三线摆方程简化及其共振问题研究

对于广泛用于测定不规则刚体转动惯量的三线摆方法,讨论了其方程的适用性和避免共振的条件。通过对扭振方程的推导与分析,得出了扭振方程线性化的条件;揭示了三线摆结构参数、被测刚体惯性与几何参数与对方程线性化的影响。通过比较扭振频率与摆振频率,得出了二者耦合的条件。这种耦合将导致惯性参数测试试验失败。结合一个测试实例,具体分析了发生振动耦合时被测刚体惯性参数与系统设计参数之间的关系,由此进一步阐述了三线摆设计与应用中的注意事项。

Simplification of Governing Equation of a Trifilar Pendulum and its Resonance Problem

For a trifilar pendulum, which is widely used to identify the inertial parameters of odd-shaped rigid bodies or structural assemblies, applicability of the governing equation and the conditions to avoid resonance are addressed. The governing equation is systematically discussed, focusing on equation simplification and the condition to ignore translational vibration. A set of clear conditions are thus obtained, which are in terms of design parameters of the trifilar pendulum, and the inertial and geometric parameters of the body under test. Under that condition, the governing equation can be linearized to a form that is now widely used for inertial parameter identification. With explicit formulae about frequencies of torsional and transversal vibration, which are typical vibration modes of any trifilar pendulum, a condition is also presented under which the two forms of vibration will be coupled. This coupling will destroy experiments due to resonance. A practical example is given to demonstrate the requirements for design parameters of the trifilar pendulum and the inertial and geometric properties of the body under test, so as to avoid resonance. Guidance for designing and applying a trifilar pendulum is listed.