If you've specified radial bushings or slides in a recent design, you may have sized them using a pressure-velocity (PV) factor — a measure of pressure and velocity between key contacting surfaces. Well, the descriptive expression can also characterize the properties of leadscrews. It's a value listed for most engineering polymers (plastics have intrinsic limiting PV ratings) though generally omitted from nut load ratings. But the PV value says a lot about a given leadscrew assembly's performance envelope.

Put simply, the more load applied to the leadscrew assembly, the slower it must be turned to avoid exceeding the nut's PV limit. The reverse is also true: More speed means less available load capacity. The PV of a leadscrew quantifies this relationship for specific running conditions.

Plastics are assigned PV ratings by the companies that formulate the compounds. Common compounds are DuPont's Delrin AF, Quadrant's Torlon, and LNP Lubriloy of GE Plastics. The compounder determines the formulation of base resin and additives that are chosen: For example, additives are commonly included to improve structural and tribological properties. PV values are then verified by sliding a sample disc of the material against a steel surface at varying load and speed. In this way, the wear inflection point (and hence, the limiting PV value) can be determined.

A base resin may have a certain PV rating, but adding lubricants and other compounds raises that rating. So, designers have considerable flexibility in achieving a suitable PV envelope for their application. That said, test methods do differ from company to company, so it is best to compare different plastics from a single compounder when selecting a material.

### System-wide PV

The primary modes of failure for leadscrews are wear and PV. By designing within the PV envelope, failure is forced to occur as a result of wear. Wear is a slower and more linear type of failure, which can be accounted for in design. The PV value is determined by helix length, approximate pressure, as well as surface velocity. So besides material modifications, the system PV can also be addressed by modifying the geometry of the leadscrew components.

The limiting PV for any given material is often represented on a PV chart. To plot values, first set the product of pressure and velocity equal to the material's PV limit. Ensure that units are consistent, either in *psi ft/min*. or *MPa m/sec* throughout:

where force is applied axially to the nut, and pressure is defined as that axial force divided by the projected bearing area and velocity *V* as the sliding speed between the surfaces. By solving for pressure (or velocity) one can plot the curve over a desired range of velocities — or pressures. To prevent failure, the system PV must be held below the material PV curve.

Geometry determines how a material's limiting PV relates to the system PV of a leadscrew assembly. Start by calculating the projected area of engagement between the threads of a nut and screw with the helix length:

where *l _{H}* = Total helix length in nut, in. or m

*l _{HR}* = Helix length per revolution

*l _{N}* = Nut length

*L* = Thread lead

*S _{t}* = Number of thread starts

This is the imaginary line running around the thread at its pitch diameter where theoretical thread engagement occurs. By “unwrapping” this helix of the screw thread, we can analyze it as a triangle, with the hypotenuse representing the helix length for one rotation of thread:

where *D _{p}* = Pitch diameter of thread, in. or m

The pitch diameter and thread lead are the base and height for the right triangle, respectively. Solve for the hypotenuse, and multiply both by the nut's number of thread turns and the number of thread starts. The result: Total helix length. This can be multiplied by the depth of thread engagement between nut and screw to calculate the area in contact between them:

where *A* = Projected bearing area, in._{2} or m_{2}

dt= Depth of thread engagement

*C _{f} = Correction factor for area, from 0.25 to 0.75.*

Surface velocity can be calculated by multiplying the helix length per turn by the speed of rotation:

where *rpm* = Speed of rotation between nut and screw.

In reality, the physical situation is a bit more complex. Due to the inherent stiffness of the polymer materials used for the nut, deflection occurs between the thread of the nut and screw. The deflection in turn causes the nut thread to rotate (as in beam bending) such that the patch of contact between nut and screw is reduced. As this happens, the patch also moves further up the flank of the screw thread, until most of the load is carried near the major diameters, and increases the pressure between the two parts under a given load.

In practice it is difficult to precisely calculate this reduction in area; unfortunately, the load-carrying area shrinks as the load increases — compounding the chances for PV related failure and increasing the importance of staying within performance envelopes. To address this issue, a correction factor (Cf) is applied to the projected area. Cf normally ranges from about 0.75 to 0.25 as loading increases from light to full-rated-load capacity.

Compare this to the PV rating of the material: A safety factor of two is recommended. Again, when system PV is more than half the limiting PV, wear is accelerated. Though the chances of sudden failure are minimized here, system life is shortened.

Alternatively, one can plot a chart of load vs. rpm or nut linear speed. By dividing pressure by the corrected contact area, the PV curve can be plotted against load. Furthermore, as we just learned, surface velocity can be translated into terms of rotational speed. The result is a handy graphical map of allowable load and speed for one leadscrew system. Keep the plot of your leadscrew assembly's motion under this curve, and life depends on wear failure alone.

In fact, there are several ways to manipulate the PV envelope. Changing the polymer compounding or base resin can raise maximum PV limits (up and to the right on the PV chart) to increase system performance. Anything that reduces friction between the components has this effect, including adding grease to the screw, infusing the plastic with lubricant beforehand, or applying a dry film lubricant. In addition, the nut geometry can be changed to lower system PV at a given load and speed. For example, a longer nut reduces pressure on the threads. (The benefits of this approach diminish as the nut length reaches about four times the screw diameter.)

### Breaking the rules

For short periods of time, if the application duty cycle is very low, the PV for a leadscrew design can be exceeded safely. But unfortunately, once friction-generated heat has been created, it takes a considerable amount of time to dissipate. Even 50% duty cycles increase the amount of time before the operating temperature of the nut is exceeded. If the application requires that you exceed the limiting PV by a significant amount, duty cycle should be held to 10 or 20% at most. Remember that if a design exceeds the load rating of the nut, it could cause a structural or mechanical failure — so consult the manufacturer for advice in these situations.

*For more information, visit* thomsonbsa.com *or call (800) 882-8857. More information can also be found at the Leadscrew Component Zone accessible from the homepage of* motionsystemdesign.com.

### Shortcut

Given the inherent complexity of calculating the PV of a leadscrew system, there is always some uncertainty in the results. However, understanding the relationships and interactions aids greatly in designing functional systems. In the absence of information from the manufacturer, the general rule of thumb is that most catalog load ratings are accurate at a rotational speed of about 500 rpm. Speeds greater than that may require some derating of the operating load. Follow this rule and you'll stay out of trouble.

### Lubrication boosts rating

If you can add lubrication to your leadscew, then do it. Reduction of friction in a leadscrew system has a greater impact on performance than almost anything else. Lowered friction coefficients improve PV ratings substantially. In fact, most load ratings stated for lead nut products assume a grease or dry-film lubricant to achieve the full capacity at 500 rpm. For any duration of operation without lubricant, consult the leadscrew manufacturer.