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where f is the workpiece feed; t the undeformed chip thickness; Z the number of active grains per revolution; and N is the wheel RPM
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Specific energy provides a useful measure of how much power (or energy) is required to remove 1 mm3 of metal during machining Using this measure, different work piece materials can be compared in terms of their power and energy requirements for machining For conventional surfaces, whether internal or external grinding, the specific grinding energy, u, required is calculated by the following equation [4][15]: u =
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The plus sign is for up grinding, and the minus sign is for down grinding Since v <<<V, the preceding equation is simplified as u = (27)
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where Ft is the tangential grinding force which is derived from measured force components FH and FV, V is the cutting speed, v is the table or workpiece speed, d is the infeed or the wheel depth of cut and b is the width of the cut The forces in a grinding process can be measured quite satisfactorily by means of a dynamometer Wheel and table speed can be adjusted on the machine controller while the remaining variables in the aforementioned equation are readily determined by using simple length The coefficient of friction, , between the grains and workpiece can be estimated from the following expression [16]: m =
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where FH and FV are the horizontal and vertical components of the grinding force in the sliding mode as illustrated in Figure 323
Mechanics of Materials Cutting
The inverse relationship between the specific energy and the grit depth of cut is often referred to as the size effect [17][15] The size effect theory attributes the apparent increase in shear stress with a reduced undeformed chip thickness Taniguchi [18] discussed the size effect in cutting and forming and the modified relationship between specific energy and chip thickness that was initially proposed by Backer et al [19] with his version by including tensile test data in the graph as shown in Figure 327 Referring to the figure, the small chip sizes in grinding (of the order of less than 1 m) cause the energy required to remove each unit volume of material to be significantly higher than conventional turning (chip size >50 m) Resisting shearing stress reduces to the order of 500 N/mm2 between the two processes The reason for this behaviour could be explained based on the defect distribution mode in materials When the chip thickness becomes less than about 1 m, the distribution of moveable dislocations (defects) in the metal crystal approaches zero, and the cutting forces have to overcome the very large atomic bonding forces within the crystals to remove the material as a chip Apart from the size effects, Groover [5] provided additional reasons for the specific energy in grinding being much higher than other conventional machining processes First, the individual grits in a grinding wheel possess extremely negative rake angles with an average of 30 and sometimes as low as 60 These very low rake angles result in low values of the shear plane angle and high shear strains, both of which imply higher energy levels while grinding Secondly, due to the random distribution and orientation of grits in the wheel, not all individual grits are engaged in the actual cutting process Some grains do not project far enough into the work piece surface and may end up rubbing, thus consuming energy without removing any material Thirdly, the combination of size effect, negative rake angles and ineffective grain actions cause the grinding process to be very inefficient in terms of energy consumption per volume of material removed
Fig 327:
Shaw s size effect relationship between chip thickness and resisting shear stress of a carbon steel [17] modified by Taniguchi [18] with the addition of tension tests
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