Energy harvesting through pendulum motion and DC generators

Abstract In this paper a mathematical model was found, and numerical results obtained for the pendulum behavior when coupled to a DC generator. A simple pendulum is vertically excited on its support and consequently exhibiting oscillations and rotations. The motion of the pendulum spins the axis of a DC generator and inducing a current. The dynamic model involving the generator and the pendulum dynamics is developed and analyzed in this article. Bifurcation diagrams demonstrate doubling-period and saddle-node bifurcations with the chaos. The presence of chaos is verified by the Lyapunov exponents applied on the time series of the pendulum speed and position. Nonideal interactions of a DC motor with a pendulum by a crank-shaft-slider mechanism is analyzed and compared with an ideal excitation of the pendulum.

摘要 本文建立了直流发电机（DC generator）耦合摆的数学模型，并给出了其运动行为的数值计算结果。单摆的支座受到垂直方向激励，因此摆体可产生摆动与旋转运动。摆体的运动将带动直流发电机的转轴旋转并产生感应电流。本文构建并分析了包含发电机动力学与摆运动学的耦合动力学模型。分岔图展示了系统存在伴随混沌现象的倍周期分岔与鞍结分岔。通过对摆的速度与位置时间序列计算李雅普诺夫指数（Lyapunov exponents），验证了系统混沌的存在性。本文还分析了通过曲柄滑块机构（crank-shaft-slider mechanism）实现的直流电机与摆的非理想耦合作用，并将其与单摆的理想激励工况进行了对比。