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A shape memory effect swashplate heat engine
Volume 7. number 3
MATERIALS LETTERS
September 1988
A SHAPE MEMORY EFFECT SWASHPLATE HEAT ENGINE
A.P. JARDINE ’ H.H. Wills Phvsics Laboratory, University of Bristol, Bristol BS8 I TL, UK Received 30 June 1988
A novel heat engine based on the shape memory effect (SME) of helical NiTi wire and utilising the swashplate geometry is described. Measurements of engine power cycled through 12°C and 80°C water baths were as high as 3 W/kg, which compare favourably with more complex SME heat engines designs.
About half of the solar radiation falling onto the earths surface is directly converted into low grade heat (temperature differences less than 100 ’ C above ambient) and is largely unused as a source of energy though the energy flux (8 x lOI W) is vast. Devices which can convert these abundant energy supplies into work will be of some importance in global energy concerns. A novel shape memory effect (SME) heat engine, the first built along swashplate principles is introduced, to exploit these low grade thermal reservoirs. The shape memory effect is a macroscopic shape change driven by a thermoelastic martensitic transformation #I. When cooled below the m~ensiti~ start temperature M,, martensitic plates composed of crystallographic twin variants of the martensitic unit cell are formed. Upon application of an external stress, the twin variant which best accommodates the elastic stress grows reversibly at the expense of the other. When the stress is removed, a strain of up to 10% can remain. Upon heating above A,, the austenitic start temperature, the twins whose growth was preferred now revert to the original orientation (the “hot shape”), thereby recovering the plastic strain, hence the realisation of shape memory. All twin variants then transform to austenite. Macroscopically, the Young modulus of the mar’ Present address: Depa~ment of Materials Science and Engineering, SUNY Stony Brook, Stony Brook, NY 11794,USA. ” An introduction to SME is given in ref. [ I], a more comprehensive source of information is ref. [ 21.
102
tensitic phase is much less than the austenitic phase due to deformation twinning to the preferred twin orientations. On heating, a large driving force is present as the deformed material transforms back to its preferred hot shape. These properties are utilised in SME heat engines. The SME alloy NiTi was chosen as its transformation temperatures are within the temperature range of the hot (80°C) and cold (1S’C) heat reservoirs, it is available in small diameter wire and it is relatively easy to set a hot shape in the form of a helix. Small diameter (0.46 mm) NiTi wire was used to promote rapid heat transfer. The time to heat this wire through the transformation was approximately 0.1 s from visual observations. On cooling, the exothermic transformation, with latent heats of transformation approaching 800 Jjmol [ 31, produced cooling times on the order 10 times longer than heating due to the difficulty in transporting heat away from the wire. Three strands of wire were braided together, thereby producing a wire of three times the force of a single wire but with the effective heat transfer properties of one wire. The braided wire was then wound and clamped on a mild steel mandril and heated to 500°C for 1 h and then furnace cooled to set the preferred hot shape in the form of a 1.10 cm diameter helix with a pitch of 0.65 cm. The swashplate geometry consists of two circular plate assemblies mounted on axles misorientated from collinearity by a small angle a!. The plates assemblies were 25.4 cm diameter, 1 mm thick Al discs bolted to 12.7 cm diameter, 4 mm thick dural flanges,
0167-577x/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 7, number
3
MATERIALS
with a moment of inertia per plate assembly (I) of 0.15 kg m2. Forty three holes per disc were drilled near the rim and identical SME NiTi helices of 2.5 turns of braided wire were inserted and bonded to the plates with epoxy. A hot water spray was located at maximum plate separation and the cold water spray 90” further along at the top of the motor. The swashplate engine is shown in fig. 1. Work was extracted from the SME in the following manner: as the motor rotated, the cold, martensitic SME helices were easily stretched axially due to plates’ misorientation. At the maximum plate gap, the helix was heated through its transformation by the hot water and attempts to contract to its preferred hot shape, though constrained by the plates. The helix was then in a higher energy state than 180” away, where the helices are relaxed, thus providing a driving force for rotation. The torque responsible for motor rotation results
LETTERS
September
1988
from the contraction of the helices having a component of force along the radius of the plates, related to the misorientation angle (Y (see fig. 2a). The SME recovery force is dependent on the wires’ extension and temperature, with the recovery force increasing with increasing helix extension [4] and decreases with increasing SME helix temperature. As the hot water stream width was x 1 cm, there were always several helices transforming though at different stages of the transformation. The instantaneous force on the plates from the transformation-staggered helices was not symmetric about the horizontal but had a net tangential component, generating the torque r, as illustrated in fig. 2b. The engine is subjected to four torques; a power torque r due to the SME helices, a dynamical frictional torque (K), a static torque from the bearings and from the helices themselves (C), and finally a loading torque (L) from which work is derived. If
Fig. 1. The SME swashplate motor, the height of the motor is 27.5 cm. For purposes of display, the source of cold water has i been rema Ived. The hc3t water SIlpply is shown, providing two streams of hot water. The SME helices arc between the plates.
103
MATERIALS LETTERS
Volume 7. number 3
September 1988
thus, the steady-state rotational speed (0,) is o,=(T-L-C)/K,
a
water
b
Fig. 2. (a) A schematic view of the engine looking down between the plates. The two discs of radius R are inclined at an angle a! to each other. When heated in an extended state, the springs generate an axial restoring force F with a radial component F,. (b) A schematic view of the engine, each small dot represents a helix. At any time, several helices will be transforming but at different strains due to the engine geometry and at different temperatures due to the differing times from immersion in the hot stream. The instantaneous radial forces are therefore different, hence there is a net tangential force, which generates the torque driving the rotation.
the helices are densely packed so that r is effectively time independent, the speed of rotation w(t) from an initial speed w. is given as #’ o(t)=wo
exp[ - (K/l)t]
+[(r-L-C)lKl{l-exp[-(K/i)ll),
(1)
tit A detailed mathematical description of the swashplate heat engine has been presented in ref. [ 51.
104
(2)
where Z,the moment of inertia of the plates, was calculated as 0.15 kg m2. The dynamic friction torque K was measured by observing the decay of the rotational speed with plates parallel, no water running, with r and L zero, and without an external load. As the motor speed decays exponentially as exp[ - (K/l)t] (from eq. (1 )), K was measured as -5.0~ 10V3 kg mz s-‘. The motor would stop after several cycles if either hot or cold water streams were interrupted. A fast stream of cold water could not rotate the misorientated plates a complete turn; convincing evidence that the motor was not acting as a water-wheel from a force imbalance between hot and cold water streams. With a m&orientation angle of 4.8” and a plate separation of 3.7 cm, motor speeds from 60 to 110 t-pm were observed with no load, the variability being due to irreproducible cooling conditions. By changing the cooling water spray, higher rotational speeds of 110 rpm were observed but were difficult to maintain or reproduce. Taking w, as 110 rpm as being representative of an optimally cooled motor, T-C was 5.76x 10e2 N m (from eq. (2)). Calculations of power-speed curves were done in parametric form for a given load. The speed is given by eq. (2 ) and the power (P) is given as P=Mgro,
(3)
where g is the gravitational constant and M is the effective mass causing the braking torque (L= Mgr) on the axle of radius r. Power measurements were made by placing a known load over the drive axis and measuring the load on a spring scale on the other side of the load. The difference between measured and actual loads gave the effective load on the engine. Power-speed curves were calculated by changing the loading torque (i.) for fixed values of r-C, K, plate separation and CLSeveral curves with different free running speeds, corresponding to different values of r- C, are shown in fig. 3. From the stated values of K and r- C, the maximum power of the motor is 166 mW at 55 rpm. To measure reproducible power-speed curves, a weak stream of cold water onto the helices at the top of the engine was employed. This impaired the ef-
Volume 7. number
MATERIALS
3
Speed
(Rpm)
Fig. 3. Power-speed relationship from eqs. (2) and (3). for (~~4.8’. Maximum power is 166 mW at 55 rpm from the observed maximum free-running speed ( 110 t-pm) performance of the engine. The observed power-speed curve for the SME swashplate motor was consistent with that predicted for free-running speed of 60 rpm. The large error bars at low revolutions are due to an unaccounted long period oscillation of speed with time. The open circle denotes the maximum observed power using irreproducible cooling conditions.
fkiency of the cooling as reproducible speeds of only 60 rpm could be obtained for the free-running engine. As shown in fig. 3, the motor performance was consistent with that predicted for I”-- Cof 3.14X 10-l N m, with peak performance a factor of 3.5 lower than for the engine free-running at 110 x-pm. However, using unstable cooling spray arrangements, power readings of 0.14 W at 30 rpm were recorded corresponding to a power density of 3 W/kg of NiTi. This value corresponds to a free-running speed of 120 rpm (r-Cz6.23~ lo-’ N m) in fig. 3. Evidently, the manner in which the helices were cooled was important. Other SME engines designs have been reviewed elsewhere [ 6,7 1. By way of comparison, the best motors to date such as Banks’ offset crank engine [ 81 gave 0.23 W at 69 rpm. Another by Hockstein [9] gave 1O-20 W at 70 rpm; a maximum power density
LETTERS
September
1988
of 133 W/kg. Turbine SME heat engines are reported to produce 0.5 W at 2500 t-pm [ 5 1. The viability of SME Nil-i swashplate heat engines has been demonstrated. Although the power measured was low, improvements in the method of applying cooling water will increase performance. Advantages inherent in the swashplate design are the intrinsic simplicity of the engine construction and the low local strains on the SME helices. (As a rule of thumb, the greater the strain per cycle, the greater the number of dislocations generated per cycle and the faster the helix fails to transform due to workhardening.) A more rigorous physical model of the engine producing more efficient designs is desired to evaluate the true potential of these engines. Power densities of 30 W/kg would not be an unreasonable expectation for these motors. The author is grateful to Mr. Harry Young for construction of the motor and to Dr. Ken Ashbee, Dr. Jeff Sargent and Dr. David Hanstead for helpful advice. The author is also grateful for sponsorship by the British Gas Corporation under a British Gas Scholarship.
References [ 1] L. McDonald
Schetky. Sci. Am. 241 (November 1979) p. 68. [ 2 ] 1. Perkins. Shape memory effects in alloys (Plenum Press, New York, 1975). [3] KMelton and 0. Mercier, J. Appl. Phys. 50 ( 1979) 5747. [4] A.A. Golestaneh, Acta Metall. 28 ( 1980) 1427. [ 51A.P. Jardine. Ph.D. thesis, Bristol University ( 1986). [6] W.S. Ginell, J.L. McNichols and J.S. Gory, Mech. Eng. 101 (May 1979) p. 28. [ 71 D.M. Goldstein and L.J. McNamara, eds., Proceedings of the Nitinol Heat Engine Conference, Silver Spring. MA (US Navy Department, 1978) NSWC MP 79-448. [S] R. Banks. Proceedings of the NiTi Heat Engine Conference, Silver Spring, MA (1977) p. 7-1: U.S. Patent 3. 913, 326 (Oct. 1975). [ 93 P.A. Hochstein, Thermal Energy Converting Assembly. IJ.S. Patent 4.037.41 I (July 1977).
105
MATERIALS LETTERS
September 1988
A SHAPE MEMORY EFFECT SWASHPLATE HEAT ENGINE
A.P. JARDINE ’ H.H. Wills Phvsics Laboratory, University of Bristol, Bristol BS8 I TL, UK Received 30 June 1988
A novel heat engine based on the shape memory effect (SME) of helical NiTi wire and utilising the swashplate geometry is described. Measurements of engine power cycled through 12°C and 80°C water baths were as high as 3 W/kg, which compare favourably with more complex SME heat engines designs.
About half of the solar radiation falling onto the earths surface is directly converted into low grade heat (temperature differences less than 100 ’ C above ambient) and is largely unused as a source of energy though the energy flux (8 x lOI W) is vast. Devices which can convert these abundant energy supplies into work will be of some importance in global energy concerns. A novel shape memory effect (SME) heat engine, the first built along swashplate principles is introduced, to exploit these low grade thermal reservoirs. The shape memory effect is a macroscopic shape change driven by a thermoelastic martensitic transformation #I. When cooled below the m~ensiti~ start temperature M,, martensitic plates composed of crystallographic twin variants of the martensitic unit cell are formed. Upon application of an external stress, the twin variant which best accommodates the elastic stress grows reversibly at the expense of the other. When the stress is removed, a strain of up to 10% can remain. Upon heating above A,, the austenitic start temperature, the twins whose growth was preferred now revert to the original orientation (the “hot shape”), thereby recovering the plastic strain, hence the realisation of shape memory. All twin variants then transform to austenite. Macroscopically, the Young modulus of the mar’ Present address: Depa~ment of Materials Science and Engineering, SUNY Stony Brook, Stony Brook, NY 11794,USA. ” An introduction to SME is given in ref. [ I], a more comprehensive source of information is ref. [ 21.
102
tensitic phase is much less than the austenitic phase due to deformation twinning to the preferred twin orientations. On heating, a large driving force is present as the deformed material transforms back to its preferred hot shape. These properties are utilised in SME heat engines. The SME alloy NiTi was chosen as its transformation temperatures are within the temperature range of the hot (80°C) and cold (1S’C) heat reservoirs, it is available in small diameter wire and it is relatively easy to set a hot shape in the form of a helix. Small diameter (0.46 mm) NiTi wire was used to promote rapid heat transfer. The time to heat this wire through the transformation was approximately 0.1 s from visual observations. On cooling, the exothermic transformation, with latent heats of transformation approaching 800 Jjmol [ 31, produced cooling times on the order 10 times longer than heating due to the difficulty in transporting heat away from the wire. Three strands of wire were braided together, thereby producing a wire of three times the force of a single wire but with the effective heat transfer properties of one wire. The braided wire was then wound and clamped on a mild steel mandril and heated to 500°C for 1 h and then furnace cooled to set the preferred hot shape in the form of a 1.10 cm diameter helix with a pitch of 0.65 cm. The swashplate geometry consists of two circular plate assemblies mounted on axles misorientated from collinearity by a small angle a!. The plates assemblies were 25.4 cm diameter, 1 mm thick Al discs bolted to 12.7 cm diameter, 4 mm thick dural flanges,
0167-577x/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 7, number
3
MATERIALS
with a moment of inertia per plate assembly (I) of 0.15 kg m2. Forty three holes per disc were drilled near the rim and identical SME NiTi helices of 2.5 turns of braided wire were inserted and bonded to the plates with epoxy. A hot water spray was located at maximum plate separation and the cold water spray 90” further along at the top of the motor. The swashplate engine is shown in fig. 1. Work was extracted from the SME in the following manner: as the motor rotated, the cold, martensitic SME helices were easily stretched axially due to plates’ misorientation. At the maximum plate gap, the helix was heated through its transformation by the hot water and attempts to contract to its preferred hot shape, though constrained by the plates. The helix was then in a higher energy state than 180” away, where the helices are relaxed, thus providing a driving force for rotation. The torque responsible for motor rotation results
LETTERS
September
1988
from the contraction of the helices having a component of force along the radius of the plates, related to the misorientation angle (Y (see fig. 2a). The SME recovery force is dependent on the wires’ extension and temperature, with the recovery force increasing with increasing helix extension [4] and decreases with increasing SME helix temperature. As the hot water stream width was x 1 cm, there were always several helices transforming though at different stages of the transformation. The instantaneous force on the plates from the transformation-staggered helices was not symmetric about the horizontal but had a net tangential component, generating the torque r, as illustrated in fig. 2b. The engine is subjected to four torques; a power torque r due to the SME helices, a dynamical frictional torque (K), a static torque from the bearings and from the helices themselves (C), and finally a loading torque (L) from which work is derived. If
Fig. 1. The SME swashplate motor, the height of the motor is 27.5 cm. For purposes of display, the source of cold water has i been rema Ived. The hc3t water SIlpply is shown, providing two streams of hot water. The SME helices arc between the plates.
103
MATERIALS LETTERS
Volume 7. number 3
September 1988
thus, the steady-state rotational speed (0,) is o,=(T-L-C)/K,
a
water
b
Fig. 2. (a) A schematic view of the engine looking down between the plates. The two discs of radius R are inclined at an angle a! to each other. When heated in an extended state, the springs generate an axial restoring force F with a radial component F,. (b) A schematic view of the engine, each small dot represents a helix. At any time, several helices will be transforming but at different strains due to the engine geometry and at different temperatures due to the differing times from immersion in the hot stream. The instantaneous radial forces are therefore different, hence there is a net tangential force, which generates the torque driving the rotation.
the helices are densely packed so that r is effectively time independent, the speed of rotation w(t) from an initial speed w. is given as #’ o(t)=wo
exp[ - (K/l)t]
+[(r-L-C)lKl{l-exp[-(K/i)ll),
(1)
tit A detailed mathematical description of the swashplate heat engine has been presented in ref. [ 51.
104
(2)
where Z,the moment of inertia of the plates, was calculated as 0.15 kg m2. The dynamic friction torque K was measured by observing the decay of the rotational speed with plates parallel, no water running, with r and L zero, and without an external load. As the motor speed decays exponentially as exp[ - (K/l)t] (from eq. (1 )), K was measured as -5.0~ 10V3 kg mz s-‘. The motor would stop after several cycles if either hot or cold water streams were interrupted. A fast stream of cold water could not rotate the misorientated plates a complete turn; convincing evidence that the motor was not acting as a water-wheel from a force imbalance between hot and cold water streams. With a m&orientation angle of 4.8” and a plate separation of 3.7 cm, motor speeds from 60 to 110 t-pm were observed with no load, the variability being due to irreproducible cooling conditions. By changing the cooling water spray, higher rotational speeds of 110 rpm were observed but were difficult to maintain or reproduce. Taking w, as 110 rpm as being representative of an optimally cooled motor, T-C was 5.76x 10e2 N m (from eq. (2)). Calculations of power-speed curves were done in parametric form for a given load. The speed is given by eq. (2 ) and the power (P) is given as P=Mgro,
(3)
where g is the gravitational constant and M is the effective mass causing the braking torque (L= Mgr) on the axle of radius r. Power measurements were made by placing a known load over the drive axis and measuring the load on a spring scale on the other side of the load. The difference between measured and actual loads gave the effective load on the engine. Power-speed curves were calculated by changing the loading torque (i.) for fixed values of r-C, K, plate separation and CLSeveral curves with different free running speeds, corresponding to different values of r- C, are shown in fig. 3. From the stated values of K and r- C, the maximum power of the motor is 166 mW at 55 rpm. To measure reproducible power-speed curves, a weak stream of cold water onto the helices at the top of the engine was employed. This impaired the ef-
Volume 7. number
MATERIALS
3
Speed
(Rpm)
Fig. 3. Power-speed relationship from eqs. (2) and (3). for (~~4.8’. Maximum power is 166 mW at 55 rpm from the observed maximum free-running speed ( 110 t-pm) performance of the engine. The observed power-speed curve for the SME swashplate motor was consistent with that predicted for free-running speed of 60 rpm. The large error bars at low revolutions are due to an unaccounted long period oscillation of speed with time. The open circle denotes the maximum observed power using irreproducible cooling conditions.
fkiency of the cooling as reproducible speeds of only 60 rpm could be obtained for the free-running engine. As shown in fig. 3, the motor performance was consistent with that predicted for I”-- Cof 3.14X 10-l N m, with peak performance a factor of 3.5 lower than for the engine free-running at 110 x-pm. However, using unstable cooling spray arrangements, power readings of 0.14 W at 30 rpm were recorded corresponding to a power density of 3 W/kg of NiTi. This value corresponds to a free-running speed of 120 rpm (r-Cz6.23~ lo-’ N m) in fig. 3. Evidently, the manner in which the helices were cooled was important. Other SME engines designs have been reviewed elsewhere [ 6,7 1. By way of comparison, the best motors to date such as Banks’ offset crank engine [ 81 gave 0.23 W at 69 rpm. Another by Hockstein [9] gave 1O-20 W at 70 rpm; a maximum power density
LETTERS
September
1988
of 133 W/kg. Turbine SME heat engines are reported to produce 0.5 W at 2500 t-pm [ 5 1. The viability of SME Nil-i swashplate heat engines has been demonstrated. Although the power measured was low, improvements in the method of applying cooling water will increase performance. Advantages inherent in the swashplate design are the intrinsic simplicity of the engine construction and the low local strains on the SME helices. (As a rule of thumb, the greater the strain per cycle, the greater the number of dislocations generated per cycle and the faster the helix fails to transform due to workhardening.) A more rigorous physical model of the engine producing more efficient designs is desired to evaluate the true potential of these engines. Power densities of 30 W/kg would not be an unreasonable expectation for these motors. The author is grateful to Mr. Harry Young for construction of the motor and to Dr. Ken Ashbee, Dr. Jeff Sargent and Dr. David Hanstead for helpful advice. The author is also grateful for sponsorship by the British Gas Corporation under a British Gas Scholarship.
References [ 1] L. McDonald
Schetky. Sci. Am. 241 (November 1979) p. 68. [ 2 ] 1. Perkins. Shape memory effects in alloys (Plenum Press, New York, 1975). [3] KMelton and 0. Mercier, J. Appl. Phys. 50 ( 1979) 5747. [4] A.A. Golestaneh, Acta Metall. 28 ( 1980) 1427. [ 51A.P. Jardine. Ph.D. thesis, Bristol University ( 1986). [6] W.S. Ginell, J.L. McNichols and J.S. Gory, Mech. Eng. 101 (May 1979) p. 28. [ 71 D.M. Goldstein and L.J. McNamara, eds., Proceedings of the Nitinol Heat Engine Conference, Silver Spring. MA (US Navy Department, 1978) NSWC MP 79-448. [S] R. Banks. Proceedings of the NiTi Heat Engine Conference, Silver Spring, MA (1977) p. 7-1: U.S. Patent 3. 913, 326 (Oct. 1975). [ 93 P.A. Hochstein, Thermal Energy Converting Assembly. IJ.S. Patent 4.037.41 I (July 1977).
105