of active contacting grains and cutting grains were determined analytically.
The grain distribution without dressing meet normal distribution and the grain distribution following dressing meet beta distribution. 2.1 Total number of grains passing through grinding area per second The grain size of an abrasive in a grinding wheel is determined by the number of meshes in the sieve.
The critical depth of indentation is then used to determine the number of active cutting grains.
Table.1 Summary of statistical parameters in one case of grinding operation Mean diameter of grains(mm) 0.39 Number of grains per unit length (grains/mm) 2.5 Number of grains per unit area (grains/mm2) 6.2 Number of grains per unit volume (grains/mm3) 15.5 Total number of grains passing through grinding area per second(grains/s) 2480000 Length of cut lc(mm) 1.732 Depth of grain indentation(mm) 0.018 Diameter of the smallest actual contacting grain(mm) 0.407 Diameter of the smallest actual cutting grain(mm) 0.417 The probability of active contacting grains 48.26% The probability of active cutting grains 13.24% Number of contacting grains passing through grinding area per second(grains/s) 1196848 Number of cutting grains passing through grinding area per second(grains/s) 333560 Number of contacting grains per unit area(grains/cm2) 299 Number of cutting grains per unit area(grains/cm2) 83 3.2 Experiment result by the means of measuring grinding temperature The analytical result above
It is found that out of a large number of grains on the surface of the wheel, only a small fraction of the grains participate in actual cutting while a large number of contacting grains merely rub or plow and not cut at all.

The changes of grain number during grain growth with different pinning particle configurations are obtained with phase field simulation, Fig. 2.
The pinning effects of particles on grain growth with different number or size of pinning particles.
The details of pinning effects of particles on grain growth with different particle size, number and total particle volume are presented.
The pinning effects of the same number pinning particle on grain growth increases with the increases of the pinning particle size.
With the constant particle volume, under different grain growth stage or grain size, different particle size and number configuration is required to obtain the best pinning effect.

On the other hand, during abnormal grain growth, a few grains grow faster than the matrix, and, as a result, the number of faces per grain increases [1].
Normal grain growth occurs when the number of faces per grain, N, decreases, even as the total grain volume increases [3], that is 0≤ dt dN
Figure 3 shows the grain boundary curvature plotted against the number of faces per grain for the energy ratios Γ=0.61, 1 and 1.414.
Figure 3 - Grain boundary curvature plotted against number of faces per grain for Γ=0.61, 1 and 1.414.
The number of grains in a real sample is large, say ≈109 grains in a 1 cm3 specimen.