Re-derivation of Laplace operator on curvilinear coordinates used for the computation of force acting in solenoid valves

• Autorzy: Goraj R.

Identyfikatory

DOI

10.17512/jamcm.2016.1.03

• Języki publikacji: EN

Abstrakty

EN

This article presents two mathematical methods of derivation of the Laplace operator in a given curvilinear co-ordinate system. This co-ordinate system is defined in the area between the armature and the yoke of a high-speed solenoid valve (HSV). The Laplace operator can further be used for the numerical solving of the Laplace’s equation in order to determine the electromagnetic force acting on the armature of the HSV. In further steps the author derived an expression for the gradient and the vector surface element of the armature side surface in this co-ordinate system. The solution of the derivation was compared with one other solution derived in the past for the computational investigations on HSVs.

Słowa kluczowe

EN

Laplace operator; solenoid valve; armature; electromagnetic force

PL

operator Laplace'a; zawór elektromagnetyczny; armatura; siła elektromagnetyczna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 1
• Strony: 25--38
• Opis fizyczny: Bibliogr. 8 poz., rys., tab.

Twórcy

autor

Goraj R.

• private means Erlangen, Germany

Bibliografia

• [1] Vogel R., Numerische Berechnung der Ankerreibung eines elektromagnetischen Schaltventils, Studienarbeit, Universität Dortmund, Dortmund 2006.
• [2] Peng L., Liyun F., Qaisar H., De X., Xiuzhen M., Enzhe S., Research on key factors and their interaction effects of electromagnetic force of high-speed solenoid valve, The Scientific World Journal 2014, p. Article ID 567242.
• [3] Huber B., Ulbrich H., Modeling and experimental validation of the solenoid valve of a common rail diesel injector, SAE Technical Paper 2014, 2014-01-0195.
• [4] Shahroudi K., Peterson D., Belt D., Indirect adaptive closed loop control of solenoid actuated gas and liquid injection valves, SAE Technical Paper 2006, 2006-01-0007.
• [5] Bronstein I.N., Semendjajew K.A., Musiol G., Mühlig H., Taschenbuch der Mathematik, Edition Harri Deutsch, Berlin 2000.
• [6] Epstein M., Differential Geometry, Basic Notions and Physical Examples, International Publishing: Springer, 2014.
• [7] McInerney A., First Steps in Differential Geometry, Riemannian, Contact, Symplectic, Springer, New York 2013.
• [8] Nguyen-Schäfer H., Schmidt J.-P., Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, Springer, Berlin-Heidelberg 2014.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.