When the infeed reaches its final feed point, the grinding force F will change with time t as the system relaxes according to the equation
Ft and power are directly related; therefore t can be determined from a log plot of the decay in power during spark-out. After 3t virtually all grinding has ceased, preventing any improvement in part tolerance, while roughness, as shown above, will not improve further. Consequently, spark-out times in internal grinding should be limited to no more than 3t.
2.2.26 G-Ratio
G-ratio is used as the primary measure of wheel wear. This is defined as
G-ratio = Volume of material ground per unit wheel width Volume of wheel worn per unit wheel width
G-ratio is dimensionless with values that can vary from <1 for some soft alox creep feed vitrified wheels to as high as 100,000 for vitrified CBN wheels. G-ratio will fall linearly with increases in Q accelerating to an exponential drop as the maximum metal removal rate for the wheel structure is reached.
2.2.27 P-Ratio
P-ratio is a closely related index that has started to be used as an alternative to G-ratio for plated superabrasive wheels.
P-ratio = Volume of metal ground per unit area of wheel surface
This allows for the fact that it is hard to define a wear depth on a plated wheel. P-ratio usually has the dimensions of (mm3/mm2). For high-speed high stock-removal applications in oil-cooled grinding crankshafts, for example, P-ratio values have reached 25,000 mm3/mm2. Since the usable layer depth on a plated wheel is only at most about 0.1 mm, a P value of 25,000 mm corresponds to a G-ratio greater than or equal to 250,000.
2.2.28 Contact Length
lc is the length of the grinding contact zone and is the length over which the heat input to the workpiece is spread. The contact length is approximately equal to the geometric contact length for rigid metal bond wheels.
2.2.29 Geometric Contact Length
c g
2.2.30 Real Contact Length
The real contact length is typically twice this value for more elastic vitrified wheels. Marinescu et al. [2004] show that
lc — V lg + lf
where
8 • R2 • F’• d
12 ______ r n e
f~ n • E
gives the contribution to the contact length due to elastic deflection between the abrasive and the workpiece due to the normal grinding force. This deflection is increased for rough surfaces such as an abrasive wheel. A typical value for the roughness factor is Rr ~ 5. The combined elastic modulus for the workpiece and abrasive materials is given by
_L _ hUL+1i_U e E E