The parallel two-dimensional piston (2D piston) flowmeter is a novel kind of positive displacement flowmeter that has been recently invented and proposed by our research group. Following an overview of the working principle of this flowmeter, a modified mathematic model was carefully established in this paper based on the analysis of the shortcomings of the presented primary model. The churning loss, as the first of two ignored parts in the previous research, is caused by the rollers rotation in oil, and it is considered a part of the torque balance equation in the pressure loss model. Besides, the flow rate of the transient leakage, which comes from the change in the leakage flow rate equation when the 2D piston rotates at a specific angle, was analytically modeled and added to the flow rate distribution equation. By comparing the experimental results from the last study, the modified mathematical model showed to be precise and became more suitable for predicting the flowmeter's performance and enhancing its measuring accuracy.

并联二维活塞（2D活塞）流量计是我们研究小组最近发明并提出的一种新型的容积式流量计。在对该流量计的工作原理进行了概述之后，本文在分析了所提出的主要模型的缺点的基础上，精心建立了一个改进的数学模型。作为先前研究中两个被忽略的部分中的第一个，搅拌损失是由油中的滚子旋转引起的，在压力损失模型中，搅拌损失被视为扭矩平衡方程的一部分。此外，对瞬态泄漏的流量进行了分析建模，该瞬态泄漏的流量是由于2D活塞旋转特定角度时泄漏流量方程式的变化而引起的，并将其添加到流量分布方程式中。