Abstract. 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.
Purpose
This paper aims to present airworthiness considerations regarding a shaft of an electric motor. A fatigue lifetime prediction analysis based on one-step load spectrum is performed during high-cycle fatigue. Time-dependent normal and shear stress components are estimated using a high-fidelity digital twin built in Siemens PLM Nx Nastran as a finite element model (FEM). Linear and centrifugal acceleration as well as gyroscopic moment, motor torque, propeller thrust and thermal loads are considered. The equivalent cyclic degree of utilisation and a safety margin against the slip of a press-fitted shaft to rotor hub connection is estimated.
Design/methodology/approach
A load analysis using FEM is presented. The numerically obtained results are verified on an analytical and a semi-empirical basis.
Findings
The shaft of the electric motor can sustain 74 h of operation if burdened with aerobatic loads. Its load capacity equals 48% for the overall safety factor of 2.25.
Practical implications
The paper presents a specific, easily identifiable advance in knowledge that can be applicable in safety flight analysis issues.
Originality/value
The work presents a rotor of a novel lightweight electric motor for aircraft applications, which is a successor of the electric motor set recently in Extra 330E. The work delivers a computational estimation of the shaft life.
A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presented at the beginning of the transformation.
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