Theory of Elasto-Hydrodynamic (EHD) Lubrication

Life calculations for ball screws assume sufficient lubrication, which means that there is an adequate lubrication film. In case of oil lubrication this means that whenever the speed is sufficient, a fluid film develops which separates the contact partners as much as possible. This requires that

  • sufficient oil is available at all times
  • contamination is minimal
  • lubricant is in adequate condition

The necessary condition to form such a fluid film is described by the theory of elasto-hydrodynamic lubrication. Whether a fluid film, able to withstand the pressure in the friction contact zone, will build depends on the actual viscosity of the lubricant and the speed and, to a lesser extent, the pressure. However, a certain minimum load is required (for example by preloading the ball screw) to cause a consistent rolling motion of the balls.

Whether an EHD film will build can be determined from the viscosity ratio k = u / u1. The operational viscosity u is the viscosity the lubricant exhibits under the conditions in the contact patch in terms of speed, temperature and pressure. The viscosity needed to build a sufficient EHD film is u1.

The viscosity ratio can be classified in 3 parts:

  • k ≥ 4 full EHD lubrication - contact partners are mostly separated
  • 0,4 ≤ k < 4 mixed friction - lubricant with wear inhibiting additives is necessary, since EHD film is only partially able to separate contact partners (EP - grease, CLP - oil)
  • k < 0,4 no separation - accelerated wear through micro welding will occur

Since a high viscosity ratio is desirable, oil with high viscosity seems to be the solution. But high oil viscosity also causes high temperatures, which in turn could lower the actual viscosity again. High viscosity oil is also difficult to deliver to all lubrication points and will not aid in cooling the ball nut.

We recommend using oil viscosities as close as possible to the ones per the following table.

recommended oil viscosity