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Heat flux estimation in journal bearings using inverse heat transfer method

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Abstract

Journal bearings are used in industrial equipment at high rotational speed. Normal and also fault operations of bearing increase the temperature of the bearing. Estimation of heat flux on the inner surface of the bearing and prediction of temperature of the bearing can prevent the damage to the bearing. In this research, these quantities are estimated in normal operation by an inverse method. The sequential function specification method is applied and the best number of temperature sensors and their positions are obtained. The temperature sensors are embedded in the bearing. The results show that the accuracy of heat flux estimation has a district relation with the number and the position of the sensors and also with the measurement frequency.

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Abbreviations

L:

Length of bearing

C r :

Radial clearance

C :

Specific heat

e :

Eccentricity

e bias :

Bias error

e rms :

Root mean square error

e var :

Variance error

H 1 :

Ambient heat transfer coefficient

H 2 :

Oil heat transfer coefficient

k :

Thermal conductivity

m :

Time index

N m :

Number of time steps

N s :

Number of sensors

N p :

Number of segments of unknown heat flux

O B :

Center of the journal bearing

O S :

Center of the shaft

P :

Pressure

q :

Heat flux vector

qin :

Inlet heat flux

R :

Radial coordinates

\({R}_{B_i}\) :

Inner radius of the journal bearing

\({R}_{B_O}\) :

Outer radius of the journal bearing

R S :

Shaft radius

r :

Number of future time steps

Sh :

Heat source

T :

Vector of calculated temperatures

\(\hat{\boldsymbol{T}}\) :

Calculated temperature

T air :

Ambient temperature

T s :

Supply oil temperature

T 0 :

Initial temperature

t :

Time

t + :

Dimensionless time

u r :

The velocity component in r

u θ :

The velocity component in θ

X :

Sensitivity coefficient matrix

X + :

Dimensionless sensitivity coefficient matrix

Y :

Measured temperature

Z + :

Kind of dimensionless sensitivity coefficient matrix

∆t :

Time step

θ:

Tangential coordinate

μ:

Dynamic viscosity as a function of temperature

μ0 :

Dynamic viscosity at 303 K

ρ :

Density

σ:

Standard deviation of fluctuation

ψ :

The dissipation function

φ :

Attitude angle

ω :

Rotational speed

α :

Coefficient of thermal expansion

i:

Time index

j:

Sensor index

mean:

Measured

opt:

Optimum

S:

Shaft

B:

Bearing

f:

Fluid

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran

    Davoud Alibeyki & Reza Mehryar

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  1. Davoud Alibeyki
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  2. Reza Mehryar
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Correspondence to Reza Mehryar.

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Alibeyki, D., Mehryar, R. Heat flux estimation in journal bearings using inverse heat transfer method. Heat Mass Transfer 57, 605–615 (2021). https://doi.org/10.1007/s00231-020-02959-x

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