# Acme Screw Selection

The selection of the correct acme screw and nut for a particular application involves four interrelated factors. Before attempting to determine the acme screw and nut combination, the following values must be known:

• Axial load measured in pounds or newtons
• Speed measured in inches or millimeters per minute
• Length between bearings measured in inches or millimeters
• End fixity type

The loads that need to be considered are the static loads, dynamic loads, reaction forces and any external forces affecting the screw. See Load definitions section on page 11 of our Precision Screw Assemblies Catalog for details.

## Speed

The travel rate (linear speed) is the rpm at which the screw or nut is rotating multiplied by the lead of the screw.

## Length

The unsupported length of the screw.

## End Fixity

End fixity refers to the method by which the ends of the screw are supported. The degree of end fixity is related to the amount of restraint of the ends of the screw. Examples of the three basic types of end fixity are:

Simple End fixity can be provided through a single bearing support. (See Image 1 in Figure 1 Below)

Multiple or spaced pairs of bearings are more rigid than a "Simple" support, but because of their compliance are not truly "Fixed".

A screw can be supported with different combinations of end fixity. (See Image 2 in Figure 1 Below)

## Critical Speed

Once the load, speed, length and end fixity are identified, the next factor to consider is the critical speed. The speed that excites the natural frequency of the screw is referred to as the critical speed. Resonance at the natural frequency of the screw will occur regardless of the screw orientation (vertical, horizontal etc.) or if the system is designed so the nut rotates about the screw. The critical speed will vary with the diameter, unsupported length, end fixity and rpm. Since critical speed can also be affected by shaft straightness and assembly alignment, it is recommended that the maximum speed be limited to 80% of the calculated critical speed. The theoretical formula to calculate critical speed in rpm is:

 N = Cs × 4.76 × 106 × d L²

WHERE:

N = Critical Speed (rpm)
d = Root Diameter of Screw (inch)
L = Length Between Bearing Supports (inch)
Cs = 0.36 for one end fixed, one end free
1.00 for both ends simple
1.47 for one end fixed, one end simple
2.23 for both ends fixed

The critical speed chart on page 17 is provided to quickly determine the minimum screw size applicable for Nook EZZE-MOUNT™ designs.

If the selected Acme screw does not meet critical speed criteria, consider the following options:

1. Increase screw lead and reduce rpm
2. Change end fixity (e.g. simple to fixed)
3. Increase screw diameter

## Column Strength

When a screw is loaded in compression (see compression load definition on page 11), its limit of elastic stability can be exceeded and the screw will fail through bending or buckling.

The theoretical formula to calculate the column strength in pounds is:

 Pcr= 14.03 × 106 ×Fc ×d4 L²

WHERE:

Fc = End Fixity Factor
0.25 for one end fixed, one end free
1.00 for both ends supported
2.00 for one end fixed, one end simple
4.00 for both ends rigid
d = Root Diameter of Screw (inch)
L = Distance between nut and load carrying bearing (inch)

The column strength chart on page 16 may be used to verify that the screw can carry the required load without buckling.

The charts show the theoretical limitations of each screw on a separate line. The lines are limited horizontally by the slenderness ratio and vertically by the maximum static capacity of the bronze nut. Actual load is limited by the maximum nut capacity.

If the selected screw does not meet compression load criteria, consider the following options:

1. Change end fixity (e.g. simple to fixed)
2. Design to use screw in tension
3. Increase screw diameter

## PV Value

For plastic nuts, the PV value needs to be checked (see the PV load definition page 11). The operating load values for the plastic nuts are based on a pressure of 1,250 lb per square inch. Any loads less than the operating load can be evaluated by using the following formula:

V is the relative speed between the nut and the screw in feet per minute. V can be calculated by using the following formula:

 V = Outside Dia. (in) of the Screw × π × Operating Speed (rpm) 12

It is recommended that P × V be limited to values less than 2,700.

Figure 1