Furthermore, ISO 3002-5:1989 defines the active grit count, Nact, as grit that are actually engaged [ISO89]. Werner expressed this as number of momentary grains per unit area, Nmom (Eq. 6.11) [WERN71].
Nmom = bs • lk • Nkin (6.11)
1 + a
Nmom number of momentary grains per unit area a empirical factor
bs wheel width
lk kinematic contact length
Nkin kinematic cutting edges
Resin or vitrified bonded grinding wheels flatten due to wheel flexibility [ROWE09, p. 82]. Tool deflection increases contact length and number of grits (Fig. 6.6) [BORK92, ROWE09, SAIN80]. Figure 6.6 shows deformations at flat grinding; similar deformations happen during cylindrical grinding operations, with the difference that the contact zone deforms as well [PEKL57].
Grits in bonding can be viewed as a spring-damper system (Eq. 6.12) [PEKL57, p. 113]. Saini and Brown derived Eq. 6.13, where grit workpiece deflection, S, results from actual depth of cut, da, and theoretical depth of cut, dt (Fig. 6.6) [SAIN80]. Measured groove length, l, deviates from the groove length, l1, that occurs when the workpiece stands still (workpiece speed vw = 0).
|
5 |
elastic grit deflection rectangular to cutting direction |
|
F n, grit |
normal force at grit |
|
c |
spring constant of bonding |
|
dt |
theoretical depth of cut |
|
da |
actual depth of cut |
|
l |
measured groove length |
|
ds |
grinding wheel diameter |
|
vw |
workpiece speed |
|
vs |
wheel speed |
Furthermore, workpiece speed affects the spring/damper system of grits and bond. Chip thickness per grit increases with higher workpiece speed vw2 (Fig. 6.7) [PEKL57, p. 113]. Higher chip thicknesses lead to higher single grit forces and larger elastic grit deviation, S (Eq. 6.12). Therefore, the grits engage less deeply and more grits have to remove the material. In addition, the distance between cutting edges gets shorter at higher workpiece speeds [PEKL57, p. 113].