barcode reader library vb.net Zeff = Z c2 2 RYc By definition, Zc is valued at d = dc, that is, Zeff = Zc when Yc = 0 in Software

Generation Data Matrix 2d barcode in Software Zeff = Z c2 2 RYc By definition, Zc is valued at d = dc, that is, Zeff = Zc when Yc = 0

2 Zeff = Z c2 2 RYc By definition, Zc is valued at d = dc, that is, Zeff = Zc when Yc = 0
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Zc = Substituting and rearranging, Zc2 = Zeff2 =
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Rdc f f
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R 2 dc 2 Rd f 2 c + f 2 2 f f R 2 dc 2 2 Rdc + f 2 2 RYc f2
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d 2 2d 2Y Zeff2 f 2 = R 2 c 2 c c f R R
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Mechanics of Materials Cutting
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2 Z eff f 2 d2 d Yc = c2 2 c 2 R f R
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2 Z eff f 2 v/s 1/f 2 gives a straight line R2
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The straight line can be defined by Y = mX + C, where m is the slope and C is the intercept Putting equation 44 in terms of a straight line, we get
2 Z eff f 2 = Y-axis R2
1/f 2 = X-axis dc2 = m ( Slope)
d Yc 2 c = C (intercept) R The square root of the slope gives us dc, and Yc can be calculated by the intercept of the line The process limit for the feed rate can be obtained from equation 42 by setting Zeff = 0, that is, the feed fmax at which damage first replicates into the cut surface Equation 44 gives for Zeff = 0
0 f 2 d2 d Yc = c2 2 c 2 R f R
0 = 0 =
dc 2 f 2 2d 2Y + 2 c + c R R f2 R dc 2 R 2 + f 4 2dc f 2 R + 2Yc f 2 R dc 2 f 2
0 = f 4 2 ( dc + Yc ) Rf 2 + dc 2 R 2 Using the quadratic formula
dc = R ( dc + Yc ) R ( dc + Yc ) 1 dc + Yc and choosing the physically correct root that corresponds to the minus sign, we have the process limit
2 f max
f max = dc
R 2 ( d c + Yc )
(45)
where it is assumed that ( dc / ( dc + Yc ) ) <<< 1
Precision Engineering
2 dc2 Z eff f 2 d + yc 2 c = 2 2 f R R
(46)
where R is the tool nose radius, and the other parameters are defined as shown on the right side of Figure 33 (right) The derivation of the equation is shown in the Appendix For a typical example, such as a [100] Ge crystal, it was found that dc = 130 nm and yc = 1300 nm when using the equation with a tool having a radius of 3175 mm and a 30 rake angle Solved examples:
Graph showing a plot of the model using R = 0762 mm tool with various rake angles
Fig 344:
Different plots of the lines depending on different rake angles of the tool [41]
Calculation for Rake angles 30 and R = 0762 mm Coordinates of the line taken are X 025 05 Y 2 6
Mechanics of Materials Cutting Intercept = 2 10 3 We know that
Z2 f 2 d2 d + Yc = c2 2 c 2 R f R
This can be expressed in terms of the equation of a straight line, that is, Y = mX + C, where m is the slope of the line and C is the intercept From the aforementioned equation and coordinate values of the line,
dc2 = m = dc2 = m = dc2
Y2 Y1 X2 X1
( 6 2 ) 10 3
05 025
= 16 10 3
Also,
dc = 0126 m
d + yc C = 2 c R 0126 + yc 2 10 3 = 2 762
Yc = 0612 m fmax = dc
R 2 ( dc + yc ) 762 2 ( 0126 + 0612 )
fmax = 0126
fmax = 28 m/rev It is possible to modify Scattergood s theory by looking at pre-existing defects Nakasuji et al [48] used a critical stress field and pre-existing defect model as depicted in Figure 345 to explain the brittle-ductile transition in chip formation during diamond turning of brittle materials When the uncut chip thickness is small, as shown in Figure 345(a), the size of the critical stress field is small enough to avoid a cleavage initiated at the defects On the other hand, when the uncut chip thickness is as large as shown in Figure 345(b), the critical stress field acts as nuclei for crack propagation, which gets initiated at the defects
Precision Engineering
Fig 345: The critical stress field is a function of the uncut chip thickness: (a) the small depth of cut avoids
cleavage initiation at the defects and thus the chip removal process by plastic deformation, (b) a large depth of cut results in cleavage initiation at the defects and production of a brittle fracture surface and (c) a schematic diagram of the cut surface [48]
Consequently, the transition of the chip removal process from brittle to ductile depends on the uncut chip thickness that subjected to the critical stress field acts on the workpiece surface during cutting This gives rise to the following relationship for estimating the critical thickness of a cut (tc) at which the brittle-ductile transition occurs: tc = R + xf
R2 +
x2
1 f 2 R
xf R
f2 2R
(47)
where R is the tool nose radius, f is the feed and x is the distance between the nose top of the tool and the point of the transition as judged from the micrograph of the shoulder region (see Figure 345 c) For a typical example, such as silicon [111], using the foregoing equation for a tool having a nose radius of 08 mm and a rake angle of 25 , 05 m/rev feed and depth of cut of 55 m, it was found that tc = 57 nm In the ductile mode grinding process, each protruding abrasive grain on a grinding wheel generates an intense local stress field on contacting the workpiece surface According to Konig and Sinhoff s model [49], chip removal in ductile machining of an optical glass is caused by a hydrostatic shearing stress as a result of flattened dull edge grains (Figure 346) The shearing stress between glass lamellas causes frictional heat and plastification of the material, which finally results in a good surface quality Whereas sharp grains that exceed the maximum depth of cut (high in feeds) cause brittle fracture, and the work piece is damaged by deep cracks Zhong and Venkatesh [50] later modified this model by relating uneven protrusion heights of the grain with the critical depth concept to ductile streak formation Figure 347 shows the modified form of Konig s model The uneven protrusion height
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