Rk, Rpk, Rvk — reading a plateau-honed surface

A plateau-honed cylinder bore has two jobs at once. Its smooth plateaus carry the piston rings; its deep honing grooves hold oil. Ra averages both into one number and says nothing about either. The Rk parameters of ISO 13565-2 were made for exactly this kind of surface: they split the profile into peaks that will wear off during running-in, a core that carries the load, and valleys that retain lubricant.

The material ratio curve

Sort all heights of the roughness profile from the highest to the lowest and plot them against the share of the evaluation length that lies above each height. The result is the material ratio curve, or Abbott–Firestone curve. At the top only the highest peak is cut (0 %); at the bottom everything is (100 %).

For a plateau-honed surface the curve is S-shaped: steep at the top where a few peaks stand out, flat through the plateau, and steep again at the bottom where the deep grooves are.

1Equivalent line2Rk3Mr1, Mr24Rpk5Rvk

Rvk: the area A2 below the core between Mr2 and 100 % becomes a triangle of equal area on the base 100 % − Mr2: Rvk = 2·A2/(100 % − Mr2).

Rk 0.58 µmRpk 0.13 µmRvk 1.68 µmMr1 6.8 %Mr2 82.5 %

The construction, step by step

1. Equivalent straight line. A secant spanning 40 % of material ratio is moved along the curve until its slope is smallest. That position marks the core of the profile.
2. Rk, the core roughness depth. Extend the line to 0 % and 100 %. The height between those two intersections is Rk.
3. Mr1 and Mr2. Horizontal lines through the two ends of the core cut the curve at Mr1, the smallest material ratio of the core, and Mr2, the largest.
4. Rpk, the reduced peak height. The area A1 between the curve and the upper core line, from 0 % to Mr1, is replaced by a right triangle of equal area on the base Mr1:

$$Rpk = \frac{2\,A_1}{Mr_1}$$

5. Rvk, the reduced valley depth. In the same way, the area A2 between the lower core line and the curve, from Mr2 to 100 %, gives:

$$Rvk = \frac{2\,A_2}{100\,\% - Mr_2}$$

Read in terms of function:

• Rpk describes the peaks that will be worn away in running-in. Small is good.
• Rk describes the core that carries the load over the long term.
• Rvk describes the valleys that hold the oil. It must be large enough to retain lubricant.
• Mr1 is the share of the length occupied by the peaks; 100 % − Mr2 is the share occupied by the valleys.

Names under ISO 21920

ISO 21920-2:2021 replaced ISO 13565-2 and -3. Rk, Rpk and Rvk keep their names; Mr1 and Mr2 became Rmrk1 and Rmrk2. The status of the filter standard differs by body: ISO lists ISO 13565-1 as current and confirmed it in 2026, while BSI and Mahr’s DIN-based summary list it as withdrawn.

ISO 13565-3 added a second family, Rpq, Rvq and Rmq, based on the material probability curve: the slopes of the plateau and valley regions on a normal-probability scale, and the material ratio at their transition. They were intended for two-component surfaces such as cylinder liners and fuel injectors.

Published target values

Engine cylinder bores (MS Motorservice)

Measured over a traverse length of 4.8 mm with a 2 µm, 90° stylus tip. Note how Rvk is several times Rpk: the surface is meant to be mostly plateau, with deep oil-holding grooves. A liner maker’s patent (Zynp) and a paper by Gruszka, Pawlus and Mathia give similar ranges; they are compared in honing and plateau honing.

Passenger carDiesel utility vehicle

Counter-surfaces for hydraulic seals

To see how feed and nose radius set the roughness of a turned surface before honing or grinding, use the theoretical roughness calculator.