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Existence and Uniqueness Problem

Consider the interacting lead screw and nut pair shown in Fig. 5.3. The equation of motion of this system is given by (5.13)  [Pg.135]

Vahid-Araghi and F. Golnaraghi, Friction-Induced Vibration in Lead Screw Drives, 135 DOI 10.1007/978-l-4419-1752-2 8, Springer Science-I-Business Media, LLC 2011 [Pg.135]

Now we consider the possibility of Painleve s paradoxes for the equation of motion of the lead screw drive given by (8.1). Define [Pg.136]

Note that we have 0 and F 0. Assume that the system s parameters are selected such that F+ 0 which requires that 0 and tan X + 7. For to be positive, coefficient of friction must be large enough such that /i tanA. If sgn(0)sgn(7 7 —mrni tan Ar) = 1, then (8.3) has no solution-, setting sgn(AI) = 1 in the RHS of (8.3) results in a negative contact force, and setting sgn(N) = — 1 results in a positive contact force. On the other hand, if sgn(0) sgn(P7— tanAr) = — 1, then (8.3) has two distinct solutions  [Pg.136]


The minimum conditions are recast into different equivalent forms in Section lOJ. Pragmatically and disregarding the theoretical existence and uniqueness problems, the reconciliation problem is reduced to finding some i obeying the conditions (10.3.11). We then expect that this x, making the constraint equation solvable by (10.3.11a), provides also the minimum (10.1.31) thus... [Pg.409]

It has been shown that existence and uniqueness problems arised even for a single-degree-of-freedom system and the conditions under which such problems occur have been determined. A graphical method has been... [Pg.288]


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