Surface Roughness: Definition, Parameters, and Engineering Applications
I. What is surface roughness?
Regardless of the machining method (turning, milling, grinding, drilling) used for parts, fine uneven tool marks will be left on the surface - the surface of rough machining is visible to the naked eye, while the surface of finishing requires a magnifying glass or microscope to observe the interlaced "peaks and valleys". This microscopic unevenness of the surface is the surface roughness (formerly known as "surface finish"). It is the core indicator for describing the microscopic geometric shape of the part surface and directly affects the function and service life of the part.
II. Core parameters of surface roughness
The state regulations stipulate that the parameters of surface roughness are divided into three categories: height parameters (describing the height of peaks and valleys), spacing parameters (describing the interval between peaks and valleys), and comprehensive parameters (describing the bearing capacity of the surface). Among them, the height parameters are the most commonly used in engineering.
1. Height parameter: Measures the "height difference" between peaks and valleys
The height parameters directly reflect the "smoothness" of the surface. There are three key points:
Arithmetic mean deviation of the profile (Ra): The most commonly used parameter. When measuring, first draw a center line m - on a profile of a certain length, make the areas enclosed by the profile on both sides of the center line and the center line equal (i.e., F₁ + F₃ + … = F₂ + F₄ + …). Ra is the arithmetic mean of the absolute values of the distances from all profile points to the center line within the measurement length l. The formula is:
$$Ra = \frac{1}{l} \int_0^l ydx$$
In practical calculations, an approximate value is often used: $Ra ≈ \frac{1}{n} \sum_{i = 1}^n y_i$ (where $y_i$ is the distance from each point to the mid - line, and $n$ is the number of measurement points).
Mean height of irregularities (Rz): Within the basic measuring length, select 5 highest peaks (h₁, h₃…h₉) and 5 lowest valleys (h₂, h₄…h₁₀). Subtract the sum of the valley depths from the sum of the peak heights, and then divide the result by 5. The formula is:
$$Rz = \frac{(h_1+h_3+h_5+h_7+h_9) - (h_2+h_4+h_6+h_8+h_{10})}{5}$$
Rz focuses more on "macroscopic unevenness" and is suitable for evaluating rough surfaces (such as castings).
Maximum height of the profile (Ry): Within the sampling length l, it refers to the vertical distance between the "peak line" formed by connecting the highest points of all peaks and the "valley line" formed by connecting the lowest points of all valleys. It reflects the "maximum undulation" of the surface and is commonly used to evaluate surfaces prone to stress concentration (such as internal fillets and grooves).
2. Spacing parameter: Measures the "interval" between peaks and valleys
The spacing parameter describes the distribution density of peaks and valleys, and there are two core aspects:
Average spacing of single peaks in the profile (S): The average value of the projection distances (Sᵢ) on the center line between the highest points of two adjacent single peaks within the sampling length. It reflects the "density" of the peaks - the smaller the S, the more densely the peaks are distributed.
Average spacing of micro - irregularities of the profile (Sm): The average value of the length of a section of the center line (Sₘᵢ) that contains one peak + one adjacent valley. The difference from S is that Sm focuses more on the interval between units of micro - undulations, while S is the interval between single peaks.
3. Comprehensive parameter: Measure the "bearing capacity" of the surface
There is only one comprehensive parameter - the contour bearing length ratio (tₚ), which is the ratio of the contour bearing length nₚ (the projected length on the center line of the contour part above the center line that can bear the load) to the sampling length l (tₚ = nₚ/l). The larger the tₚ is, the larger the "effective bearing area" of the surface is, and the stronger the wear resistance is.
III. Correspondence between surface roughness and "surface finish"
The previous "surface finish" standard was divided into 14 grades (designated as 1 to 14). The larger the number, the smoother the surface (corresponding to a smaller roughness value). For example:
- Surface finish grade 14 → Ra ≈ 0.012μm (mirror surface);
- Surface finish grade 1 → Ra ≈ 100 μm (Surface after rough turning).
Although the parameter of "surface roughness" is now used, the workshop still customarily uses the popular term "surface finish". For example, "The surface finish of this shaft should reach Grade 6" (corresponding to Ra ≈ 0.8μm).
IV. Measurement methods of surface roughness
Two measurement methods are commonly used in engineering:
1. Template comparison method: This is the most commonly used method in the workshop. Compare the surface of the machined part with a standard roughness template (a metal sheet engraved with different grades) - observe the "degree of reflection" with the naked eye (the smoother the surface, the stronger the reflection), or feel the "concavity and convexity" with your fingers (the smoother the surface, the finer the touch) to quickly estimate the grade.
2. Instrument measurement method: In high-precision scenarios, use professional instruments (such as profilometers and roughness meters). Scan the surface with a stylus to accurately measure parameters such as Ra, Rz, and Ry. The error can be controlled within 0.01 μm.
V. Engineering Significance of Surface Roughness: Balance between Performance and Cost
Surface roughness directly affects the service performance and processing cost of parts.
Performance advantages: The smaller the roughness value (the smoother the surface), the higher the contact accuracy of the mating surface, the less the friction and wear, and the longer the service life of the part (for example, when the Ra of the bearing inner ring decreases from 1.6 μm to 0.8 μm, the service life can be extended by 2 to 3 times).
Cost: The smaller the roughness, the greater the processing difficulty. It requires finer cutting tools (such as diamond tools), higher machine tool precision (such as grinding machines), and longer processing time (for example, precision grinding requires repeated passes). The cost will increase exponentially.
Therefore, the core logic of reasonably selecting the roughness value is to select the largest possible value under the premise of meeting the technical requirements to reduce costs.
VI. Selection principles for surface roughness
When designing parts, the selection of roughness values needs to be combined with the function, fit type, and load conditions of the parts. Specifically, the following five principles should be followed:
1. Working surface
Working surfaces (surfaces involved in functions, such as the mating surface of a shaft and the tooth surface of a gear) need to be in frequent contact or bear forces, so the roughness value is smaller; non - working surfaces (such as the side and bottom surfaces of a part) do not participate in functions, and the value can be 1 - 2 grades larger (for example: the mating surface of a shaft has Ra = 0.8μm, and the side surface has Ra = 3.2μm).
2. Friction surface
Friction surfaces (such as pistons and cylinder liners, gear tooth surfaces) need to reduce wear, and the values should be smaller.
- The higher the friction speed (e.g., high-speed motor shaft) and the greater the unit pressure (e.g., heavy-duty bearing), the smaller the value should be (for example: Ra = 0.4μm for high-speed gears and Ra = 1.6μm for low-speed gears).
- Rolling friction (e.g., ball bearings) has a smaller value than sliding friction (e.g., sliding bearings) (the wear of rolling friction is more dependent on surface smoothness).
3. The fit type determines the value
Clearance fit (the movable connection between the shaft and the hole, such as the valve stem and the sleeve): The smaller the clearance, the smoother the surface is required (to prevent jamming), and the smaller the value is (for example: when the clearance is 0.01mm, Ra ≤ 0.4μm; when the clearance is 0.1mm, Ra ≤ 1.6μm).
Interference fit (press-fit connection between the shaft and the hub, such as that between the coupling and the shaft): The greater the load, the smoother the surface is required (to avoid stress concentration at the bumps), and the smaller the value should be (for example: for heavy loads → Ra ≤ 0.8μm; for light loads → Ra ≤ 3.2μm).
- Usually, the values of clearance fits are smaller than those of interference fits (clearance fits are more prone to jamming).
4. Matching of dimensional accuracy and size
The higher the accuracy, the smaller the value: The higher the fitting accuracy (e.g., IT5 level → Ra ≤ 0.4μm; IT8 level → Ra ≤ 1.6μm).
The smaller the size, the smaller the value: Under the same accuracy level, the value of small-sized parts (such as a φ5mm shaft) is smaller than that of large-sized parts (such as a φ50mm shaft) (the error of small parts has a more sensitive impact on the fit).
The value of the shaft is smaller than that of the hole: especially for the accuracy levels from IT5 to IT8. It is easier for the shaft to achieve high precision during processing (the tool has good rigidity during turning), while the processing of the hole (such as boring) has poor rigidity, and the value is usually one level larger than that of the shaft (for example: when the Ra of the shaft is 0.8μm, the Ra of the hole is 1.6μm).
5. The stress concentration areas need to be smoother
- Surfaces subjected to cyclic loads (such as the crankpin of a crankshaft and the connecting rod bearing bush): A small roughness can reduce the generation of "fatigue cracks" (stress concentration is likely to form at the protrusions).
- Parts with internal fillets and grooves (such as the undercut of a shaft and the root circle of a gear): A small surface roughness can prevent stress concentration at the convex points and avoid breakage.
VII. Corresponding table of commonly used surface roughness values
The following table shows the corresponding relationship between "surface finish symbols and roughness parameters" commonly used in engineering (some data are reference values):
Surface finish symbol Maximum height of the profile Ry (μm) Average height of the irregularities Rz (μm) Arithmetic mean deviation of the profile Ra (μm) Sampling length l (mm)
ssss 0.05 0.05 0.013 -
0.1 0.1 0.025 0.2
0.2 0.2 0.05 0.4
0.4 0.4 0.10 0.8
0.8 0.8 0.20 0.25
sss 1.6 1.6 0.40 0.8
3.2 3.2 0.80 -
6.3 6.3 1.6 -
12.5 12.5 3.2 2.5
ss 18 (Reference) 18 (Reference) 6.3 -
25 25 35 (for reference) -
s 50 50 12.5 -
70 (reference) 70 (reference) 25 -
100 100 140 (reference) -
200 200 280 (Reference) 50
400 400 560 (reference) -
Summary
Surface roughness is an "invisible indicator" for part design and machining - it can't be seen but can be felt, yet it directly determines the service life and cost of parts. In engineering, it is necessary to reasonably select the roughness value in combination with functional requirements, fit types, and dimensional accuracy to achieve the optimal balance between "performance and cost". For example:
- Tooth surface of heavy-duty gears → Ra = 0.4μm (to reduce wear);
- The head of the ordinary bolt → Ra = 6.3μm (non-working surface, to reduce costs);
- The inner surface of the engine cylinder liner → Ra = 0.8μm (sliding friction, requires smoothness).
Understanding the core parameters and selection principles of surface roughness is one of the basic skills of mechanical engineers.