2D (Profile) Stylus Parameters
Stylus (X,Y) Δq
Stylus (X, Y) Δq is the Root Mean Square Slope Along (X,Y). The Stylus X Δq and Stylus Y Δq calculations find the rms (standard deviation) of the profile slope given by:
From Fourier analysis, the surface texture is composed of a series of sine waves in all directions with different spatial frequencies (i.e. 1 /spatial wavelength) and amplitudes. The power spectrum is a measure of the amplitude of each sine wave for a particular spatial frequency, along a given direction. Thus for a 3D surface, the power spectrum would be displayed as a “3D” function in which the X and Y axes represent the various spatial frequencies for a given direction. The amplitude of the power spectrum (displayed on the Z axis) represents the amplitude of the sine wave at a particular spatial frequency direction. The angular power spectrum is found by integrating the amplitudes of each component sine wave as a function of angle.
The figures below demonstrate a crosshatched surface, the power spectral density of the surface and the angular power spectral density function.
Depiction of two surfaces with similar overall roughness but different surface texture slopes along the X and Y directions as a result of the presence or absence of finer spaced features.
Application
The Δq measurements along the X and Y directions provides a quantitative assessment of the rate of change of the surface heights over the profile length. Since the slope values are squared prior to integration, the polarity (i.e. positive or negative) of the slope is lost in the calculation. The Δq measurements may be useful in applications where a machining process is producing parts with nominally correct amplitude parameters (e.g. Ra) but has other functional or process problems. For machining operations, parameters associated with the materials or machine setup may be manifested in significant changes in the surface slopes, easily measured by Δq. The wetting characteristics of a surface and the surface area of a texture may be related to Δq.