Thermal optimization of a tubular linear oscillating motor for directly driven LEHA application

ABSTRACT

Efficient cooling method is important to improve the output performance of electric motors. This paper presents three kinds of cooling methods for tubular linear oscillating motor (TLOM) in directly driven linear electro-hydrostatic actuator (LEHA) applications, i.e., cooling with heat sinks, water cooling and forced-air cooling, and compares the cooling efficiency in quantity systematically. The result shows that heat sink is suitable for the TLOM. Then, a detailed thermal model is proposed to analyze the temperature characteristics of the TLOM with/without heat sinks. Based on the thermal model, an optimized motor structure with a parabolic-profile heat sink is proposed, which helps the heat dissipation significantly. The heat dissipation property is validated with numerical results. Finally, thermal experiments under different current inputs are conducted, and the good agreement of experimental results with the thermal model and simulation results confirms the validity of the thermal model and the design of the linear machine.

Nomenclature

a	=	constant in correlation
A	=	cross-section area, m2
b	=	constant in correlation
c	=	constant in correlation
cp	=	fluid-specific heat capacity, J/(Kg · °C)
d	=	equivalent diameter of vent, m
g	=	acceleration of gravity, m/s2
Gr	=	Grashof number
h	=	convection heat transfer coefficient, W/(m2 · °C)
Ie	=	current input of coil, A
k	=	fluid thermal conductivity, W/(m · °C)
Kc	=	volume proportionality coefficient
L	=	characteristic length, m
Lc	=	length of the cylinder, m
Nu	=	Nusselt number
PCui	=	heat source (i = A, B … , H) of part i, W
Pr	=	Prandtl number
Re	=	electric resistance of the coil, Ω
Ri	=	inner radius of the cylinder, m
Ra	=	thermal resistance including conduction and convection of heat sinks, °C/W
Rij	=	element thermal resistance of part i, (i = A, B … , H; j = 0,1,2 …), °C/W
Ro	=	outside radius of the cylinder, m
t	=	thickness of the element, m
Tambient	=	ambient temperature, °C
Tij	=	node temperature of part i, (i = A, B … , H; j = 0,1,2 …), °C
T1	=	average winding temperature of one separate sectional part, °C
T2	=	average air gap temperature of one separate sectional part, °C
ΔT	=	temperature difference, °C
u	=	fluid velocity, m/s
v	=	kinematic viscosity, m2/s
λ	=	thermal conductivity, W/(m · °C)
β	=	coefficient of cubical expansion
ρ	=	fluid density, Kg/m3

Nomenclature

a	=	constant in correlation
A	=	cross-section area, m2
b	=	constant in correlation
c	=	constant in correlation
cp	=	fluid-specific heat capacity, J/(Kg · °C)
d	=	equivalent diameter of vent, m
g	=	acceleration of gravity, m/s2
Gr	=	Grashof number
h	=	convection heat transfer coefficient, W/(m2 · °C)
Ie	=	current input of coil, A
k	=	fluid thermal conductivity, W/(m · °C)
Kc	=	volume proportionality coefficient
L	=	characteristic length, m
Lc	=	length of the cylinder, m
Nu	=	Nusselt number
PCui	=	heat source (i = A, B … , H) of part i, W
Pr	=	Prandtl number
Re	=	electric resistance of the coil, Ω
Ri	=	inner radius of the cylinder, m
Ra	=	thermal resistance including conduction and convection of heat sinks, °C/W
Rij	=	element thermal resistance of part i, (i = A, B … , H; j = 0,1,2 …), °C/W
Ro	=	outside radius of the cylinder, m
t	=	thickness of the element, m
Tambient	=	ambient temperature, °C
Tij	=	node temperature of part i, (i = A, B … , H; j = 0,1,2 …), °C
T1	=	average winding temperature of one separate sectional part, °C
T2	=	average air gap temperature of one separate sectional part, °C
ΔT	=	temperature difference, °C
u	=	fluid velocity, m/s
v	=	kinematic viscosity, m2/s
λ	=	thermal conductivity, W/(m · °C)
β	=	coefficient of cubical expansion
ρ	=	fluid density, Kg/m3