Abstract:
Arrays of magnets configured to create linear or rotary magnetic springs with multiple equilibrium points. Some of the equilibrium points are stable, while others are unstable. No mechanical contact is required between moving and stationary elements of the magnetic springs, resulting in a virtually unlimited lifetime. The magnetic springs can be utilized in conjunction with low force electromagnetic actuators to implement multi-step linear or rotary actuators with high force, very short movement time between unstable equilibrium points, and with near-zero holding power required to maintain actuator position at any unstable equilibrium point. Specific applications that embody the present invention may include, but are not limited to, optical filters, linear valves, or any mechanism that would benefit from an efficient magnetic spring.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims priority from U.S. Provisional Patent Applications Nos. 60/535,803 filed on Jan. 13, 2004 and 60/543,865 filed on Feb. 10, 2004. 

   FIELD OF THE INVENTION 
   This invention relates to apparatus and methods for creating linear or rotary magnetic springs with multiple equilibrium positions. More specifically, such magnetic springs can form multi-position linear or rotary actuators. 
   BACKGROUND OF THE INVENTION 
   Electric motors of various types are commonly used to rapidly move an object linearly from one stationary position to another or to rotate an object from one stationary angular position to another by accelerating and then decelerating the object. The motor converts electric energy into the kinetic energy of the moving object during acceleration, and then brakes the object by converting that kinetic energy into another form such as heat during the deceleration. However, in some applications such motors are incapable of providing adequate speed of movement while also limiting their power consumption, size, and control complexity to acceptable levels. Such electric motors may serve as rotary or linear actuators and have been used in various applications such as, but not limited to, internal combustion engine valves. 
   Another method commonly used to rapidly move or rotate an object is to employ a mechanical spring. The initial position of the object is set by stretching or compressing a spring, or set of springs, such that a certain amount of potential energy is stored in the springs. When the spring is released the object is accelerated and the potential energy is converted into kinetic energy. After the object passes the position where all potential energy has been converted, it begins to decelerate and the kinetic energy is converted back to potential energy. The object can be captured at the end of its travel with the same potential energy as it had at the start, at the cost of only a small input of energy to compensate for energy lost to friction and heat, for example. In comparison with motor-driven switching, a spring mechanism involves greatly reduced power consumption due to its ability to efficiently convert potential energy to kinetic energy, and vice-versa, in a passive manner. In many applications a spring mechanism is also simpler and smaller. 
   Conventional mechanical springs are shown in  FIGS. 1   a  and  1   c .  FIG. 1   a  shows a conventional coil spring system  10 . Assuming the left end of spring  16  is attached to stationary element  12 , when moving element  14 , attached to the right end of spring  16 , is moved laterally, left or right, the spring produces a linear force as depicted in the graph of  FIG. 1   c . Specifically, when the spring is stretched to the right it produces a negative force, proportional to the offset or distance of movement, which tends to restore the spring to its original length. When the spring is compressed to the left it produces a positive force, proportional to the offset or distance of movement, which again tends to restore the spring to its original length. 
     FIG. 1   b  shows a known arrangement of magnets  20  that exhibits behavior analogous to that of a coil spring. Note that permanent magnets are depicted in  FIG. 1   b , but electromagnets can be conventionally substituted in any such arrangement to produce the same effect as permanent magnets. Examples of such magnetic springs may be found in the linear magnetic springs of U.S. Pat. No. 5,017,819 issued to Patt et al. and U.S. Pat. No. 5,148,066 issued to Beale et al. and the rotary magnetic spring of U.S. Pat. No. 5,038,063, each of which are herein incorporated by reference. 
   With continued reference to  FIG. 1   b , it is shown that if the leftmost magnet  22  and the rightmost magnet  26  are fixed in stationary positions and the center magnet  24  is moved left or right, within a limited range of movement the interaction of the magnetic fields of the three magnets produces a restoring force similar to that depicted in the graph of  FIG. 1   c . In  FIG. 1   d , a graph shows the preferred force characteristics versus offset of an idealized, hypothetical high performance switching mechanism. Mechanical spring-based mechanisms are unable to achieve this type of performance, whereas such high performance is more likely via magnet-based mechanisms. 
   A major drawback that limits the achievable switching speed and utility of a mechanical spring-based switch is the large force or torque typically required to hold the object in position prior to or after the switching movements. If switching speed requirements are too high to allow mechanical capture at the end of travel, an electric actuator such as an electromagnet is needed to provide the holding force or torque, producing a constant power drain when the object is stationary. The force or torque of a mechanical spring increases in proportion to the displacement, as depicted in  FIG. 1   c . As the required switching speed increases, the force capability of the spring must also increase, which increases the required holding force or torque, which increases the required current in the electric actuator, which can quickly lead to unacceptable levels of power consumption. The high force that accompanies large displacements also makes it exceedingly difficult to achieve “soft landing”—i.e., a low impact speed at the end of travel. 
   Although the holding force in a mechanical spring system can sometimes be reduced through a complicated combination of springs and other mechanisms, such as in a compound bow, the complexity of those devices limits the switching speed and also brings about issues of size, cost, reliability, and so forth. Another drawback of a mechanical spring system relates to the periodic deformation of the spring that induces high-frequency internal friction in the spring material. This not only causes energy loss, but also is a potential source of fatigue failure in high speed switching applications. 
   It is desirable to have a switching mechanism that eliminates the need for significant holding force or torque at the stationary positions as well as the fatigue and energy loss characteristics of a spring, while retaining the advantages of a spring mechanism. Preferably, it would possess a force-displacement characteristic as shown in  FIG. 1   d . Here, the curve AOB represents a switching process between two stationary positions, A and B, where the spring force/torque is zero so that no hold force/torque is required. Since these points are located at the maximum displacements in a switching cycle, they correspond to the maximum potential energy and thus unstable equilibrium. Therefore, if the object is displaced a short distance from point A in the positive direction it would encounter a force/torque in the same direction that would tend to drive the object further from point A. When moving from point A to point  0 , the object would be accelerated as potential energy is converted into kinetic energy. From point  0  to point B, the object would be decelerated as kinetic energy is converted back into potential energy. Virtually no energy input would be needed to accomplish the switching process. The middle point  0  is a stable equilibrium position. 
   SUMMARY OF THE INVENTION 
   Arrays of magnets are configured to create linear or rotary magnetic springs with multiple equilibrium points. Some of the equilibrium points are stable, while others are unstable. No mechanical contact is required between moving and stationary elements of the magnetic springs, resulting in a virtually unlimited lifetime. The magnetic springs can be utilized in conjunction with low force electromagnetic actuators to implement multi-step linear or rotary actuators with high force, very short movement time between unstable equilibrium points, and with near-zero holding power required to maintain actuator position at any unstable equilibrium point. Specific applications that embody the present invention may include, but are not limited to, linear valves, or any mechanism that would benefit from an efficient magnetic spring. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1   a  shows a conventional mechanical spring. 
       FIG. 1   b  shows a magnetic analog to the mechanical spring of  FIG. 1   a.    
       FIG. 1   c  is a graph of the force characteristics versus offset of the moving end of the spring in  FIG. 1   a.    
       FIG. 1   d  is a graph of the preferred force characteristics versus offset of a high performance switching mechanism. 
       FIG. 2   a  shows fixed and moving arrays of magnetic dipoles with the moving array constrained to lateral motion in accordance with the present invention. 
       FIG. 2   b  is a graph of the lateral force experienced by the moving array of  FIG. 2   a  in relation to its offset from the center of the fixed array. 
       FIG. 2   c  is a graph of the potential energy of the moving array of  FIG. 2   a  in relation to its offset from the center of the fixed array. 
       FIG. 3   a  shows fixed and moving Halbach arrays of magnets with the moving array constrained to lateral motion in accordance with another embodiment of the present invention. 
       FIG. 3   b  is a graph of the lateral force experienced by the moving array of  FIG. 3   a  in relation to its offset from the center of the fixed array. 
       FIG. 4   a  shows concentric circular arrays of magnetic dipoles with the inner array configured to rotate with respect to the outer array in accordance with another embodiment of the present invention. 
       FIG. 4   b  is a graph of the torque experienced by the inner array of  FIG. 4   a  in relation to its rotation with respect to the outer array. 
       FIG. 5   a  shows concentric circular Halbach arrays of magnets with the inner array configured to rotate with respect to the outer array in accordance with another embodiment of the present invention. 
       FIG. 5   b  is a graph of the torque experienced by the inner array of  FIG. 5   a  in relation to its rotation with respect to the outer array. 
       FIG. 6   a  shows a partial cutaway view of concentric cylindrical arrays of magnets configured to provide magnetic spring force in the axial direction in accordance with another embodiment of the present invention. 
       FIG. 6   b  shows a perspective view of concentric cylindrical Halbach arrays of magnets to provide magnetic spring torque in response to rotary motion of one array with respect to the other in accordance with another embodiment of the present invention. 
       FIG. 7   a  shows a variation of the rotary magnetic springs depicted in  FIGS. 5   a  and  6   b  in accordance with another embodiment of the present invention. 
       FIG. 7   b  is a graph of the torque experienced by the shaft and inner magnet subassembly of  FIG. 7   a  as they rotate clockwise with respect to the outer magnet subassembly. 
       FIG. 8   a  shows a torque modification assembly to be used in combination with the rotary magnetic spring of  FIG. 7   a  in accordance with another embodiment of the present invention. 
       FIG. 8   b  is a graph of the torque experienced by the shaft and inner magnet subassembly of  FIG. 8   a  as they rotate clockwise with respect to the outer magnet subassembly. 
       FIG. 9   a  shows a side view of a rotary actuator utilizing the primary magnet assembly of  FIG. 7   a  and the torque modification magnet assembly of  FIG. 8   a  in accordance with another embodiment of the present invention. 
       FIG. 9   b  is a graph of the torque experienced by the shaft of the rotary actuator of  FIG. 9   a  as the shaft and the two inner magnet subassemblies rotate with respect to the outer magnet subassemblies. 
       FIG. 9   c  is another graph of the torque experienced by the shaft of the rotary actuator of  FIG. 9   a  as the shaft and the two inner magnet subassemblies rotate with respect to the outer magnet subassemblies, this time using increased torque modification. 
       FIG. 9   d  is a graph of the potential energy at the shaft of the rotary actuator of  FIG. 9   a  as the shaft rotates. 
       FIG. 10   a  shows a partial cutaway view of concentric cylindrical magnets configured to form a valve spring for a cam-driven engine in accordance with another embodiment of the present invention. 
       FIG. 10   b  shows a partial cutaway view of concentric cylindrical Halbach magnet arrays configured to form a high-force valve spring for a cam-driven engine in accordance with another embodiment of the present invention. 
       FIG. 11  is a cross-section of a cylinder head illustrating for the sake of comparison both a conventional mechanical spring on the intake valve and a magnetic spring in accordance with the present invention on the exhaust valve. 
       FIG. 12  is a graph comparing the force vs. valve position of a conventional valve spring and three magnetic valve springs in accordance with the present invention. 
       FIG. 13   a  is an enlarged cross-section of a magnetic valve spring with the valve in the closed position. 
       FIG. 13   b  is an enlarged cross-section of the magnetic valve spring of  FIG. 13   a  with the valve in the open position. 
       FIG. 13   c  is a graph comparing the compression force vs. spring compression distance for the magnetic spring of  FIGS. 13   a  and  13   b.    
       FIG. 14   a  is an enlarged cross-section of another magnetic valve spring with the valve in the closed position. 
       FIG. 14   b  is an enlarged cross-section of the magnetic valve spring of  FIG. 14   a  with the valve in the open position. 
       FIG. 14   c  is a graph comparing the compression force vs. spring compression distance for the magnetic spring of  FIGS. 14   a  and  14   b.    
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   With reference to the drawings,  FIG. 2   a  shows an arrangement of magnetic dipoles  30  according to the first embodiment of the invention. Here, a row of dipoles  32  is configured in a fixed or stationary array with each dipole rotated 180 degrees with respect to adjacent magnets. The poles depicted are horizontal but other angles would be acceptable as long as the rotation requirement is met. Such rotation requirement is utilized within Halbach arrays as discussed within U.S. Pat. No. 6,374,746 issued to Fiske on Apr. 23, 2002, U.S. Pat. No. 6,684,794 issued to Fiske et al. on Feb. 3, 2004, and U.S. patent application Ser. No. 10/412,082 filed on Apr. 10, 2003 by Fiske et al. and published on Oct. 16, 2003 as US Patent Application Publication No. 2003-0192449, each document of which is herein incorporated by reference. Accordingly, arrays  32  and  34  of  FIG. 2   a  can be considered as Halbach arrays with a rotation increment of 180 degrees. 
   A movable array of magnets  34 , using a similar configuration of alternating poles, is positioned in close proximity to fixed array  32 .  FIG. 2   b  graphs the net lateral force on movable array  34  caused by the interaction of the magnetic fields produced by the magnets in both the fixed and movable arrays. In this graph, positive lateral force is assumed to mean force that tends to accelerate movable array  34  to the right. Negative force is assumed to mean force that tends to accelerate movable array  34  to the left. As depicted in  FIG. 2   b , this lateral force exhibits cyclical behavior. In the zero-offset position shown in  FIG. 2   a , the lateral force is zero. However, if the offset is increased in either direction the lateral force will tend to accelerate the movable array away from the zero-offset position. In other words, this is an unstable equilibrium position. Positions  38   a - e , as labeled in the graph, are all unstable equilibrium positions. At an offset of plus one or minus one, where one unit of offset is equivalent to one dipole length, the lateral force is again zero but here a small change in offset will produce lateral force tending to oppose movement. These are stable equilibrium points. Positions  36   a - f , as labeled in the graph, are all stable equilibrium positions. In essence, this magnet configuration produces a periodic spring in which the direction of force changes at each equilibrium point. The total number of equilibrium points are determined by the length of the fixed array. Equilibrium points near the end of the fixed array produce lower force than intermediate equilibrium points due to the reduced number of magnets involved. 
     FIG. 2   c  provides another way of looking at the interaction of the two arrays. Here the potential energy of the movable array is graphed as a function of offset. Potential energy is highest at unstable equilibrium points  42   a - e —i.e., the movable array is “balanced on a peak” and only a small force input is needed to induce it to “roll downhill”. Such a small input force may be provided, for example, by a motor or some similar motive source with an external power supply in either a linear or rotary configuration as necessary. Ideally, in the absence of impediments such as excessive friction or physical barriers the movable array will pass through a stable equilibrium point  44   a - f  and then climb the next potential energy hill almost to the peak. At that point only a small force is needed to “capture” the array in position, and very low power is sufficient to stabilize the array in position. As explained in more detail below, this cyclical behavior can be exploited to create highly useful actuators with unique characteristics. 
     FIG. 3   a  shows an arrangement of magnets  50  similar to that of  FIG. 2   a  but modified according to the second embodiment of the invention. Here the magnets are configured as Halbach arrays, in which the direction of magnetization of each magnet within the movable array  54  is rotated clockwise as the array is traversed from left to right and the active surface faces downward toward fixed array  52 . The direction of magnetization in fixed array  52  is rotated counterclockwise as the array is traversed from left to right with the active surface facing upward toward movable array  54 . This has the effect of focusing the field produced by each array toward the opposing array to produce higher force per unit of mass of magnet material. Arrays  52  and  54  shown in  FIG. 3   a  use 90 degrees of rotation from one magnet to the next, or four magnets per wavelength (360 degrees). However, it should be understood that more or less degrees of rotation may be used in order to produce shorter or longer wavelengths. The lateral force characteristics of arrays  52  and  54  in  FIG. 3   a  are graphed in  FIG. 3   b . Stable equilibrium points  56   a  and  56   b  are one wavelength apart, as in  FIG. 2   b . Unstable equilibrium points  58   a - c  are also one wavelength apart.  FIG. 4   a  shows a magnetic spring  60  according to the third embodiment of the invention. Here, concentric circular arrays of magnetic dipoles are arranged with inner array  64  configured such that it can be rotated with respect to outer array  62 , or vice-versa. In  FIG. 4   a , the magnetic poles are oriented radially with alternating directions of magnetization, though the only requirement is that the magnetization direction alternates from one magnet to the next. This produces torque on movable inner array  64  that varies analogously to the lateral force on movable array  34  of  FIG. 2   a .  FIG. 4   b  is a graph of the torque on inner array  64  of  FIG. 4   a  in relation to its rotation with respect to outer array  62 . Positive torque is assumed to be in the clockwise direction. The torque exhibits a cyclical, alternating behavior that produces stable equilibrium points  66   a - e  and unstable equilibrium points  68   a - d  similar to those in  FIG. 2   b . The configuration of  FIG. 4   a  produces a periodic rotary spring in which the direction of the torque produced by the spring changes at each successive equilibrium point. The total number of unstable equilibrium points equals the number of magnet wavelengths contained in the circular arrays, as does the total number of stable equilibrium points. 
     FIG. 5   a  shows an arrangement of magnets  80  similar to that of  FIG. 4   a  but modified according to the fourth embodiment of the invention. Here, the magnets are configured as concentric Halbach arrays, in which the direction of magnetization of each magnet in outer array  82  is rotated clockwise as the array is traversed clockwise. The direction of magnetization in inner array  84  is rotated counterclockwise as the array is traversed clockwise. Again, this has the effect of focusing the field produced by each array toward the opposing array to produce higher torque per unit of mass of magnet material. Arrays  82  and  84  shown in  FIG. 5   a  use six magnets per wavelength and three wavelengths per array for a total of 18 magnets per array. However, it should be readily understood that more or less magnets may be used to produce shorter or longer wavelengths without straying from the intended scope of the present invention. Arrays  62  and  64  of  FIG. 4   a  can be considered Halbach arrays with a rotation increment of 180 degrees. The torque experienced by inner array  84  of  FIG. 5   a  as it rotates with respect to outer array  82  is graphed in  FIG. 5   b . Stable equilibrium points  86   a - c  are one wavelength (120 degrees) apart. Unstable equilibrium points  88   a  and  88   b  are also one wavelength apart. 
     FIG. 6   a  is a partial cutaway view of magnetic spring system  100  in accordance with another embodiment of the present invention. Magnetic spring system  100  includes concentric cylindrical arrays of magnets  102  and  104  configured to provide spring force in the axial direction—i.e., a linear magnetic spring of the type depicted in  FIG. 2   a . Although shown as a cylinder in  FIG. 6   a , it should be understood that variations are well within the intended scope of the present invention such that the arrays could be square, “unrolled” flat, or configured in any other arrangement as long as the two magnet arrays are configured to provide multiple equilibrium points as one array moves linearly past the other. 
     FIG. 6   b  is a perspective view of magnetic spring system  120  in accordance with still another embodiment of the present invention. Magnetic spring system  120  includes concentric cylindrical Halbach arrays of magnets  122  and  124  configured to provide spring torque in response to rotary motion of one array with respect to the other as depicted in  FIG. 5   a.    
     FIGS. 7 through 10  depict one application of the rotary magnetic spring in accordance with the present invention and reveal some additional methods to extend capabilities of such an application. Specifically,  FIGS. 7   a  and  8   a  show subassembly portions designed in accordance with the present invention and that are further combined within the apparatus of  FIG. 9   a  to increase the advantageous characteristics of the present invention. While specific configurations are shown and described below, other configurations are possible without straying from the intended scope of the present invention. 
     FIG. 7   a  shows a cross-sectional view of primary magnet assembly  140  similar to that shown in  FIGS. 5   a  and  6   b . Outer magnet array  144  is mounted on the inside of stationary structural shell  142 . Inner magnet array  146  is mounted on rotating axle shaft  148 . These particular array configurations contain three magnetic wavelengths with three magnets per wavelength. The resulting torque characteristics for this configuration are graphed in  FIG. 7   b , with stable equilibrium points  152   a - d  and unstable equilibrium points  154   a - c  labeled. 
     FIG. 8   a  shows a cross-sectional view of torque modification magnet assembly  160  that can be used in combination with a rotary magnetic spring such as that in  FIG. 7   a . Within the torque modification magnet assembly  160 , the inner subassembly  166  consists of three magnets mounted on the same rotating shaft  148  depicted in  FIG. 7   a . The outer subassembly  164  consists of three additional magnets mounted on the inside of stationary structural shell  142 . The poles of all six magnets in arrays  164  and  166  are pointing radially inward, but they could all be pointed radially outward and produce the same effect. Indeed, any direction of magnetization is possible so long as the effect is that the inner and outer arrays  164 ,  166  are attracted to one another when in close proximity to one another.  FIG. 8   b  graphs the torque characteristics of assembly  160  with stable equilibrium points  172   a - c  labeled accordingly. 
     FIG. 9   a  shows a cross-sectional view of rotary actuator  180  employing primary magnetic assembly  140  in conjunction with torque modification assembly  160 . Both assembly  140  and assembly  160  are mounted on rotating shaft  148 , which is held in position by bearings  182 . As shown, bearings  182  are ball bearings, but magnetic or other types of bearings can be used instead in a manner well known by one skilled in the motor/generator art. Ideally, such bearings should impart minimal friction. Motor  184  connects to one end of shaft  148 , and works in conjunction with a control processor (not shown) and a rotary position sensor such as a shaft encoder (not shown). Such control processors and rotary position sensors may include, for example, a chip level central processing unit and hall effect sensor or some similar types of devices and will control motor movements based upon sensed positions. Such devices are well known in the motor/generator art and details of such are therefore not repeated here for purposes of clarity. 
     FIG. 9   b  graphs the torque versus rotation angle of the combined assembly  180 . Without torque modification magnet assembly  160 , the 60, 180, and 300 degree points in  FIG. 9   b  would be unstable equilibrium points, as described previously. With torque modification magnet assembly  160 , however, those points ( 194   a - c ) are now marginally stable equilibrium points—i.e., it takes significantly more torque to destabilize them. If, instead, magnets of increased power are used in torque modification assembly  160 , the graph of the torque versus rotation angle of the combined assembly will change to that shown in  FIG. 9   c . Here the marginally stable equilibrium points  194   a - c  have become stable equilibrium points  204   a - c  as illustrated in  FIG. 9   d  in terms of potential energy. 
   In  FIG. 9   d , the 60, 180, and 300 degree points  204   a - c  are “shallow” stable equilibrium points—i.e., a relatively small torque from the motor will push the rotating assembly “over the edge” and out of stable equilibrium. Once out of stable equilibrium, the rotating assembly will accelerate rapidly, pass through one of the “deep” stable equilibrium points  202   a - d , and decelerate as the rotating assembly approaches the next shallow equilibrium point. At this point, another small torque input from the motor will push the rotating assembly over the peak and into the shallow equilibrium point  204   a - c.    
   By monitoring the shaft encoder, the control processor can determine when to activate the motor so as to provide the torque pulses required to achieve the desired motion. The result is a rotary actuator that will maintain specific angular positions corresponding to the shallow equilibrium points or “operating detents”, with no torque required from the motor and thus no power consumption while in such shallow equilibrium. When desired, a relatively small torque input from the motor will cause the actuator to “snap” to the next detent at high speed, where it is captured by another small torque input from the motor. In spite of its high speed, this movement between shallow equilibrium points  204   a - c  requires no power input other than the small torque pulses necessary to destabilize and subsequently recapture the rotating assembly and to compensate for friction or drag. If the rotating assembly is stuck in one of the “deep” equilibrium points  202   a - d  when the unit is first powered up or due to a control malfunction, even a low torque motor can “bounce” it back and forth, gradually increasing the angular extent of each spring bounce, until the rotating assembly reaches one of the operating detents and can be captured there in the shallow equilibrium point  204   a - c . Although the actuator  180  and its related primary magnetic assembly  140  and torque modification assembly  160  are shown as a rotary configuration, it should be readily apparent that an “unrolled” or otherwise linear arrangement is possible without straying from the intended scope of the present invention. Such a linear variation would exhibit the same characteristics as detailed in  FIGS. 9   a - c.    
     FIGS. 10 through 14  describe an implementation of the linear format of a magnetic spring in accordance with the present invention. Specifically, this involves direct replacement of a conventional mechanical valve spring used in internal combustion engines with a magnetic valve spring in accordance with the present invention. 
     FIG. 10   a  shows a cylindrical magnetic spring  220  similar in principles to design  100  depicted in  FIG. 6   a . In magnetic spring  220  of  FIG. 10   a , the vertical thickness of each magnet ring in inner array  222  and outer array  224  has been doubled, thereby doubling the magnetic wavelength, and the number of rings in each array has been decreased. This increases the travel distance of the moving assembly without reversing the direction of magnetic force. In linear magnetic spring  240  of  FIG. 10   b , Halbach arrays with 90° rotation increments are used in inner array  242  and outer array  244  both to increase the amount of force delivered per unit of magnet mass and to increase the wavelength of the array. Magnet rings with radial magnetization can be approximated using ring segments with transverse magnetization, as is conventionally done. 
   As shown in cylinder head assembly  260  of  FIG. 11 , magnetic springs of this type would be installed in an engine in a manner similar to conventional valve springs. Specifically, the linear magnetic spring  220  of  FIG. 10   a  is used in  FIG. 11 . While both a conventional valve spring and a magnetic valve spring are shown, it should be understood that this is for purposes of illustration and not meant to suggest mixed use of a conventional valve spring with a magnetic valve spring. 
   In  FIG. 11 , the intake cam  264  provides the force required to open intake valve  274 , allowing fuel and air to enter the cylinder through intake port  268 . Conventional valve spring  278  provides the force required to close intake valve  274 . Exhaust cam  266  provides the force required to open exhaust valve  276 , allowing exhaust gases to leave the cylinder through exhaust port  272 . Magnetic valve spring  282  provides the force required to close exhaust valve  276 , much like a conventional valve spring. However, magnetic valve springs are quite different from conventional mechanical springs in several respects and offer significant potential advantages as discussed above in regard to magnetic springs in accordance with the present invention. While  FIG. 11  is generally illustrative of a magnetic spring valve, specific operational details are shown and described in regard to  FIGS. 12 ,  13   a - c , and  14   a - c.    
   The force characteristics of conventional and magnetic springs are compared in  FIG. 12 . A conventional mechanical spring can be selected to provide a particular force when the engine valve is closed (100 lbs in this case), and a larger particular force when the valve is open and the spring is compressed (350 lbs in this case). The spring force exhibited in between those two points is described by straight line  292 . With a magnetic spring, on the other hand, the force at valve closed, the force at valve open, and the shape of the force curve in between can all be selected over a wide range by varying the wavelength of the magnet arrays and the phase relationship of the moving and stationary assemblies at the valve closed position. In the example as shown, magnetic spring  294  is designed to provide about 50 lbs of force with the valve closed, about 50 lbs of force with the valve open, and a peak of about 175 lbs in between. The curve shown for magnetic spring  294  corresponds to part of one half-wavelength of the magnetic spring curve shown in  FIG. 2   b . Magnetic spring  296  also provides about 50 lbs of force at each end, but its peak force is 350 lbs in between. Magnetic spring  298  has the same force as conventional mechanical spring  292  at each end of its travel, but a higher force everywhere in between. An important point to note is that magnetic spring force characteristics can be designed to more closely approximate the needs of a particular engine than can a mechanical spring. 
   Due to their higher force over most of the range of movement, both magnetic springs represented by curves  296  and  298  in  FIG. 12  can provide substantially higher rpm capability before onset of valve float than will conventional spring  292 —without increasing the peak spring force. Specifically, the peak force of magnetic spring  296  could be decreased by 50-100 lbs while still providing performance equal to or better than conventional spring  292 , when combined with a cam profile optimized for use with the magnetic spring. Such a cam profile would be designed in such a manner so as to provide slower onset and release of valve acceleration (reduced jerk), decreasing engine vibration and valve touchdown speed. Lower forces on the cam would lower friction losses, increasing engine power and efficiency. In addition, magnetic springs will not suffer from metal fatigue or contact wear, thus providing the potential for increased reliability and longevity, and will allow the use of tuned eddy-current damping to suppress resonances and vibration. However, it is important to note that the magnets must not be overheated and care must be taken in the design of applications utilizing magnetic springs in accordance with the present invention so as to reduce heating of the magnets themselves. If such magnets exceed maximum working temperature (up to 180° C. for neodymium and 350° C. or higher for samarium cobalt) they will lose their magnetization and cease to provide any spring force. 
     FIG. 13   a  is an enlarged cross-section of a magnetic valve assembly similar to the engine valve shown in  FIG. 11 .  FIG. 13   a  shows one configuration of magnets suitable to create a magnetic spring  296 , as graphed in  FIG. 12 . In  FIG. 13   a , the valve is in the closed position with the magnetic spring forced to the limit of its mechanically allowable travel. This alignment of the two magnet arrays of magnetic spring  296  is near a stable equilibrium point, comparable to point  56   a  or  56   b  in  FIG. 3   b . In  FIG. 13   b , the valve is in the open position with magnetic spring  296  extended to the opposite limit of its mechanically allowable travel. This alignment is near an unstable equilibrium point, comparable to point  58   a  or  58   b  of  FIG. 3   b .  FIG. 13   c  is a graph comparing the compression force vs. spring compression distance for magnetic spring  296 , with the “valve closed” and “valve open” points (the limits of mechanically allowable travel) indicated on the curve. 
     FIG. 14   a  is an enlarged cross-section of an engine valve assembly showing one configuration of magnets suitable to create a magnetic spring  298 , as graphed in  FIG. 12 . This configuration includes fewer magnet elements, each of which are of increased length in the vertical dimension to increase the wavelength of the magnetic spring. In  FIG. 14   a  the valve is in the closed position, with the magnetic spring forced to the limit of its mechanically allowable travel. Again, this alignment of the two magnet arrays of magnetic spring  298  is near a stable equilibrium point, comparable to point  56   a  or  56   b  in  FIG. 3   b . In  FIG. 14   b  the valve is in the open position, with magnetic spring  296  extended to the opposite limit of its mechanically allowable travel. This alignment corresponds to the maximum force point halfway between an unstable equilibrium point and a stable equilibrium point such as points  56   a  and  58   b  of  FIG. 3   b .  FIG. 14   c  is a graph comparing the compression force vs. spring compression distance for magnetic spring  298  with the “valve closed” and “valve open” points (the limits of mechanically allowable travel) indicated on the curve.