Plain Bearing Pressure (p·v Value) Calculator
Determine the bearing pressure, sliding velocity and p·v value of a maintenance-free dry-sliding or mixed-friction plain bearing: from the radial force, bearing diameter, bearing width and speed (or swing angle and frequency for oscillating operation) the tool derives the three key values and their utilization against the selected bearing material, live with every input.
Calculation
Model: p·v rating method (Roloff/Matek) for maintenance-free dry-sliding/mixed-friction bearings, not a hydrodynamic verification (Sommerfeld number, DIN 31652 is a separate method). Temperature and break-in effects are manufacturer-specific. Sizing tool for mechanical engineering.
Results
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Formulas and fundamentals
Projected area and bearing pressure
Plain bearings are not rated against the actual, curved contact area between shaft and bushing, but against the projected area - the area of the rectangle formed by diameter d and width b, on which the radial force F acts. It is easy to determine and has become the established reference dimension for plain bearing load capacity:
The bearing pressure p is therefore an average value over the projected area, not a local peak pressure - which is sufficient for the approximate sizing done with the p·v method.
Sliding velocity: rotating and oscillating
For rotating operation, the sliding velocity is the circumferential velocity of the shaft:
with d in mm and n in rpm, v results in m/s (the factor 60000 converts mm/min to m/s). For oscillating (swinging) operation, the shaft travels the distance phi_rad · d per double stroke (forward and return), with the swing angle phi in degrees converted to radians:
with f as the double-stroke frequency in cycles per minute. This average sliding velocity is the value used by the p·v method; the actual instantaneous velocity varies during the swing between zero (at the reversal points) and a maximum.
p·v value and utilization ratios
The p·v value is the product of bearing pressure and sliding velocity:
It is a measure of the frictional power generated per unit area in the bearing and therefore of wear and heating - a bearing can be overloaded at low pressure and high speed just as much as at high pressure and low speed. The calculator compares p, v and p·v individually against the material's allowable values and forms three utilization ratios (p/p_allow, v/v_allow, (p·v)/(p·v)_allow). For each criterion: utilization up to 80% is green (pass), 80 to 100% amber (marginal), above 100% red (fail) - the overall rating is the worst of the three individual ratings, since each criterion can overload the bearing on its own.
Distinction from hydrodynamic lubrication
The p·v rating method applies to maintenance-free plain bearings with mixed or dry friction (sintered bronze, composite bearings, plastics) - cases where no load-carrying hydrodynamic lubricant film forms. Fully hydrodynamically lubricated plain bearings (oil bath, circulating lubrication), by contrast, are sized using the Sommerfeld number per DIN 31652: there, a self-generating oil film carries the load, and allowable values are based on the minimum lubricant film thickness rather than on p and v alone. The two methods are not interchangeable; this calculator covers the p·v method only.
Material selection
Solid bronze (CuSn8) and gunmetal are suited to higher pressures and speeds at moderate cost but generally require basic lubrication. Sintered bronze (oil-impregnated) stores lubricant in its pores and therefore runs with less maintenance. Composite bearings with a PTFE sliding layer (DU bushings) run dry, tolerate high bearing pressure at low speed, and suit applications without relubrication. POM composite bearings (DX type) need initial greasing but are cost-effective and tolerate somewhat higher speeds than PTFE. Polyamide (PA6) has the lowest allowable values of the group but is lightweight, damping and very low-cost - suited to lightly loaded, slow applications.
Worked example
Given: a bronze bushing (CuSn8) with diameter d = 30 mm and width b = 30 mm carries a radial force F = 4500 N, rotating at n = 120 rpm.
Projected area A = d · b = 30 · 30 = 900 mm². Bearing pressure p = F/A = 4500/900 = 5 N/mm². Sliding velocity v = pi · 30 · 120/60000 = 0.19 m/s. p·v value = 5 · 0.19 = 0.94 N/mm²·m/s.
CuSn8 reference values: p_allow = 25 N/mm², v_allow = 8 m/s, (p·v)_allow = 1.8 N/mm²·m/s. Utilization: p 5/25 = 20%, v 0.19/8 ≈ 2%, p·v 0.94/1.8 ≈ 52%. All three criteria are below 80% - overall rating green, the bearing has comfortable margin for these operating conditions.
Frequently asked questions
What does the p·v value mean for plain bearings?
The p·v value is the product of bearing pressure p and sliding velocity v, and it measures the frictional power generated per unit area in the bearing - it is the key driver of wear and heating in maintenance-free dry-sliding or mixed-friction bearings. Because p and v act together, a bearing can be overloaded at low pressure and high speed just as at high pressure and low speed; the calculator therefore rates p, v and p·v individually against the material's allowable values.
When to use a plain bearing versus a rolling bearing?
Plain bearings are often preferable under shock and vibration loads, at high temperatures, in aggressive media, at very high speeds (turbines), or when installation space and noise are decisive - they tolerate misalignment better and run quieter. Rolling bearings are more common where low starting friction, a defined fatigue-life calculation (ISO 281) and standard applications with moderate load are needed. The p·v rating method used here applies to maintenance-free plain bearings with mixed/dry friction, not to rolling bearing life calculations.
Why is the projected area used instead of the actual contact area?
The actual contact area between a cylindrical shaft and a bushing is curved, and its exact size depends on clearance, deformation and load distribution - for an approximate, practical sizing method the projected area A = d · b is used instead (the area of the rectangle on which the radial force acts). It is unambiguously determined from the bearing dimensions and has become the established reference for p and p·v, even though the actual local pressure at the load peak is higher than the average p.
What to do if p, v or the p·v value exceed the allowable limits?
The most direct options are: a larger bearing (increasing diameter or width directly lowers p), a material with higher allowable values (e.g. solid bronze instead of polyamide), a lower speed or swing frequency if the design allows it, or switching from dry to mixed friction via additional lubrication. For a marginal exceedance (amber rating), targeted lubrication or a slightly larger bearing is often enough; for a significant exceedance (red), the sizing should be reworked.
How is the sliding velocity calculated for oscillating (swinging) operation?
In oscillating operation, the shaft swings back and forth through an angle phi; per double stroke (forward and return), a point on the circumference travels the distance phi_rad · d (phi_rad = phi · pi/180 in radians). With the double-stroke frequency f in cycles per minute, the average sliding velocity is v_m = phi_rad · d · f/60000 m/s. This is a time-averaged value; the instantaneous velocity is zero at the reversal points and higher in between.
Do break-in behavior and temperature matter beyond what the calculator shows?
Yes. The p·v rating method gives reference values for run-in, steady-state operation at moderate ambient temperature; break-in behavior (initially higher wear until the surfaces conform), the actual operating temperature (allowable values drop at higher temperature, especially for plastic plain bearings), and shock loading, contamination and misalignment are manufacturer-specific and not part of this approximate calculation. For safety-relevant or marginally loaded applications, consult the catalog data and test recommendations of the specific bearing manufacturer.
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