Abstract:
An electromagnetic valve apparatus with nonlinear springs for variable valve timing in an internal combustion engine. The apparatus includes a valve, floating spring assembly, translational cam, and motor. The cam and spring serve to minimize lash and valve stem bending forces. During opening and closing of the valve, spring potential energy is converted into valve kinetic energy and then back into potential energy at the end of the motion. The potential energy is then available for the next opening/closing event. The motor initiates motion, replaces friction and vibration losses, and terminates motion. However, the motor supplies minimal energy as the valve opens and closes, and vice-versa, naturally due to combined effects of system inertia and the nonlinear spring. In addition to valve control, the apparatus may be applied to fuel injectors, or any reciprocating linear or rotary mechanism where electronic control is used.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of Application No. PCT/US13/22080 filed on 18 Jan. 2013 which claims priority from U.S. Provisional Application No. 61/661,244 filed on 18 Jun. 2012. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with U.S. Government support under grants IIP-0945595 and IIP-1058556 awarded by the National Science Foundation. The U.S. Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to an apparatus for electronic engine valve operation. More particularly, the present invention relates to electromagnetic valve assemblies with nonlinear springs and involving electronically controlled linear actuators for driving valves. 
     BACKGROUND OF THE INVENTION 
     There are various types of linear electric motors and electromagnetic actuators that can move an object along a limited length linear path and are controlled electronically. These actuators utilize electric energy and convert it into kinetic energy of a moving object when accelerating the object from a stationary position. They also compensate for any motion-related losses and decelerate the object to a stop at the end of travel while dissipating the kinetic energy of the object or converting it partially back to some other form of energy. 
     Utilization of such electric and electromagnetic actuators for driving of intake and exhaust poppet valves of an internal combustion engine is one of the many applications of these actuator mechanisms. Many such known actuators are designed for controlling the opening and closing of engine valves for implementation of variable valve timing (VVT) and variable valve lift (VVL). This significant attention to VVT and VVL is explained by corresponding performance improvements of a conventional internal combustion engines in terms of improved fuel efficiency and reduced emissions when VVT and VVL are used. 
     One embodiment of an electronically controlled linear actuator for a valve mechanism involves direct utilization of a linear electric motor for opening or closing the valve during the engine operation. Due to a very short interval of time allowed for the opening and closing events, on the order of few milliseconds, the electric motor that can open or close a conventional engine valve in the required amount of time would be too big and inefficient for practical implementation in the engine. This inefficiency arises mainly due to ohmic losses in the motor coils. In addition, if the motor is required to counter a spring force, there are likewise ohmic losses in countering the spring force in addition to the inertial forces for accelerating the valve. 
     With reference to  FIG. 1 , there is shown a prior art electronic valve system with the valve  100  oriented roughly in a half-open position. The valve controls the flow of gas through manifold  102  as part of, for example, an internal combustion engine. The net force of the springs  104  and  106  is roughly zero in this configuration. Computer-controlled electromagnets  108  and  110  act on the armature  112  to form a simple linear motor that works in conjunction with the springs  104  and  106  on the valve stem  114  to cause valve transitions. Valve closure is accomplished when the valve  100  is brought into contact with the valve seat  116 . The upper spring  104  is constrained by a stationary retainer  118  and the lower spring  106  is constrained by the stationary cylinder head  120 . Hash marks  122  are used to emphasize that a component is stationary for illustrative clarity, but not all stationary components have hash mark in the figures. 
       FIGS. 2A and 2B  show possible generic spring force  200  and spring energy profiles  252  which are generally indicative of the relationship between the valve displacement and the spring restoring force such as that shown in  FIG. 1 . During operation of the valve  100  of  FIG. 1 , the upper electromagnet  108  holds the armature  112  in an upper position with the valve  100  closed while a relatively large spring force is pulling the valve  100  downward. To open the valve  100 , the upper electromagnet is turned off and the valve  100  is released. The combined mass/spring system of valve  100 , valve stem  114 , armature  112  and springs  104  and  106  begins a nearly sinusoidal oscillation. Following a half-cycle of motion, the lower electromagnet is activated and latches the valve in the open position. Since the spring force is large in the open position, the acceleration of the valve  100  is largest just as it latched. A similar sequence closes the valve  100 . The electromagnets  108  and  110  together with the armature  112  therefore form a kind of linear motor. 
     Because the electronic engine valve of  FIG. 1  has maximum spring forces when the electromagnets  108  and  110  latch the valve  100  open or closed, the valve  100  undergoes an impulse in its 3 rd  derivative of motion known as the “jerk.” This impulse is associated with vibration and noise even when the valve  100  is latched at zero velocity. In practice, the latching forces can cause the armature  112  to impact the electromagnets  108  and  110  causing additional noise and vibration. Moreover, the valve  100  must contact the valve seat  116  at nearly the same time that the armature  112  contacts the upper electromagnet  108 . Otherwise the valve  100  may leak or may impact the valve seat  116  with excessive velocity. This creates a tolerance problem that increases the cost of manufacturing and complicates the control of the electronic engine valve. The problem of positioning the valve seat  116  accurately relative to other components (e.g., the face of upper electromagnet  108 ) is common and the present discussion refers to it as the “valve seat positioning problem” when it occurs. 
     The generalized solid curve  252  in  FIG. 2B  can be seen to specifically illustrate the total spring potential energy in the springs  104  and  106  of  FIG. 1 . In the middle position, the potential energy is defined to be zero, and as the armature  112  is deflected in either direction from this middle position the spring potential energy grows in a characteristic quadratic form of curve  252  for ideal springs obeying Hooke&#39;s law. The motion of the valve  100  under the forces of the springs  104  and  106  is analogous to the motion of ball  250  rolling in the energy well defined by the total potential energy curve  252  of the springs  104  and  106 . As may be clearly understood from  FIG. 2B  by one of ordinary skill in the art, the intersection of the axis labeled spring potential energy, the axis labeled displacement, and the curve  252  represents a state in which the valve  100  tends to return after being disturbed and which point is commonly understood as stable equilibrium. Accordingly, the middle position  212  at the bottom of the potential energy well is a stable equilibrium point. The fact that the ball  250  is on a steep incline as shown is consistent with the large restoring force being applied to the valve  100  in the open position. The large restoring force of the spring  104  and  106  implies that the linear motor (i.e., electromagnets  108  and  110  together with the armature  112 ) must apply large holding forces to maintain the valve  100  in the open or closed position which is often undesirable as this requires electrical power. 
     In light of the above, a more desirable ideal shape for a potential energy function is that shown by the dashed curve  254  in  FIG. 2B  and corresponding ideal nonlinear restoring force curve  202  in  FIG. 2A . Potential energy curve  254  reaches a peak at the open and closed positions corresponding to zero force in  FIG. 2A  where correspondences are indicated with dashed lines  206 . If such an ideal nonlinear spring were created, the holding forces of the linear motor of  FIG. 1  would be minimal and the associated jerk in the valve motion would also be minimized. In order to operate a valve with total spring potential energy of the ideal form shown as  254 , such a linear motor would have to apply a small push to move the valve off the peaks of potential energy during valve transitions. 
     It is also known that the ideal nonlinear restoring force curve  202  in  FIG. 2A  can be, for example, accomplished with a cam and spring. The present discussion refers to any mechanism where the magnitude of the force or torque required to hold the valve open or closed is less than a peak spring force as a “nonlinear spring.” Nonlinear springs are usually designed using cams in combination with springs generally abiding by Hooke&#39;s law. The ideal nonlinear restoring force curve  202  has a peak value which occurs at  204  and there is an intersection  210  where the curves  204  and  202  cross the displacement axis (with positive slope) and a corresponding zero total spring restoring force at the crossing point. Such intersection  210  is the point at which the valve  100  tends to return after being disturbed and which point is commonly understood as stable equilibrium. Accordingly, the intersection  210  is a stable equilibrium point. Whether the spring characteristic is linear or nonlinear, it is readily apparent that the given linear motor must supply any energy lost to friction, impacts, and vibration. 
     One example of a nonlinear spring can be realized with the prior art system of  FIG. 3A . Cam  300  works in conjunction with cam followers  302  and  304 , and two springs  306  and  308  to create the potential energy characteristic of  FIG. 3B  which has an associated nonlinear spring curve (not shown) similar to  202 . Note that the ordinate in  FIG. 3B  is the motor displacement angle θ. The motor  310  is coupled to the cam  300  in any known manner (e.g., by gears, belts, or direct co-axial drive) as generally indicated by the dashed line  312 . The motor executes a reciprocating motion and causes a reciprocating rotary motion of +/−45° in the cam relative to the θ=0° reference angle  314 . The cam  300  is shown in the +45° position. An important property of this design is the fact that a positive follower force is applied consistently to the cam  300  during operation as the springs  306  and  308  are always under some level of compression. The present disclosure refers to such a follower and cam combination a “lashless cam.” In contrast, a follower and cam combination whose contact force becomes less than or equal to zero at some point during its operation is called a “lashing cam.” Lashing cams have the undesirable property of having impact between the follower and the cam which cause wear, vibration and energy loss. 
     It should be noted that the positive contact force in  FIG. 3A  is applied intrinsically by the energy storing springs  306  and  308  rather than extrinsically with a separate preload mechanism whose primary function is to apply force or absorb lash in the system. The present disclosure refers to any follower and cam combination held in positive contact using an energy storage spring as an “intrinsic lashless cam.” Such cam and follower combinations are desirable due to their simplicity in addition to the reduction in impact, vibration, and noise associated with the elimination of lash in the valve system. 
       FIG. 3B  shows the curve  350  for the total potential energy in the springs  306  and  308  for the system of  FIG. 3A . The symmetry of the curve follows from the symmetry of the cam  300 , followers  302  and  304 , and identical maximum compression and spring constants of the springs  306  and  308 . All of these factors can be varied to shape the total potential energy curve. For example, one prior art design aims to minimize the peak energy  352  in order to minimize the torque supplied by the motor. Further, the 90° angle shown between the springs  306  and  308  can be varied to shape the total potential energy curve. In addition to the compressive force that the cam  300  applies to the followers  302  and  304  and springs  306  and  308 , the cam  300 , at some points in the cycle, also disadvantageously applies a tangential force to the followers  302  and  304  and a bending force the valve stem  315  and pin  316 , induces bending vibrations in the valve stem  315  and pin  316 , and increases frictional forces in the valve guide  318  and pin guide  320 . Because the valve guide  318  often serves as a gas seal, it is difficult to mitigate frictional losses with rolling element bearings or other such mechanisms in the valve guide  318 . In the present disclosure, this type of cam follower producing tangential or bending forces is described as a “non-zero tangential force cam” and those that do not produce tangential or bending forces are described as a “zero tangential force cam.” It should be understood though that exactly zero tangential force is not attainable due to manufacturing and other imperfections. 
       FIGS. 4A, 4B, and 4C  depict another prior art electronic valve system.  FIG. 4B  is a section of the disk cam  400  in  FIG. 4A  along section  4 B- 4 B.  FIG. 4C  shows the total potential energy function  460  for springs  402  as a function of motor angle θ in  FIG. 4A . 
       FIG. 4A  shows the half-open position for valve  404  corresponding to the minimum total potential energy of the springs  402 . Motor  406  drives the disk cam  400  in a rotary oscillatory fashion.  FIG. 4B  shows section  4 B- 4 B of  FIG. 4A . The cam follower  408 , typically a roller follower, follows the cam slot profile  430  during valve transitions. The cam slot profile surface is nearly tangent to a concentric circle at  432  in the valve open position, and nearly tangent to a second concentric circle at  434 . The axis of cam rotation in  FIG. 4B  corresponds to the center of the concentric circles  432 ,  434 . This near tangency condition at  432  and  434  implies that the motor torque required to hold the valve closed or fully open is advantageously nearly zero. The flats  462  and  464  in  FIG. 4C  correspond to the mentioned tangencies in the cam profile. 
     With further regard to  FIG. 4A , as one of the equilibrium positions of the springs  402  is the half-open position, the follower  408  applies an upward force along the positive Z direction (shown by arrow at bottom of  FIG. 4A ) when the valve  404  is closed and a downward force along the negative Z direction when the valve  404  is fully open. As a consequence, the cam  400  and follower  408  combination is a lashing cam. The follower must alternately contact the inner and outer profile surfaces of the cam slot  430 . This lash disadvantageously causes impact, vibration, and energy losses in the valve system. In addition, the force  436  applied to the follower  408  by the cam  400  has a non-zero tangential component  415 . Thus, such cam system is a non-zero tangential force cam. Accordingly, it applies a bending force to the valve stem  410  thereby creating bending vibrations of the valve stem  410 , and contributes to friction in the valve guides  411 . Another drawback of this design is the valve seat positioning problem associated with maintaining tolerance on dimension  412  between the seat and the cam profile surface at  434 . 
       FIGS. 5A, 5B, and 5C  show another known variation of that shown in  FIG. 4A  which can overcome the valve seat positioning problem because the cam profile is parallel to the valve motion in the seated position.  FIG. 5B  shows section  4 B- 4 B of  FIG. 5A . Rotary spring  500  together with disk cam  502  and cam follower  504  create the spring potential energy curve  558  shown in  FIG. 5C . Note that the ordinate in  FIG. 5C  is the vertical displacement Z of the valve and linear motor  506 . The minimum of curve  558  corresponds to the valve half-open position. The cam profile  530  is tangent to radial lines  532  and  534  at the ends of the motion so that the spring potential energy has flats  560  and  562  respectively. Consequently, the motor force opposing the spring force when the valve is closed or fully open is nearly zero. The linear motor must counter any gas forces on the valve in contrast to the design of  FIG. 4A . Near the ends of the valve motion, the spring displacement forces are high. Hence, there is a large cam follower force  536  shown in  FIG. 5B  and a large tangential force  538 . Thus, this prior art design provides a non-zero tangential force follower with the associated problems of bending forces and vibration and increased friction in the guides  508 . Finally, this is a lashing cam system as the cam torque switches sign at the half-open point. Thus, there is impact, vibration, and energy loss as the cam follower moves from one surface of the cam slot to the other. 
     Thus, it is desirable to create a mechanical valve mechanism with a natural motion that is nearly the desired opening/closing motion of the valve and to augment this mechanism with an electric motor to control timing and compensate for losses due to friction, impacts, mechanism lash, vibration and other loss occurrences. It is desired, in addition, to have such an electrically actuated valve mechanism that has minimal friction, minimal bending forces on the valve stem, minimal jerk in the valve motion, minimal unwanted vibration, and minimal impacts to due to lash in the mechanism. It is also desired that the valve mechanism have minimal mass because the motor is needed to initiate the opening/closing of the valve and to stabilize the valve motion upon closing. Finally, it is desirable to have motor current waveforms that achieve the desired opening and closing times of the valve and also minimize the electrical power consumed by the electric motor. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to obviate or mitigate at least one disadvantage of previous electrically actuated valve mechanisms. 
     In a first aspect, the present invention provides an electromagnetic valve apparatus, the assembly including: a valve stem having a longitudinal axis, the valve stem including a valve located on an end thereof; a motor providing displacement of the valve stem; a spring mechanism symmetrically providing force for translation to the valve, the spring mechanism being pivotably attached to a stationary section, the force providing positive contact pressure to the valve stem between a fully open position of the valve and a fully closed position of the valve; a first reduced force point corresponding to the fully open position and at which the force acts upon the valve stem to maintain the fully open position; and a second reduced force point corresponding to the closed position and at which the force acts upon the valve stem to maintain the fully closed position. 
     In further aspect, the present invention provides an electromagnetic valve apparatus, the assembly including: a valve stem having a longitudinal axis, the valve stem including a valve located on an end thereof; a motor providing displacement of the valve stem; a pivoting spring type nonlinear spring; a first reduced force point corresponding to the fully open position and at which the force acts upon the valve stem to maintain the fully open position; and a second reduced force point corresponding to the closed position and at which the force acts upon the valve stem to maintain the fully closed position. 
     According to the present invention there is a translational camshaft (i.e., cam) attached to a valve and a spring biased follower tracking the cam profile. Such a valve/cam/spring system creates a vertical force component along the axis of the valve stem such that the valve naturally opens subsequent to a small initial input force from a linear motor that pushes, or otherwise releases, the valve from the initial position. Once the motion is initiated, the natural motion of the valve/cam/spring system is such that the valve accelerates in the opening direction as potential energy in the spring is converted to kinetic energy of the valve. Then, as the valve approaches the open position, the valve decelerates, loses kinetic energy which is converted to potential energy in the spring by the cam profile. The linear motor applies relatively small forces to control the motion from the closed position, to compensate for losses due to friction, impacts, vibration, and other losses in the mechanism, and to control motion to the open position. The closing of the valve follows a similar sequence of events. For purposes of the present invention, this application refers to the operations of valve closing and valve opening as “valve transitions.” There is substantial similarity in the opening and closing operations and, for brevity and illustrative clarity, it is therefore useful to introduce this notion of valve transitions. 
     Because external power is required for the motor to compensate for losses, it is important that losses due to friction, impacts between the cam and follower, and vibration throughout the mechanism be minimized. Accordingly, the valve/cam/spring system embodied in the inventive valve apparatus having a floating spring assembly is symmetric so that negligible lateral and bending forces are applied to the valve stem which would cause friction in the valve guides. Also, the cam follower contact is preloaded by the energy storing springs so that there are no losses due to lash impacts of the cam follower. 
     Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present invention will now be described, by way of example only, with reference to the attached Figures. 
         FIG. 1  shows a prior art electromagnetic valve system. 
         FIGS. 2A and 2B  show possible generic spring force and spring energy profiles. 
         FIGS. 3A and 3B  describe one prior art electromagnetic valve system. 
         FIGS. 4A, 4B, and 4C  describe another prior art electromagnetic valve system. 
         FIGS. 5A, 5B, and 5C  describe yet another prior art electromagnetic valve system. 
         FIGS. 6A and 6B  show the preferred embodiment of the present invention. 
         FIGS. 7A and 7B  show flexure elements useful in the invention. 
         FIG. 8  shows another alternative embodiment of the present invention. 
         FIG. 9  shows yet another alternative embodiment of the present invention. 
         FIGS. 10A and 10B  show cam profiles. 
         FIGS. 11A and 11B  show a rotary embodiment of the present invention. 
         FIGS. 12A and 12B  describe yet another alternative embodiment of the present invention. 
         FIGS. 12C and 12D  describe yet still another alternative embodiment of the present invention. 
         FIGS. 13A, 13B, 13C, and 13D  describe preferred motor current profiles for the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Generally, the present invention provides an apparatus for electronic engine valve operation that includes nonlinear springs and an electronically controlled actuator for driving valves in a manner which minimizes losses due to friction, impacts between the cam and follower, and vibration throughout the electronic engine valve. The present invention accomplishes this by providing an arrangement of the valve, cam, and spring that is symmetric so as to avoid lateral and bending forces typically otherwise applied to the valve stem and thereby avoid friction in the valve guides. The present invention also preloads the cam follower contact via the energy storing springs so as to preclude losses due to lash impacts of the cam follower. 
       FIGS. 6A and 6B  show a first embodiment of the present invention. This inventive arrangement overcomes problems in prior art designs regarding the valve seat positioning problem, lashing cam, non-zero tangential force, and incorporates an intrinsic lashless cam. The inertia of the moving masses is also minimized. Further, the inductance of the motor coil is minimized to enable the high-speed electronic control of the valve. 
     With specific reference to  FIG. 6A , there is shown a symmetric translational cam  600  having a symmetric surface profile which produces an ideal nonlinear spring characteristic similar to that of curve  202  in  FIG. 2A .  FIG. 6B  shows a section along  6 B- 6 B in  FIG. 6A . Roller followers  602  and  604  are pressed via expansion forces toward the lateral surfaces of cam  600  by springs  606  and  608  which are held under compression. The cam profile has four identical flats (one identified as flat  601 ). Each flat  601  provides for minimal holding force by the motor (described in more detail herein below) in the fully open and closed positions. Thus, the minimal holding force at each flat  601  may be alternatively described and identified as a reduced force point. Moreover, the cam flats  601  eliminate any valve seat position problem as previously described in the background section. It should be understood that the flats  601  may alternatively be only nearly flat and that various trade-offs on holding force and switching time of the valve  634  can be optimized in the cam profile design. 
     On the lower ends of the inner rocker arms  610  and  612 , there are included stationary pivots retained in the engine head  628  and which position the roller followers  602  and  604  on the upper end of the inner rocker arms  610  and  612 . Thus, the roller followers  602  and  604  are restricted to an arcuate motion which is largely horizontal for small lateral displacements. While there is some vertical motion of the roller followers  602  and  604 , the combined cam, rocker, roller follower system is configurable to accomplish a desired force curve such as  202 . For example, if a cam is first designed based on the assumption that the roller followers follow a purely horizontal motion, a modest reshaping of the cam will produce the desired force curve in the presence of arcuate roller follower motion. Springs  606  and  608  are held in position with inner spring retainers  614  and  616 , and outer spring retainers  618  and  620 . The outer spring retainers provide a compressive load on the springs and roller via cross members  622  located behind and in front of the springs as shown in  FIG. 6B . The cross members  622  preferably consist of rigid bars that serve to maintain the orientation of spring retainers  614 ,  616 ,  618  and  620  in addition to providing the compressive load on the springs. The outer spring retainers  618  and  620  are supported with outer rocker arms  624  and  626  so that negligible lateral load is transmitted to the engine head  628  by any of the rocker arms  610 ,  612 ,  624 , or  626 . Further, the length of the rocker arms  610 ,  612 ,  624 ,  626  may be increased to minimize any vertical motion in the roller followers  602  and  604  as necessary. 
     Springs  606  and  608  form a spring mechanism symmetrically providing force for translation to the valve  634 . However, it should be readily apparent from  FIG. 6A  that the symmetry of the spring mechanism and the use of rockers  624  and  626  will accommodate any residual asymmetry due to an assortment of variables such as mechanical variations or manufacturing imperfections. Examples of such variables could be slight differences in stiffness between the two springs  606  and  608  or variations in their equilibrium length. It should therefore further be apparent that the use of rockers  624  and  626  are important components in that they provide the “floating” aspect for the spring mechanism due to the fact that the springs  606  and  608  are not rigidly attached to the engine head  628 . 
     Still further, some or all of the rocker arms  610 ,  612 ,  624 ,  626  may be replaced with flexures to constrain the motion of the roller followers and the flexures may serve some or all of the spring function as well.  FIG. 7A  depicts a flexure  702  made from elastic material such as, but not limited to, spring steel or titanium, mount  704 , and attachment  706  where spring retainers are attached rather than to rocker arms. The flexure in  FIG. 7B  is shown displaced to the right relative to the equilibrium configuration of the flexure which lies along a straight line segment. As the flexure bends, there is a small amount of vertical motion that can be accounted for in the design of the cam profile.  FIG. 7B  shows another type of flexure support system incorporating a folded-beam flexure. This flexure support system incorporates four flexures of the type indicated at  710 . Mount  712  is connected by supports  714  and  716  to two flexures which, in turn, are connected via floating body  718  to two more flexures connecting to the attachment  720  where the spring retainers are attached. 
     In the inventive embodiment including either the rocker arms or folded-beam flexures, there is negligible lateral load transmitted to the valve stem  630  due to the rocker arms (or folded-beam flexures) and the symmetry of the double translational cam system. Thus, such an electronic valve system in accordance with the first embodiment has a zero tangential force cam in the sense that the only source of bending forces on the valve stem is parasitic frictional force in the rocker arms (or folded-beam flexures), minor imbalances in the spring masses, and similar second order effects. While the present description uses the term “spring” in the aforementioned and the following embodiments and illustrates such spring in particular as a coil spring, it should further be understood that any similar device that stores potential energy in the elastic deformation of a solid or gas may be used. For example a wave spring, torsion spring, leaf spring, cantilevered elastic beam, elastic flexures, or gas springs are within the scope of the intended invention so long as there is a positive contact force between the followers and the symmetric translational cam. This positive contact ensures lateral forces from the spring for continuous contact pressure between the cam and follower(s). 
     With continued reference to  FIG. 6A , the outer rocker arms  624  and  626  allow the cross members  622  and outer spring retainers  618  and  620  to move to a minimum spring energy position so that there is no net tangential bending force on the valve stem  630  and valve guide  632 . Because of the effect of the outer rocker arms  624  and  626 , the present invention is described as an electronic valve apparatus which has, as previously mentioned above, a “floating” spring assembly that applies negligible net bending force on the valve stem  630 . The floating spring assembly is itself formed by at least a spring mechanism having one or more springs where such springs may be of varying type. Indeed, the springs may vary independently from one another in structure and design so long as the spring mechanism collectively provides negligible net bending force of the valve stem  630  thereby enabling the floating spring assembly to function as intended. It should further be understood that the outer rocker arms  624  and  626  and cross members  622  can be replaced with two rigid supports for the outer spring retainers without affecting the symmetry of the spring and cam system and without straying from the intended scope of the present invention. Moreover, the floating spring assembly can minimize bending forces on the valve stem even when there are differences in stiffness between the two springs  606  and  608  due to manufacturing errors. Still further, the floating spring assembly is arranged in such a manner that precludes unfettered movement due in large part to the tethering aspect of the rocker arms which also form part of the floating spring assembly. Such tethering provides smooth action of the floating spring assembly and avoids random and clumsy motions such as would occur via typical guides. 
     Referring again to  FIG. 6A , the linear motor will now be further described. Such motor is shown in the form of a generally axisymmetric moving coil actuator (frequently called a voice-coil actuator in the linear motion case) which is used to actuate the valve stem  630  and hence the valve  634 . The voice coil actuator includes a wire coil  640  wound on bobbin  642 . A radial magnetic field is provided for the conductive wire coil  640  using annular magnet  644 , iron core  646 , and iron pole  648 . The iron core  646  and iron pole  648  incorporate, respectively, inner conductive shields  650  and outer conductive shields  652 . Eddy-currents induced in the conductive shields  650  and  652  by time-varying currents supplied to the conductive wire coil  640  serve to confine time-varying magnetic fields produced by the coil  640 . Hence, the inductance, and more generally the impedance, of the coil  640  is reduced in magnitude so that high currents in the coil  640  can be changed more quickly and with lower control voltages. The conductive shields  650  and  652  are typically made from copper or aluminum, and their dimensions are optimized to balance the positive effects of shielding and the negative effects of reduced flux through the coil  640  due to their low magnetic permeability. The conductive shields  650  and  652  can also be made from alternating layers of thin copper and iron rings stacked vertically to provide shielding and high average magnetic permeability. Other approaches readily apparent to one of skill in electrical motor design related to mixing conductive and permeable materials and alternative embodiments of a linear motor are possible as well without straying from the intended scope of the present invention. 
     In  FIG. 6A , there is also shown sensor  654  which is in communication with valve stem  630 . The sensor  654  monitors movement characteristics such as the position, velocity, and/or acceleration of the valve stem  630  for feedback control of the voice coil actuator or other embodiments of a linear motor. The sensor  654  may be inductive, capacitive, optical or any other form of sensor mechanism so long as it provides the requisite measurement for control. One cost-effective form of sensing is to use the back electromotive force (or “back-EMF”) voltage generated by the motion of the coil to estimate its position. Similar approaches have been applied to so-called “sensorless” motor control and the present disclosure uses such terminology in the same way herein. The method of estimating the position may employ what is known as an “observer” to those skilled in the art of control engineering. 
     Referring to  FIG. 6B  which is a cross-sectional view taken from line  6 B- 6 B in  FIG. 6A , it should be readily understood that there are a total of four roller followers  602 ,  604  in this embodiment, though there need only be at least two followers. One advantage of the configuration as shown and described is that this arrangement serves to prevent rotation of the valve  634  which protects the power supplying flexible wiring or flat cable (not shown) that connects to the conductive wire coil  640 . 
       FIG. 8  depicts a further embodiment of the present invention. In this embodiment, the positions of cams  855  and followers  859  are interchanged relative to the previous embodiment. Here, the resulting nonlinear spring energy has the same preferred ideal curve  254  as shown in  FIG. 2B . Another difference in this embodiment is that the cams  855  are rigidly attached to spring retainer  856  versus rigid attachment to the valve stem. The spring retainer  856  is rigidly attached to rocker arms  857  which are attached to pivot  858 . Followers  859  are attached to the valve stem. As in the previous embodiment, this alternative embodiment is symmetric and functions in a similar manner as before. 
       FIG. 9  is yet another embodiment of the present invention with a cam design identical the first embodiment shown in  FIG. 6A . While the linear motor, cam, and valve components remain unchanged from the first embodiment, the floating spring assembly in the form as shown and described in the preceding embodiments has been replaced with flexible element  960 . The flexible element  660  is itself a spring movably affixed at a centrally located pivot. Here, the symmetrical spring energy is stored in flexible element  960  provides generally equal lateral compression of the followers  962  and  963  against the cam  964  so as to provide positive contact pressure on the cam. Thus, an effective floating spring assembly is accomplished by supporting the flexible element  960  on the pivot  961 . 
       FIG. 10A  is the cam profile for the first embodiment as seen in  FIG. 6A  which produces potential energy plateaus at  1062  and  1063 . With such potential energy plateaus at  1062  and  1063 , the linear motor can hold the valve in the open and closed position with little or no effort to counter the nonlinear spring forces. Further, the potential energy plateau at  1063  near the closed position eliminates any valve seat positioning problem because a feedback control system can, through sensing provided by sensor  654 , learn the valve seat position and control the closing velocity in response to physical variables including, but not limited to, manufacturing errors, thermal expansion, and wear. 
       FIG. 10B  illustrates possible cam profile modifications that accomplish certain beneficial functions. For example, an opening variation  1064  may indicate a corresponding mechanical stop feature which will limit the motion of the valve near the open position, and a profile closing variation  1068  may indicate a different physical cam feature configured to create a small closing force on the valve when the linear motor is not energized. Note that the closed position can vary somewhat and the profile closing variation  1068  will still provide a small closing force. 
     The aforementioned embodiments and cam configurations are equally applicable to rotary cam implementations. As such,  FIGS. 11A and 11B  illustrate one possible rotational embodiment of the present invention. This rotational embodiment is analogous to the embodiment of  FIGS. 6A and 6B  with the linear motor replaced with a rotary motor, the symmetric translational cam replaced with a symmetric rotary cam, and the linear poppet valve replaced with a rotary ball valve. Accordingly, most of the components in  FIGS. 11A and 11B  can be understood in terms of the detailed description of  FIGS. 6A and 6B  with explanations as noted herein below. 
     With reference to  FIG. 11A , a rotary motor  1100  rotates valve stem  1101  supported by bearings  1102  and  1103 . The valve stem  1101  is connected to a rotary ball valve  1104  whereby rotation is monitored with sensor  1105  mounted on the valve stem  1101 . The rotary ball valve  1104  consists of an input port  1106 , an output port  1108 , and a flow passage  1110  in the ball  1112 . As should be readily apparent, when the flow passage  1110  in the ball  1112  is aligned with ports  1106  and  1108 , the valve is therefore open as shown and non-alignment occurs during valve closure. The ball valve housing  1114  may incorporate fluid or gas seals (not shown) as is customary in the art. To enable rapid switching between the fully open and fully closed positions of the valve—roughly 90° rotation—a nonlinear spring operates with regard to a cam  1116  attached to the valve stem  1101 . The nonlinear spring is described with reference to  FIG. 11B  below along with other components. 
       FIG. 11B  is a cross section representing a plane  11 B- 11 B as indicated in  FIG. 11A . Here, there are illustrated the cam profile of rotary cam  1116 , cross members  1122 , support  1120 , rockers  724 ,  726 ,  728 ,  730  and roller followers  732 ,  734 , and springs  736  and  738 . The section  11 A- 11 A of  FIG. 11B  is that section depicted in  FIG. 11A . For the cam angle shown, the springs are in their most compressed state. By rotating the cam in the clockwise direction from the open position, spring potential energy is transformed into rotary kinetic energy and then back into spring potential energy as the valve moves to the closed position. Negligible lateral loads from the springs are translated to the valve stem due to the symmetry of the system and the use of a floating spring assembly accomplished with the rocker arms shown. 
       FIG. 12A  shows yet another embodiment of the present invention wherein the nonlinear spring is formed of upper springs  1202 , lower springs  1204 , and eight pivots  1206 . A linear motor  1200  is provided in a similar manner to the linear motor components described in regard to  FIG. 6A . Each pivot  1206  is located at the end of each spring  1202  and  1204 . Four pivots are relatively stationary in that they are located in a fixed manner on a mounting structure  1207  and four pivots are movable in that they are located on the reciprocating valve stem  1208 . In the configuration shown, lower springs  1204  are at their natural length and apply no force to the pivots  1206  to which they are attached. Upper springs  1202  are compressed, but apply no net force to the valve stem so that the valve is in an equilibrium position relative to the potential energy in the springs  1202  and  1204 . For purposes of this description, this nonlinear spring configuration is referred to as a pivoting spring type nonlinear spring. As the valve is opened by linear motor  1200 , the upper springs release their potential energy and help accelerate the valve toward the open position shown in  FIG. 12B . In this movement, the kinetic energy of motion is converted back to potential energy in the springs. Accordingly, the springs and pivots create a desirable ideal nonlinear spring energy curve similar to  254  in  FIG. 2B . 
       FIG. 12C  shows a variation on the alternative embodiment of  FIGS. 12A and 12B . In this embodiment, the upper spring  1210  and lower spring  1212  are formed by disk springs. For purposes of illustrative clarity, such a disk spring is show in isometric  FIG. 12D . The disk springs  1210  have rolled edges  1214  and  1216  which form bearing surfaces and fit in grooves such as  1218  in cylindrical housing  1220  and similar grooves in the valve stem. The grooves  1218  serve to function as pivot points. The natural uncompressed form of disk spring  1212  is that form depicted in  FIG. 12C  where the disk spring  1212  has a conical form pointed upward. The natural uncompressed form of disk spring  1210  is a similar conical form pointed downward. It should be understood therefore that either disk spring in its compressed form represents an unstable equilibrium position. Slots  1222  shown in  FIG. 12D  facilitate the construction of the electronic valve system in that the disk spring can be pressed onto the valve stem and the rolled edges such as  1214  will snap into place thereby effectively forming pivot points on the valve stem. 
     Operation of the first embodiment as shown in  FIG. 6A  will now be described in terms of valve movement in relation to  FIGS. 13A through 13D . 
       FIG. 13A  graphically depicts a typical velocity waveform for the closing of the valve in  FIG. 13A . The time interval for a transition T is taken to be [−T/2, T/2] so that the midpoint is 0.  FIG. 13B  graphically depicts a corresponding current waveform for the linear motor in  FIG. 13A  with an initial pulse to start the motion and a final pulse to stop the motion - with a significant fraction of the forcing coming from the nonlinear spring. The dashed curve  1300  depicts an enlarged initial pulse necessary to compensate for friction or other losses in the electromagnetic valve system.  FIG. 13C  shows an alternative and desired current signal shape that should be added to the solid curve of  FIG. 13B  to compensate for friction and other losses.  FIG. 13D  shows a typical current waveform which is the sum of start and stop pulses ( FIG. 13B ) and a compensation waveform ( FIG. 13C ) for friction and other losses. Mathematically, such energy transfer to the moving components as graphically depicted can be postulated as follows. 
     Consider the force produced by permanent magnet linear motors of the type shown in  FIG. 6A  can be approximated by
 
 F ( t )= KI ( t )  (Eq.1)
 
     Where F(t) is the force in the positive Z direction (e.g., in Newtons), K is the force constant of the motor (e.g., in Newtons/Amp), and I is the coil current (e.g., in Amps). The power lost in the coil due to ohmic heating is
 
 P   ohmic ( t )= I ( t ) 2   R   (Eq. 2)
 
     where R is the coil resistance. The mechanical power delivered to the valve stem is
 
 P   mechanical ( t )= F ( t ) v ( t )  (Eq.3)
 
     Where F(t) where v(t) is the velocity of the valve. There are many formulations of the optimal control problem involving efficiency, voltage and current limits on the drive electronics and so forth, but a simple measure of performance that points to an aspect of the present invention is the maximization of mechanical energy to the ohmic loss in the coil. Preferably, for the sake of convenient normalization, the ratio of mechanical energy to the square root of the ohmic loss in the coil will be optimized: 
     
       
         
           
             
               
                 
                   
                     
                       
                         ∫ 
                         
                           
                             - 
                             T 
                           
                           / 
                           2 
                         
                         
                           T 
                           / 
                           2 
                         
                       
                       ⁢ 
                       
                         
                           F 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           v 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅆ 
                           t 
                         
                       
                     
                     
                       
                         
                           ∫ 
                           
                             
                               - 
                               T 
                             
                             / 
                             2 
                           
                           
                             T 
                             / 
                             2 
                           
                         
                         ⁢ 
                         
                           
                             
                               I 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             2 
                           
                           ⁢ 
                           R 
                           ⁢ 
                           
                             ⅆ 
                             t 
                           
                         
                       
                     
                   
                   = 
                   
                     
                       K 
                       
                         R 
                       
                     
                     ⁢ 
                     
                       
                         
                           ∫ 
                           
                             
                               - 
                               T 
                             
                             / 
                             2 
                           
                           
                             T 
                             / 
                             2 
                           
                         
                         ⁢ 
                         
                           
                             I 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                             v 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ⅆ 
                             t 
                           
                         
                       
                       
                         
                           
                             ∫ 
                             
                               
                                 - 
                                 T 
                               
                               / 
                               2 
                             
                             
                               T 
                               / 
                               2 
                             
                           
                           ⁢ 
                           
                             
                               
                                 I 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               2 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ⅆ 
                               t 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     Using the notions of norms and inner products in Hilbert spaces, the rightmost term in previous equation is a constant multiplied by an inner product divided by a norm. Assuming that the desired velocity waveform v(t) is fixed, the Cauchy-Schwarz inequality reveals that the optimal loss compensating current waveform is proportional to velocity:
 
 I ( t )∝ v ( t )  (Eq.5)
 
     Normally, the sign of the friction compensating current is such that it enhances the motion of the valve and the current and velocity have the same sign. However, in some cases gas forces on the valve may overcome friction and act to accelerate the valve transition. In this case, the desired compensating current will tend to slow the valve and will have the same shape as the velocity waveform but have opposite sign. 
     This heuristic derivation of the optimal compensating current can be validated with more detailed optimization calculations that incorporate the cam profile, friction models, coil inductance, current/voltage limits of the drive electronics. In spite of the simplicity of the formulation of equations (1-5), the utility of a loss compensating current of the form shown in  FIG. 9C  persists under a range of conditions. The start/stop current has a largely antisymmetric form with peaks at the ends of the switching time interval, and the loss compensating current has a largely symmetric form with a broad peak. 
     Near optimal waveforms like that of  FIG. 9D  can be characterized more quantitatively as follows. The symmetric part, I s (t), and antisymmetric part, I a (t), of the total current waveform, I(t), are given by 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       s 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           I 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         + 
                         
                           I 
                           ⁡ 
                           
                             ( 
                             
                               - 
                               t 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       I 
                       a 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           I 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         - 
                         
                           I 
                           ⁡ 
                           
                             ( 
                             
                               - 
                               t 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
     Observe that I(t)=I s (t)+I a (t). The antisymmetric part is largely the start/stop signal, and the symmetric part is largely the friction compensation signal. Define a normalized standard deviation for the symmetric part to quantify the spread of the compensating current as follows. The area under the absolute value of the symmetric part is given by 
     
       
         
           
             
               
                 
                   
                     
                        
                       
                          
                         
                           I 
                           s 
                         
                          
                       
                        
                     
                     1 
                   
                   = 
                   
                     
                       ∫ 
                       
                         
                           - 
                           T 
                         
                         / 
                         2 
                       
                       
                         T 
                         / 
                         2 
                       
                     
                     ⁢ 
                     
                       
                          
                         
                           
                             I 
                             s 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                          
                       
                       ⁢ 
                       
                         
                           ⅆ 
                           t 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     Define a normalized symmetric current by 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       sn 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                        
                       
                         
                           I 
                           s 
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                        
                     
                     
                       
                          
                         
                            
                           
                             I 
                             s 
                           
                            
                         
                          
                       
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
     The area under this positive-valued function is 1 so that it is similar to a probability density function. Finally, define a normalized standard deviation of the symmetric part by 
     
       
         
           
             
               
                 
                   
                     σ 
                     sn 
                   
                   = 
                   
                     
                       
                         ∫ 
                         
                           
                             - 
                             T 
                           
                           / 
                           2 
                         
                         
                           T 
                           / 
                           2 
                         
                       
                       ⁢ 
                       
                         
                           
                             I 
                             sn 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               t 
                               T 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           ⅆ 
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     It thus forms part of the present invention to use efficient current signals with broad symmetric parts located near the middle of the time interval. Such symmetric parts generally have either positive or negative sign, and have normalized standard deviations of less than ¼ and preferably near ⅕. 
     The above-described embodiments of the present invention are intended to be examples only. Alterations, modifications and variations may be effected to the particular embodiments by those of skill in the art without departing from the scope of the invention, which is defined solely by the claims appended hereto.