Probabilistic Thermal and Electromagnetic Analyses of Subsea ...

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)11, 665-672Table 1. Statistical characteristic of material properties and dimensionsProperty Description Unit Mean COV Distributionk 316 Thermal conductivity of 316L stainless steel W/(mK) 15 0.06 Gaussk 440 Thermal conductivity of 440C stainless steel W/(mK) 24.2 0.06 Gaussk oil Thermal conductivity of conduction oil W/(mK) 0.111 0.02 Gaussh sea Convection heat transfer coefficient of seawater W/(m 2 K) 200 0.01 Gaussμ 440 Relative permeability of 440C stainless steel – 10000 0.05 GaussR pl Radius of plunger (see Fig. 2) m 0.0063 0.004 GaussR psi Inside radius of plunger sleeve (see Fig. 2) m 0.0065 0.003 GaussR pso Outside radius of plunger sleeve (see Fig. 2) m 0.0080 0.003 GaussR mr Radius of magnetic ring (see Fig. 2) m 0.0155 0.002 GaussU Applied voltage V 16 0.010 Gaussof variables are expressed as the product of meanvalves and Coefficient of Variations (COV).For both of the probabilistic thermal andelectromagnetic analyses, the Latin HypercubeSampling was selected for MCS due to the fact thatthis technique avoids repeating samples that have beenevaluated, and also forces the tails of a distributionto participate in the sampling process. The centralcomposite design was used to locate the samplingpoints in the design space for RSM.2 EXPERIMENTSIn order to verify the finite element analysis results,the temperature within the subsea solenoid valveand electromagnetic force as a function of air gapwere measured. Four resistance thermometer sensors(ZYWRNK-191, ZhongYiHuaShi, China) were fixedin Point A, B, C and D when the coil was wound andthe valve was installed, as shown in Fig. 2. The steadystate temperatures in the four points were measuredwhen the solenoid was energized by applied DCvoltage of 16 V in the constant temperature bath of10 °C.A static experiment was performed to measurethe relationship between the electromagnetic forceand the air gap. The applied DC power was alsosupplied by a switching power supply (RXN-3020D),which is set to 16 V. The displacement of the plungerwas determined by an eddy current displacementsensor (JX70-04-B-M16*1-75-03K), and the forcewas measure by an S-shape force sensor (PST-20).By recoding the voltage outputs of the force sensorand eddy current sensor, the relationship between themagnetic force and the air gap could be calculated.a) b) c)Fig. 4. Distributions of a) temperature, b) magnetic flux line, and c) magnetic flux density668 Cai, B. – Liu, Y. – Ren, C. – Abulimiti, A. – Tian, X. – Zhang, Y.