Abstract
The conversion of rotary to translational motion in a lead screw system occurs at the meshing lead screw and nut threads. The contacting threads slide against each other creating a friction force opposing the direction of motion. The three main friction-induced instability mechanisms in dynamical systems were introduced in Chap. 4. In this chapter, the role of the velocity-dependent friction coefficient on the stability of lead screw systems is studied. We have seen in Sect. 4.1 that a decreasing coefficient of friction with relative sliding velocity can effectively act as a source of negative damping causing instabilities that lead to self-excited vibration. The 1-DOF model of Sect. 5.3 is used in this chapter, which captures all the essential features of the lead screw system dynamics pertaining to the negative damping instability mechanism.
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Notes
- 1.
In chapter 8, it will be shown that in systems with constant coefficient of friction, there are situations where a different instability mechanism can lead to negative damping instability.
- 2.
Violation of this inequality also leads to instability, which is known as the “kinematic constraint instability mechanism.” This instability mechanism is the subject of Chap. 8.
- 3.
See Sect. 3.6.
- 4.
See the footnote on page 36.
- 5.
This is the consequence of the initial assumption \(\Gamma\;>\;0.\)
- 6.
For simplicity of notation, from this point on, prime denotes differentiation with respect to ϕ.
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Vahid-Araghi, O., Golnaraghi, F. (2010). Negative Damping Instability Mechanism. In: Friction-Induced Vibration in Lead Screw Drives. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1752-2_6
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DOI: https://doi.org/10.1007/978-1-4419-1752-2_6
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Publisher Name: Springer, New York, NY
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