Working with Critical Speeds and Lead Screws

There are a variety of factors that must be considered before screw selection is determined in any type of application. One factor that should not be overlooked when it comes to selecting lead screws is critical speed. Lead screws, like any object in our environment, have a natural frequency.

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There are a variety of factors that must be considered before screw selection is determined in any type of application. One factor that should not be overlooked when it comes to selecting lead screws is critical speed. Lead screws, like any object in our environment, have a natural frequency. When an object is excited at its natural frequency it will vibrate excessively. Critical speed is the rotational speed in revolutions per minute (rpm’s) that matches the screw’s natural frequency, thus causing excessive vibration.

At what point in the screw selection process should critical speed be determined? Critical speed is typically considered after the load, speed, length and end fixity are identified. Here is a quick overview of these factors:

EndFixity-acmeLoad: Choices include dynamic, static, reaction forces, and any other external forces that may have an impact on the screw itself.

Speed: The travel rate, or linear speed of the lead nut. The travel rate is the is the rpm of the screw multiplied by the lead of the screw.

Length: This is the unsupported length of the screw itself (distance between bearing supports).

End Fixity: This refers to how each end of the screws is supported. Each end of a screw can have a different type of end fixity. The following are some common types of end fixity.

  • Free – no bearing support, the end of the screw is “floating” in space
  • Simple - single bearing support
  • Fixed - multiple and spaced bearings

In addition to the above factors, critical speed is also impacted by shaft straightness and assembly alignment. Therefore it is recommended that the maximum speed of the screw does not exceed 80% of the calculated critical speed.

(It is also worth noting that the resonance of the screw will occur no matter the screw orientation or system design. So it doesn't matter if you're dealing with a vertical or horizontal orientation or even if the system is designed so that the nut is driven and the screw translates - resonance will occur.)

Below, you'll see the formula for calculating critical speed in rpm:

N=

Cs X 4.76 X 106 X d

L2

Where:

"N" is the critical speed in (rpm)

"" refers to the root diameter of the screw (inches)

"L" is the length between bearing supports (inches)

"Cs" is the end condition factor

0.36 - for one end fixed/one free
1.00 - for both ends simple
1.47 - for one end fixed/one end simple
2.23 - for both ends fixed 

A common question that we often get asked here at Helix Linear is what should be done if a selected screw fails to meet critical speed criteria. If this is the case, there are several options that can be considered.

  • Increase the screw lead: This will allow the same translation speed of the nut with reduced rpm
  • Modify the end fixity: Increasing the rigidity of the system. For example, going from simple to fixed support(s) increases the critical speed
  • Increase the screw diameter

When it comes to selecting lead screws for your application, do not neglect critical speed when making your determination. It is very important to operate your lead screw below it’s critical speed for optimum system performance and life.

Download this handy engineer's reference guide to critical speeds in lead screws - inch and metric sizes. We think you'll find it useful.