Tool life between conditioning is measured in time, per number of machined workpieces or workpiece volume removal [PAUC08, p. 343]. The G-ratio is a common parameter for describing the tool lifespan as ratio of machined workpiece volume, Vw, and worn grinding tool volume, Vs (Eq. 6.20) [MALK08]. The G-ratio depends on the machined material, tool design, grinding operation and parameters, cooling lubricant, machine tool, etc. Therefore, no certain value can be given for a generic application, but literature provides ranges of G-ratios (e. g. Table 6.1 or [PAUC08, p. 350]). In addition, tool suppliers have databases on case studies (Fig. 6.13).
In precision grinding of steel, maximum values for the G-ratio of about 50 mm3/mm3 can be reached with alumina wheels and G-ratios of more than 10,000 mm3/mm3 with CBN wheels [HELL05a]. In contrast, a G-ratio of
|
Grinding alumina |
Grinding steel |
Grinding nickel |
Grinding titanium |
|
|
100,000 |
1000 |
100 |
500 |
|
|
CBN (4500 HV) |
1000 |
10,000 |
5000 |
100 |
|
Alox (1800 HV) |
<1 |
5-10 |
10 |
1 |
|
SiC (2800 HV) |
10 |
1-5 |
1 |
10 |
|
Table 6.1 Typical G-ratios or relative wear resistance values for grain types [JACK11, p. 9 f.] |
The highly complex and multivariant grinding setup complicates modeling of the wear rate, although Werner claims that the high number of simultaneous grit engagements decouple the process results from the failure of a single cutting edge [WERN73, p. 67]. A wear rate model is necessary for calculating waste streams and tool costs.
Decneut et al. [DECN74] relate the G-ratio to the equivalent chip thickness, heq (Eq. 7.9), with charts. Werner [WERN73, p. 80 ff] built a wear model by multiplicative superposition. He included the four wear criteria of contact pressure,
friction velocity, engagement time, and engagement frequency and derived Eq. 6.21 [WERN73, p. 90]. Factor P includes the grinding wheel diameter, cutting edge density and edge shape factor and was derived through experimental tests [WERN73].
(6.21)
W wear cross-sectional area
P linear factor from grinding wheel specifications in [mm2/mm*kp]
e, h, i, m system constants (0.5 < m < 1.5; 0.5 < i < 1.0)
Vw specific workpiece volume [mm3/mm]
Bierlich [BIER76, p. 83] derived the tool life volume, V’stand, between two dressing operations in Eq. 6.22. This criterium can be integrated easily as cost function. Osterhaus [OSTE94] combined regression models of wheel wear in cylindrical and surface grinding processes.
Vstand = C4(Qw)“4 (vs)^4 (6.22)
Vstand tool life volume per mm wheel width
C4, a4, p4 constants Qw specific material removal rate
vs wheel speed
G-Ratio and maximum material removal rate are often contradictory, so Helletsberger proposes to regard the performance factor, L, as factor from G-ratio and specific material removal rate, Q’w, (Eq. 6.23) [HELL05a]
Performance factor L = G • Qw (6.23)
G G-ratio
Q’w specific material removal rate
Interrupted cuts increase the number of entry and exit impacts on the grinding tool leading to higher tool wear, so that uninterrupted cuts are preferable [METZ86, p. 78 ff].
Literature mostly disregards that tools can have the same G-ratio but with different machined workpiece volume, such as G = Vw/Vs = 10/0.1 = 500/5 = 2000/20 = 100. If the same G-ratio is achieved in the same time, the tool performance varies greatly. Figure 6.14 shows an example where the grinding forces propagate differently and the dressing intervals vary, although the G-ratio is similar. Although high G-ratio is
desirable, a highly wear-resistant tool may generate higher forces and grinding energies, thus increasing the potential of thermal workpiece damage.