Based on the reasoning discussed before, three conditions can be established. If 180°-в gives a half-wavelength, 360° gives a multiple of a whole wavelength, and a gives a multiple of a whole wavelength, waviness will persist. These three conditions follow.
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The number of waves, n, is an integer.
where n1 and n2 are other integers.
Miyashita [1965] gave the conditions for convenient waviness as
n. a/180 = even number (19.43)
and
n ■ (180 — в)/180 = odd number (19.44)
Moriya, Kanai, and Miyashita [1994] recommended that а/в should be equal to an odd number to avoid convenient waviness.
It is important to avoid geometry vulnerable to convenient waviness. In the above example, changing the workrest angle to 30° and changing the tangent angle to 7° greatly reduces the risk of convenient waviness. This conclusion can be checked using a spreadsheet or a calculator to check a range of values of n for near-integer values of n and n2.
From a practical viewpoint, it is important to avoid a workspeed that aligns a known source of excitation with a convenient waviness. For example, if n = 22 is a convenient waviness and wheel speed is 20 rev/s, it would be important to avoid a workspeed of 1.1 rev/s since any change in wheel unbalance will directly excite the convenient waviness.
Another practical possibility for reducing roundness errors is to vary the set-up geometry during the grinding operation [Harrison and Pearce 2004]. Perhaps the simplest way to do this is to employ a larger tangent angle for roughing than for finishing. However, it is suggested that if two set-up geometries are employed, both setups should provide a strong rounding tendency.
The analysis of rounding geometries is explored further in Sections 19.12 and 19.13 with reference to process stability.