barcode reader library vb.net Grit Depth of Cut in Software

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342 Grit Depth of Cut
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The value of the grit depth of cut, tmax, or sometimes also called maximum undeformed chip thickness, t, depends on both machine and wheel parameters Although the nominal or wheel depth of cut in a grinding operation as set by the down feed on a grinding machine is not in itself an important
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Mechanics of Materials Cutting
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variable for determining grinding characteristics, it is instead the average depth of cut taken by each individual abrasive grain that is of prime importance [4] The formation of ductile streaks on the ground surface of hard and brittle materials, for example, is a clear indication of the role of abrasive grains in providing a ploughing action when their protrusion heights are within the critical depth of cut region The equation for tmax was proposed by Reichenbach et al [13] Figure 324 illustrates various process variables involved in the surface grinding operation to determine tmax: tmax
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where tmax is the grit depth of cut (maximum undeformed chip thickness, t); C is the number of active cutting points per unit area of the wheel periphery; r is the ratio of the chip width to the average undeformed chip thickness; V is the wheel peripheral speed; v is the work piece speed (table speed); d is the wheel depth of cut and D is the wheel diameter
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Fig 325: A schematic illustration of the surface grinding operation showing various process variables involved
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for determining the maximum grit depth of cut [5]
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Based on the chip geometry, l = BC = (CF )2 + d 2 d = wheel depth of cut D (1 cos q ) d = 2 D CF = sin q 2 (7)
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(8) (9)
Precision Engineering
Fig 326: A scheme of the chip formation during surface grinding
Thus, from equation (7), (8) and (9) l = The maximum thickness, tmax
(10)
CF tmax = CE sin = CE D 2 But from equation (7) and (10),
CF =
2 l2 + 2 =
(11)
Dd 2 d 2
(12) (13)
tmax = 2CE
d d 1 can be neglected D D
d d D D
Since
Since CE is the distance, the table advances during the time it takes the cutter to make revolutions (K = number of teeth) CE = tmax =
V KN
(14)
2V KN
d D b (constant width throughout its length) t2
(15)
Substituting the value of K = pDbC and r =
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4V d 2 tmax = DNCr D Using the volume removed (another concept to calculate the undeformed chip thickness)
(16)
1 l l b t (17) 3 2 = 1 b t l (18) 6 1 The average volume removed per chip removed = bmax t max l Number of chips produced 6 bmax per unit time = (pNDbC) Now taking r = t max
Volume of the pyramid =
NDbC
1 b t l = vdb (total volume removed per unit time) 6 max max 1 6
(19) (20)
NbDC r t max 2 l = vdb
6v d 2 tmax = DNCr D Power = u MRR = tw
(21)
= u bdv = Fc = Fc = =
D 2 N 2 1000
(22) (23) (24)
u b d v 1000 DN
Fn = 2 Fn 2Fc Fc
The value of r is reported to be in the range of 5 20 [4] or 10 20 [1] Malkin [12] has suggested that the scratch method can be used to determine the r value as it provides the most detailed picture of the cross sectional shape of a grinding grit The values of C, however, must be determined experimentally Mayer and Fang [14] have measured the grit surface density by means of an optical microscope sighting on the grit flats after wheel truing and dressing Other ways are (1) imprint methods by rolling a grinding wheel over a soot-coated glass slide or a glass coated with dye, (2) by placing a carbon paper between the wheel surface and the glass, (3) scanning electron microscopy by observing wear flat per unit area after dressing, (4) dynamometer and thermocouple techniques by
Precision Engineering
analysing force and thermal pulses, respectively during grinding and (5) by using profilometry methods to obtain a profile trace on the wheel topography [12] A study carried out by Mayer and Fang [14] has shown that flexural strength of hot pressed silicon nitride reduced when the grit depth of cut is beyond a critical value (016 m) in traverse grinding using a diamond wheel For plunge grinding, the undeformed chip thickness can be expressed as t =
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