Triboelectric nanogenerators (TENGs) are superb candidates to harvest low-frequency energy from water waves, wind, and ambient vibrations. They consist of triboelectrically-charged dielectric materials in relative motion and have been realized experimentally in several configurations and geometries. In this work, we provide a detailed mathematical analysis and fast computational method for designing spherical TENG devices to realize optimal performance. The method provides a self-consistent analysis to determine the charge distribution on spherical electrodes in compliance with the physical constraint of uniform potentials over the electrode surfaces. It is shown that the difference between the assumptions of a uniform potential vs. uniform charge density on electrodes for spherical TENG model parameters increases with the spatial dimensions of the electrodes relative to other characteristic dimensions of the TENG. For typical spherical TENGs the difference in harvested energy can be several percentages. A major benefit of the present model of a spherical TENG is its applicability to design large TENG network systems for which 3D methods, such as the finite element method, are computationally far too demanding.

摩擦纳米发电机 (TENG) 是从水波、风和环境振动中获取低频能量的绝佳候选者。它们由相对运动的摩擦带电介电材料组成，并已在多种配置和几何形状中通过实验实现。在这项工作中，我们为设计球形 TENG 器件以实现最佳性能提供了详细的数学分析和快速计算方法。该方法提供了一种自洽分析，以确定球形电极上的电荷分布，符合电极表面上均匀电位的物理约束。结果表明，均匀电位假设与均匀电位假设之间的差异。球形 TENG 模型参数的电极上均匀电荷密度随着电极的空间尺寸相对于 TENG 的其他特征尺寸而增加。对于典型的球形 TENG，收集能量的差异可能是几个百分比。目前的球形 TENG 模型的一个主要优点是它适用于设计大型 TENG 网络系统，其中 3D 方法（例如有限元方法）在计算上的要求太高了。