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Choosing an arbitrary abrasive grain on the surface of tool, the equations of motion can be expressed as follows : Rotary motion of spindle： (1) Where R is tool radius(mm); n is spindle speed (r/min); α is initial phase angle； Lateral feed motion: (2) Where v is lateral feeding speed (mm/s); Axial ultrasonic vibration: (3) Where A is amplitude; f is ultrasonic frequency KHz; β is initial phase angle; So the three dimensions motion equations of abrasive grain can be expressed as follows: (4) In order to show the trajectory of abrasive grain visually, the paper simulates the path of grain by Matlab.
It can been seen in fig.1 that the motion of abrasive grain is helical motion, the cutting length is longer than ordinary mill-grinding and material removal rate increase dramatically, cutting depth of abrasive grain decreases and unit grinding force decreases, which are all help to achieve high surface quality.
The periodic separation between grain and workpiece give coolant chances to enter into grinding area.
Fig. 1 3D trajectory of grain Fig. 2 2D trajectory of grain on finished surface Experiments Experimental conditions This paper adopts orthogonal experiments and mainly investigate the influences to surface roughness of four factors: spindle speed, feeding speed, cutting depth and amplitude.
Fig.5 SEM photographs of machined surface (a) (b) n=7000 r/min, v=250mm/min, ap=2μm, A=60% (c) (d) n=7000 r/min, v=250mm/min, ap=6μm, A=30% Conclusions The paper analyzes the movement of abrasive grain, establishes 3D moving equations of grain and simulates the moving trajectory of grain by Matlab and qualitatively explains the reason for ultrasonic vibration mill-grinding improving surface roughness.

After a given number of cycles, quenching was carried out in water.
The number of cycles varied from two to four.
After a given number of cycles, a low vacation was carried out.
Hardness distribution over the cross-section of steel samples 40: 1-traditional hardening; 2-two cycles; 3-three cycles; 4-four cycles The size of the grain and the grain size distribution after each cycle indicate the grinding of the grain, a decrease in grain diversity (Fig. 3).
Distribution of austenite steel 40 grains by size depending on the number of cycles: 1-after traditional hardening; 2-after three cycles; 3-after four cycles Due to the fact that changes in nonequilibrium systems occur in local volumes, the distribution of microhardness was studied.

Small grain sizes lead to a significant increase of active cutting edges, decrease of the single grain chip thickness and accordingly, to the decrease of the load in each grain.
In this way, the variation of the wheel grain size implies at the same time a variation of the dressing roll grain size.
Results and Discussion The abrasive grain size has the greatest influence on the edge quality in comparison with feed and cutting speeds, as a result of the influence on the number of active edges in the grinding wheel layer and the single grain chip thickness.
Fig. 3 shows that small diamond grains lead to a reduced edge chipping, i.e. a better edge quality of the PCBN insert, due to a decrease of the single grain chip thickness and, accordingly, the forces per grain.
Fig. 3 Edge chipping under variation of grinding wheel grain size and bonding Aiming to investigate the influence of the wheel bonding on the insert edge quality and the possibility of reaching lower values of Rk by using larger grain sizes, a resinoid bonded wheel with grain size D36 was applied and compared with a vitrified bonded wheel with the same grain size and concentration.

In Eq. 3 the distinction between curvature and radius of curvature is used with correction as reciprocal numbers.
Then using Eq. 2 for a number of metals with Burgers vector b=(3¸5)10-10 m and angular misorientations of cells q=0.01 rad, the average cell size about d ~ 2¸3 nm was obtained.
Dimensions and angular misorientations of grains.
Regarding multi-phase alloys containing a large number of stable particles, their scale factor is not determined by the size of the deformation macrozone, i.e. sample section, but by the distance between particles.
Experimental dependences of angular misorientations of grains cover a wide range.

The results show that barrier dams composed of coarse-grains or well-graded fills are more stable than those composed of fine-grained fills; coarse-grain-dams are more sensitive to the rising of water level than fine-grain-dams; the failure mode of coarse-grain-dams is usually overflowing-erosion and the barrier dams usually fail from the top of dams; the failure mode of fine-grain-dams is sliding and the barrier dams fail initially from the slope downstream.
There are 3 earth pressure monitoring points numbering TY1~TY3 and 3 pore pressure monitoring points numbering KY1~KY3.
Its maximum monitoring number is 1000 and minimum sampling interval is 1 s.
The porosity of fills of fine particles is bigger than that of coarse particles, so the increase of the pore pressure in fine-grain-dams is bigger than that in coarse-grain-dams.
Failure mode is usually overflowing-erosion in coarse-grain-dams.

As x increases from 0 to 0.008, ceramic grains growth gradually improved, particles size becoming larger, porosity decreasing, density increasing, grains growing regularization.
Changes in εr affected by grain boundarys and grain phase structures.
For the above reasons, the number of polarization particles increased per unit volume, resulting in increase of εr .
The variation of tanδ depend on grain size, pore and defect.
When the maxing amount more, the grain size has been ruduced, promopting an increase in charges on grain boundaries,resulting in tanδ’s increased.

EBSD shows that the continuous small angle grain boundaries are produced during the fatigue.
The growing number of aircraft accidents is due to low cycle fatigue failure of the engine turbine disk, so the low cycle fatigue has become a typical failure form for the turbine disc[1-2].
A substantial increase in the percentage of low angle grain boundaries when the test temperature is 720 ℃, while the large angle grain boundaries at an angle substantially reduce.
The higher the strain amplitude , the greater the pertcentage of low angle grain boundaries.
EBSD shows that the continuous small angle grain boundaries are produced during the fatigue.

Intensities of the texture components as well as deviations from their ideal shear positions vary from the top to the bottom of the billet and with the number of passes.
This continuous process of coarsening, subdivision and shearing yields a steady state microstructure of constant average grain size, aspect ratio, grain shape foliation and fraction of HAGBs.
If grain boundary migration is high, i.e. the time a grain boundary moves a distance of the order of the grain radius is short compared to the transformation of LAGBs to HAGBs, then this mechanism is called discontinuous dynamic recrystallization (DDRX) [2].
Focus is put on the influence of DDRX on texture formation with respect to the number of ECAP passes and texture gradient.
Tóth, in: Ultrafine Grained Materials IV, edited by Y.T.

Natural aging can fundamentally change the precipitation near the grain boundaries, and is an optimization, precipitation hardening of high-strength aluminum alloys with very small grains [5].
Figure 8 (a) shows that the grains of 5083 are small and tightly ordered, and are round and spherical.
The crystal grains of 7075-T6 are composed of large strips and relatively small strips.
It can be found from Figure 8 (c) that different precipitates lead to different crystal grains.
C. for their financial support under grant number MOST 109-2221-E-168-002.

In sample D, different grain shapes are seen, this is probably caused by recrystallization or grain growth.
Grain Size of Sample A, B, C, and D Figure 3 shows the grain size of all samples.
Smaller grain sizes increase the number of grain boundaries so that they are more susceptible to grain boundary corrosion.
This larger number of grain boundaries causes sample B to be more susceptible to grain boundary corrosion.
In a corrosion reaction, the grain acts as an anode and matrix as a cathode so that corrosion occurs at the grain boundary.