Gear pumps represent the majority of the fixed displacement machines used for flow generation in fluid power systems. In this context, the paper presents a review of the different methodologies used in the last years for the simulation of the flow rates generated by gerotor, external gear and crescent pumps. As far as the lumped parameter models are concerned, different ways of selecting the control volumes into which the pump is split are analyzed and the main governing equations are presented. The principles and the applications of distributed models from 1D to 3D are reported. A specific section is dedicated to the methods for the evaluation of the necessary geometric quantities: analytic, numerical and Computer-Aided Design (CAD)-based. The more recent studies taking into account the influence on leakages of the interactions between the fluid and the mechanical parts are explained. Finally the models for the simulation of the fluid aeration are described. The review brings to evidence the increasing effort for improving the simulation models used for the design and the optimization of the gear machines.

Models for Flow Rate Simulation in Gear Pumps: A Review

A new curve for application to the rotor profile of rotary lobe pumps

Numerical analysis of theoretical flow in external gear machines

Discrete optimization of a gear pump after tooth root undercutting by means of multi-valued logic trees

To improve the system performance of hydraulically assisted mechatronic systems, the research investigates the instantaneous pressure of the meshing action in the external gear pumps and motors. The undesired large pressure overshoots or spikes could be excited by virtue of the sudden volumetric change of meshing pockets. In practice, the spikes cause the gear machines to be noisy, inefficient, and have fatigue problems. The study employs the optimization theorem to analyze the nonlinear dynamical equations to define the instantaneous flow area overlapped by the wear-plate profiles and control volumes. The approach can also be applied to determine the backlash area to avoid large pressure variations between two meshing volumes. System noise may consequently be reduced and the mechanical efficiency is improved in gear machines. However, the volumetric efficiency may be compromised. Thus, all these issues have to be considered to achieve the optimal design.

The Optimal Design in External Gear Pumps and Motors

Kinematic flowrate characteristics of external spur gear pumps using an exact closed solution

To increase volume displacement is always concerning in designing external gear pumps (EGPs). Therefore, an approach of optimization analysis intending to enhance their displacement capability is proposed in this study. Through that, design parameters of the spur gears in the pumps are systematically resulted to achieve their optimal volume displacements. Parametrically, a CAD model to visualize the designed gear of the optimal design is also created. Firstly, the study derives tooth profile equations by using the coordinate transformation and equation of meshing for gears on a rack cutter profile. Then, an analytic formula represented the enveloping area by an involute curve is derived. Next, volumes of output and trapped backflow of the EGP are achieved. Therefore the net output volume can be calculated accurately and efficiently. After that, the optimization analysis to maximize the volume displacement is performed. Through that, optimal design parameters for the pumps are achieved under assigned constraints for considerations of design and manufacturing. Additionally, influences of module, pressure angle, and addendum correction factor for the gears in the pumps on their displacement capability are also investigated. Additionally, flowrate fluctuation characteristics under different pressure angles of gears are finally discussed.

Wun Chuan Lian

Papers

Kinematic flowrate characteristics of external spur gear pumps using an exact closed solution

An Optimization Approach to the Displacement Volumes for External Spur Gear Pumps