Über Die Stabilität Von Schwingungen in Gelenkgetrieben
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Die dynamischen Untersuchungen von Gelenkgetrieben f�hren u. a. zu der Frage nach den Schwingungen der als elastisch anzusehenden Glieder und Wellen. So wurden die Gestellschwingungen untersucht [1], ferner die Schwingungen, die bei elastischer Bettung der Lager oder bei Beachtung der Biegungselastizit�t von An-und Abtriebs- wellen auftreten [2], die Torsionsschwingungen in An-und Abtriebswellen unter ver- einfachenden Annahmen [1], bei genauer Durchrechnung und experimenteller Pr�fung [3]. Schlie lich wurde auch die Koppel als elastisches Glied betrachtet, und zwar gewisserma en als L�ngsfeder aufgefa t [4] - aber bereits 1939 hat GEIGER [5] rein versuchsm� ig und qualitativ die Schwingungen betrachtet, welche bei sehr weichen elastischen Gliedern einer Kurbelschwinge auftreten. Es wurde hieran anschlie end und ausgehend von den Biegungsschwingungen eines Stabes darauf hingewiesen, da man die einzelnen Glieder, insbesondere die Koppel als Kontinuum betrachten mu und die besonders interessierenden Biegeschwingungen auf eine partielle Differential- gleichung 4. Ordnung f�hren m�ssen [6]. Sp�ter wurde das Problem erneut aufgegriffen, die Differentialgleichung aufgestellt und ihre L�sung unter vereinfachenden Annahmen angegeben [7,8]. Dabei wurde insbesondere darauf hingewiesen, da in der Differential- gleichung zeitlich ver�nderliche Koeffizienten auftreten. W�hrend der genauen Untersuchung fr�her gro e Schwierigkeiten entgegenstanden, da weder elektronische Digital-noch Analogrechner zur Verf�gung standen, hat sich die Situation in dieser Beziehung grundlegend ge�ndert. So wurde vom Unterzeichneten angeregt, die Differentialgleichung f�r die Biegungsschwingungen bei Gelenkgetrieben aufzustellen, zun�chst unter Beachtung der Elastizit�taller drei bewegten Glieder, aber unter Betonung der Schwingungen und der Stabilit�tsfragen der Koppel [9]. Die vorliegende Arbeit meines Mitarbeiters Dr. -Ing. H.
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