Contact: bistabledomes at gmail.com
FLEX-ACTUATED BISTABLE DOME PUMP
barkingpo at earthlink.net
Presented at the 3rd European Wave Energy Conference, Patras, Greece, Sept. 1998.
A flexible pump that pumps when bent is suggested as means for using a wide range of motion for pumping, including wave motion. The pump mechanism is a row of shallow stainless steel bistable domes that invert and switch back and forth from the inside of a curvature to the outside in response to repeated bending. Alternating dome displacement in an enclosed space is used to draw liquid or gas and then force it out as directed by check valves. The relationship between degree of curvature and volume pumped was examined. Simplicity of dome structure and pump construction suggests versatility and economy for a wide range of scale and applications. Construction, theory, and applications are discussed.
Shallow bistable domes that switch sides when the material around them is bent can be used to make flexible pumps that utilize a wide range of natural and mechanical motion. The dome structure acts like the diaphragm in a common diaphragm pump but no separate mechanism is needed to move it, only leverage created by flexure along its edges.
Bistable domes function best when they are formed in hard, flexible materials and have a very shallow profile. When the material around such a dome is bent toward the same side as the dome, flexural forces cause it to buckle and invert to its opposite stable state (fig. 1).
The increment of flexure necessary to collapse and invert a single dome is determined by its structural and material characteristics.
When a row of bistable domes is formed so that their perimeters overlap, as in fig. 2, they create a common dynamic structure along which the flexural forces created by bending can be shared.
This structure through the middle of the dome row is longer than the edge of the domes and occupies a slightly larger radius of curvature (fig. 3).
When flexed this difference in length creates flexural forces proportional to the radius of curvature as long as the switching forces are not absorbed by the dome material and the edge is properly contained in the neutral flex axis of a stiffer overall structure. The bistable domes are forced from one side to the other in patterns determined by location, direction, and amount of curvature (fig. 3).
If the domes didn't overlap, the flexural forces that switch them would largely dissipate in the material between them.
Minimum functional radius is reached when all the domes are oriented to one side or the other. When the edge of the dome row is flattened approximately every other dome is on the same side (fig. 3).
Large numbers of very small bistable domes have previously been suggested for measuring surface flexure1. In that application arrays of bistable domes are used in a flexible circuitry laminate to form a paper-thin sensor of flex-activated on/off switches. The laminate can provide a computer with a digital approximation of the shape or changing shape of a surface parallel to the edge of the dome layer.
For a pump application flex-activated bistable domes can be formed in materials such as hardened stainless steel. Alternating dome displacement caused by bending the dome layer back and forth is used to draw liquid or gas into an enclosure and then force it out. Check valves are used to direct the flow. Such a pump can be constructed using a single dome (fig. 4) or rows of overlapping domes.
In this paper the construction of a row of overlapping stainless steel bistable domes is described. The row of domes is then used as a pump mechanism to construct a small-scale flexible pump that pumps when bent.
A motorized device was constructed to bend the pump between convex and concave states and volumes pumped were compared for a selection of curvatures.
Characteristics of bistable dome behavior as described above suggest that a pump made with overlapping bistable domes would demonstrate proportionality between amount of curvature and volume pumped. The smaller the radius the more bistable domes would switch sides and the greater the volume pumped.
MATERIALS AND METHOD
The pump mechanism is a row of 50 overlapping bistable domes formed in a band of hardened stainless steel approximately 12mm wide and .152mm (.006") thick.
The bistable domes were formed by stamping the stainless steel band between a tool and die whose contact surfaces approximate the dome profile. Bistability was achieved by stamping both sides.
The domes were approximately 10mm in diameter and spaced approximately every 7mm, center to center. The row of 50 domes was 35cm long. Dome displacement was approximately .17mm.
The dome row was inserted into flexible polyvinyl chloride tubing. The inner diameter of the tubing (approximately 8mm ID, 12mm OD) was slightly smaller than the width of the dome row and the tubing had to be flattened slightly to allow insertion of the dome row. After insertion the tubing was allowed to relax and became tight enough along the edge of the dome row to create a watertight seal between the two sides.
Simple check valves were made from short lengths of rubber tubing and thin rubber flaps glued to one end. The check valves were used to create one-way flow through one of the chambers between the dome row and the tubing.
The pump bending device consisted of a motor-driven arm which moved the ends of a flexible plastic strip (3mm x 5cm x 75cm) up and down in relation to two fixed points on the strip approximately 20cm from each end so that the middle of the strip alternated between convex and concave curvature. The fixed points were spaced approximately 35cm apart, a distance which is equivalent to the length of the pump mechanism.
The pump was attached to the plastic strip between the two fixed points so that it remained parallel to it when flexed by the pumping device.
The motorized pumping device was used to bend the pump repeatedly between equally convex and concave curvatures to approximate flexure that might be caused by floating such a device on a water surface with waves with wavelength larger than pump length.
Water volumes pumped were compared for ten curvatures. The mechanics of the motorized device did not allow precise selection of any particular curvature but did provide a range of 9 distinct curvatures between but not including the minimum functional radius, when all bistable domes were oriented to one side, and the large radius limit, a curvature at which the pump was no longer able to pump. The motorized device was unable to bend the pump to its minimum functional radius so those volumes were determined by hand bending.
The pump was also used to pump water up a vertical tube with an internal cross-sectional surface area of approximately 33mm2 at an altitude of approximately 1646m.
Another device was built in which the row of domes was replaced by a band of stainless steel without bistable domes but it could not be used to pump water.
Figure 5 shows volumes pumped for 10 different curvatures.
Fig. 5 Pump results
The pump did not require priming and was able to push the water column to a height of 5.7m before failure. It was determined that the volume pumped per bistable dome was approximately .02 ml.
Due to inefficiencies in the check valves it was not possible to determine volume figures for small amounts of curvature. It was observed, however, that small numbers of domes switch sides even for very slight curvatures.
The pump was also capable of utilizing curvature for which the concave curvature was different from the convex curvature as well as bending between curvatures on the same side of flat. Only a change in curvature was necessary to pump.
General The results suggest that flex-activated bistable domes can utilize a wide range of two-dimensional flexure for pumping. Consistent with overlapping bistable dome behavior observed for applications related to sensing flexure, volume increased as radius decreased.
The sudden volume change between minimum functional radius at approximately 22cm radius, which was obtained by hand bending, and the minimum radius obtained with the motorized pumping device at approximately 32cm radius cannot be adequately explained here.
It was observed during dome construction that sensitivity to flexure varies with characteristics such as relative dimensions, materials, and percentage of overlap.
Efficiency for a particular application may largely be determined by balancing available flexing forces and displacement ranges with pump length, dome diameter, and dome sensitivity.
It may be practical to use single large bistable domes for pumping in applications where higher pressure is required. For other applications rows or arrays of smaller overlapping domes may be more useful, as well as being easier and more economical to manufacture and transport.
Whereas a single large dome requires mechanical extension for leverage and reacts only when a single increment of flexure is exceeded, smaller overlapping domes provide their own leverage mechanism and are more sensitive. They might pump the same volume by utilizing smaller increments of flexure and/or less force at a higher frequency. Arrays of overlapping domes are able to convert motion more variable in magnitude and direction, as is often found in nature.
With regard to bistable dome life, common snap-acting stainless steel domes that are used in the membrane switch industry can exceed 5 million collapses/cycles but bistable domes are more shallow. A good pump design may allow replacement of the dome row.
There is considerable tolerance for flexing a dome row (such as the one used in this study) past its minimum pumping limits but permanent damage may result from sharp radius bending. Overall pump construction should offer protection from this possibility.
Wave energy Wave applications suggest floating the dome pump on or near the water surface but there may be other options. Dome pumps with a thin, flat cross section might be repeatedly flexed by subsurface motion near shore, for example.
A floating wave pump might use the difference between trough and the crest for leverage. The number or domes that switch sides when a wave passes will depend largely on wave steepness and the sensitivity of the dome to flexure. The domes would switch at approximately the speed of the wave. Flow can be controlled by spacing check valves appropriately. Orientation of multiple connected pump rows/arrays in relation to wave length and direction might also be used to manage flow and pressure. Long rows of domes might be divided into shorter segments with stiff joints to simplify manufacture and handling.
Short segments of overlapping domes that are all switched by any wave exceeding a certain low amplitude may be deployed in a staggered array that provides an even flow in a variety of wave conditions.
If sensitive enough for low wave heights, bistable dome pumps may be well suited for small-scale localized applications including freshwater lakes and reservoirs.
Structural considerations will effect size extrapolation, especially for pumping fluids. With respect to volume extrapolation only, overlapping domes of similar proportions to those used in this study but with diameters of 40cm, 1m, and 2m might displace, respectively, approximately 1, 18, and 146 liters. A 4m diameter dome could displace more than 1100 liters.
Other applications Simplicity of dome structure and pump construction, versatility, and modular design possibilities suggest a variety of customized uses.
Easy, low-cost construction with common materials might make it an alternative in developing countries where low-tech, low-maintenance pumping systems are necessary. Inexpensive small-scale versions might utilize almost any animal, water, or wind-driven motion for gradual pumping to a water storage tank, for irrigation, etc. Wind and bicycle-driven pistons, blowing tree branches, as well as river and stream motion can be used.
An overlapping bistable dome with a diameter of 4cm could displace approximately 1ml of water. A movement that could displace 10 such domes every 10 seconds could pump almost 100 liters per day. 8cm diameter domes could displace approximately 9ml each.
Further research Subjects for further research include: (1)Limits of sensitivity for utilizing large radius curvature, (2)Pressure generated by dome displacement in relation to dome characteristics, (3)Pump housing materials and construction, (4)Fatigue and other effects of long-term use, (5)Efficiency studies (6)Spacing and use of check/control valves relative to wavelength and pump length, (7)Cost studies, (8)Design for minimizing damage, (9)Flotation materials and construction, (10) Effects of scale changes.
Thanks to M. Ericson, L. Conroe-Luzius, and M. Luzius for their thoughtful comments and help.
Ericson, P. L. 1996. US Patent # 5563458. Apparatus and Method For Sensing Surface Flexure.
Ericson, P. L. 2000. US Patent # 6132187. Flex-actuated Bistable Dome Pump.
A flexible pump that pumps when bent
This pump utilizes any natural or mechanical motion that causes it to bend. For wind and wave energy, medical, lubrication, siphoning, water supply, etc. Volume pumped is proportional to change in curvature.
See US Patent #6132187. Flex-actuated Bistable Dome Pump (expired). The pump has also been described in a paper presented at the 3rd European Wave Energy Conference held in Patras, Greece in Sept., 1998 (Flex-actuated Bistable Dome Pump) (right).
How it works: The pump mechanism is a row of shallow overlapping flex actuated bistable domes formed in hard flat materials such as stainless steel. When bent, domes on the inside of the curvature are forced to buckle and invert toward the outside in numbers proportional to that curvature. Alternating dome displacement caused by bending the dome layer back and forth is used to draw liquid or gas into an enclosure and then force it out. The further it is bent the more it will pump. Check valves are used to direct the flow. The domes function essentially like a series of diaphragm pumps- but without the pistons and driving mechanisms. Only leverage created by bending it is required to pump. Single bistable domes may also be used.
Construction: One of the simplest pumps. Besides one way valves, connectors, etc., the pump has only two components: 1) the dome row, which can be made of small or large domes and can be short or long and 2) a continuous flexible housing around the domes, or for one side of the dome row. Housing must flex with the dome row without collapsing/expanding. One very simple and inexpensive version uses common plastic tubing for a housing. Simplicity of dome structure and pump construction, versatility, and modular design possibilities suggest a variety of customized uses. See "Flex-actuated Bistable Dome Pump" below for more detail.
Versatility in utilizing renewable energy sources: Instead of needing to reach a certain threshold amount of motion or force to pump, a multi dome pump only has to be bent back and forth anywhere between its minimum radius limits. This sensitivity makes it well suited to utilize the wide range of natural motions found in nature, such as those available when utilizing wind and water.
Volume monitoring: As described in US Patent 5563458- Apparatus and Method for Sensing Surface Flexure and at the web page available through www.bistabledome.com, small bistable domes can be made into switches so that pumping behavior can be monitored at the same time. Besides using such a combination to monitor volume a sensor could be used to predetermine the pumping requirements for customizing pump design for a particular application.
Medical: very small thin flex actuated pumps may be possible.
Lubrication/Industrial: automated, passive, measured lubrication of machinery. May be actuated by relative motion between two moving parts. Might be used to pressurize a reservoir.
Siphon pump: might screw onto the end of garden hose and draw fluid with a whipping motion, for example.
Small scale water supply: easy, low-cost construction with common materials might make it an appropriate technology for situations where low-tech, low-maintenance pumping systems are necessary. Inexpensive small-scale versions might utilize almost any animal, water, or wind-driven motion for gradual pumping to a water storage tank, for irrigation, etc. For example, bicycle-driven pistons, blowing tree branches, as well as natural river and stream fluid motion might be used.
Wave energy applications
Power generation: May provide enough pressure to power a turbine or pump water to a reservoir. May be suitable for a wide range of wave sizes and conditions. Flexibility and low profile may make it less vulnerable to destruction by large waves, a concern for many wave power devices. Bistable dome pumps capable of utilizing small waves may also be suited for inland applications such as freshwater lakes, reservoirs and bays.
Desalination: The pump might be useful for augmenting water supply for desalination. Large domes may also provide enough pressure to directly desalinate water using membrane methods.
Re-oxygenation of lakes, reservoirs, bays: long term passive pumping may help restore polluted water bodies.
Utility boating applications: small scale power, water, pressure supply.
Mariculture, aquaculture: water supply, nutrient cycling.
Oil spill: might provide a large scale means for moving or pumping oil, cleaning.
Offshore facilities: small scale water and pressure supply.
Extrapolating from small scale working prototypes an overlapping flex actuated bistable dome with a diameter of 4cm could displace approximately 1ml of water. A wind or water generated motion that could displace 10 such domes every 10 seconds could pump 3.6 liters per hour. 8cm diameter domes could displace approximately 9ml each, or approximately 32 liters per hour. With respect to volume extrapolation only, overlapping domes with diameters of 40cm, 1m, and 2m might displace, respectively, approximately 1, 18, and 146 liters. A 4m diameter dome might displace more than 1100 liters each time a wave passes it (see parer FLEX-ACTUATED BISTABLE DOME PUMP- right).
Contact: Paul Ericson
barkingpo at earthlink.net