Grinding wheel rotation leads to centrifugal forces and stresses within the tool body. For a generic homogeneous cylinder, the tangential stresses, atx, at the diameter Dx follow (Eq. 5.1); the radial stresses, arx, follow (Eq. 5.2) [HELL05b, FRAN67].
The tangential stress has its maximum at the inner hole diameter, H = Dx; the radial stress reaches the maximum at T(DH) = Dx [HELL05b]. Equations 5.1 and
5.2 show that the stresses increase with the square of the wheel speed, v?, and with the ratio of hole diameter to outer diameter, (Я/D)2. Helletsberger [HELL05b] discusses several body designs and composite bodies in detail.
Because the wheel speed has such a big influence on the internal stresses, high-speed applications have particular requirements for the grinding tool body [FERL92, p. 66]:
• High strength of body material,
• Quasi isotropic material behavior,
• Small radial elongation,
• Small weight,
• Good damping ability.
High wheel circumferential speeds, vs, are favored for low cutting forces and wheel wear. High wheel speed can be achieved with a large wheel diameter, ds, or a high number of revolutions, ns (Eq. 5.3).
High numbers of revolutions require special tool spindles. Not only do these spindles have to provide a high number of revolutions (such as 10,000-30,000 min-1), but they should have high maximum power, convenient compliance behavior, high radial and axial runout accuracy, smallest axial deviation, and small space for installation [FERL92, p. 59 f.].
Large wheel diameters go along with large wheel perimeters and high volumes of abrasive grits. Tool life increases with diameter, however, not always in the same proportion as tool costs rise with the grit costs [FERL92, p. 53]. Whereas the grinding wheel perimeter, P, and the number of grits increase linearly to the tool diameter, ds, (Eq. 5.4), the mass rises with the square of the diameter (Eq. 5.5). Heavier tools are harder to handle for the machinist during clamping and machine set-up. Moreover, additional disadvantages lie in the higher rotational energy and higher loss drive power [FERL92, p. 53].
The rotational energy depends on the wheel diameter to the power of 4 (Eq. 5.6) [FERL92, p. 53]. The higher the rotational energy of the tool, the more worker protection and machine encapsulation needs to be in place.
Air friction and grinding wheel mass increase the loss power of the tool drive. Ferleman [FERL92, p. 55] gives an equation for the loss drive power by air friction for turbulent flux. Here, the loss drive power depends on the wheel diameter to the power of 4.6 and the number of wheel revolutions to the power of 2.8. This emphazises that the diameter should be as small as possible for high-speed grinding operations.
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Tool perimeter P = p ■ ds |
(5.4) |
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P 2 Tool mass m = ■ p ■ bs ■ d2 |
(5.5) |
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Rotational energy Erot = K1 ■ p ■ bs ■ d4 ■ n;2 |
(5.6) |
p wheel density bs wheel width ds wheel diameter K1 constant factor ns number of wheel revolutions
An increase in grinding wheel circumferential speed induces a decrease in the single grit chip thickness. This can be used for two different principles, enhancing quality or performance. With smaller chip thickness, the grinding process achieves similar or higher material removal rates, but with higher surface quality and extended tool life compared to lower speed applications [GUHR67]. In addition, high efficiency grinding with much higher material removal rates is possible and often substitutes turning, milling or reaming applications [FERL92, p. 1].
Resonance vibrations can be calculated via Finite Element Analysis and measured through laser holography [FERL92, p. 66]. The number of spindle
revolutions as excitation frequency should have a security distance of 20 % to the first resonance frequency of the tool body [FERL92, p. 66]. However, the centrifugal forces are much higher than the grinding forces and need to be the focus of design optimizations for high-speed grinding operations [KIEN63].
Strain builds around the inner hole, so wheels without inner holes or special reinforment around the hole are in use. Already in the 1930s, Krug suggested to counter the strain around the inner hole by strengthing the material by resin [KRUG35]. In 1963, Kienzle et al. suggested a two material grinding wheel with an internal ring of a material with higher Young’s modulus than the abrasive layer [FERL92, p. 5, KIEN63]. Thus, the rupture circumferential speed of the grinding wheel increases in comparison to a conventional wheel with the ratio between the adhesive layer strength to the abrasive layer strength [KIEN63]. A larger inner ring increases the rupture speed further [KIEN63].
In 1967, Guhring increased the cutting speed up to vc = 90 m/s with the usage of conventional vitrified grinding wheels with an optimized shape [GUHR67, FERL92, p. 6]. The tools taper off from the inner boring to the rim to reduce the centrifugal forces. Konig and Ferlemann [KONI90] examined grinding wheel bodies for cutting speeds up to vc = 500 m/s and define design features for high-speed grinding wheel bodies (Fig. 5.1).
The cutting speed has increased from 1935 to 1990 from 25 to 200 m/s; simultaneously, the specific material removal rate increased from 8 to 110 mm3/ mms or even 800 mm3/mms in special cases [FERL92, p. 5]. The success of high-speed grinding applications between 1980 and 1990 was combined with the use of superabrasives, especially CBN [FERL92, p. 1].
The use of high grinding wheel speeds is tied to the development of appropriate bondings. Table 5.1 gives a range of possible wheel speeds and material removal rates for different bonding systems.
Oliveira et al. [OLIV09] found in 2009 that still a comparably low proportion of grinding machine tool manufacturers use high grinding wheel speeds with CBN.
Optimized shape Bonding type through changing (electroplated) the thickness along the radius
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Table 5.1 Wheel and bonding types, wheel speeds, and specific removal rates in 1997 [KLOC97]
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Around 39 % of the 23 interviewed manufacturers use cutting speeds of mainly vs = 40-80 m/s, only 13 % of up to vs = 200 m/s [OLIV09]. The major reasons given for the comparably low proportion of high wheel speeds were the complex machine tools needing additional systems and economic reasons.