Having chosen the track-bound principle for force generation, the functional requirements arise to hold the workpiece, provide the cutting speed and feed of the grits, and reduce the mechanical impact that is not crucial for the cutting action (Fig. 7.17). The workpiece can be held by mechanical or magnetic clamping, or the centerless principle can be applied for cylindrical parts that are machined on their external circumference or the inner diameter (Fig. 7.17 left). In addition, deflections, bending of cylindrical workpieces, etc. have to be considered as sources of errors, so that additional counter-measures have to be taken [ROWE09].
The cutting speed results from the wheel spindle rotation and the grinding wheel diameter (Fig. 7.17 middle). The grit feed is generated by the tool axis movement and the process kinematics, such as face or circumference grinding, transverse or plunge cut grinding, external diameter, internal diameter, etc. (Fig. 7.17 right). Mechanical impact on the workpiece is a side effect of the chip formation and has to be minimized (Fig. 7.18). A low normal force per single grit and a small number of grit contacts both reduce the mechanical impact on the workpiece (Fig. 7.18). The normal single grit force is decreased by having a small load per grit and by changing the chip formation process to be more effective.
Fig. 7.17 Track-bound principle (diagram follows Fig. 7.12)
The maximum undeformed chip thickness, hcumax, is directly tied to the single grit load (Fig. 7.19). Chip thickness is related to statistical cutting edge density, Cstat, workpiece speed, vw, grinding wheel speed, vs, depth of cut, ae, and equivalent grinding wheel diameter, deq (Eq. 7.8) [WERN71, TONS92]. Factors, k, а, в, у, have to be found empirically, and Eq. 7.8 does not account for elastic and plastic material deformation. A common assumption is a = P = 1/3, у = 1/6, showing that the factor (ae/deq) is of smaller significance than the other factors [WERN71]. A simplified approximation for the chip thickness is the equivalent chip thickness, heq (Eq. 7.9).
In reality, the real chip thickness is smaller than the maximum undeformed chip thickness [KLOC09, ROWE09]. This results from the elastic and plastic deformation effects overlaying the chip formation process (Fig. 7.20). The grit cutting depth, TM, is the grit engagement depth, at which chip formation starts. A high chip thickness increases the effectivity of the chip formation process, because the grit cutting depth T^ is reached sooner. The same applies for the down-grinding mode in comparison to up-grinding and the use of a cooling lubricant with low lubrication properties to increase friction.
k constant depending on grinding wheel; e. g. k = 0.695 [WERN71]
CStat static cutting edge density; e. g. Cstat = 4420 mm-3 for A46 [WERN71]
к half of the cutting edge angle; e. g. к = 82.4° [WERN71] vw workpiece speed
vs wheel speed
ae depth of cut
deq equivalent grinding wheel diameter (Eqs. 6.15, 6.16 and 6.17)
а, в, у empirical coefficients
a — shearing zone, c ■
deformation work d
b — rake face, friction work e ■
Fig. 7.20 Three phases of ductile chip formation [KLOC09] including the different contact types rubbing, plowing and cutting [ROWE09, TONS92], reprinted from [LINK12c] with permission from Elsevier