DESIGN OF HIGH-SPEED WHEELS

1.4.1 Trend toward Higher Speeds

Vitrified CBN wheel speeds have risen significantly in the last 10 years. In 1980, 60 m/s was considered high speed; by 1990, 80 m/s was becoming common in production; by 1995, the speed reached 120 m/s; and then by 2000, the speed was 160 m/s. At the time of this writing several machines for vitrified wheels have been reported entering production for grinding cast iron at 200 m/s. Speeds of up to 500 m/s have been reported experimentally with plated CBN [Koenig and Ferlemann 1991]. Such wheel speeds place increased safety demands on both the wheel maker and machine tool builder.

Conventional vitrified bonded wheels generally default to a maximum wheel speed of 23 to 35 m/s depending on bond strength and wheel shape. Certain exceptions exist; thread and flute grinding wheels tend to operate at 40 to 60 m/s and internal wheels up to 42 m/s. (A full list is given in ANSIB7.1 2000 Table 23.)

1.4.2 How Wheels Fail

To achieve higher speeds requires an understanding of how wheels fail. Vitrified bonds are brittle, elastic materials that will fail catastrophically when the localized stresses exceed material strength. Stresses occur from clamping of the wheel, grinding forces, acceleration and deceleration forces on starting, stopping, or changing speed, wheel unbalance, or thermal stresses. However, under normal and proper handling and use of the wheel, the greatest factor is the centrifugal stresses due to constant rotation at operating speed.

1.4.3 Hoop Stress and Radial Stress

Подпись: 0 d2U du T1 r dh r2 + r U + dr2 dr h dr Подпись: du r + U ■ v dr DESIGN OF HIGH-SPEED WHEELS

The stresses and displacements created in a monolithic grinding wheel can be readily calculated from the classic equations for linear elasticity. The radial displacement U is given by

Подпись: E U U (1 - v2) _ r + v dr Подпись: E dU U_ (1 - v2) _ dr + V r

This can be solved using finite difference approximations to give radial displacements at any radius of the wheel. The circumferential or hoop stress and radial stress equations are given by the following, where it is assumed the wheel outer diameter is >10 times wheel thickness.

The solutions to these equations are given by Barlow and Rowe [1983], Barlow et al. [1995], and Barlow, Jackson, and Hitchiner [1996] as

— (1 _ v2)

Подпись: 8

(1 _ v) • — _ (1 + v) • -2- _ p a2 • r

n C2 3 + v 2

^rr = — + 77——— ^ p’®2 ^

Подпись: -L _ V rr 8 ^ca = C1 _ ~L ~^FP®2 ^2

The constants — and C2 are subject to the appropriate boundary conditions:

• Radial stress at the periphery of the wheel is zero.

• Free radial displacement at the bore.

The second boundary condition concerns the displacement of the bore and depends on the level of clamping of the wheel. It is usual in the design of wheels to assume the worst-case situation, which is free radial displacement, as this gives the highest level of circumferential stress. The maximum hoop stress occurs at the bore. In this case, the radial stress is zero.

Full constraint at the bore leads to zero displacement but the radial stress is now nonzero. Figure 4.5 gives an example of the stress distribution for the two extremes.

Updated: 24.03.2016 — 12:02