What are p, v and PV?
Pressure p is the radial load spread over the projected area of the bore. Speed v is how fast the two surfaces slide past each other. Their product, PV, is a stand-in for the frictional heat generated per unit of surface: friction force is proportional to pressure, and heat is friction force times sliding speed. The actual PV is compared with a permitted PV, which depends on the shaft material, the ambient temperature and the duty cycle.
A material can fail on any of the three numbers. The permitted PV is only roughly constant over a range of speeds. At low speed the pressure limit controls the design, because the material can only carry so much pressure however slowly it moves. At high speed the speed limit controls it, and PV is what limits the heat in between. That is why a slow pivot can pass the PV check and still fail on pressure. A design is workable when p, v and PV are all within the limits of the chosen material, with a margin for shock, misalignment and dirt.
How do you calculate them?
In newtons and millimetres:
- Pressure p = F ÷ (d × L), in N/mm² (the same as MPa). F is the radial force, d the bore and L the loaded length.
- Speed, rotating v = π × d × n ÷ 60,000, in m/s, with n in rpm.
- Speed, oscillating v = 2 × (θ ÷ 360) × π × d × f ÷ 60,000, with θ the total swing angle in degrees and f the cycles per minute (one cycle is out and back).
- PV = p × v.
Worked example, a 25 mm shaft in a bushing 30 mm long, with 1,500 N radial load and 300 rpm:
- p = 1,500 ÷ (25 × 30) = 2.0 MPa
- v = π × 25 × 300 ÷ 60,000 = 0.393 m/s
- PV = 2.0 × 0.3927 = 0.785 MPa·m/s
Supplier-typical continuous PV for unfilled acetal is 0.25 to 0.35 MPa·m/s, and for nylon 66 or cast nylon 0.30 to 0.45 (Quanda Plastic). Test methods differ a great deal between suppliers, with different speeds and temperature-rise limits, so use these as an order of magnitude only. The rotating case above is well over them, which means it needs a modified grade or a solid-lubricant-filled compound. For converting units, 1 MPa·m/s is about 28,550 psi·ft/min, so the 10,000 psi·ft/min often quoted for acetal is about 0.35 MPa·m/s.
Most pivots swing rather than turn. Same bushing and load, but swinging 60° in total at 20 cycles a minute:
- v = 2 × (60 ÷ 360) × π × 25 × 20 ÷ 60,000 = 0.0087 m/s
- PV = 2.0 × 0.0087 = 0.0175 MPa·m/s
That is far below the continuous PV limits above, but the pressure p = 2.0 MPa must still be within the material's own pressure limit. All the numbers here are examples.
What can raise the permitted PV?
Three things.
- Short runs. A bearing that runs only for short periods, with pauses long enough to cool, can be allowed a higher PV than continuous running, because the heat never reaches steady state.
- Lubrication. Lubrication carries heat away and lowers friction. Published correction factors for particular polymers run from 1 for dry running up to about 5 for continuous oil. These factors belong to specific materials, so do not carry them to another grade (Q1-06).
- The shaft. A shaft that conducts heat away well keeps the bearing cooler. Typical thermal conductivities are about 46 W/m·K for carbon steel, 204 for aluminium, 16 for 304 stainless steel, and only about 0.24 for the polymer itself, so almost all the heat leaves through the shaft. The shaft's hardness and surface finish matter too (Q1-05).
What about the load capacity on its own?
The load a plastic bushing can take is set by its surface pressure, from the projected area. The permitted static surface pressure applies at very slow speed, of the order of 0.01 m/s. Short-term overload capacity differs by material, so take it from the datasheet. The permitted pressure also falls as temperature rises (Q1-16).
What happens if PV is exceeded?
Heat builds up at the sliding surface, the polymer softens, its size changes and wear accelerates, and in the end the bushing can seize. Leave a margin.