FLEXIBLE SPINDLE POLISHING

Abstract

Precise surface treatment and finishing of an enclosed, non-linear channel through a 3-dimensional printed, additively manufactured or machined part or workpiece results from insertion of a grinding wheel on a flexible shaft and controlling an orbital movement though rotational speed, grit selection and fluid viscosity of a liquid medium in the channel. Drive logic rotates the flexible shaft for controlled rotation as the orbital movement or pattern achieves controlled contact with the interior channel surface. Rotational contact by the grinding wheel removes material based on a grit size, while the orbit is controlled through the rotation, viscosity and grit size for achieving uniform coverage of the interior surface. An internal geometry, typically circular or elliptical, is preserved while attaining a smooth surface through precise material removal resulting from the controlled orbit.

Claims

1. A polishing device for surface treatment of an interior surface of a conduit, comprising: a grinding wheel adapted for rotation; a flexible shaft attached to the grinding wheel; an abrasive surface geometry defined by an exterior of the grinding wheel; and a drive source responsive to drive logic for rotating the flexible shaft, the flexible shaft configured for a rotation speed for attaining an orbit of the grinding wheel based on the abrasive surface geometry.

2. The device of claim 1 wherein the abrasive surface geometry further comprises a grit size, the flexible shaft configured for a rotation speed for attaining the orbit of the grinding wheel based on the grit size of the abrasive surface geometry.

3. The device of claim 2 further comprising a fluid within the conduit, wherein the drive logic is configured for controlling the rotation speed based on at least the grit size and a viscosity of the fluid.

4. The device of claim 1, further comprising a fluid source, the fluid source configured to deliver a fluid having a viscosity and a density into the conduit, the orbit responsive to at least one of the viscosity and density for achieving a predetermined percentage of coverage of the interior surface based on consistent grinding wheel dynamics.

5. The device of claim 1 wherein the abrasive surface further comprises an abrasive height, the abrasive height indicative of a variation of the abrasive surface geometry based on the grit size.

6. The device of claim 5 wherein the abrasive surface geometry further comprises a distribution, orientation and patterning of an abrasive material adhered to the surface of the griding wheel.

7. The device of claim 1 wherein the rotation induces an elastic force in the flexible shaft, the elastic force resulting from a nonlinear path of the conduit, the orbit based on the abrasive surface geometry and the elastic force.

8. The device of claim 3 wherein the drive logic is further configured to generate, based on the rotational speed, grinding forces and hydrodynamic forces, the drive logic configured to ensure the grinding forces and hydrodynamic forces are unequal and opposed.

9. The device of claim 3 wherein the drive logic is further configured to generate, based on the rotational speed, grinding forces and hydrodynamic forces; and generate a net force acting in the direction of an intended orbital motion.

10. The device of claim 3 wherein the drive logic is further configured to generate, based on the rotational speed: a hydrodynamic force resulting from the viscosity and the grit size, the hydrodynamic force having components normal and outward to the interior surface, and tangential to the interior surface; and a grinding force having components inward and normal to the interior surface, and tangential to the interior surface and aligned with a rotation of the grinding wheel.

11. The device of claim 1 wherein the orbit defines a cyclic path around the interior of the conduit, the orbit having a radius less than a radius of the conduit.

12. The device of claim 11 wherein the orbit defines an irregular path, the irregular path based on at least the rotation speed, the abrasive surface geometry, a viscosity of fluid in the conduit, and a shape of the grinding wheel.

13. The device of claim 1 wherein the shape of the grinding wheel includes at least one of an ellipsoid with a circular cross section, sphere, fluted, finned and triangular with radiused edges.

14. The device of claim 1 wherein the conduit has an internal diameter of between 0.5-300 mm.

15. The device of claim 1 wherein the grit size defines the abrasive surface geometry with a grit height between 40-120 microns.

16. In a material fabrication environment for forming internal channels with curvilinear portions in a machined body, a method for smoothing a surface of the internal channels, comprising: attaching a grinding wheel at a distal end of a flexible shaft; engaging a drive source with a proximal end of the flexible shaft for rotation of the grinding wheel via the flexible shaft; inserting the grinding wheel into the channel; creating a fluid media in communication with the channel and the grinding wheel; and rotating the flexible shaft at a rotation speed for controlling an orbit of the grinding wheel against the surface of the channel.

17. The method of claim 16 further comprising: selecting an abrasive surface geometry on an outer surface of the grinding wheel; selecting a viscosity of a fluid flowing through the channel; and controlling the orbit of the grinding wheel based on the abrasive surface geometry and the selected viscosity.

18. The method of claim 17 further comprising generating a down-grinding orbit of the grinding wheel by engaging the grinding wheel against the surface of the channel in a direction the same as a rotation of the grinding wheel.

19. The method of claim 17 further comprising generating an up-grinding orbit of the grinding wheel by engaging the grinding wheel against the surface of the channel in a direction opposite to a rotation of the grinding wheel.

20. The method of claim 17, further comprising: selecting a rotation speed, fluid viscosity and grit size for controlling an orbital path of a grinding wheel; and operating the drive logic and a fluid supply for flowing the fluid based on the selected rotation speed, fluid viscosity and grit size.

21. A system for surface treatment of an interior surface of a conduit, comprising: a grinding wheel adapted for rotation; a flexible shaft attached to the grinding wheel and responsive to drive logic for rotation of the grinding wheel; a fluid supply for providing fluid to an interior of the conduit; and an abrasive surface geometry on an exterior of the grinding wheel, the drive logic for rotating the flexible shaft, the flexible shaft configured for a rotation speed for attaining an orbit of the grinding wheel based on a grit size of the abrasive surface geometry, a rotational speed of the grinding wheel and a viscosity of the fluid.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The foregoing and other features will be apparent from the following description of particular embodiments disclosed herein, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

[0008] FIG. 1 is a context diagram of a polishing and grinding environment suitable for use with configurations herein;

[0009] FIGS. 2A-2C show movement aspects of the grinding wheel of FIG. 1;

[0010] FIG. 3 shows an example apparatus for performing orbital control of the grinding wheel as in FIGS. 1-2C;

[0011] FIG. 4 shows orbital and rotational control for generating upgrinding or down- grinding in the apparatus of FIG. 3;

[0012] FIGS. 5A-5D show a cross section of a grinding wheel disposed inside a conduit or tube;

[0013] FIG. 6 shows the forces acting on the grinding wheel of FIGS. 5A and 5B;

[0014] FIGS. 7A-7D show example shapes of the grinding wheel; and

[0015] FIG. 8 shows variation of orbital frequency and direction of the grinding wheel for different viscosities.

DETAILED DESCRIPTION

[0016] Configurations disclosed below present a fixed abrasive, flexibly driven device capable of uniformly polishing surfaces of complex internal channels. Many precision industrial devices such as injection molds, turbine blades, and fuel nozzles include small, high aspect ratio cooling channels which must be polished to maximize cooling, fatigue life, and corrosion resistance.

[0017] Technology such as MAM enable the fabrication of complex internal channels with designs optimized for weight reduction, and thermal and fluid transfer efficiency. In one use case, conformal cooling channels for injection molds can increase productivity via reducing mold cooling time by up to 70%. Integrated fuel channels of jet engines increase fuel delivery efficiency by 15% while enhancing the heat transfer to the fuel through the optimized path of the channels. These complex channels with optimized designs, featuring small diameters, high aspect ratios, high tortuosity, and varied diameters and geometries, challenge the traditional casting and machining processes, and are amenable to one-piece constructions via MAM. As-built MAM parts often need post-processing for surface finishing. The average areal surface roughness (Sa) of as-built MAM parts ranges from 10 to 30 m with maximum peak to valley heights (Sz) of more than 150 m. High surface roughness negatively affects the fatigue life, corrosion resistance, and dimensional tolerance. For as-built MAM parts, the fatigue life can be reduced by 75% compared to conventional wrought or polished components; the corrosion resistance is diminished with surface protrusions as potential nucleation sites for metastable pitting, and the dimensional accuracy can be poor due to layer stratification, partially melted powders, and spatters, altering surface geometry. To address these challenges in as-built MAM parts, post-processing, including surface milling and grinding, laser machining, and shot peening, has been used to improve the surface finishing. Such post-processing techniques are mostly limited to exterior surfaces, due to line of sight and tooling restrictions, and not suitable for internal surface polishing.

[0018] Conventional internal surface polishing methods for MAM parts with complex channels include abrasive flow machining, hydrodynamic cavitation-assisted finishing, magnetic abrasive finishing, chemical polishing, and electrochemical polishing. Conventional approaches to interior surface polishing and grinding fail to utilize a hydrodynamic effect to control a driven device such as a polishing wheel. While some approaches employ a rotational driven impact, conventional approaches fail to embrace orbital control, particularly based on a grit size and rotational responses due to viscosity of a hydrodynamic fluid.

[0019] In another use case, internal cooling channels are essential to turbine blades for high efficiency power generation. The cooling channels lower the peak temperature experienced by the turbine blades, reduce thermal stresses within the blades, allow higher turbine entry temperature, and enhance efficiency and safety. These cooling channels, subjected to high-temperature, high-velocity air flow, need protective aluminide coating on the inner surface for corrosion and fatigue resistance. The aluminide coating of the cooling channels degrades due to oxidation. The accumulation of the aluminum oxide narrows the channels, limits the air flow and cooling, and leads to reduced efficiency and turbine blade failure. It is important to remove the aluminum oxide buildup and restore patency of the cooling channels to refurbish the turbine blades.

[0020] A uniform, adaptable method for quickly reducing surface roughness while maintaining dimensional integrity is significant to the adoption of MAM fabricated channels and similar structures. The disclosed approach satisfies this need by utilizing an adaptable drive system, a controllable high Material Removal Rate (MRR) grinding wheel, and a hydrodynamic effect which causes the grinding wheel to orbit the channel maintaining uniformity and dimensional integrity. A particular feature is the control of the grinding wheel orbit speed and direction through manipulation of the hydrodynamic effect. Orbit speed control directly correlates to the uniformity and consistency of the polishing process and can be altered to vary grinding mechanics to effect MRR and surface roughness. Orbit direction relative to the rotational direction fundamentally changes the grinding mechanics allowing for both up grinding and down grinding modes. Each method has specific process advantages which are detailed below. However, direct control of the orbit is not feasible due to the flexible nature of the drive system and indirect control through manipulation of system and process parameters. However, orbital control derives from controllable parameters and features of a shaft driven grinding wheel through rotation speed, grit size, fluid viscosity within the tube or vessel, and a shape of the grinding wheel, to name several.

[0021] FIG. 1 is a context diagram of a polishing and grinding environment suitable for use with configurations herein. Referring to FIG. 1, a grinding and polishing device 100 for surface treatment of an interior surface 105 of a conduit 110, channel or pipe includes a grinding wheel 120 adapted for rotation, and a flexible shaft 112 or spindle attached to the grinding wheel 120. An abrasive surface 122 on an exterior of the grinding wheel 120 is selected for grinding and/or polishing the interior surface 105. A rotational drive source is responsive to drive logic for rotating the flexible shaft 112 according to predetermined control parameters discussed further below, such that the flexible shaft 112 is configured for a rotation speed for attaining an orbit of the grinding wheel based on at least a grit size of the abrasive surface. A fluid 124 within the conduit 110 facilitates a hydrodynamic effect on the grinding wheel 120, such that the drive logic is configured for a rotation speed, in which the rotation speed is based on at least the grit size and a viscosity of the fluid. The fluid 124 in the conduit 110 has a viscosity selected such that the orbit is responsive to the viscosity for achieving an orbit to provide a predetermined percentage of coverage and abrasion of the interior surface.

[0022] The device 100 of FIG. 1 depicts a flexible spindle polishing approach that utilizes a high-speed rotational fixed-abrasive grinding wheel 120 driven by a flexible shaft 112 or spindle for internal polishing and grinding of a workpiece such as the conduit 110. The fluid 124 also serves as a coolant delivered via a non-rotational sleeve 114 outside of the flexible shaft 112 to evacuate swarf from a grinding zone formed at a contact point 126 of grinding wheel 120 abrasive contact with the interior wall 105. The coolant or fluid 124 in the channel, driven by the high speed rotation of the grinding wheel 120, develops a hydrodynamic swirling flow that carries the grinding wheel 120 to orbit and polish around the interior surface 105 of the channel. The assembly including the grinding wheel 120, flexible shaft 112, and sleeve 114 is translated to polish through the channel, and may ride on a concentric non-rotational guiderail 116. Alternatively, the flexible shaft 112 may advance the grinding wheel 120 with sufficient rigidity. The grinding wheel exhibits an abrasive surface geometry, including the abrasive surface 122 but also defined by characteristics of abrasive particles on the exterior surface, and on a shape or macro geometry of the grinding wheel. The abrasive surface geometry further comprises a distribution, orientation and patterning of the abrasive material adhered to the surface of the griding wheel. This includes the height or variations in the surface, how closely spaced the particles occur (distribution) and an arrangement in placement (patterning).

[0023] FIGS. 2A-2C show movement aspects of the grinding wheel of FIG. 1. Referring to FIGS. 1 and 2A-2C, the manipulation of the grinding wheel 120 motion inside the conduit 110 is accomplished through an approach which leverages a relationship between the hydrodynamic force and the cutting force at the contact point 126 between the grinding wheel 120 and the interior surface 105. Referring specifically to FIG. 2A, it is important to distinguish between the rotation 130 of the grinding wheel 120 and the orbit 132 within the conduit 110. Rotation 130 refers to movement about an axis 134 of the cutting wheel defined by the shaft 112. Orbit 132 refers to movement of the axis 134 withing the conduit 110. The orbit 132 therefore defines a cyclic path around the interior of the conduit 110, where the orbit 132 has a radius less than a radius of the conduit 110. When the grinding wheel 120 has a diameter approaching the diameter of the interior surface 105, orbit and rotation tend to merge. A greater deviation of the diameter of the cutting wheel 120 and the diameter of the interior surface 105 defines an available range of the orbit 132. Large cutting forces with comparatively small hydrodynamic force results in a net force exerted on the cutting wheel 120 at the boundary in an opposite direction of rotation, causing the wheel to orbit the channel in opposite direction of rotation, causing the wheel to orbit the channel in an opposite direction to its rotation or climb. This results in a grinding process referred to as down-grinding in which the linear velocity of the wheel periphery at the surface and the linear velocity of the wheel center with respect to the contact point are opposite. This process is linked to larger uncut chip thickness which is has a higher efficiency whilst producing a rougher surface. Conversely, when hydrodynamic force and the wall exceeds the cutting force, the wheel orbits in the same direction as the as it rotates. This process is referred to as up-grinding and is has characteristics such as smaller uncut chip thickness, which is less efficient but produces a smoother surface. Due to the inherent advantages in both up-grinding and down-grinding, the ability to control orbit direction is advantageous for minimizing surface roughness (Sa), while maximizing efficiency.

[0024] Configurations herein demonstrate control based on various parameters affecting the orbit, such as grinding wheel geometry, fluid medium, and grit size. Grinding wheel abrasive surface geometry could be altered in such a way as to increase the fluid flow to the contact area, increasing the hydrodynamic force. On this rationale, direct correlation of wheel design and orbital frequency can be obtained. Different grinding wheels with tailfins of different sizes may be employed for control of orbit direction based on geometry selection, disclosed further in FIGS. 7A-7D below.

[0025] FIG. 2B shows a cross section of a conduit 110 section. The fluid 124 is introduced by the sleeve 114, which delivers fluid media having a viscosity and for cooling purposes. The viscosity may be defined the to manipulate both the cutting force and the hydrodynamic reaction. Using highly lubricious cutting fluids 124, the cutting force at the wall 105 is reduced due to the low surface energy boundary layer between the wheel and the wall (slippery wall). Additionally, hydrodynamic force is modifiable by controlling fluid viscosity with higher viscosities producing higher forces. Using this rationale, different combinations of viscosity and lubricity could be used to change the relationship of the cutting and hydrodynamic forces. Low lubricity, low viscosity fluids have been shown to produce down-grinding by maximizing cutting force and minimizing hydrodynamic force. Additionally, high lubricity, high viscosity fluids tend to change the grinding direction to up-grinding as the hydrodynamic forces increased and the cutting forces decreased. Using these observations and demonstrations, fluid media could be tailored to achieve a narrow window of orbit parameters and control orbit direction based on an intended orbit 132.

[0026] The rotation may also induce an elastic force in the flexible shaft 112. The elastic force typically resulting from a nonlinear path of the conduit, as in FIG. 2B, such that the orbit is based on the abrasive surface geometry and the elastic force. The flexible shaft 112 has a flexural stiffness or rigidity, and bends or turns in the conduit 110 often result in contact of the flexible shaft with the interior surface 105.

[0027] A third parameter involves selection of abrasive grit on the surface 122 of the grinding wheel 120, as one example of altering the grinding wheel abrasive surface among other parameters. Changing the grit size is preferable in many applications, with larger abrasive sizes increasing MRR and wheel life, while smaller sized produce better Sa. However, increase in grit size is accompanied by increase in cutting force which has been previously observed to affect orbit. Using this association, grit size may be modified or combined with different fluid media and wheel geometries to further control grinding wheel orbit. A relation of grit size 201 to orbit 203 is shown in FIG. 2C for several rotational speeds.

[0028] FIG. 3 shows an example apparatus for performing orbital control of the grinding wheel as in FIGS. 1-2C. Referring to FIGS. 1-3, a variety of configurations may be employed for generating orbital control using rotation speed, cutting wheel geometry, grit size and fluid viscosity. In a material fabrication environment as shown in FIG. 3 for forming internal channels with curvilinear portions in a machined body, a method for smoothing a surface of the internal channels includes attaching a grinding wheel 120 at a distal end 144 of a flexible shaft 112. A drive source 140 engages with a proximal end 142 of the flexible shaft for rotation of the grinding wheel 120 via the flexible shaft 112. A spool 146 advances the distal end 144 for inserting the grinding wheel 120 into the channel or conduit 110 of a workpiece 110. An adjustable arm 148 orients the shaft 112 and grinding wheel 120 for insertion. Control logic 150 rotates the flexible shaft 112 at a rotation speed for controlling the orbit 132 of the grinding wheel 120 against the surface 105 of the channel.

[0029] Overall results for orbital control as in FIGS. 103 demonstrated Sa improvement, geometric integrity and uniformity, and efficiency on several use cases with popular MAM alloys including AlSi10Mg, 316L SS, and Ti6Al4V channels with 3.8 mm inner diameter and 40:1 aspect ratio. The channel inner surface Sa was improved by over 90% in all tests with sub-micron roughness achieved in the AlSi10Mg specimen after a process time of just 5 minutes. Final Sa in all channels varied by less than 7% along the length of the channel which was a 21% reduction from as-built condition. This indicates uniform surface finish and material removal. Direct control material removal and reduction of geometric restrictions as compared to conventional methods resulted in minimum diameter widening of 0.2% during orbitally controlled grinding, demonstrating a promising advantage in maintenance of dimensional integrity. Cylindricity, which is a measure of an internal channels deviation from a perfect cylinder was found to increase by 43%, rendering the polished channels smoother and closer to as-designed geometry. The cylindricity improvement of channels may be further exploited in the design process allowing for manufacture of more stable non-circular channels which could later be shaped. Additionally, appreciable improvements in the required polishing and grinding time per linear distance were also achieved.

[0030] As disclosed above, orbital control allows manipulation to favor an up-grinding or down-grinding orbital movement. FIG. 4 shows orbital and rotational control for generating up-grinding or down-grinding in the apparatus of FIG. 3. Orbit 132 is responsive to the abrasive surface 122 of the grinding wheel 120. The abrasive surface 122 further comprises an abrasive height, where the abrasive height is indicative of a variation of the abrasive surface based on the grit size of an abrasive medium forming the abrasive surface 122. Referring to FIGS. 1-4, orbit 132 control using different values of viscosity, grit size, and rotational speed defines two distinct grinding modes: down-grinding, shown by arrow 152 in which wheel tangential velocity 156 at the wheel-workpiece contact 126 and material feed are in the same direction, and up-grinding, shown by arrow 154, in which the directions are opposite. Down-grinding was generally observed in low viscosity fluids, at low rotational speed and using higher grit sizes. In these situations, hydrodynamic forces are theorized to be significantly smaller than grinding forces since hydrodynamic forces decrease with decreasing viscosity and rotational speed. Because of this, down-grinding scenarios can be labeled as grinding- force dominated and the resulting orbital frequency and direction and direction can be attributed to the tangential grinding force acting on the wheel periphery. Conversely, up-grinding occurs at high fluid viscosities and wheel rotational speeds and can be considered hydrodynamic-force dominated motion with orbital motion occurring due to hydrostatic pressure and viscous force acting on the wheel surface 122.

[0031] In operation, down-grinding creates a shorter, thicker chip (the name for the material removed by an individual abrasive grain), whereas up-grinding creates a longer, thinner chip. Due to chip geometry, down-grinding produces slightly higher material removal rates and grinding efficiency, with a rougher overall surface. Conversely, up-grinding generally produces a smoother surface, but with less efficiency.

[0032] FIGS. 5A-5D show a cross section of the grinding wheel 120 disposed inside a conduit 110, channel or tube. Referring to FIGS. 1-4 and 5A-5B, the orbit 132 may define an irregular path based on at least a rotation speed, a grit height, a viscosity of fluid in the conduit, and a shape of the grinding wheel. FIG. 5A shows an ideal or average orbit 132, while FIG. 5B shows an orbit 132 that follows a generally circular, irregular path that smooths to a more uniform orbit 132 over time.

[0033] FIGS. 5C and 5D show a detail of the conduit 110 interior surface as the abrasive surface geometry of the grinding wheel 120 responds to rotation in the fluid or liquid 124. FIGS. 5C and 5D show the forces due to coolant viscosity, grinding forces, and spindle (flexible shaft 112) forces. The spindle elastic force tends to push the grinding wheel 120 into the wall 105. This force, which is dependent of spindle flexural stiffness, can overcome the forces from grinding and viscosity, preventing orbital motion in highly complex channels with a lot of curvature. Configurations herein demonstrate that controlling shaft 112 flexibility allows for more consistent orbit in channels with high curvature.

[0034] FIG. 6 shows a more general view of the forces acting on the grinding wheel of FIGS. 5A-5D. Referring to FIGS. 1-6, the drive logic 150 is further configured to generate, based on the rotational speed: grinding forces 160 and hydrodynamic forces 162, such that the drive logic is configured to ensure the grinding forces and hydrodynamic forces are unequal and opposed. In particular, grit size contributes directly to the grinding force 160 by increasing the amount of grain interacting with the workpiece and thus the force on each grain. Fluid viscosity increases hydrodynamic forces 162. Configurations herein demonstrate that consistent grinds occur when the grinding force 160 dominates (down-grinding) or when the hydrodynamic force 162 dominates (up-grinding). Poor grinding may result when these forces are similar in magnitude. Using observation and measurement of these forces 160, 162, the drive logic 150 can predict the consistency of an orbit 132 for a combination of viscosity and grit size by determining the forces and comparing them.

[0035] Therefore, the drive logic 150 is further configured to generate, based on the rotational speed, a hydrodynamic force 162 resulting from the viscosity and the grit size, such that the hydrodynamic force has components normal and outward to the interior surface, and tangential to the interior surface. The drive logic 150 may also manage the grinding force 160 having components inward and normal to the interior surface, and tangential to the interior surface and aligned with a rotation of the grinding wheel.

[0036] FIGS. 7A-7D show example shapes of the grinding wheel. FIG. 7A-7D demonstrate that the shape of the grinding wheel includes at least one of an ellipsoid with a circular cross section in FIG. 7A, a fluted shape in FIG. 7B, in which flutes or fins extend along a majority of the longitudinal dimension that respond to fluid viscosity, a tail flute shape in FIG. 7C, with flutes or fins along a small rear portion, and a triangular shape with radiused or rounded edges in FIG. 7D.

[0037] FIG. 8 shows the orbital frequency and direction of the grinding wheel for a set of four viscosities, varying from 2.1 cSt (double the viscosity of water) to 14.5 cSt (half the viscosity of motor oil). Positive orbital frequency in the graph corresponds to down grinding, whereas negative orbital frequency corresponds to up-grinding. For 8.8 cSt, it can be seen that at low rotational speeds (<30 krpm) the wheel rotates at a high frequency in the down-grinding direction. However, as the rotational speed increased, the wheel orbital direction changes to up-grinding at a much lower frequency. This is due to the effect of fluid viscosity in the channel on hydrodynamic forces acting on the grinding wheel. From this graph, it can be seen that fluid viscosity and rotational speed can be used to predictably control both the grinding wheel orbital frequency AND the orbital direction.

[0038] While the system and methods defined herein have been particularly shown and described with references to embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.