1
What you measured, as a volume
Every wear rate starts from a volume of material that is gone. Four measurements are common and they need four different conversions. Pick the one you did. The three disc routes open on the same track, so switching between them should agree to within the error of each; the ball route measures the other body in the contact, which wears far less. The contact geometry behind these formulas, including the flat-pin case, is worked out in module 8 of How to measure wear; this page is about what you do with the volume once you have it.
2
Every wear rate at once
The volume above, with the load and the sliding distance, gives all of them. They are not alternatives: each answers a different question, and only one of them is close to a material property.
| Quantity | Value | Unit | What it is for |
|---|
The specific wear rate k = V/(F·s) is the one to quote if you quote one number: dividing out both the load and the distance is what makes two tests comparable. It still is not a material property, because it depends on the counterface, the atmosphere, the speed and the contact geometry, which is why the conditions belong beside it. The dimensionless Archard coefficient K = k·H goes one step further and divides out the hardness, which is how mild and severe wear are usually separated.
3
The unit map
Most of the confusion in this subject is one table wide. These are the forms the same measurement appears in, and what to multiply by to move between them.
| Written as | Units | Really means | To get mm3/N·m |
|---|---|---|---|
| Wear volume | mm3 | Material gone. Says nothing until the load and the distance come with it. | divide by F·s |
| Wear rate | mm3/m | Volume per metre slid, at one load. Comparable only between tests at the same load. | divide by F |
| Wear rate | mm3/h, mg/h | Per hour, so it also carries the sliding speed. Common in industrial reports, hard to compare. | divide by F and by speed (and by density for mg) |
| Specific wear rate k | mm3/N·m | Volume per newton per metre. The comparable one. | this is it |
| Wear factor, also k | mm3/N·m | The same quantity under another name, common in the polymer literature. | this is it |
| Specific wear rate | m3/N·m or m2/N | The SI form of the same thing. | multiply by 109 |
| Wear coefficient K | dimensionless | Archard: k times the hardness. The fraction of asperity contacts that produce a wear particle. | divide by H in N/mm2, times 1000 |
| Wear depth rate | µm/h, nm/m | Depth per time or distance over the apparent contact. What a design engineer needs; depends on the contact area. | multiply by the apparent area, divide by F |
| Mass loss | mg | Easiest to measure, useless between materials of different density. | divide by density, then by F·s |
“Wear rate” on its own means volume per unit sliding distance in some papers and specific wear rate in others, and both are written mm3/N·m by mistake often enough that you cannot rely on the unit alone. If a number looks a thousand times off, check whether the distance was in metres or millimetres before you conclude anything about the material.
4
What ASTM G99 actually specifies
G99 is the pin-on-disc standard, and it is shorter than people expect. It fixes the geometry and the reporting, and deliberately leaves the test conditions to you. That division is the reason two laboratories can both follow G99 and get answers that differ by an order of magnitude.
| The standard fixes | The standard leaves to you |
|---|---|
| The geometry: a pin (ball or flat-ended) loaded perpendicular against a flat rotating disc, tracing a circular track. | The load, the sliding speed, the track radius and the total sliding distance. |
| That wear is reported as a volume loss, for the pin and for the disc separately. | The materials, their finish and their hardness. |
| How to get those volumes: a scar diameter on a ball, a profile across the disc track, or a mass loss converted with the density. | The atmosphere: humidity, temperature, and whether there is a lubricant. |
| What must be reported for the test to mean anything: materials, geometry, load, speed, distance, atmosphere and temperature. | How many repeats, and what counts as agreement between them. |
| That the result describes the system, and does not predict service life. | Whether to record friction at the same time, which most rigs do anyway. |
The two volume formulas, worked out
The ball. A worn ball has a flat circular scar of diameter d. What is gone is a spherical cap. Its height is h = R − √(R² − d²/4), and its volume is πh(3d²/4 + h²)/6. When the scar is small compared with the ball, which it usually is, that collapses to the form most papers quote: V ≈ πd4/(64R). The calculator above uses the exact cap and shows the approximation beside it, so you can see when the shortcut stops being safe: at d/R above about 0.6 it is out by more than 5%.
The disc. A profile across the track gives the cross-section area A that is missing. The track is a circle of radius Rt, so the volume is that area swept around it, V = 2πRtA. Two things go wrong here in practice. Material displaced into the shoulders rather than removed must be excluded from A, or the wear is overstated: integrate below the original surface only. And a track whose depth varies around the circle needs several profiles averaged, not one profile trusted.
Specific wear rate in mm3/N·m, with the load, the speed, the sliding distance, the counterface material and radius, the atmosphere and the temperature, and the number of repeats with their spread. Everything else can be recomputed from that; nothing else can be recomputed without it.
Sources
Show the six references
- J. F. Archard, “Contact and rubbing of flat surfaces,” J. Appl. Phys. 24, 981 (1953): the wear equation and what K means.
- ASTM G99, Standard Test Method for Wear Testing with a Pin-on-Disk Apparatus: the geometry, the volume-loss measurements and the reporting requirements summarised above.
- ASTM G40, Standard Terminology Relating to Wear and Erosion: the definitions behind the unit map, including wear rate and specific wear rate.
- I. M. Hutchings, P. Shipway, Tribology: Friction and Wear of Engineering Materials, 2nd ed., Butterworth-Heinemann (2017): wear regimes, the mild to severe transition, and the ranges the scale on this page uses.
- K. Kato, K. Adachi, in Modern Tribology Handbook, CRC Press (2001): wear mechanism maps and the conditions that move a system between them.
- M. Woydt, R. Wasche, “The history of the Stribeck curve and ball bearing steels,” Wear 268, 1542 (2010): on why a wear number belongs to a system and not to a material.