The present invention relates to a rotary device and to a method of designing and making a rotary device. Typically the rotary device might be an engine, a compressor, an expander or a supercharger. When used herein, the term “rotary device” includes but is not limited to,any or all of the above.
Rotary engines are known that use a pair of rotors to achieve compression or expansion by displacement. The engines typically utilise the interaction between pairs of lobed and recessed rotors, in which the volume change applied to a compressible working fluid is achieved in a manner determined by the cross-sectional shape of the rotor pairs.
In WO-A-91/06747, the entire contents of which are hereby incorporated by reference, there is disclosed an internal combustion engine comprising separate rotary compression and expansion sections. Each of the compression and expansion sections is a rotary device comprising a first rotor rotatable about a first axis and having at its periphery a recess bounded by a curved surface, and a second rotor counter-rotatable to said first rotor about a second axis, parallel to said first axis, and having a radial lobe bounded by a curved surface. The first and second rotors are coupled for intermeshing rotation. The first and second rotors of each section intermesh in such a manner that on rotation thereof, a transient chamber of variable volume is defined. The transient chamber has a progressively increasing (expansion section) or decreasing (compression section) volume between the recess and lobe surfaces.
The manner of the interaction relies on the fact that the surfaces are contoured such that during passage of said lobe through the recess, the recess surface is continuously swept, by both a tip of said lobe and a movable location on the lobe. The moving tip and location on the lobe can each be said to define a locus. The location on the lobe progresses along both the lobe surface and the recess surface, to define the transient chamber. Thus, in such devices the form of the rotors is important and it is necessary that they should conform with the requirement to provide a sweep of the lobe through the recess, in which two minimum clearance points (at the tip and the movable location on the lobe) are maintained for the duration of the volume change cycle from a maximum volume at the start of the cycle to an effectively zero volume at the end of the cycle (for a compressor) and an effective zero volume increasing to a capacity limited maximum volume in the case of an expander.
These devices work well in that the low friction function means they are comparatively efficient as compared to other known rotary devices or indeed other engines. They are “low friction” in that the rotors do not actually contact each other but instead there is a minimum clearance between the rotors at the two points mentioned above.
Subsequent improvements and modifications to the basic form of such devices added new features. In WO-A-98/35136, the entire contents of which are hereby incorporated by reference, there is disclosed the use of helical forms of the rotors in the axial direction and a variable maximum possible volume for the transient chamber. Furthermore, in WO-A-2005/108745, the entire contents of which are hereby incorporated by reference, there is disclosed a method and apparatus by which the port flow area of such devices is increased. Indeed, in WO-A-2005/108745, an endplate was provided at the axial end of the recess rotor that enclosed the transient chamber of variable volume. A valve was provided in the endplate and an opening was provided in the surrounding housing. As the recess rotor rotates, the valving action between the endplate and the housing serves to control the flow of working fluid into and out of the transient chamber during an operating cycle. The sizing and positioning of the valve in the endplate and the opening in the housing enables accurate control of the rotary device.
The modifications and additions of WO-A-98/35136 and WO-A-2005/108745 did not change the form of the rotors nor their manner of interaction.
Rules were established which governed the distance apart of the central axes of rotation of the rotors and the magnitude of the outer radius of both rotors. In the case of the distance between axes of rotation, it was known that if this was reduced beyond a certain extent, then rotor forms could not be devised which would complete the interaction without either fouling or creating unavoidable leakage areas. Where this limit precisely lay in geometrical terms which could be related to other geometrical rotor parameters however, was unknown. It was therefore considered unsafe to reduce it arbitrarily below one and one third times the outer radius of the lobe. Once this parameter was fixed, then any reduction in the outer radius of the lobe rotor alone, without change in the radius of the recess rotor, would necessarily reduce the maximum 2-dimensional area swept by the lobe and therefore would reduce the swept volume of the machine. Subsequent models were therefore developed in which equality of outer radius dimensions for each of the recess and lobe rotors was retained.
This limitation, together with the limited value of the distance between the rotor axes, necessarily constrained the inner radius of the lobe rotor, i.e. the radius of the lobe rotor core, in order to provide rolling contact with the segments of the circumference of the recess rotor between the recesses. It also determined the maximum penetration of the lobe into the recess rotor.
According to a first aspect of the present invention, there is provided a rotary device comprising a first rotor rotatable about a first axis and having at its periphery a recess bounded by a curved surface, and a second rotor counter-rotatable to said first rotor about a second axis, parallel to said first axis, and having a radial lobe bounded by a curved surface, the first and second rotors being coupled for intermeshing rotation, wherein the first and second rotors of each section intermesh in such a manner that on rotation thereof, a transient chamber of variable volume is defined, the transient chamber having a progressively increasing or decreasing volume between the recess and lobe surfaces, the transient chamber being at least in part defined by the surfaces of the lobe and the recess; the ratio of the maximum radius of the lobe rotor and the maximum radius of the recess being greater than 1.
Thus, the present rotary device provides for a radius of the lobe rotor to be larger than that of the recess rotor and therefore enables the working volume of the device to be increased on a per cycle basis. This change to the previously established form of the rotor geometry increases the 2-dimensional sweep area through the interaction cycle. When translated into a 3-dimensional design, this change allows the maximum swept delivery volume per revolution to be increased by more than 100 per cent when compared with rotors of the same overall dimensions but following the previously established rules.
Previously, if the radial length of the lobe were to be increased by making the outer radius of the lobe greater than the radius of the recess rotor, then there could be no certainty that an effective interaction between the rotors could be achieved. In the present case, it has been recognised that the outer radius of the lobe can be greater than the radius of the recess rotor whilst still providing a functioning rotary device. Furthermore, the increased radius of the lobe provides for a greater swept area during each cycle.
There is a desire to generate a means by which the interaction of the rotors could be modelled and then to use the generated means to provide a new engine having optimised rotors such that swept volume and therefore power-per-cycle can be maximised.
The nature of the constraints discussed above emphasizes the lack of a clear mathematical model by which the interaction between the rotors could be understood or by which rules could be established to distinguish rotor forms with characteristics capable of supporting effective gas displacement without leakage and without fouling.
Preferably, the geometry of the or each lobe is determined by the inner radius of the lobe ρLi, the outer rotor radius at the tip of the lobe ρLo, the outer radius of the recess rotor ρPo and a circular arc segment Al of radius Rl defining a bulk of the lobe.
In one embodiment, the geometry of the or each lobe is, in addition, determined by a circular arc segment Ac of radius Rc wherein the arc segment Al defines the bulk of the lobe from its tip to an inflection point and the circular arc segment Ac defines a base of the lobe connecting between the arc segment Al and the core of the lobe.
In one embodiment, the position of the centre of the circular arc segment Al is defined in dependence on the separation of the centre of the circular arc segment Al from the centre of the lobe rotor.
Thus, in the absence previously of a basis for determining rotor shape, new physical models developed for practical applications could only be reasonably assured of success provided that they conformed to the parametric relationships of the geometrical entities which defined their predecessors, i.e. by ensuring equality of outer radius dimensions for both rotors.
According to a second aspect of the present invention there is provided a method of designing the rotors for a rotary device having a lobe rotor and a recess rotor coupled for intermeshing rotation, wherein the lobe and recess rotors intermesh in such a manner that on rotation thereof, a transient chamber of variable volume is defined, the transient chamber having a progressively increasing or decreasing volume between the recess and lobe surfaces, the method comprising: determining the geometry of the or each lobe in dependence on the inner radius of the lobe ρLio the outer rotor radius at the tip of the lobe ρLo, the outer radius of the recess rotor ρPo and a circular arc segment Al of radius Rl defining a bulk of the lobe. Preferably the method also comprises making a lobe rotor having the determined geometry.
In a preferred embodiment, the geometry of the or each lobe is, in addition, determined by a circular arc segment Ac of radius Rc wherein the arc segment Al defines the bulk of the lobe from its tip to an inflection point and the circular arc segment Ac defines a base of the lobe connecting between the arc segment Al and the core of the lobe.
A method and device is provided by which rotors can be designed and built so as to provide a functioning engine capable of improved performance as compared to previous engines. A means is provided to realise designs of the rotor interaction which conform to the characterisation requirement established in the aforesaid prior art but which are not necessarily constrained by the arbitrary limits to which the prior art was subject.
In the present case, the search for improved performance from rotors of given overall size, has led to an exploration of the general rules which limit the size and shape of lobe and recess rotors which are capable of interaction in the manner defined as acceptable in the prior art cited above. A 2-dimensional mathematical model is hereby provided, in which the geometrical form of the pair of interacting rotors is represented by a minimum number of key parameters whose relative magnitudes determine the properties of an effective pair of interacting rotors.
Use of this mathematical model to explore the potential for improved performance has led to the recognition that effectively interacting rotor forms are possible in which the maximum radius of the lobe rotor can be advantageously extended to a value substantially greater than that of the recess rotor. This change to the previously established form of the rotor geometry increases the 2-dimensional sweep area through the interaction cycle. When translated into a 3-dimensional design, this change allows the maximum swept delivery volume per revolution to be increased by more than 100 per cent when compared with rotors of the same overall dimensions but following the previously established rules.
The mathematical model that is preferably used to determine parameters for the rotors to enable the present rotary device to operate is set out in detail in the Appendix forming part of the description of this patent application.
According to a third aspect of the present invention, there is provided a rotary device having a lobe rotor and a recess rotor in which the lobe rotor has an outer radius and an inner radius and the inner radius is minimised so as to maximise swept area or volume of the lobe.
Preferably, the swept area is maximised in accordance with the equation:
in which
ρpo is the outer radius of the recess rotor;
ρLi is the inner radius of the lobe rotor;
ρMl is the separation between the centre of the lobe rotor and the centre of the circle from which the arc that at least in part defines the shape of the lobe is taken;
q is the ratio of angular velocities of the recess and lobe rotor; and
Rl is the radius of the arc defining at least in part the shape of the lobe.
This may be thought of as a condition on the curvature of the main lobe segment Al .
Embodiments of the present invention will now be described in detail with reference to the accompanying drawings, in which:
In contrast, in the present rotary device the radius of the lobe rotor and the radius of the recess rotor are different such that an increased swept area (in 2D) and consequently, volume (in 3D) can be achieved without increasing the overall size of the rotary device.
In an example, the two rotors are sized and configured in such a way that it is possible to increase the outer radius of the lobe rotor so that it is larger than that of the recess rotor. Comparing this with the previous arrangement using a pair of intermeshing rotors of given equal outer radius and given distance between the rotor axes, then the change is seen only as an increase in the tip radius of the lobe rotor. Thus, the arc described by the lobe tip describes a larger circular area than the recess rotor. It has been recognised by the inventors that it is possible that the close contact point remote from the tip of the lobe, i.e. near to the base of the lobe, is able to maintain close proximity to successive points on the surface of the recess to enable the familiar displacement of 2 dimensional area between the lobe and recess to be executed in the same manner as was previously possible.
The result of making this change in geometry is significant. The result is to effect a substantially increased swept volume from the paired rotor device on each cycle of operation. As an example, when comparing the new geometry with a previous design, it is shown that the swept volume delivery per revolution of the lobe rotor is twice that of the previous design for rotors having the same shaft centre distance.
In a previous design with shaft centre distance set at a value such that the maximum possible volume of the transient chamber of variable volume was 125 cc, the lobe rotor had four lobes and the recess rotor had six recesses, each interaction yielding a swept volume of 120 cc, thus making a total of 480 cc. per revolution of the lobe rotor.
Using the geometry of embodiments of the present invention in which the ratio of the maximum radius of the lobe and the maximum radius of the recess is greater than 1, the increased penetration of the lobe also increases the length of the arc traversed by the lobe tip from the start of the cycle. Thus, in this particular example, it is only possible to accommodate two lobes which requires a matching three-recessed complementing rotor. Nevertheless, the cycle swept volume for the new geometry is 500 cc. per lobe which means that the new design can deliver 1 Litre per revolution of the lobe rotor.
Rotor lengths are preferably kept constant between previous and new geometries in this comparison.
In the example shown, the y-axis of the co-rotating coordinate system (x, y) in the recess frame is chosen such that it pierces T at this instant. The shape of the lobe is, in this example, defined by the two circles of Radius Rl and Rc for the bulk of the lobe and its base. As shown there are various angles near centres of the lobe OL and the centre of the recess OP.
These angles are defined by triangles of named points, namely
φMl=/(Ml, OL, T),
φMc=/(Mc, OL, T),
φlc=/(Ml, OL, Mc),
αL=/(OP, OL, T), and
αP=/(OL, OP, T),
where the angle defined is near the second of each triple of points.
With reference to the parameters defined above with respect to
As explained above and also in section D in the appendix, a general condition can be recognised for validity of a rotor configuration. The parameters that are most favourable in order to maximize the maximum possible volume of the transient compression or expansion chamber of variable volume are now considered. As explained in detail in the appendix (section E, entitled “Maximising the Lobe Length”), a large fraction of the volume is swept by the lobe rotor and it is thus useful to increase the length of the outer lobe radius ρLo. An alternative or additional way of achieving this, i.e. other than increasing ρLo, involves reducing ρPo followed by a resealing of all length parameters such as to recover the same overall size of the rotary device.
Independently, minimizing the inner lobe radius ρLi also contributes to an increase of the total swept volume. Thus an independent aspect of the present invention (which may of course be combined with other aspects or embodiments of the invention) provides a rotary device having a lobe rotor and a recess rotor arranged for intermeshing interaction in which the lobe rotor has an outer radius and an inner radius and the inner radius is minimised so as to maximise swept area or volume of the lobe. Preferably, the rotary device comprising a first rotor rotatable about a first axis and having at its periphery a recess bounded by a curved surface, and a second rotor counter-rotatable to said first rotor about a second axis, parallel to said first axis, and having a radial lobe bounded by a curved surface, the first and second rotors being coupled for intermeshing rotation, wherein the first and second rotors of each section intermesh in such a manner that on rotation thereof, a transient chamber of variable volume is defined, the transient chamber having a progressively increasing or decreasing volume between the recess and lobe surfaces, the transient chamber being at least in part defined by the surfaces of the lobe and the recess.
As explained in section E of the appendix, a criterion which limits both these types of change is the condition on the curvature of the main lobe segment Al, as formulated in equation (26) and which is reformulated as equation (30). Rotor configurations that maximize swept volume correspond to parameters such that equation (30) is nearly satisfied as an equality, i.e. is approximately satisfied as an equality. Thus by satisfying this condition it is possible to maximise the swept volume in such a way as to increase the effective working volume of the rotary device per cycle without necessarily requiring a difference in the outer radii of the lobe and recess rotors. Greater detail on this is given in the appendix.
The rotor pairs may be provided within a housing such as that shown in and described above with reference to
It will be appreciated that the above examples are non-limiting and any suitable form may be used for the rotors. What is important is that the radius of the lobe rotor and the recess rotor is not the same which then enables an increased swept volume to be achieved with the same overall size of device. In summary and with reference to the description above of
As set out in the prior art referred to above, an efficient rotational displacement device, is obtained by helically extruding a single two-dimensional cross sectional area of the lobe and recess rotors. By extension and reference to the prior art it is therefore sufficient to describe the parameters defining their two-dimensional shapes, as well as the constraints to which the different parameters are subject.
In summary, the model operates by defining some fundamental parameters and in dependence on these determining a shape for a lobe rotor and the corresponding recess rotor. From the fundamental parameters, a number of others may be derived including a number of angles and further lengths. These two forms of parameter may be referred to as “fundamental geometrical parameters” and “derived geometrical parameters”. The model discussed in the appendix below uses one specific example as shown in
Once the rotors have been designed using the method described above the lobe rotor and the corresponding recess rotor are made. These may be made using appropriate materials such as steel and using any known method such as die casting, injection moulding, extrusion of appropriate materials etc.
Embodiments of the present invention have been described with particular reference to the examples illustrated. However, it will be appreciated that variations and modifications may be made to the examples described within the scope of the present invention.
The defining element of the rotational displacement device (which we shall also refer to in short as the engine) is the geometry of the lobe(s). The pocket rotor is obtained as the involute form of the lobe geometry. The lobe rotor consists of a nL, identical lobes, offset relative to each other by an angle 2π/nL. Similarly, the pocket rotor features nP identical pockets, offset by an angle 2π/nP. Both rotors are linked by a pair of gears such that they rotate at a fixed ratio of angular velocities q=nL/nP, given by the ratio of the number of lobes nL to the number of pockets nP. As shown in
The length parameters given above uniquely define the geometry. For convenience we derive from these a number of angles and further lengths. Additional lengths which we shall refer to below are given by the distance between the axes of the two rotors
R
O=ρPo+ρLi, (1)
the separation of M1 and Mc
R
lc
=R
l
+R
c, (2)
and the separation of Mc and OL h
ρM
Various angles are obtained by application of the cosine law in the triangles present in the geometry. In particular, we define two angles αL and αP, which relate to a special state of rotation of the system. These two angles are realized in the configuration where the tip of the lobe T first penetrates into the interior of the pocket rotor. Considering the triangle Δ(Op, OL, T) at this instant, we define the two angles αL∠(Op,OL,T), and αP=∠(OL, OP, T) (where the angle defined is near the second of each triple of points), such that
at the corner OL, and
at the corner OP. Further angles are defined for the lobe geometry and do not imply a particular state of rotation. All of these angles are measured near the centre of the lobe OL, and are defined by triangles of points named in
These angles equate to
Prior patents NO-A-91/06747, GB98/003451 have described specific geometries of this type using the offset d of the point Ml from the radius towards the tip {right arrow over (OLT)}. This quantity can be used interchangeably with ρM
C. The Pocket Geometry
The shape of the pocket rotor follows by imprinting the shape of the lobe under revolution of the two rotors. There are two points of contact between the two rotors. The first point of contact is located initially at the base of the lobe defined by the intersection of Ac and {right arrow over (OL Mc)} and is travelling towards the tip T of the lobe as the lobe penetrates the pocket rotor. The second point is given by the tip of the lobe. These two points are referred to below as the inner and outer locus. The movement of these two loci defines the geometry of the pocket. However, some conditions need to be verified by the lobe geometry to assure that a functional pocket exists, which are considered in the subsequent section. Here, we first demonstrate how to construct the shape of the pocket.
First, we need to define a convenient coordinate system in which to express the pocket shape. We choose the system (x, y) shown in
A second useful frame of reference (ξ, η) can be defined for the lobe rotor, such that the unit vector {right arrow over (e)}ξ continually points towards the origin of the pocket rotor, and {right arrow over (e)}η is obtained by rotating this vector by π/2 (counterclockwise), i.e., {right arrow over (e)}η={right arrow over (e)}z×{right arrow over (e)}ξ, with {right arrow over (e)}z the unit vector pointing outwards of the plane of projection of
where φO
Consequently, the (time-dependent) unit vectors of the system (ξ, η) are given by
The reference system (ξ, η) is not attached to the rotating frame of the lobe. Instead, angles of points in the lobe system decrease linearly with the time variable, t=0 corresponding to {right arrow over (OLMc)}=ρM
The motion of single points in the lobe system, such as the lobe tip T, as well as the center points Ml and Mc can now be straightforwardly expressed:
{right arrow over (r)}
T(t)={right arrow over (r)}O
{right arrow over (r)}
M
(t)={right arrow over (r)}O
{right arrow over (r)}
M
(t)={right arrow over (r)}O
The outer locus is identical with {right arrow over (r)}T(t), while the inner locus is traced out as the involute form of circles with centers {right arrow over (r)}M
{right arrow over (r)}
C
(t)={right arrow over (r)}M
{right arrow over (r)}
C
(t)={right arrow over (r)}M
where we have introduced the tangent vectors {right arrow over (r)}M={right arrow over ({dot over (r)}M/∥{right arrow over ({dot over (r)}m∥ (using the notation
for the time derivative, and ∥{right arrow over (r)}∥ to denote the norm of a vector).
As stated above, the inner locus moves from the base of the lobe towards its tip during the compression cycle. The curve delineating the pocket is given as the union of three segments, defined by {right arrow over (r)}C
{right arrow over ({dot over (r)}
M
(tcl)·[{right arrow over (r)}M
The solution can be found analytically, and it is of the form
abbreviating recurrent expressions
For times tcl<=t <=tend, the inner locus is described by {right arrow over (r)}C
{right arrow over ({dot over (r)}
M
(tend)·[{right arrow over (r)}M
It solution has a similar form as Eq. (18), but with one change in sign:
and with the parameters
In the previous section, we have derived mathematical expressions for the curves defining the pocket geometry, Eqs. (12), (15), and (16). However, not all choices of parameters {ρLi, ρLo, Rl, Rc, ρM
For a successful compressor geometry, the inner locus, as seen in the rest-frame of the pocket rotor, performs a continuous movement, which excludes any momentary reversals of the velocity as well as intersections of its trajectory with itself. A valid trajectory can be ensured by requiring a negative initial velocity (contrary to the sense of rotation of the pocket rotor), a touching point of the curves Cc and Cl at time tcl and the absence of reversal of the velocity within curve Cl. In addition, there are some trivial geometric contraints which we consider first.
On the level of basic geometry, the lengths defining the lobe geometry have to be chosen such that the two fundamental triangles Δ(OL, T, Ml) and Δ(OL, Mc, Ml) can be spanned, as described by the triangle relations |a−b|<c<a+b [for a generic triangle Δ(a, b, c)]. Six inequalities follow, namely
R
l+ρM
ρLo+ρM
R
l+ρLo>ρM
for the first of the two triangles, and
ρM
R
l+2Rc+ρLi>ρM
ρLi+ρM
for the second.
In order for the initial velocity of the inner locus to be negative (i.e., moving in the direction from the base to the tip) it is sufficient to demand that the movement of its center has a positive velocity at t=0. The trajectory ρM
By construction, the arc segments defining the lobe Ac and Al share a common tangent where they join. Consequently, the involutes of both arcs generically yield parallel curves Cc and Cl at their touching point. However, Cc has an inflection point accompanied with a reversal of local velocity. This feature must occur after the time of intersecting with Cl, in which case it does not affect the geometry. This leads to a condition, which is equivalent to demanding a positive argument of the root in Eq. 18. Simplifying this expression, we arrive at the condition
Note all the factors in parentheses for the first term are positive by virtue of the triangle relations.
Finally, one needs to ensure that the curve Cl is well formed. It is typically dominated by a point of inflection where the inner locus remains nearly stationary, and can even reverse its direction. The latter case leads to leakage and should be avoided. Algebraically, this can be expressed as the velocity of the touching point {right arrow over ({dot over (r)}C
The bound on the signed curvature kl(t) can only be satisfied if its absolute maximum maxtkl(t) satisfies the bound. A pleasingly simple criterion ensues.
In total, the pocket rotor has to be able to carry np pockets. This imposes a limitation on the maximal angle of opening of the pocket. The total opening angle of the pocket θP is given by
This criterion only tests for the size of the pockets on the circumference of the lobe rotor. In addition, the pockets need to be well separated in the interior of the rotor as well. This can be checked easily by drawing a given shape of the pockets for a set of input parameters.
So far, we have not mentioned the shape of the trailing edge of the lobe. As this element has no function other than ensuring mechanical stability of the lobe, it can be designed freely except having to avoid colliding with the pocket rotor. The maximum allowed angle between the tip of the lobe and its trailing edge at the base γL is therefore limited to the value
Typically, mechanical stability will require at least γLmax>0. To extend this discussion, we consider the constraint arising from the need that the lobe evacuates the interior of the pocket rotor quickly enough to prevent a collision with the trailing edge of the pocket rotor. The most protruding feature of the trailing edge of the pocket is the point {tilde over (T)} on the outer radius of the pocket which meets the tip of the lobe T at time t=φM
introducing the abbreviation β(t)=αP+q(φM
Given the criteria for validity of a rotor configuration discussed in section D, we may now ask which parameters are most favorable in order to maximize the volume of the transient compression chamber. A large fraction of the volume is swept by the lobe rotor. It is thus useful to increase the length of the outer lobe radius ρLo. Rather than thinking of increasing ρLo, we may equivalently reduce ρPo followed by a resealing of all length parameters such as to recover the dame overall size of the engine. Independently, minimizing the inner lobe radius ρLi also contributes to an increase of the total swept volume.
The criterion which limits both these types of change is the condition on the curvature of the main lobe segment Al, Eq. (26), which we can reformulate equivalently to read
Rotor configurations that maximize swept volume correspond to parameters such that (30) is nearly satisfied as an equality. In particular, previously disclosed rotor configurations in patents WO-A-91/06747 and GB98/00345 did not approach this criterion very closely. Even while keeping the ratio of the outer lobe radii ρLo/ρPo constant, the maximal 2D area for a system of rotors with ρPo=ρLo can be increased substantially by reducing ρLi. To illustrate the effect of this modification, we modify the parameters of the engine previously disclosed in U.S. Pat. No. 6,176,695. One can easily achieve ρLi/ρLo=1/4 as opposed to the value ρLi/ρLo=1/2 given in prior art. In
With regard to the other criteria, Eq. (23) can always be fulfilled by choosing Rc sufficiently large. However, the remaining constraints are non-trivial. In particular, when ρLi is minimized, this may lead to violations of the triangle relations (22a-c), such that ρM
Above, we have given an explicit construction of a geometry which implements the concept of a rotary displacement device with a compression chamber formed by a lobe and pocket rotor that are touching in two points of close contact. The lobe geometry described above consists of precisely two arc segments Al and Ac, however, this is not the only possible way of constructing a geometry in the spirit of patent no. WO-A-91/06747.
As a special case of the construction presented in this appendix, it is possible to obtain a geometry in which the lobe consists of a single arc segment Ai, which touches the lobe core tangentially. In this case, the points Ml, Mc and OL lie on a single line, and the arc Ac does then not define any portion of the lobe and Rc is not a relevant parameter (can be formally chosen to be any positive number). In addition, the triangle relations (22a-c) can be disregarded, and ρM
Following the same geometrical principles, a lobe can be built up from multiple arc segments of different curvature. Generalising the construction given above, the condition defining whether a geometry can be realized is the criterion of non-reversal of the velocity of the inner locus akin to Eq. (26). The main difference arising in the case of multiple arc segments is to replace this equation by a condition of the momentary curvature of the trajectory of the relevant center point for a given segment of the lobe. Generally, the structure of the lobe will be similar to that given in the model of two arcs: the base of the lobe is a convex piece either given by the inner core or a circle segment tangential to it as in the case of the single arc structure in section F1. The next portion of the lobe is concave, and the portion near the lobe tip is again convex. Each of these portions can in principle be composed of multiple arc segments of varying curvature.
To display the versatility of the given construction with two arc segments, a number of possible configurations are included in the section of drawings.
Number | Date | Country | Kind |
---|---|---|---|
0921968.4 | Dec 2009 | GB | national |
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/GB10/52128 | 12/17/2010 | WO | 00 | 12/20/2012 |