Spatial Roughness Parameters: Understanding RSm, Spacing, and Surface Feature Frequency

Like height-based values, 2D spatial parameters are defined and formalized under international standards to ensure consistency, traceability, and comparability across measurement systems:

• ISO 21920 for linear profile parameters
• ASME B46.1 for surface texture specification and reporting

Mathematically:

Where:

• S_i = horizontal spacing between irregularity boundaries
• n = number of spacing intervals in the evaluation length

RSm answers the question:

“How frequently do peaks and valleys occur along the surface?”

While roughness parameters like Ra describe how tall surface features are, RSm describes how far apart those features are. That spacing turns out to be just as important—if not more so—when it comes to preventing leaks.

Surfaces with small RSm values have tightly packed features, which may improve sealing and lubrication performance. Larger spacing suggests smoother flowing surfaces with reduced friction and lower wear rates.

For a seal to work, two things have to happen at the interface. First, the surfaces need to conform to each other under load. Second, they must block any continuous paths that would allow gas or fluid to flow across the interface. RSm directly influences this second requirement by controlling the lateral width of the channels that can form between surface features.

Low RSｍ = 50 µm

When RSm is low, surface features are closely spaced. This means there are many peaks and valleys packed into a short distance, creating narrow grooves and short flow paths. Under compression, these closely spaced asperities deform or collapse more easily, allowing the surfaces to make contact across a larger area. Any remaining gaps tend to be narrow and discontinuous, which makes it difficult for air or fluid to pass through. As a result, surfaces with low RSm generally seal more effectively, especially in applications involving elastomer seals, gaskets, or metal-to-metal contact under sufficient load.

High RSｍ = 400 µm

In contrast, a high RSm surface has features that are spaced farther apart. There are fewer peaks per unit length, and the valleys between them are wider and longer. These wide valleys can act as continuous leakage channels, allowing air or gas to bypass the contact points between peaks. Closing these gaps often requires much higher clamping forces, and even then, leakage can persist. This is why surfaces with high RSm are more prone to sealing failures, particularly in gas or vacuum applications, even if the surface appears smooth based on Ra alone.

This highlights an important limitation of relying solely on Ra for sealing specifications. Two surfaces can have the same average roughness yet behave very differently. A surface with low Ra but high RSm may look smooth, but its wide grooves can form effective leak paths. Meanwhile, a surface with a slightly higher Ra but low RSm may seal better because its closely spaced features disrupt flow paths more effectively. This mismatch is a common reason seals fail when Ra is the only parameter specified.

It’s also important to consider directionality, as strongly directional surface textures can create straight-through leakage paths even if RSm is low in one direction. For best results, RSm should be evaluated alongside other functional parameters such as Rpk and Rvk for bearing and valley behavior, skewness (Rsk) to understand peak dominance, and areal parameters like Sal and Str to capture surface texture direction and isotropy.

• Predicting lubrication retention
• Evaluating cutting and grinding tool behavior
• Diagnosing machining vibrations
• Assessing surface fatigue behavior

Grinding wheel wear causes spacing between cutting points to expand progressively. Even if Ra remains constant, a shifting RSm value may indicate loss of surface uniformity, leading to higher friction and greater risk of surface burn.

Peak count reflects how many surface peaks exceed a filter threshold per evaluation length:

• Wear interface design
• Roller bearing lubrication analysis
• Consistency checks in precision grinding

In optical polishing, an increase in peak density typically signals successful texturing control. In contrast, low peak count may produce glare, scatter, or haze. Even if Ra is identical, the number of peaks affects optical behavior significantly.

Represents the average wavelength of surface waviness or roughness features along the profile.

Gives more weight to large wavelength features than λa.

Wavelength parameters are especially sensitive to machining dynamics, and they are excellent indicators of process health and stability.

• Cutting tool vibration
• Chatter frequency
• Machine tool harmonics

In precision turning, excessive λq wavelength often reveals tool chatter caused by instability in feed rate or cutting forces. Engineers may use wavelength analysis to correlate machine vibration events with surface texture patterns to prevent premature tool failure.

• λa vs RSm:
  Both describe spacing, but λa is statistical/spectral, while RSm depends on explicit peak and valley identification.
• λq vs λa:
  λq highlights irregular spacing that λa averages out.
• Pc vs spacing parameters:
  Pc is roughly the inverse of spacing, but it lacks information about spacing consistency.
  “Higher Pc ⇒ smaller spacing”

The VK-X3000 Series 3D Surface Profiler analyzes over 40 roughness parameters to provide users with a comprehensive data set for understanding a surface. Our software can also automatically compare multiple surfaces and extract the key quantitative differences between them so that you don’t have to spend your time staring at data to accurately determine the next best step.

Spatial roughness trends reveal melt pool pattern shifts, porosity distribution, and post-processing tool stability — especially during grinding and polishing steps.

In every case, spatial parameters provide context that height metrics alone cannot.

The VK-X3000 Series 3D Surface Profiler is ideal for any industry or application. With three different measurement techniques, users can accurately measure the surface of any type of material, regardless of the shape, from millimeters to nanometers. Request an onsite or virtual demo to see how this system can work for you.