Compact and efficient elastocaloric heat pumps—Is there a path forward?

By 2050, global energy use for space cooling is projected to increase threefold¹ due to emerging economies, income rise, and population growth resulting in significant increases in economic and environmental impacts. Caloric cooling, more specifically elastocaloric (eC, also known as thermoelastic) cooling, has been identified as one of the most promising non-vapor-compression technologies with a high potential to improve efficiency and eliminate greenhouse gas emissions.² Although the technology shows great promise, there are no known commercial elastocaloric cooling systems. Several research-scale devices for both single-stage cooling^3–5 and active elastocaloric regeneration⁶ were demonstrated; however, they are far from achieving the performance and size parameters needed to be competitive with vapor-compression systems.

While research and development of elastocaloric (eC) heat pump systems is on the rise, elastocaloric cooling has not yet reached the level of maturity of competing caloric technologies such as magnetocaloric (MC) cooling. Learning from 20+ years of MC development^7,8 and its main barriers to commercial adoption⁹ can help rapidly advance eC technology. Many promising MC systems have been demonstrated;¹⁰ however, the technology has not been widely adopted largely due to the high cost of producing magnetic fields. Unlike MC systems where permanent magnet arrays or coils are the only practical choices to produce magnetic fields that control magnetocaloric effects, there is a wide range of actuators available to apply stresses to control strains and elastocaloric effects.

The majority of demonstration systems that have achieved measurable cooling power employ hydraulic actuators¹¹ and linear motors.^5,6 In all of these cases, the actuators are hundreds of times larger than the amount of active material.¹² For comparison, in MC systems, the ratios of permanent magnet volume to active regenerator volume are on the order of 10:1 or less. A similar target value for elastocaloric systems, less than 10:1 actuator volume to active material volume, is needed in order for these systems to be competitive in size with vapor-compression systems.

Qian et al.³ considered piezoelectric, linear motor, screw jack, hydraulic, and pneumatic actuators for elastocaloric systems, however, without detailed analysis of actuator selection. Shape memory alloy (SMA) actuation of elastocaloric materials has the potential to achieve a small actuator to active material volume,¹² but this approach uses thermal energy, is slow, and is therefore unsuitable for most cooling applications. Considering the wide array of actuator technologies available, establishing reliable methods to match actuator capabilities with requirements of active elastocaloric regenerators is needed for compact cooling solutions.

In this work, we identify metrics that can be used to select actuators for eC systems for best performance by evaluating a broad range of actuator technologies using established methods.¹³ For specific elastocaloric materials, we evaluate possible actuator technologies on the basis of energy density and power density. We further show the potential for compact, inexpensive actuators in two case studies of regenerative elastocaloric systems.

The most widely used eC materials are nearly stoichiometric nickel–titanium (NiTi) alloys, commonly known as Nitinol, due to their large eC effect and commercial availability. Near-adiabatic temperature changes of 23 K have been reported for applied tensile stresses of 570 MPa and strains of 6%.¹⁴ NiTi alloys do have drawbacks such as large hysteresis and fatigue-related failure.^15,16 To address fatigue in NiTi, operating with pre-strain and a relatively low oscillating strain has been proposed.¹⁵ Other known elastocaloric materials, the majority of which are not commercially available, are mostly variations of nickel-based and copper-based alloys, magnetic shape memory alloys (MSMAs), man-made and natural polymers, and ferroelectric ceramics. Selected eC materials and their achievable actuation stresses and strains are listed in Table I along with their reported adiabatic temperature changes including two cases of NiTi materials with pre-strain. Strain energy density of a linear elastic material is half of the product of stress and strain,¹⁷ and we use this as a first-pass estimate of the energy density required to actuate the materials.

From the wide array of actuation technologies available, we list the technologies deemed most appropriate for elastocaloric actuation in Table II.^3,13 Actuator types include both direct actuation of active materials (e.g., piezoelectrics, magnetostrictives, SMAs, and ferromagnetic SMAs) and conventional actuators (e.g., hydraulic, pneumatic, and electromagnetic). Evaluating the inherent stress and strain of actuators and actuator materials provides insights into selecting the best technology to use. We apply the technology-independent metrics for actuators and actuator selection suggested by Huber and Fleck¹³ to the case of elastocaloric systems. For a linear actuation material, the maximum mechanical energy density is calculated as one quarter of the product of maximum stress and strain,^13,35

While considering the full load curve, including nonlinearities, would be more accurate, the simplicity of this method makes it attractive as a first approximation in comparing active material requirements with actuation capabilities. It is applicable to low-frequency actuation and provides an order-of-magnitude evaluation tool for matching actuator technologies to key parameters of elastocaloric materials collected in Table I.

At the full-actuator level, the actuator energy density, E_a,max, describes the maximum force it can provide, F_max, and its maximum travel, x_max, making it a better system-level metric,

where V is the volume of the actuator. For some active materials, actuator size is strongly application dependent; these technologies were evaluated based on the energy density of the actuating material [Eq. (1)] where indicated in Table II.

The maximum actuator energy per unit volume provides an accurate measure of the size of the actuator needed to meet requirements of direct actuation for low-frequency elastocaloric heat pump operation. Practically, however, actuators commonly operate indirectly at the system level; working through, e.g., gearboxes and lever arms. For these cases, considering the frequency of operation, f, allows matching the power density of the actuator, P_a,max, to the requirements of a given eC system,

Because power density is proportional to frequency for the regime of interest, this opens up a range of possible actuation technologies, provided the power can be shifted efficiently from high to low frequency.

Figure 1 shows the stress–strain capabilities of many common actuation materials and actuators along with the requirements for several elastocaloric materials; our focus is on Ni-based alloys and NiTi with pre-strain because of their commercial availability and large eC effect. Lines of constant energy density are provided on the plot as an indicator of the volume ratio of active material required to actuate elastocaloric material. The Ni-based eC materials fall largely along the 10 MJ/m³ line; actuators and active materials in the 1–10 MJ/m³ range fall within the 10:1 target range. Interestingly, thermally actuated NiTi (shape memory effect) provides a very close match to the energy density requirements of elastocaloric (superelastic) NiTi.¹² The only other technology that meets or exceeds the energy density requirements is hydraulics albeit with a lower stress and higher strain. Magnetic shape memory alloys (MSMAs) overlap a small portion of the actuation requirements for NiTi with pre-strain and pneumatics fall within the 10:1 energy density range. Based purely on stress and strain requirements, SMAs and MSMAs would result in the most compact actuators for Ni-based alloys and NiTi with pre-strain, respectively. Although hydraulics are in the same range of energy density as elastocaloric materials, they would require force amplification and stroke de-amplification to meet the requirements because of their low stress and large strain. Without this, hydraulic actuators need to be oversized to meet the force requirements as done eslewhere.¹¹ Figure 1 does not account for power, efficiency, or cost of the actuator; so it only provides part of the information needed in actuator selection. It is promising, however, that there are multiple actuator technologies in the target 10:1 volume range.

When designing an energy-efficient eC heat pump system, efficiency of the actuator will be critical to the overall system efficiency. Thus, we can safely exclude technologies with efficiencies less than 50% in Table I from further consideration, leaving piezoelectrics, magnetostrictives, magnetic SMAs (MSMA), solenoids, moving coils, and linear motors. These higher efficiency technologies are evaluated on the basis of frequency and power density to match the requirements of elastocaloric materials.

Evaluating actuators based on power provides another dimension in actuator selection (Fig. 2). While piezoelectric and magnetostrictive actuators have higher power density than required for most eC materials, they tend to have very high operating frequencies. There are some methods to frequency-shift their operation;^40,41 however, this comes at the expense of low efficiency and complex controls. Linear motors, solenoids, and moving coil actuators suffer from low power density in the frequency range of interest. MSMAs are a good match in power density and frequency. The power density is calculated only at the material level; however, actuators based on MSMAs are not widely available because they are not a mature technology.

In the power density plot, we add a new category of actuators, rotary electric motors. While rotary motors cannot directly actuate elastocaloric regenerators, their rotary motion can be converted to linear reciprocating motion using any number of mechanisms such as slider-cranks or Scotch yokes.⁴² Motors are ubiquitous and inexpensive, and their frequency of operation is easily changed with gears at reasonable efficiencies making them a good choice of actuators for eC applications.

We look at theoretical design cases for elastocaloric cooling, including the regenerator configuration that drives requirements for actuation. For case 1, an actuator is based on a DC electric rotary motor with a rotary-to-linear oscillation mechanism sized to operate the regenerator. Case 2 uses the same actuation method but includes improved regenerator design to reduce the actuation requirements.

The eC regenerator, in particular, the amount and configuration of eC material (plates, wires, etc.) and their arrangement, directly influences the force and displacement requirements of the actuator. For both studies, we assume a regenerator with 20.7 g of NiTi material in the form of 20 plates with active length of 75 mm, width of 10 mm, and thickness of 200 μm attached to a polyether ether ketone (PEEK) base structure. With a target operating frequency of 1 Hz, the rotational speed of the motor is 60 rpm for both cases. In case 1, the target strain for the plates is about 0%–1%, requiring approximately 0–325 MPa tensile stress applied along the active length, normal to the direction of motion as illustrated by the minor loop depicted with filled green circles in Fig. 1. Under these conditions, approximately ±3.5 K temperature changes are achieved for loading and unloading, respectively.¹⁴ 

We use a unique bending configuration as described by Czernuszewicz et al.¹⁴ to match the requirements of the regenerator with a rotary motor (Fig. 4). Using Young's modulus of 32.5 GPa estimated from the data of Fig. 3 for the minor 0%–1% loop, we employed a two-dimensional finite element model in Comsol® to assess the force and displacement of the structure when operated as a cantilever with the fixed region and forced portion as shown in Fig. 4 (more details are provided in the supplementary material). For case 1, we estimate the target force and displacement requirements to be 2423 N and 13 mm, respectively. These force and displacement requirements are highly dependent on the base structure material and geometry, NiTi geometry, and boundary conditions, and can be readily matched to an actuator.

Actuation forces and displacements required by the regenerator are supplied by a rotary motor driving a Scotch yoke mechanism to convert rotary to oscillating linear motion schematically illustrated in Fig. 4; this mechanism was selected because of its compact nature and its ability to be readily adapted for different requirements.⁴³ The estimated average torque needed from the motor is 15.9 Nm and an average estimated power of 100 W. We selected a readily available brushless DC motor with a 223:1 gearhead (Portescap, 22ECT82 Ultra EC with R22HT planetary gearbox). As shown in Fig. 4 and Table III, the actuator volume to active material volume ratio for case 1 is 15.7:1 which is a significant improvement over hydraulics.¹¹ 

The case 2 design employs two design concepts to further reduce the actuator to active material volume ratio. The regenerator structure discussed above can readily be used in a push–pull configuration (two regenerators acting in opposite directions) for mechanical energy recovery⁴⁴ and to provide an offset strain for the eC material,¹⁵ both of which can drastically reduce the force and strain requirements to achieve the same temperature change. During assembly of the regenerator, both sets of strips are assembled in tension with a specific pre-strain so that, at either end of the range of motion, releasing tension on one side (lowering its temperature) can partially supply the stress for applying tension on the other side (increasing its temperature). For the case 2 design, the actuator only needs to supply the alternating stress and strain and not the total stress and strain. With a target mean strain of 2%, an alternating strain of ±0.5% results in approximately ±3.5 K temperature change,¹⁴ which requires ±93 MPa stress because the material is operating as shown by the corresponding minor loop (red circles in Fig. 3). This minor loop is entirely in the superelastic region as illustrated by the larger stress–strain loop (black circles in Fig. 3).⁴⁵ 

This modified regenerator configuration for case 2 shown in Fig. 6 has NiTi strips on both sides of a PEEK support for a symmetric structure with energy recovery and offset strain. It has the same number and geometry of NiTi strips as in case 1. Using the case 2 regenerator geometry, stress/strain targets, and Young's modulus of 19.1 GPa estimated from the data depicted in Fig. 3, we calculate the target force and displacement requirements to be 585 N and 14 mm, respectively, using finite element analysis with the structure operated as a cantilever (refer to the supplementary material for details). The estimated average torque needed from the motor is 4.0 Nm with an average estimated power of 25 W. We selected a readily available 34 W brushless DC motor with a 204:1 gearhead as an option that can provide the torque and speed needed for actuation (Portescap, 22ECT35 Ultra EC with R22HT planetary gearbox). As listed in Table III, the motor volume to active material volume for case 2 is 9.7:1, which meets our target size of 10:1 (Fig. 6).

If the Scotch yoke mechanism is balanced properly to minimize torque⁴³ (i.e., operating at a mechanical resonance), the motor power and size can be reduced even further for the same regenerator assembly. The motor can also be used to provide additional functions such as pumping heat transfer fluid and operating fans. These additional functions should not add significantly to the overall motor requirements and will help ensure that the motor operates at its peak efficiency.³⁸ 

We demonstrate two methods that can be employed to match actuation technologies with elastocaloric regenerators, namely, the energy density based on stress and strain and the power density that further takes into account operating frequency. The energy density method is appropriate for selecting actuator technologies to directly strain elastocaloric materials. Shape memory actuators match the stress, strain, and energy density requirements; however, low efficiency and slow response time eliminate them as a viable option. While hydraulics and pneumatics are close to the energy density requirements, they do not meet the stress and strain, thus requiring force amplification. Actuation with magnetic shape memory alloys matches the strain and is within a factor of 10 for stress, providing an interesting option for directly driving elastocaloric materials.

Using power density and frequency as selection criteria allows for actuation methods that do not directly strain the elastocaloric material but, rather, act through some transduction mechanism. For this second analysis, we did not consider technologies with efficiencies less than 50%, thus eliminating hydraulics, pneumatics, and shape memory actuators. Some technologies, such as piezoelectrics and magnetostrictives, have very high power densities only at high operating frequencies. We show that rotary motors with rotary-to-linear mechanisms are promising as actuators in select regenerator configurations because they are ubiquitous, efficient, and extremely flexible; frequency of operation is readily shifted using gears or belts/pulleys and rotary-to-linear converters provide the necessary oscillating motion.

Actuators based on magnetic shape memory materials meet the stress, strain, energy density, power density, and frequency ranges for elastocaloric applications and warrant future exploration as a long-term solution. While a system based on a magnetic shape memory actuator has the potential to be much simpler than the design cases considered in this work, their technical immaturity and lack of commercial availability are a hindrance to their immediate widespread use in elastocaloric cooling technologies.

Electric rotary motors fall within the target range for power density, thus providing a promising path forward for effective actuation of elastocaloric regenerators. We presented two theoretical design cases with off-the-shelf electric rotary motors and a Scotch yoke to convert rotary to linear motion driving a regenerator in a unique bending configuration. Without energy recovery, an actuator to active material volume can be as low as 15.7:1, which is an improvement over hydraulic actuators. Modifying the regenerator geometry to include energy recovery and pre-strain reduces the power requirements, lowers the ratio of actuator to material volume to 9.7:1, and demonstrates a feasible path forward to compact and efficient elastocaloric heat pumps.

See the supplementary material for information on finite element analysis of the regenerator structure.

This work was performed with joint funding from the Advanced Manufacturing Office and the Building Technologies Office of the Office of Energy Efficiency and Renewable Energy of the United States Department of Energy. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358.