Research Papers

The Theoretical Volumetric Displacement of a Check-Valve Type, Digital Displacement Pump

[+] Author and Article Information
Noah Manring

Mechanical and Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: ManringN@missouri.edu

Christopher Williamson

Danfoss Power Solutions,
Ames, IA 50010
e-mail: cwilliamson@danfoss.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 11, 2018; final manuscript received September 5, 2018; published online November 22, 2018. Assoc. Editor: Youngsu Cha.

J. Dyn. Sys., Meas., Control 141(3), 031014 (Nov 22, 2018) (8 pages) Paper No: DS-18-1184; doi: 10.1115/1.4041713 History: Received April 11, 2018; Revised September 05, 2018

This paper has been written to develop closed-form equations for describing the theoretical displacement of a check-valve type, digital displacement pump. In theory, the digital displacement pump is used to alter the apparent volumetric displacement of the machine by short circuiting the flow path for reciprocating pistons within the machine that would ordinarily deliver a full volumetric flow rate to the discharge side of the pump. The short circuiting for the pistons is achieved by opening and closing a digital valve connected to each piston chamber at a desired time during the kinematic cycle for each reciprocating piston. Experience with these machines has shown that the expected volumetric displacement for the machine tends to decrease with pressure. This paper presents a theoretical explanation for the reduced volumetric displacement of the pump and quantifies the expected behavior based upon the digital valve command, the residual volume of fluid within a single piston chamber, and the fluid bulk modulus-of-elasticity. In summary, it shown that the apparent volumetric displacement of the machine may be reduced by as much as 10% for high-displacement commands and by as much as 30% for low-displacement commands.

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Grahic Jump Location
Fig. 1

An operational schematic of the digital displacement pump

Grahic Jump Location
Fig. 2

Nondimensional reduction in displacement for x=0.2, 0.4, …, 1.0 and Vt/ΔV=1.3 as the pressure drop increases

Grahic Jump Location
Fig. 3

Percent reduction in displacement for x=0.2, 0.4, …, 1.0 and Vt/ΔV=1.3 as the pressure drop increases



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