Field of the Invention

The field of the invention is motor impact rings. Background

The background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.

Pistons have long been used in various motor designs in order to turn the drive shaft of pneumatic motors. Pistons generally function by sealing two cavities within the motor, which cooperate to push a drive shaft when the air pressure of one cavity exceeds the air pressure of the other cavity. The classic piston geometry is the axial piston geometry used in a traditional crankshaft, which was first patented by Maxime Guillaume in FR534801. The more air that is displaced when increasing the air pressure of one of the engine cavities, the more force that is imparted upon the drive shaft.

Many different piston geometries have been developed in order to maximize the air displacement when operating with increased cavity air pressure. US8162621 to Walker teaches radial piston geometries that increase the amount of air pressure that could be handled by the engine cavity, thereby increasing the amount of force induced upon the drive shaft. Depending upon the number of pistons compressed serially one after another, Walker's design creates ebbs and flows when using a non-combustion power source, such as water or steam. In addition, by operating a drive train with multiple pistons, Walker's design drastically reduces the size of the cavity that can be compressed.

Walker and all other publications herein are incorporated by reference to the same extent as if each individual publication or patent application were specifically and individually indicated to be incorporated by reference. Where a definition or use of a term in an incorporated reference is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply. US7713042 to Rodgers teaches a rotary vane piston that pushes vane pistons about a drive using a combination of (i) an irregularly shaped chamber and (ii) vanes that vary their length depending upon their location within the irregular chamber. By using vanes that are evenly distributed about the driveshaft, however, Rodgers' design limits the volume of air that can be displaced when increasing the air pressure of one of the cavities.

US201 10185998 to Murphy, the Applicant's own work, teaches toroidal pistons rotating serially about the drive shaft to increase/decrease the volume of air that is displaced when increasing/decreasing the air pressure of one of the cavities. Murphy's toroidal engine uses impact rings to prevent the pistons from hitting one another and to promote energy transfer between pistons. The wedge-shaped protrusions on Murphy's impact ring, however, undergo a great deal of wear-and-tear by suffering collision after collision, and need to be replaced rather frequently.

WO201 1/040869 to Svenska teaches an engine system having one or more stop rings that increase the amount of friction imparted to a clutch before the impact ring is engaged. If, however, the stop rings of Svenska were used to slow down a piston before it hits an impact ring, the increased friction would dramatically reduce the amount of force imparted on the drive shaft.

Thus, there is still a need for improved systems and methods for minimizing wear and tear of impact rings in toroidal piston engines. Summary of The Invention

The inventive subject matter provides apparatus, systems and methods in which a pair of impact rings that transfer kinetic energy between rotors are modified to reduce stresses upon the impact rings during collisions. Generally, each impact ring has a pad, and is coupled to a rotor such that when a rotor rotates, the pad of one impact ring strikes the pad of another impact ring, transferring kinetic energy between the rotors, while preventing pistons coupled to the rotors from striking one another directly.

While the faces of the striking surfaces of the impact ring pads are generally square in shape, the faces of the striking surfaces could be altered to have many different sizes, for example circular, elliptical, rectangular, hexagonal, triangular, or pentagonal with rounded or pointed corners. Preferably, the faces of the striking surfaces are rectangular in shape, and preferably have a length and width ratio between 1 :2 and 1 : 1. As used herein, the length of the striking surface refers to the distance from the outer face of the impact ring to the outer face of the striking surface, while the width of the striking surface refers to the thickness of the striking surface. Referring to the drawings shown herein, the length of the striking surface is shown as the distance between inner edge of the striking surface to the outer edge of the striking surface, and the width is shown as the distance between the inner circumference of the impact ring and the outer circumference of the impact ring. Preferably, the ratio between the length and width of the striking surfaces are between 6: 11 and 9: 1 1. In an exemplary embodiment, the striking surfaces of the impact rings are shaped to have a length of 6 mm and a width of 1 1 mm.

While the junction between the striking surface of the impact ring and the outer face of the impact ring is generally a sharp, 90 degree angle, that corner could be filleted or angled to further distribute impact forces. Preferably the fillet has a radius of at least 2 or 3 mm. An exemplary fillet has a radius of 3.175 mm. In alternative embodiments, the junction between the outer face of the impact ring and the striking surface has a plurality of smaller angles, such as two 45 degree angles, three 30 degree angles, six 15 degree angles, and so on and so forth. Generally the outside corner of the striking surface is also filleted or angled to substantially match the fillet of the inside corner, and preferably has a radius within 2 mm, lmm, or 0.5mm of the fillet of the inside corner. The striking surface of the pad generally has a "superior plane" that is the largest area on the striking surface that is substantially flat and receives a majority of the stress during collision with the striking surface of the opposing pad. While the angle between the superior plane of the striking surface and the outer face of the impact ring is generally a 90 degree angle, the striking surface is preferably angled to reduce shearing forces and to evenly distribute stress distribution during collision with the opposing pad. The angle could be sloped to less than 80, 70, 60, 50, 40, or even 30 degrees, but is preferably between 40 to 70 degrees. A preferred angle for the striking surface of the pad is 40 degrees. In a preferred embodiment, the entire striking surface of the pad is curved without having a superior plane at all, for example, having a Cartesian cross-section as shown in the right-side of Fig. 33. In such an

embodiment, preferably none of the angles of the striking surface exceed 80, 70, 60, 50, 45, 40, or 30 degrees. In an exemplary embodiment, the maximum angle of the striking surface is 45 degrees from the outer face of the impact ring. Generally, the better the coupling between the impact ring and the rotor, the less vibration occurs throughout the apparatus during collision. The impact ring could be coupled to the rotor by inserting a projection of the impact ring into a recess of the rotor, or vice-versa, but providing a plurality of such projections distributes the load more evenly, and increases the contact surface area between the impact ring and the rotor. The impact ring is generally fastened to the rotor using bolts, screws, snaps, or other mechanical means to securely couple the impact ring to the motor while also allowing the impact ring to be removed and replaced due to wear and tear. While as few as one or two fasteners could be used, increasing the number of fasteners to four, eight, or more, also improves the coupling between the impact ring and the rotor and reduces vibration.

In a preferred embodiment, the impact pad of the impact ring could also be configured to mate with the recess of the rotor, allowing the projections on either side of the impact ring to be used interchangeably as a "key" to the recess or as an impact pad. The impact pad and projection could have different geometries, or identical geometries, and preferably have at least substantially similar geometries that do not vary from one another by more than 10%. In some embodiments, the impact pad and the opposing projection on the other side of the impact ring are located in the same location on opposing sides of the impact pad, and in other embodiments the impact pad and the opposing projection are "staggered" along the surface of the impact pad to further distribute stresses along the surface of the impact ring. Various objects, features, aspects and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components.

Summary of the Drawing

Fig. 1 is an illustration of the piecewise modeling process Fig. 2 is an illustration of an exemplary impact ring

Fig. 3 is a list of geometric simplifications and implications to a model of the exemplary impact ring of Figure 2.

Fig. 4 is an illustration of the model of the exemplary impact ring of Figure 2.

Fig. 5 is an illustration of an exemplary rotor. Fig. 6 is a list of geometric simplifications and implications to a model of the exemplary rotor of Figure 5.

Fig. 7 is an illustration of the model of the exemplary rotor of Figure 5. Fig. 8 is an exemplary impact ring element distribution mesh. Fig. 9 is a table that lists impact ring meshes used in a convergence study. Fig. 10 is an illustration of boundary conditions imposed on a static model. Fig. 1 1 is an illustration of a node and element chosen for the convergence study. Fig. 12 is a graph showing stress convergence data. Fig. 13 is a graph showing displacement convergence data. Fig. 14 is an exploded view of an assembly used for dynamic modeling. Fig. 15 is an illustration of an unstable contact in a dynamic model. Fig. 16 is an illustration of a stable contact in the dynamic model. Fig. 17 is a graph of elastic dynamic model system energies.

Fig. 18 is a graph that compares model system energies between course and fine mesh in the elastic model.

Fig. 19 is a graph of initial energy of an impact ring and duration of contact as a function of initial velocity with an elastic material model.

Fig. 20 is a Von Mises stress plot of an impact ring at peak deformation in an elastic model at 250 rad/s (stresses in Pa). Fig. 21 is a graph comparing elastic and elastic-plastic system energies at 250 rad/s.

Fig. 22 is a graph of initial energy of an impact ring and duration of contact as a function of initial velocity with an elastic-plastic material model.

Fig. 23 is a Von Mises stress plot of impact ring at peak deformation in elastic-plastic model at 250 rad/s (stresses in Pa). Fig. 24 shows the effective plastic strain of impact ring after contact in elastic-plastic model at 250 rad/s (strain in mm/mm).

Fig. 25 is an exploded view of an exemplary impact ring and rotor assembly including integral keys in the impact ring. Fig. 26 shows the failure of an impact ring with ends of integral keys fixed in the Y-axis.

Fig. 27 shows the Y-axis displacement of the impact ring FEM model with the outer most ends of the integral keys constrained in the y-axis.

Fig. 28 is an exploded view of an impact ring assembly with integral keys and screws to fix the ring to the face of rotor. Fig. 29 is an illustration of results of a pad length study for pad lengths of 1 1mm, 9mm, 7mm, 5mm, and 3mm with a fixed spacing of 0.76mm between the face of the ring and the end of the pad on the opposing rotor assembly.

Fig. 30 is a graph showing the relationship of the percentage of contact elements in compression over l OOMPa and 500MPa for various pad lengths of 1 1mm, 9mm, 7mm, 5mm, and 3mm with a fixed spacing of 0.76mm between the face of the ring and the end of the pad on the opposing rotor assembly.

Fig. 31 is a graph showing the relationship of the peak and average von Mises stresses in the corners between the ring and the pad in tension and compression for various pad lengths of 1 l mm, 9mm, 7mm, 5mm, and 3mm with a fixed spacing of 0.76mm between the face of the ring and the end of the pad on the opposing rotor assembly.

Fig. 32 is an illustration of three different pad shapes.

Fig. 33 shows FEM model results of a filleted pad an angled pad with fillets.

Detailed Description of the Drawing

The following description provides many example embodiments of the inventive subject matter. Although each embodiment represents a single combination of inventive elements, the inventive subject matter is considered to include all possible combinations of the disclosed elements. Thus if one embodiment comprises elements A, B, and C, and a second embodiment comprises elements B and D, then the inventive subject matter is also considered to include other remaining combinations of A, B, C, or D, even if not explicitly disclosed.

Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims. As used herein, and unless the context dictates otherwise, the term "coupled to" is intended to include both direct coupling (in which two elements that are coupled to each other contact each other) and indirect coupling (in which at least one additional element is located between the two elements). Therefore, the terms "coupled to" and "coupled with" are used

synonymously. In some embodiments, the numbers expressing quantities of ingredients, properties such as concentration, reaction conditions, and so forth, used to describe and claim certain embodiments of the invention are to be understood as being modified in some instances by the term "about." Accordingly, in some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some

embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some

embodiments of the invention may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements.

As used in the description herein and throughout the claims that follow, the meaning of "a," "an," and "the" includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of "in" includes "in" and "on" unless the context clearly dictates otherwise. The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. "such as") provided with respect to certain embodiments herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention.

One should appreciate that the disclosed techniques provide many advantageous technical effects including providing impact rings for at least a dual rotor motor where the impact rings have reduced tensile stresses and peak compressive stresses during collisions.

The Application's work disclosed in US201 10185998 to Murphy describes a toroidal motor design generally that has two intermittently rotating bodies, which are not mechanically linked. The bodies transmit rotational energy between one-another during the transition between the engine cycles through an impact mechanism of impact ring against impact ring. However, the disclosed impact rings suffer from excessive wear. Each of the rotating bodies is constructed with a rotor, pistons, and impact ring. The rotor and pistons are the bulk of the mass, and are preferably constructed of Aluminum 6061-T6, due to the high strength-to- weight ratio, and good corrosion resistance when exposed to moisture, when compared to low-carbon steel. Further, using lighter weight materials can improve the power density of the motor. Each impact ring is fastened to the rotor with a set of screws, and the two impact rings (one attached to each of the rotors) strike against one another, imparting kinetic energy from one rotor to the next during impact.

A finite element (FE) model was develop to study the stresses and energy transfer associated with the collision of two rotationally impacting bodies could help to improve the

understanding of the mechanics occurring between the two bodies, in particular the stresses in the impact ring and the energy transfer between the two bodies. Such a model could be progressively built to allow comparison of results between incremental steps as the model progresses to a more advanced state. Further, such a model could help determine if improvements of the geometry would reduce the stresses experienced by the impact rings, and evaluate whether common materials could be selected to withstand the predicted stresses. Exemplary models could be developed using the LS-DYNA Hydracode.

A flow chart illustrating a process that could be used to develop an FE model can be seen in Figure 1. A simplified static model could be developed and used for a convergence study. The results of the convergence study could then give a starting point for a mesh to use in a dynamic model during the next step. Since this does not necessarily ensure that the dynamic model had numerically converges with the element size of the static model, it is sometimes necessary to compare the mesh used for the dynamic model with a finer mesh once a stable model has been completed. It is advantageous to use a coarse mesh to develop the model in order to minimize computational time for iterations in the process. The results could then be tested with a finer mesh that takes longer to compute to ensure the model has consistent results.

In order to mesh the parts of the model consistently and to simplify calculations, some geometrical simplifications could be made. The parts being studied could be constructed in imperial (inch) units, and could contain detailed features such as fillets, countersunk screw holes, and keyways. All of these parts could, of course, be converted to metric (m) units for continuity in modeling and detailed features could be removed for simpler meshing

Figures 2-4 illustrate geometrical simplifications that could be made to an exemplary impact ring. The fillets on the pad of the ring are removed, and the swept angle of the ring is reduced by 9%. The calculated stress in the model will be more than in the exemplary impact ring because the model has sharper geometry and smaller impact areas. Therefore, these are conservative simplifications.

The bolts between the impact ring and the rotors have been removed from the model. This causes differences between the loading simulated in the model and those experienced by the exemplary impact ring. The tensioned bolts would cause slight deformation and stresses in the body of the exemplary impact ring. This is acceptable in this model, however, if the effect of bolt tension on the exemplary impact ring is not the focus of the study of the model. The removal of the bolt system probably does not significantly change the calculated stresses in the pad of the model, or affect the simulated energy transfer between the impact ring and rotor in the model. Figures 5-7 illustrate geometrical simplifications that could be made to an exemplary rotor. It is important to note that the functions of the model of the rotor and the model of the impact ring are not the same. The model of the impact ring is used to evaluate stresses and energy transfer with a reasonable degree of accuracy during impact in a dynamic simulation.

Conversely, the model of the rotor is used to simulate the inertia in the system. Therefore, the rotor's geometric simplifications reduce the number of elements, in order to minimize computational time.

The features removed from the exemplary rotor to reduce the number of elements required in the mesh are the outer shoulders and keyways. Removal of these features generally has no direct effect to stress transferred between the rotor and impact ring. However, removing these features can increase the volume, mass, and inertia of the rotor. In the model of Fig. 7, the volume is increased by 30% and the radius of gyration is increased by 6%. This model could be used to evaluate the stress distribution in the impact ring and observe the dynamics of the collision between the two assemblies. Since the rotors are symmetric, the inertial effects are equal for each body. Therefore, variation from the actual volume of the rotor should have minimal effects on the qualitative results desired. However, this limits the possibility of verifying the dynamics of the collision experimentally using the exemplary rotor. In order to verify the dynamics of the collision experimentally, the model should be built with more accurate rotor geometry would be required. Furthermore, it may be desirable to evaluate the effects of modifying the distribution of mass (inertia) of the rotor on the dynamics of the collision between the two assemblies.

With such models, a static convergence study could be conducted to establish an element size to use with dynamic modeling. The impact ring could be discretized to contain an equal number of elements around the radius of the ring throughout the part. This gives an even distribution of elements throughout the part. The size of the elements will likely depending on the radius from the center of the part, with larger elements located closer to the circumference of the part. Generally, the meshes are formed such that the elements on the inner and outer surfaces of the ring are cubic, and the elements in between are generally cubic. An example of such a mesh can be seen in Fig. 8. Fig. 9 lists the angle between elements (i.e. angle displaced by each element) of six different meshes and the total number of elements in each mesh. As the mesh number increases, the element density increases. Generally, each mesh is a derivative of the previous mesh by dividing each element into 8 elements. However, mesh number three (3) was adjusted in order to keep the element biasing consistent throughout each mesh.

A simple loading scenario could be applied to the impact ring for the static convergence study. Fig. 10 illustrates the loads and boundary conditions applied in each of the models. In the each of the models, a 20 kN force is applied to each of the pads of the impact ring, as seen in the figure. This surface is known as the striking surface of the pad. The load is generally applied perpendicular to the striking surface of the impact ring and is distributed evenly across all the nodes on the face. In addition, all the nodes on the back face of the rotor are constrained in all directions. Preferably, the material used in the model would be Aluminum 6061-T6 to match the material preferably used on actual impact rings and rotors.

In order to provide a consistent comparison for the convergence study, the location could remain consistent for each mesh. One could then evaluate the convergence of the

displacement of the node at the center of interface between the body and the pad of the impact ring and the stress in the element adjacent to this node. Fig. 11 illustrates an exemplary location of a node and element in one of the meshes that could be used in a convergence study.

Fig. 12 and Fig. 13 show the element stress and node displacements of meshes modeled using the parameters outlined above. It could be seen that the stress and displacement converge with reasonable tolerance after mesh number two (2). It should be noted that since a considerable force was applied to the model, the element stresses are beyond the maximum yield strength of the material. However, the magnitude of the stresses would not be pertinent in a study to gain understanding of the numerical convergence of the model and element sizes.

The computational time of the models also tends to increases considerably with the finer meshes (See e.g. numbers 5 and 6). Since the chosen mesh is to be used in a dynamic model with larger parts, the computational time is considered an important factor when selecting the mesh to use in further models.

By analyzing such results, a researcher could come to the conclusion that the impact ring static loading converges within reasonable tolerances from mesh number two (2) onwards. Since the results are for a static, not a dynamic, model, a conservative selection of mesh number three (3) could be made to use in a dynamic model. Also, in order to verify that changing from a static model to a dynamic model does not have unforeseen effects on the numerical calculations of the model, the results of a simple dynamic model with mesh number four (4) could be used and then compared to the results of the same model with mesh number three (3). When developing a dynamic model, generally the mesh selected for the impact ring could be used to build the mesh of the rotor. This mesh could then be brought into LS-Dyna and the boundary conditions and initial velocity of the body could then be imposed. Such a model could form the master rotor and have the driving conditions and energy of the model. A second mesh could then be formed by positioning an additional rotor and impact ring into the assembly. These parts would form the slave rotor, as this body is driven by motion of the master rotor. Contact conditions could then be imposed between the two bodies and the initial velocity in the system could then be reduced until the contact interference is stabilized. An exploded view of such an assembly used for dynamic modeling is shown in Fig. 14.

The front and back faces of the rotor are preferably constrained to have no translational movement in the y-axis (along the rotation axis) in order to simulate the constraints imposed by the thrust bearings used in the assembly. Only the back face of the rotor could be constrained for most tests, or both the back and front faces of the rotor could be constrained to prevent undesired contact between the two front faces of the rotors.

The initial velocity of the master rotor could be set by specifying a boundary prescribed motion in the x-z plane. This would specify the rotational velocity of the desired nodes in radians per second (rad/s). This velocity could then be applied to all of the nodes of a master rotor model and impact ring model.

To ensure that the units are specified correctly and the initial kinetic energy of the system are simulated correctly, an elementary validation could be performed by comparing the calculated energy from the geometry used to mesh the rotor, to the energy calculated in the system. In the model discussed above, the kinetic energy of the aluminum model at 250 rad/s is 8.33 Joules. This compares to a calculated value of 7.76 Joules for the exemplary system upon which the model is based, which is a 7.5% error. Although the values are not exact, they are within a reasonable degree of accuracy when developing the model. Therefore, it can be said that the units used in the model, and the resulting initial energy conforms to what is expected analytically. One should appreciate that the disclosed values are representative of the prototype system. One skilled in the art will appreciate that the values can vary will still falling within the scope of the inventive subject matter. All practical sizes, dimensions, and values for the disclosed impact rings are contemplated.

Since the dynamic model results are generally based upon the contact conditions between the two bodies, at the early stages of development it is important to verify that the contact between the two bodies is stable throughout such a simulation. The contact conditions could be stabilized by observing the model results and by making appropriate changes to the model to eliminate errors. For example, in the early stages of the dynamic model, the contacting faces of the impact rings may deform in obscure patters (i.e. not as a solid surface), which would cause the model to eventually drop the surface contact condition.

Fig. 15 illustrates an example of incorrect contact conditions between the two bodies. In the illustration, the contacting surface of the master impact ring (shown as solid) implodes, and breaks through the surface of the opposite impact ring (shown as wireframe). This is a clear illustration of unstable contact conditions, as the surfaces are deforming irregularly. Such instability could be caused by nodes aligning with opposing nodes or by using such a high rotational speed for the mater rotor relative to the time step. If the initial velocity of the master rotor is too high relative to the time step, the surface of the impact ring could move past the point of contact before the model can calculate the resulting deformation in the impact rings. The instability could then be fixed by offsetting the element depth along the rotational axis to ensure that the nodes align with a surface rather than an opposing node, and by reducing the initial speed of the master rotor (i.e. 250 rad/s). Fig. 16 illustrates an example of correct contact conditions between the two bodies after such modifications are made.

A purely elastic aluminum model could be used in a study to verify that the model is operating correctly. In such a model, all of the kinetic energy in the system should result in a distribution of kinetic energy after the collision between the two bodies. Alternatively, an elastic-plastic model could be used for high-velocity impact computational material models. Such a model could use a strain-rate relationship which gives more accurate material properties for high-velocity impact computations. Other material models could be used without departing from the scope of the invention. Using either model, many materials could be used, for example 2024-T351 Aluminum, 7039 Aluminum, 1006 Steel, 4340 Steel, and S- 7 Tool Steel. The primary observation and validation of an elastic material model could be from the energies in the system throughout the collision of the two rotors. By analyzing the relative kinetic energy of the rotors and internal energy of the impact rings, conclusions could be drawn from the model. Fig. 17 shows the energies in the system as a collision occurs in an exemplary elastic model. As shown, the master rotor (M-Crank) contains all the energy in the system before contact. The initial contact occurs after 0.0002 s, and as the kinetic energy in the master rotor begins to decline, the internal energies in the impact rings begins to increase, and the kinetic energy in the slave rotor (S-Crank) begins to increase. At approximately 0.0003 seconds, the impact ring reaches the peak internal energy (deformation), and springs back to the original shape.

In general, it is seen that all the energy is transferred from the master rotor to the slave rotor through the impact ring in the elastic model. However, it should be noted that not all the energy is transferred through deformation of the impact ring; rather, the deformation of the impact ring absorbs some of the shock loading between the rotors. Therefore, in order to improve these results and increase the accuracy, higher level material models could be used.

Since there are uncertainties in the accuracy of the static convergence study, when applied to a dynamic model, it is useful to compare the results of one mesh against another. Fig. 18 shows a comparison of the model energies between mesh three (3) (course mesh) and mesh four (4) (fine mesh). The results from the fine mesh are shifted on the graph in order to view the two results separately.

It can be seen that there are no major differences in the dynamics of the two meshes with this model. There is a slight reduction of the peak impact ring internal energy, but the values are within reasonable accuracy. Therefore, using mesh three (3) for modeling would probably be about as accurate as mesh four (4). In order to gain some elementary understanding of the relationship between the initial speed of the master rotor and the dynamics of the impact, the elastic model could be tested at incremental speeds decreasing from 250 rad/s. In particular, the peak internal energy of the impact ring and the duration could then be plotted, as shown in Fig. 19.

It is seen that the internal energy of the impact ring increases as the initial velocity (energy) in the system increases. However, the duration of contact remains the same, independent of the initial velocity of the system. From these results, it is unclear whether this model accurately predicts this relationship, but comparison to the results of the elastic-plastic material model could give more insight to the accuracy of such results.

In order to gain understanding of the accuracy of the elastic model, one could evaluate the stresses calculated in the impact ring. Fig. 20 shows the stress distribution in the impact ring at peak deformation. It is seen that the maximum stresses occur at the outer edges of the pad of the impact ring, and the magnitude of these stresses are approximately 1.2 GPa. Since the yield stress of aluminum is approximately 207 MPa, it is clear that plastic deformation would probably occur at this velocity. Therefore, an elastic-plastic model would be more accurate than a purely elastic model. Fig. 21 demonstrates the variation of the energies in different material models of the system. It can be seen that the elastic-plastic material model could change the dynamic results of the simulation. In particular, the duration of contact is increased and energy is permanently absorbed by the impact ring, i.e. plastic deformation. Plastic deformation is expected at the initial velocity of 250 rad/s. In addition, the peak internal energy in the impact ring is larger in the elastic-plastic model than the values seen in the elastic model.

It is seen in Fig. 22 that the results are similar to the elastic model. However, there is slightly more variation in the contact time of the two bodies. From both sets of results, it can be seen that that the duration of contact is probably independent of the initial velocity of the master rotor. Fig. 23 illustrates the stress distribution of an elastic-plastic model at 250 rad/s. It is seen that the maximum stresses calculated in this model are an order of magnitude less than that of the elastic model. In addition, it is seen that the maximum stress is distributed across a larger area in the elastic-plastic model. This is probably due to the effects of the plastic strain in the model, as the material model limits the stress by permanently deforming the material Fig. 24 illustrates the plastic strain experienced by the impact ring in this model. It is seen that the face of the impact ring permanently deforms during the impact collision. The maximum strain could be seen at the edge of the pad, and is approximately equal to 0.0051 mm/mm. This result correlates to the reduced stress (when compared to the elastic model) seen in Fig. 23, as the energy absorbed by plastic deformation, reduces the overall stress experienced by the body. However, validation of this result is difficult as an extensive experimental setup would be required. The impact rings and rotor assembly are one of the most critical and complex system of components in the motor. There are high impact loadings and stresses, and some of the models could indicate contact forces between the rotors in the order of 104 to 105 N. Fig. 25 illustrates a design of the rotor assembly and the main components. This design uses screws to tighten the face of the impact ring to the face of the rotor to transfer the torque. However, by using such a design, the screws could fail in shear, due to the high contact forces between the impact rings. It can be seen that the impact rings have two integral square projections that mate with recesses in the rotor and sleeve. These projections are intended to transfer the majority of the torque from the pad of the impact ring to the rotor and sleeve, as well as from the rotor to sleeve (and the drive shaft).

The rings shown in Fig. 25 could work without failure at first, but after multiple tests, various signs of wear could be observed, and the rings could ultimately fail, as shown in Fig. 26. The failure of such a design could be due attributed to the screws that held the integral projections on the rings in to the back face of the rotors. The screws in such a design would likely tend to loosen due to vibrations and gouge the contacting areas of the rotors. This would ultimately lead to ring failure across the ring, which indicates a fatigue failure from the ring flexing and deforming.

A FEM model could be tested to observe the tendency of the rings to deform, if the back faces of the recesses that receive the projections were constrained in the y-axis. This constraint is similar to the design shown above, as the screws holding the rings to the back face of the rotors are the only component holding the rings in the y-axis. Fig. 27 illustrates the y-axis displacement of the rings at the peak contact stress. Note that the deformations have been scaled on the image 2X for visualization purposes.

It is seen from the FEM results that the ring in the model tends to flex by almost 0.2 mm in the y-axis during contact. From observations of the model and the failed ring, this freedom of movement could ultimately lead to further ring failures and design alterations may be used to improve the design. In particular, it is advantageous to constrain the face of the ring to the face of the rotor to prevent this deformation from occurring.

Fig. 28 illustrates an improved design of the ring to reduce the fatigue on this area of the ring. This design reduces the stresses experienced in the ring of the part, and could operate without failure for a much longer time than the design shown in Fig. 25. However, such a design could further be improved by conducting a FEM study to determine the best pad length for the current rotor design.

Fig. 29 illustrates the stresses of the contacting face of the impact ring at peak contact force when the pad length is altered between 3 mm, 5 mm, 7 mm, 9 mm, and 1 1 mm while the width is held constant at 1 1 mm. As shown, all the contact pads have the same general trend of compressive stress on the outer part of the pad, and tension in the inner corner between the striking surface of the pad and an inner face of the ring. However, as the pad length decreases, the area of elements in considerable contact stress increases. Preferably, the contact force is spread over the whole face as evenly as possible. Furthermore, with longer pad lengths, the faces of the pads can be less effective since the contact forces are concentrated to the outer most regions of the pads. The relationship between the number of contact elements in compression and the pad length can be seen in Fig. 30. It can be seen that as the pad length decreases, the percentage of elements in contact increases.

Fig. 30 shows that for pad lengths of 6mm to 9mm, the number of elements in stress over lOOMPa is around 70%, while the number of elements in stress over 500MPa remains below

6%. Therefore, if the intent is to have the majority of elements in compression in the range of l OOMPa to 500MPa, then this range of pad lengths is a preferred choice. Furthermore, Fig.

31 shows the peak and average tensile and compressive stresses in the corners between the pad and ring. It is seen that, generally, the peak and average tensile stresses and the peak compressive stresses increases with pad length. Therefore, when combined with the observations of the number of contact elements in compression, a preferred length is 6mm. It is also seen that 6mm has the lowest peak tensile stress.

Further to the pad length study, the geometry of the pad on the impact ring could also be altered. Fig. 32 shows three exemplary shapes that could be used for the contact pad. The pad shapes are a straight pad, straight pad with fillets, and an angled pad with fillets.

Fig. 33 illustrates FEM model results of an 1 1mm long pad with 3.175mm radius fillets, and a 1 1mm long pad with a 40° pad angle. As shown from the model, the angled pad has an even stress distribution across the contact area of the pad, and reduced stress in the corner between the pad and the ring. These two characteristics are desirable to reduce the fatigue stresses that occur in the part. From these modeling and testing results, it can be seen that using such models can play a critical role in driving the design of the impact rings. In particular, the model could qualitatively predicts the locations of stress concentrations in the model, the shape of the impact pads and the method of securing the rings to the rotors influences the stress and fatigue experienced by the impact ring, and the shape of the pads can be adjusted to greatly reduce the stress concentrations in the corners between the pads and the ring. Therefore, the model could be a useful tool for the development of this component, arid the stresses experienced by the impact rings can be reduced by modifying the geometry, particularly by modifying the dimensions of the contact pad, the severity of a fillet carved in the inner corner between the striking surface and the outer face of the rotor, and the angle of the striking surface with respect to the outer face of the rotor.

It should be apparent to those skilled in the art that many more modifications besides those already described are possible without departing from the inventive concepts herein. The inventive subject matter, therefore, is not to be restricted except in the spirit of the appended claims. Moreover, in interpreting both the specification and the claims, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms "comprises" and "comprising" should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. Where the specification claims refers to at least one of something selected from the group consisting of A, B, C .... and N, the text should be interpreted as requiring only one element from the group, not A plus N, or B plus N, etc.