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An up-grinding operation involves a rubbing and plastic flow to the side without removal (ploughing) until the undeformed chip thickness reaches a critical value sufficient for penetration and chip formation According to Figure 324, rubbing occurs from A to A between the workpiece and the wear flats which develop on the grinding wheel grits The friction thus generated absorbs power but does no useful work Ploughing is a process whereby the abrasive grit plastically ploughs a groove and leaves small particles of highly distorted material alongside this groove During this stage, some materials are displaced, whereas others are completely removed, but this is an inefficient method of material removal This argument slightly contradicts with those of Malkin [12] and Grover [5] who have suggested that the work surface deforms plastically during a ploughing action and that energy is consumed without any material removal As shown in Figure 324, full chip formation occurs from B to C where chips form ahead of the abrasive grits



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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

(12-226)

Fig. 14-16.





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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

Fig. 14-17.

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

Fig 325: A schematic illustration of the surface grinding operation showing various process variables involved

When you build this mechanism, it will reach the desired positions precisely, as shown in Fig. 14-17.

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for determining the maximum grit depth of cut [5]

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)

Try This: The oscillator in Fig. 14-7 provides a smooth, reciprocal motion that looks something like Fig. 14-18. Coupling two cranks together to drive a follower link can provide a more complex, harmonic motion. One such mechanism is shown in Fig. 14-19. An estimate of its motion pro le is given in Fig. 14-20.

(8) (9)

Fig. 14-18.

(10)

CF tmax = CE sin = CE D 2 But from equation (7) and (10),

Fig. 14-19.

(11)

(12) (13)

Fig. 14-20.

Since CE is the distance, the table advances during the time it takes the cutter to make revolutions (K = number of teeth) CE = tmax =

If you spend some time browsing through online patents, either via the Patent O ce (www.uspto.gov) or some other patent portal like Delphion (www.delphion.com, and yes they have a free version buried in there), you will see numerous clever and unique mechanisms to achieve many di erent mechanical goals. Some examples are illustrated here.

(14)

(15)

While the the crank-and-piston arrangment can create linear motion from rotation, the cardan gear does this in less space and with a completely di erent technique (Fig. 14-21). The cardan gear is actually two gears. The outside ring is a gear turned inside out and it provides a xed framework for the moving gear. The inside gear has exactly half as many teeth as the outside gear. A post positioned over one tooth of this inside gear follows a straight line. This post can be used to drive additional machinery.

4V d 2 tmax = DNCr D Using the volume removed (another concept to calculate the undeformed chip thickness)

(16)

Fig. 14-22.

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

(19) (20)

Try This: A gear with a post on it can be used to drive other mechanisms; for example, in a quick-return (Fig. 14-22), the gear pushes the link back and forth. At the top of its arc the post moves the link slowly, along a large radius. At the bottom of its arc the post moves the link quickly since it is closer to the link s axis of rotation.

(21)

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