Physical Modeling of a Water Hydraulic Proportional Cartridge Valve for a Digital Twin in a Hydraulic Press Machine

Abstract

Digital twins are an emerging technology that can be harnessed for the digitalization of the industry. Steel industry systems contain a large number of electro-hydraulic components as proportional valves. An input–output model for a water proportional cartridge valve was derived from physical modeling based on fluid mechanics, dynamics, and electrical principles. The valve is a two-stage valve with two two/two-way water proportional valves as the pilot stage and a marginally stable poppet-type cartridge valve as the main valve. To our knowledge, this is the first time that an input–output model was derived for a two-stage proportional cartridge valve with a marginally stable main valve. The orifice equation, which is based on Bernoulli principles, was approximated by a polynomial, which made the parameter estimation easier and modeling possible without measuring the pressure of the varying control volume, in contrast with previous studies of similar types of valves situated in the pilot stage part of the valve. This work complements previous studies of similar types of valves in two ways: (1) data were collected when the valve was operating in a closed loop and (2) data were collected when the valve was part of a press mill machine in a steel manufacturing plant. Model parameters were identified from data from these operating conditions. The parameters of the input–output model were estimated by convex optimization with physical constraints to overcome the problems caused by poor system excitation. For comparison, a simple linear model was derived and the least squares method was used for the parameter estimation. A thorough estimation of the parameters’ relative errors is presented. The model contains five parameters related to the design parameters of the valve. The modeled position output was in good agreement with experimental data for the training and test data. The model can be used for the real-time monitoring of the valve’s status by the model parameters. One of the model parameters varied linearly with the production cycles. Thus, the aging of the valve can be monitored.