Methodologies towards approximating the volume displacement by a roller in a roller-type peristaltic pump

Abstract

The roller volume displacement (RVD) is the volume that a roller displaces within the tube of a roller-type peristaltic pump when it is being occluded by the roller, not to be confused with the pump volume displacement. The RVD is generally measured in order to model and simulate the pump by means of first principle modeling. The rate of change of this volume displacement (referred to as the roller induced flow rate) gives rise to the pulsatile flow rate and pressure commonly associated with roller-type peristaltic pumps. In addition to this, the volume displaced by the roller reduces the amount of transported fluid per revolution of the motor, effectively altering the average volume flow rate of the pump. The ability to obtain this flow rate without physically measuring it is advantageous for both design and modeling applications. This paper provides methods of approximating the volume displaced by the roller in a roller-type peristaltic pump. The approximations are derived from the pump and process tube dimensions. Several methods of varying complexity and accuracy are provided for approximating the maximum volume displaced by the roller. An angle dependent approximation allows for approximating this volume for both partial occlusion and compressed occlusion of the tube. The approximations are validated by testing the RVD of a roller-type peristaltic pump with specified geometries. Validation is achieved by means of measuring the RVD of the physical pump, as well as pump volume displacement over various motor speeds and comparing these values to modeled values. Additionally, the variable occlusion approximation is used to simulate the pressure response of the pump’s inlet and outlet and compared to the same simulation using the measured RVD. The variable occlusion approximation was found to have a normalized root-mean square error (NRMSE) of 6.09% when compared to the experimental average over the entire angle of engagement. Comparing the approximated RVD simulation results to that of the measured RVD simulation results revealed an average NRMSE of 6.35% and 6.62% for the inlet and outlet pressures respectively for the entire span of simulated motor speeds.