When the spring pointer mechanism exhibits a hard characteristic, as the damping of the system increases, the common amplitude value of the pointer gradually increases, and the resonance range also expands; when the spring pointer mechanism exhibits soft characteristics, as the damping of the system increases, The dynamic error of the pointer increases, but when the amplitude increases to a certain extent, the frequency curve tends to a line.
Hard stiffness amplitude frequency response soft stiffness amplitude frequency response hard stiffness force amplitude response soft stiffness force amplitude response can get the following characteristics (1) by, can get the following characteristics: when the spring pointer mechanism is machine hard stiffness, with the system As the stiffness increases, the frequency curve gradually moves to the upper right. When the spring pointer mechanism exhibits soft stiffness, the resonance curve gradually moves to the upper left. When the system stiffness increases, its common amplitude value also increases. Large, and the resonance range has also expanded.
(2) Features: When the spring pointer mechanism exhibits a hard characteristic, as the stiffness of the system increases, the frequency curve shifts to the right, but to a certain amplitude, the curve is similar to the soft stiffness. When the spring pointer mechanism exhibits soft characteristics, as the system damping increases, the dynamic error of the pointer increases.
Since the frequency curve obtained by the variation of the external excitation F0 or F is similar to the curve obtained by the variation of the system stiffness k, it will not be discussed here. The soft stiffness force amplitude response can be obtained from 05. (1) There are only two resonance curves of the hard stiffness and soft stiffness force measuring mechanisms. And as the absolute value of the harmonic value increases, the curve generally moves to the right.
(2) The resonance characteristics of the rigid stiffness measuring force mechanism are completely opposite to those of the soft stiffness measuring force mechanism. The resonance characteristic of the force measuring mechanism with a hard stiffness corresponding to a value greater than zero is the same as the resonance characteristic of the force measuring mechanism with a soft stiffness corresponding to a harmonic value less than zero. vice versa.
(3) When the force measuring mechanism exhibits hard stiffness, when R>0, the common amplitude value increases with the increase of the harmonic adjustment value; when R<0, the common amplitude value decreases with the increase of the harmonic adjustment value, and the resonance curve The change exhibits an approximately linear change. When the spring force measuring mechanism exhibits a soft stiffness, it has properties opposite to the hard stiffness.
Conclusion The Lagrangian equation in analytical mechanics is used to establish a class of differential equations for a damped spring force-measuring mechanism subjected to harmonic excitation. This equation is a typical Dffuing-Mathieu equation, applying multi-scale method of nonlinear vibration. Three superharmonic resonance analyses were performed. Some amplitude-frequency response and force-amplitude response curves are obtained by the parameters such as the stiffness of the system and the external excitation harmonics. The curves are analyzed in combination with the actual situation, and some conclusions are obtained. The conclusions of this paper have guiding significance for the dynamic design of such institutions.
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