Various factors must be considered before lead screw or ball screw selection is determined in any 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 lead 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:
Load: Choices include dynamic, static, reaction forces, and any other external forces that may impact the screw itself.
Speed: The travel rate or linear speed of the lead nut. The travel rate 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, the 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)
"d" 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
We often get asked here at Helix Linear what should be done if a selected screw fails to meet critical speed criteria. If this is the case, several options 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 selecting lead screws for your application, do not neglect critical speed when making your determination. It is crucial to operate your lead screw below its critical speed for optimum system performance and life.