TECHNICAL FIELD

[0001] The present invention concerns a volumetric pump capable of transferring fluids from an inlet to an outlet at accurately controlled flow rates without pulsations or sudden gushes of fluid spurting out through the outlet. The delivery of fluid to the outlet can be controlled at a constant flow rate, dV / dt, during a whole transfer operation or, alternatively, the flow rate may be varied in a controlled manner, and even interrupted for periods of time. Fluids of viscosities varying from highly fluid to highly viscous can be used with the volumetric pump of the present invention, with a very limited generation of shear stresses allowing the reduction of wear rate of pump parts as well as the preservation of the integrity of unstable fluids, such as sols, gels, or even liquids contained in a membrane, such as egg yolk. Thanks to its precision and versatility the volumetric pump of the present invention can be used in a variety of applications including, albeit not restricted to, 3-D printing heads, medical fluids delivery systems, metering heads in industrial production lines of products requiring an accurate dosing and/or mixing of fluid components in industries such as pharmaceutical, cosmetics, food, paper, building, and the like.

BACKGROUND OF THE INVENTION

[0002] Positive displacement pumps are volumetric pumps. They include rotary-type positive displacement pumps, reciprocating-type positive displacement pumps, and linear-type positive displacement pumps. Rotary-type positive displacement pumps (hereinafter referred to as rotary pumps) move fluid using a rotating mechanism that creates a vacuum that captures and draws in the liquid in transfer volumes, transporting the captured fluid towards the outlet by rotation of the rotating mechanism.

[0003] For some applications, it is critical to limit shear stresses in the liquid to preserve the integrity of the fluid such that the properties of the fluid at the outlet are as similar as possible to the properties of the fluid at the inlet. It can also be important to limit the amplitude of pulsations and vibrations in the flow to preserve the installations (e.g., the piping system, the tanks, the valves), to prevent surging noises, or to reach a smooth continuous output as opposed to successive blasts of medium surging out of the pump. For example, a continuous, pulsation free flow is required for the continuous deposition of a liquid ink or of paste according to a predefined pattern, or for homogeneously feeding a mixer for mixing several fluids. Syringes do not generate pulsations, but they are ill-fitted for continuous dispensing applications. By contrast, rotary-type positive displacement pumps can be used in a continuous mode over time, but generally generate small variations of flow rate in time, forming pulsations in the output of the pump. The amplitude of the pulsations can be reduced by coupling a pulsation damper to the rotary pump, but pulsation dampers increase the cost of the pumping system, they are bulky, and pulsations are not eliminated, but merely dampened at the expenses of a loss in accuracy of the volumetric flow rate.

[0004] US1892217A filed in 1931 describes a“gear mechanism adapted to be used as a [rotary] pump,” still in use to date and sometimes referred to as“Progressing Cavity Pump.” This pump combines a rotation and a translation of a single screw type rotor into a matching threaded sleeve having an extra thread compared to the rotor.

[0005] This type of pumps reduces the problem of pulsations associated with rotary pumps, but the intricate structure of this pump increases the complexity and costs in manufacturing and maintenance and reduces the freedom of design required for adapting to different pumping configurations. Universal joints are required, and the rotor and the sleeve are complex to manufacture, with tight tolerances for proper sealing. This type of pump is also limited to one geometry that has a much higher space claim than any other pumps, especially in the axial direction.

[0006] WO2017055497A1 describes a pump having a rotor that is rotatable about a rotation axis and comprises a rotor hub and a rotor collar that extends from the rotor hub in the radial direction and encircles it in an undulating manner. As the hub rotates, so does the collar forming a sinusoidal wave oscillating in the axial direction. A sleeve consisting of a portion of a straight cylinder closed at its ends forms with the disc and hub the cavities for transporting fluid. A vane pinching the disc is rotatably fixed and rides over the disc, which rotation drives a reciprocating translation of the vane along the axial direction of the rotor. The vane is used to prevent recirculation of the fluid from the outlet side to the inlet side.

[0007] This type of pumps can limit the pulsations in the flow it generates with a much shorter rotor than the one of the gear mechanism described above, and it also generates low shear stresses. This pump is, however, also complex to manufacture, in particular because of the 3D geometry of the disc. Here again, the design freedom of this pump is very limited to a single geometry and cannot be scaled down easily to small size pumps. [0008] US2717555A describes a pump comprising a pair of identical radial cams comprising two noses and mounted in rotation on an axis of rotation reducing the level of pulsations. The author of this document states that“an absolute uniform discharge rate [i. e. , no pulsation] can be obtained theoretically with proper rotor shape and proper arm relationship ,” . He concludes, however, that“in practice absolute uniform rate of discharge is not obtained [...] but a sufficiently close approximation of uniform discharge rate is obtained for all practical purposes The theoretical fluctuation of the flowrate of a pump according to US2717555A can be calculated, and it was found that the geometry described in said document theoretically yielded pulsations of the order of ±4 to ±4.5%. Such levels of fluctuations may have been considered as sufficient for all practical purposes back in 1945, but there are many applications today which require substantially lower levels of fluctuations, such as precision dosing, printing, and in particular 3D-printing.

[0009] US2754762 and US2609754 describe volumetric pumps comprising two cams mounted on a common axle of rotation with an angular offset. The cams are complementary in that, R + r = R _L + ri, thus yielding a practically constant combined instant fluid displacement produced by rotation of the two complementary rotors. Flowrate fluctuations increase with increasing value of the radius ratio, (R _{L -} n ) / R _L .

[0010] There therefore remains a need for a pump suitable for continuously delivering a fluid devoid of the foregoing drawbacks. The present invention proposes a volumetric pump suitable for continuously or intermittently delivering a fluid at an accurately controlled flow rate over time. The nominal flowrate fluctuation can be reduced to below ± 0.05%, and even down to zero. The pump of the present invention reduces shear stresses in the fluid compared with other rotating pumps, and is of simple construction, allowing for cheaper manufacturing conditions. The geometries and dimensions of the pumps of the present invention can be varied to adapt to the specific requirement of each application.

SUMMARY OF THE INVENTION

[0011] The appended independent claims define the present invention. The dependent claims define preferred embodiments. In particular, the present invention concerns a volumetric pump comprising a chamber having a chamber breadth, B, comprising an inlet volume provided with an inlet and an outlet volume provided with an outlet, the inlet volume being separated from the outlet volume by m pumping systems enclosed in the chamber, with m e N, and m > 1 , each pumping system comprising, • at least a portion of one of m / k radial cams with k £ N and k ¹ 0, comprising at least two noses, i.e., each radial cam comprises p > 2 k noses, wherein all of the m / k radial cams are mounted on an axis of rotation, Zl, parallel to the chamber breadth, B, such that the radial cam and chamber can rotate relative to one another about the corresponding axis of rotation, Zl, and

• a vane or vane portion movingly mounted in the chamber such as to keep permanent contact with a circumferential track (3t) of the radial cam or cam portion, and together with the radial cam or cam portion, permanently fluidly separating the inlet volume from the outlet volume,

wherein each pumping system delivers by rotation of the corresponding cam a volume, Vi, of fluid from the inlet volume to the outlet volume at a flow rate, Qi = dVi / dt, characterized in that, the sum of the nominal flow rates, d Vi / dt, of fluid delivered at any time to the outlet volume by a synchronized rotation of the radial cams of the m pumping systems is constant, within a tolerance of not more than ± 1%, preferably not more than ± 0.5%, more preferably not more than 0.2%,

and wherein a sum of volumetric displacements, Di, of the m pumping systems generated by the rotation of the m radial cams is constant for any azimuthal angle, a, of rotation about the axis of rotation, Zl, within a tolerance of not more than ± 1%, preferably not more than ± 0.5%, more preferably not more than 0.2%:

wherein the volumetric displacement, Di = dVi / da, is defined as the volume of fluid displaced through the cross-sectional opening per unit angle of rotation (in radians) of one pumping system.

[0012] In a preferred embodiment, the chamber comprises first, and second lateral walls separated by a joining wall of breadth, B, wherein

(a) The radial cams,

• comprise a set of r consecutive external cams or a set of s consecutive internal cams, all radial cams of a given set being rigidly coupled to one another and rotatably mounted on the axis of rotation, Zl, and wherein • together with the dividing walls defined below, they extend over substantially the whole chamber breadth, B, measured parallel to the axis of rotation, Zl,

• have a first and second peripheral rims separated from one another by the circumferential track of breadth, bi, measured parallel to the axis of rotation, Zl, and defining first and second planes normal to the axis of rotation, Zl, said first and second peripheral rims having a periodicity of p, defining p identical sectors of central angle 2p / p rad, and having a radius, Rri, and Rli, extending from the corresponding axis of rotation, Zl, to the first and second peripheral rims, periodically varying between a nose radius equal to Rlni, Rmi, defining p noses of the radial cam, and a belly radius equal to Rlbi, Rrbi, defining p bellies of the radial cam, the first and second peripheral rims being characterized by a same variation of the radius with respect to an azimuthal angle, a, dRri / da = dRli / da, wherein i = 1 to m, and wherein p is a natural number greater than 1 (p £ N, and p > 1),

• comprise a circumferential track (3ti) defined by a track profile joining the first and second peripheral rims, and defined by a distance, Ri(a, z) = Rli(a) + ri(z), from the axis of rotation, Zl (wherein z is measured along the axis of rotation, Zl).

(b) the circumferential tracks,

• of each of the r consecutive external cams or s internal cams are separated from one another by (r- 1) or (s - 1) dividing walls (3wi), each dividing wall being normal to the axis of rotation, Zl, and comprising at least a circular ring having an outer radius and an inner radius, wherein for external cams, the outer radius is equal to the largest of the nose radii, Rmi, Rln(i+l), and the inner radius is equal to or smaller than the smallest of the belly radii, Rrbi, Rlb(i+l), of two adjacent radial cams (3i, 3(i+l)) separated by said dividing wall, and for internal cams the outer radius is equal to the largest of the belly radii, Rrbi, Rlb(i+l), and the inner radius is equal to or smaller than the smallest of the nose radii, Rmi, Rln(i+l), of said two adjacent radial cams (3i, 3(i+l)),

• adjacent to the first or second lateral walls of the chamber are referred to as outer circumferential tracks, which are optionally provided with an outer dividing wall separating the outer circumferential tracks from the first or second lateral walls,

(c) each of the m vanes or m vane portions comprises a leading edge having a vane profile mating the track profile of the corresponding circumferential track, wherein said m vanes or m vane portions are radially mounted in the chamber fluidly separating the inlet volume from the outlet volume, such as to radially translate while the leading edge keeps at all time a sealed contact with the corresponding circumferential tracks of the m radial cams, each vane or vane portion having a height, di, at least equal to the absolute value of the difference between the nose radius Rlni and the belly radius Rlbi, of the corresponding radial cam (di > |Rlni - Rlbi|),

(d) each of the m pumping systems comprises a liner or a liner portion, rigidly coupled to the chamber and circumscribing a corresponding radial cam, wherein each of the m liners and/or liner portions,

• has a geometry of revolution, about the axis of rotation, Zl, of largest radius substantially equal to and slightly larger than the largest value of Ri(a, z) at the level of a nose of the corresponding circumferential track, and having a liner profile extending parallel to the axis of rotation, Zl, which mates the track profile of the corresponding circumferential track, such that the m radial cams can rotate about the corresponding axis of rotation with respect to the corresponding m liners,

• extends from an upstream end located in the inlet volume, to a downstream end located in the outlet volume, and has a peripheral length equal to or larger than the length of a circular arc comprised between two consecutive noses of the corresponding radial cam, and

(e) m cross-sectional openings each having an area, Ai, on a downstream plane, Pi, comprising the axis of rotation, Zl , of a given radial cam and passing by a point of the downstream edge of the corresponding liner and/or liner portion which is located furthest away from the outlet, said cross-sectional opening being bounded, on the one hand,

• between the corresponding liner and/or liner portion, and the corresponding circumferential track and, on the other hand;

• between the two adjacent dividing walls or, for the outer circumferential tracks, between a dividing wall and either an outer dividing wall or the first or second lateral walls,

wherein, the volumetric displacement, Di, of each pumping system generated by the rotation of the corresponding radial cam is for any azimuthal angle, a, of rotation about the axis of rotation, Zl : Rlnf — Rif (a) bi

Di = b _t + ( Rlrii - Rl _t {a )) r _f (z) dz

2 J o (3)

[0013] In one embodiment, the volumetric pump comprises,

• r = m = 2 external cams or s = m internal cams, wherein all the r or s radial cams are rigidly coupled to one another along the axis of rotation, Zl, with an azimuthal offset, Da > 0, measured at the corresponding axis of rotation, Zl, and wherein p is preferably comprised between 2 and 4, more preferably p = 2 or 3, and

• m = 2 liners (7i) or liner portions (7i), wherein the downstream ends of the liners are azimuthally flush, and

• the azimuthal distance separating the downstream end of a liner from the corresponding vane or vane portion is equal for all pumping systems

[0014] In an alternative embodiment, the volumetric pump comprises,

• r = m = 2 external radial cams or s = m internal cams, wherein all the r or s radial cams are rigidly coupled to one another along the axis of rotation, Zl, with no azimuthal offset, Da = 0, and wherein p is preferably comprised between 2 and 4, more preferably p = 3 or 4, and

• m = 2 liners (7i) or liner portions (7i), wherein the downstream ends of the m liners are offset by an azimuthal angle, Da > 0, and

• the azimuthal distance separating the downstream end of a liner from the corresponding vane or vane portion is equal for all pumping systems.

[0015] In yet an alternative embodiment, the volumetric pump comprises,

• r = m / k external radial cams or s = m / k internal cams, wherein all the r or s radial cams are rigidly coupled to one another along the axis of rotation, Zl, and form in total m = r · k or m = s k pumping systems, with k > 1 , preferably, k = 2, and wherein the number of noses of each radial cam is equal to or greater than 2 k (p > 2 k), and is more is more preferably a number comprised between 4 and 7, more preferably p = 4 or 5, and

• k liners (7i) or liner portions (7i) per radial cam, wherein the downstream ends of the k liners shared by a same cam are offset by an azimuthal angle, Da = 2p / k rad, and the azimuthal distance separating the downstream end of a liner from the corresponding vane or vane portion is equal for all pumping systems.

[0016] In this embodiment, it is preferred that,

• each radial cam comprises an odd number p of noses, and the volumetric pump comprises one or more radial cams (if p = 2u + 1 , with u G N, then s or r > 1), or

• each radial cam comprises an even number p of noses, and the volumetric pump comprises two radial cams, offset by an offset azimuthal angle, Da (if p = 2u, with u G N, then s or r = 2).

[0017] It is preferred that the r external radial cams or s internal radial cams have the same periodicity p, with an azimuthal offset of p / p rad. For reducing production costs, it is preferred when the m cams are identical in geometry. The peripheral edges of the m cams can be symmetric at the level of theirs noses, so that the direction of rotation can be inverted while maintaining the same stress levels on the vanes while yielding the same flowrate as a function of absolute value of the rotation rate, |co|, Q(co) = Q(-co) = Q(|co|).

[0018] The volumetric pump can comprise more than one inlet, opening into the inlet volume. Similarly, it may comprise more than one outlet, opening out of the outlet volume, and/or comprise an outlet which is in fluid communication with a manifold comprising more than one outlet.

[0019] The relative rotation of the radial cam and chamber can be according to any of the following configurations:

• The m radial cams rotate about the axis of rotation, Zl, and the chamber is static, or

• The m radial cams are static, and the chamber rotates about the axis of rotation, Zl, together with the vanes or vane portions, and liners or liner portions, or

• The m radial cams rotate about the axis of rotation, Zl, at a velocity, col, and the chamber rotates about the axis of rotation, Zl , together with the vanes or vane portions, and liners or liner portions at a velocity, co2, wherein col ¹ co2, and col and co2 ¹ 0.

[0020] In a preferred embodiment, the relative height DRn of a transfer volume is defined as, AR _n = wherein F = 0.5%, preferably F = 1%.

⁷¹ ’ ^{1 J} [0021] Several volumetric pumps can be assembled to form a high accuracy mixing pump, comprising at least two volumetric pumps as defined supra, lodged in a common chamber, wherein,

• each volumetric pump comprises a separate inlet and inlet volume fluidly separated from the inlets and inlet volumes of the other volumetric pumps, and

• all volumetric pumps share a single outlet volume and outlet.

BRIEF DESCRIPTION OF THE FIGURES

[0022] For a fuller understanding of the nature of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings in which:

Figure 1: shows the principle of combining complementary pulsed flowrates to yield a constant overall flowrate over time at a given rotation rate, co,

(a) m = r = 2 external cams, p = 3, symmetric (= S), different cams, no offset (Da = 0);

(b) m = r = 2 external cams, p = 3, asymmetric (= NS), identical cams, offset by an angle Da = p / p;

(c) m = r = 2 external cams, p = 2, asymmetric (= NS), identical cams, offset by an angle Da = p / p;

(d) m = r = 2 external cams, p = 2, symmetric (= S), identical cams, offset by an angle Da = p / p;

(e) m = s = 2 internal cams, p = 2, asymmetric (= NS), identical cams, offset by an angle Da = p / p;

(f) m = s = 2 internal cams, p = 4, symmetric (= S), identical cams, no offset (Da = 0);

(g) m = k = 2 internal cam portions, with s = m / k = 1 internal cam, p = 5, symmetric (= S);

(h) m = 4 internal cam portions, with s = m / k = 2 internal cams, p = 4, asymmetric (= NS);

(i) m = k = 2 external cam portions, with r = m / k = 1 external cam, p = 5, asymmetric (= NS); and

(j) m = r = 3 external cams, p = 2, symmetric (= S), different cams.

Figure 2: shows various external radial cams, (a)-(c) perspective views, (d)-(f) cut views. Figure 3: shows a transverse cut of a chamber parallel to the axis of rotation of a pump according to the present invention, with m = r = 2 external cams, with the leading edges of the vanes in contact (a) with noses of the radial cams and (b) with bellies of the radial cams.

Figure 4: shows perspective views of pumps comprising m = r = 2 external cams of periodicity, p = 3, wherein (a) the radial cams are offset by an azimuthal angle, 2p / (p m) = p / 3, and the upstream ends of the liners are flush, and (b) the radial cams are flush and the upstream ends of the liners are offset by an azimuthal angle, 2p / (p m) = p / 3.

Figure 5: shows two embodiments of mixing pumps comprising more than one inlets.

Figure 6: shows one way of designing a pair of identical complementary cams.

Figure 7: shows examples of external cams comprising a dwell region.

DETAILED DESCRIPTION OF THE INVENTION

[0023] The present invention concerns a volumetric pump of the type of rotary positive displacement pumps comprising a chamber (1) having a chamber breadth, B, measured along a direction parallel to an axis of rotation, Zl, comprising an inlet volume provided with an inlet and an outlet volume provided with an outlet and wherein the inlet volume is separated from the outlet volume by m pumping systems enclosed in the chamber, with m e hi, and m > 1. All the pumping systems share the axis of rotation, Zl. Each pumping system comprises,

• At least a portion of one of m / k radial cams (3i) with k £ N and k ¹ 0, comprising at least two noses, i.e., each radial cam comprises p > 2 k noses, wherein all of the m / k radial cams are mounted on an axis of rotation, Zl, parallel to the chamber breadth, B, such that the radial cam and chamber can rotate relative to one another about the corresponding axis of rotation, Zl,

• a vane or vane portion movingly mounted in the chamber such as to keep permanent contact with a circumferential track (3t) of the radial cam or cam portion, and together with the radial cam or cam portion, permanently fluidly separating the inlet volume from the outlet volume,

[0024] Each pumping system delivers by rotation of the corresponding cam a volume, Vi, of fluid from the inlet volume to the outlet volume at a flow rate, Qi = dVi / dt, wherein the sum of the nominal flow rates, d Vi / dt, of fluid delivered at any time to the outlet volume by a synchronized rotation of the radial cams of the m pumping systems is constant, within a tolerance of not more than ± 1%, preferably not more than ± 0.5%,

[0025] To achieve this goal, the geometry of the radial cams of the volumetric pump of the present invention is defined such that a sum of the volumetric displacements, Di, of the m pumping systems generated by the rotation of the m radial cams is constant for any azimuthal angle, a, of rotation about the axis of rotation, Zl, within a tolerance of not more than ± 1%, preferably not more than ± 0.5%:

[0026] The volumetric displacement, Di = dVi / da, is defined as the volume of fluid displaced through the cross-sectional opening per unit angle of rotation (in radians) of one pumping system

[0027] In a preferred embodiment, each pumping system comprise,

• a corresponding radial cam (31) or a cam portion shared with (k - 1) other pumping system(s) (3i, i = 2 to m), rigidly coupled with the respective cam or cam portion of the other (m - k) pumping systems, mounted on the axis of rotation, Zl, such that the radial cams or cam portions of the m pumping systems and the chamber can rotate relative to one another about the axis of rotation, Zl, and having a geometry defined as follows: o first and second peripheral rims (3ri, 3li) separated from one another by a cam breadth, bi, measured parallel to the axis of rotation, Zl, and defining first and second planes normal to the axis of rotation, Zl, said first and second peripheral rims having a periodicity of p, defining p identical sectors of central angle 2p / p rad, and having a radius, Rri, and Rli, extending from the corresponding axis of rotation, Zl, to the first and second peripheral rims, periodically varying between a nose radius equal to Rmi, Rlni, defining p noses of the radial cam, and a belly radius equal to Rrbi, Rlbi, defining p bellies of the radial cam, the first and second peripheral rims being characterized by a same variation of the radius with respect to an azimuthal angle, a, dRri / da = dRli / da, wherein i = 1 to m, and wherein p is a natural number greater than 1 (p £ N, and p > 1), o a circumferential track (3ti) defined by a track profile joining the first and second peripheral rims, and defined by a distance, Ri(a, z), from the axis of rotation, Zl (wherein z is measured along the axis of rotation, Zl). • a vane (5i) or vane portion movingly mounted in the chamber such as to keep permanent contact with the circumferential track of the radial cam or radial cam portion, and together with the radial cam or radial cam portion, permanently fluidly separating the inlet volume from the outlet volume,

• a liner (7i) and/or liner portion (7i), rigidly coupled to the chamber, which is associated to a corresponding radial cam or cam portion, wherein said liner or liner portion,

o has a geometry of revolution, about the axis of rotation, Zl, has a breadth substantially equal to the cam breadth, bi, and has a liner profile extending parallel to the axis of rotation, Zl, mating the circumferential track profile at the level of a nose of the corresponding radial cam or cam portion, such that the corresponding radial cam can rotate about the axis of rotation with respect to the liner,

o extends from an upstream end (7u) located in the inlet volume, to a downstream end (7d) located in the outlet volume, and has a peripheral length equal to or larger than the length of a circular arc comprised between two consecutive noses of the corresponding radial cam,

• a cross-sectional opening comprised on a downstream plane, Pi, and bounded between the corresponding circumferential track and the liner and having an area Ai. The downstream plane, Pi, is a radial plane comprising the axis of rotation, Zl, and passing by a point of the downstream edge of the liner and/or liner portion which is located furthest away from the outlet. The area Ai varies with the azimuthal angle between 0, when a nose is level with the downstream end of the liner (i.e., intersects the downstream plane), and |Rlni - Rli| · bi, when a belly is level with the downstream end of the liner.

[0028] In continuation, unless otherwise specified, the expressions“ radial cam”,“liner”, and “vane” used alone shall be construed as“ radial cam or cam portion”,“ liner or liner portion ,” and“ vane or vane portion”, respectively.

[0029] When a radial cam or cam portion has a first nose level with the upstream end of the corresponding liner, fluid present in the inlet volume is carried in a volume created by the rotation about the axis of rotation, Zl, of the radial cam, which is comprised between the circumferential track and the corresponding liner. A transport chamber is thus formed which capacity evolves as a function of the azimuthal angle, a, of rotation and reaches a maximum capacity when the first nose and an adjacent downstream nose separated by a belly are all located within the peripheral length of the corresponding liner. When the first nose reaches the downstream end of the liner, the fluid present in the transportation chamber is dispensed into the outlet volume through the cross-sectional opening comprised between the circumferential track and the liner. The flowrate, Ql of a first pumping system formed by a radial cam, a liner, and a vane (or portions thereof) and rotating at a constant rotation rate, co, varies with time creating periodical pulsations of fluid flow. The gist of the present invention is to combine m pumping systems, each characterized by its own periodical pulsations, in such a way that the periodical pulsations of the (m - 1) pumping systems compensate the periodical pulsations of the first pumping system, to yield an overall constant flowrate with time, without (or very limited) pulsation. This result can be achieved as described below.

[0030] The flowrate pulsations referred to in the present document are nominal pulsations or theoretical pulsations, which are calculated as a function of the geometries of the various radial cams and their relative positions. It is clear that the reduction to zero of the nominal flowrate pulsations may lead in practice to a certain level of pulsations of an actual flowrate measured on an actual pump manufactured based on the geometry yielding a zero -pulsation nominal flowrate, since the calculation to determine the nominal flowrate pulsations of a given volumetric pump neglects frictional losses and assumes perfect sealing between moving parts of the pump, which in practice cannot be achieved. This is common practice in the art and in line with the literature. To our best knowledge, however, the volumetric pumps of the prior art do not reach a theoretical zero value of the flowrate pulsations. This in spite of some allegations to the contrary, as for example in US2717555A, which claims to have a pump (theoretically) generating zero pulsations, then admits that it yields merely“a sufficiently close approximation of uniform discharge rate,” and it can easily be calculated that the (theoretical) flowrate pulsations generated by such pumps exceeds ±4 or ±4.5% and more.

Flowrate Fluctuations of a Cam

[0031] Because the m radial cams or cam portions are rigidly coupled to one another and share a common axis of rotation, Zl, they all rotate at the same rotation rate, co. As illustrated in Figure 1, for a constant rotation rate, co, each pumping system is characterized by a periodic fluctuation of the volumetric flow rate Qi = dVi / dt, it delivers through the cross-sectional opening over a full rotation of 2 p rad. The volumetric displacement, Di = dVi / da, defined as the volume of fluid displaced through the cross-sectional opening per unit angle of rotation (in radians) of one pumping system, is related to the volumetric flow rate Qi through the rotation rate of the pumping system w = da / dt, by Qi = Di co. It follows that each pumping system can be characterized by the fluctuation of its volumetric displacement, Di(a), independently from the rotation rate, co.

[0032] As shown by the horizontal mixed- lines of the graphs of Figure l(a)-l(j), representing as a function of the angle of rotation, a, the gist of the present invention is to combine two or more (m >l) pumping systems such that the sum, of the fluid flow rates delivered to the outlet volume by a synchronized rotation of the m radial cams of the m pumping systems is constant at any time, at a given rotation rate, co,

[0033] Equation (1) can be rendered independent of the rotation rate, co, and time, t, by expressing it in terms of the volumetric displacement, Di(a) = Qi(a) / co(a), with co(a) = da / dt. The geometries of the m pumping systems are thus interrelated to one another through the relation defined by Equation (2), as

wherein a is the azimuthal angle at a given time at the rotation rate, co, of the cams (3i) with the azimuth reference taken for each cam (3i) e.g., at the initial relative position of this cam and the corresponding downstream plane Pi. When Equation (2) (or (1)) is fulfilled, the m cams are complementary and are thus according to the present invention; they are said to have“flow complementary geometries

[0034] A height of the cross-sectional opening measured radially varies from zero, when a nose of a radial cam intercepts the downstream plane, Pi, to a maximum value when a belly of the radial cam intercepts the downstream plane. A distance, Rci, from the centroid (or geometric centre) of the cross-sectional opening to the axis of rotation, Zl, therefore varies with the azimuthal angle, a, of the radial cam intercepting the downstream plane. As is common in the art, the centroid (or geometric centre) of a plane figure is defined as the arithmetic mean position of all the points in the shape. The volumetric displacement, Di(a), is the product of the cross- sectional opening area, Aΐ(a) , and the distance, Rci(a), of the centroid to the axis of rotation, Zl, expressed as follows: Di (a) = RCi(a) - Ai(a)

[0035] The variation of the circumferential track profile from the peripheral rim radius Rli along the direction of the longitudinal axis, Z 1 , can be defined by a function ri(z), with z varying parallel to the axis of rotation, Zl, from 0 at the first lateral peripheral rim to bi at the second lateral peripheral rim, in such a way that any point on the circumferential track profile is located at a distance, Ri(a, z) = Rli(a) + ri(z), to the axis of rotation, Zl. The volumetric displacement, Di, can be expressed as follows:

[0036] Since

It follows that,

[0037] Equation (3) can be simplified when considering specific geometric configurations of the radial cams. For example, in an embodiment illustrated in Figure 2(d), the circumferential track can have a flat cross-section, i.e., the distance of any point of the circumferential track to the axis of rotation, Zl, at a given azimuthal angle is independent from its transverse position z and is equal to Rli(a), Vz. It follows that r _L (z) = 0, Vz, and Equation (3) simplifies to:

Rlnf — Rif (a)

D b,· (3a)

[0038] In an alternative embodiment illustrated in Figure 2(f), the circumferential track can have a concave, semi-circular geometry. This geometry is defined by the function r^z) = It follows that Equation (3) simplifies to:

[0039] The same exercise can be repeated with any profile of the circumferential track, by integrating the function ri(z) corresponding to the desired profile. In some instances, an algebraic solution of Equation (3) is possible, like in Equations (3a) & (3b) supra. For more complex profiles, a numerical solution may be required.

Constant Overall Flowrate

[0040] A radial cam geometry of the present invention is fully defined by three (3) constant: dimensions Rlni, Rlbi, bi, and by two (2) variation laws: Rli(a) and ri(z). The Rli(a) law can be expressed as,

Rli d) = Rlrii - ( Rlrii - Rlb^. U^a) where Ui(a) is a continuous and smooth function comprising no comer point, and periodically varying between 0 and 1 with a period 2p / p (p > 1), such that the peripheral rim profile Rli(a) varies periodically between p nose radii, Rlni, and p belly radii, Rlbi. A function is defined herein as comprising a comer point if the function is not differentiable at that point. In other words, the smooth function Ui(a) must be differentiable at all points.

[0041] As discussed supra, to satisfy Equation (2), = D ₀ = const., all the flow complementary radial cams must have inter-dependent geometries. It follows that by choosing a number n < m of reference cams each having a predefined geometry, and having an overall volumetric displacement, Dln = å Di, the geometries of the (m - n) remaining radial cams can be determined by determining DO and applying Equation (2) as follows, Dln + Dnm = D0., wherein Dnm = Di. In a preferred embodiment discussed below, n = 1 is defined as the reference cam and Dln = Dl .

[0042] In a preferred embodiment, the n reference cams have a smooth function Ui(a) which is an even function with Ui(-a) = Ui(a), such that each cam has symmetric noses and symmetric bellies which are symmetrical with respect to a corresponding radial plane. This geometry yields non-oriented cams which give similar outputs regardless of the direction of rotation, because the rising parts of the flowrate curves illustrated in the diagrams of Figure 1 are symmetrical with the descending parts of said curves. For example, a typical smooth function can be Ui(a) = ½ (1 - cos(p · a)). Other typical smooth functions traditionally used in cam manufacturing that can be used in the present invention are cycloidal functions or second or third harmonic functions.

[0043] In practice, to simplify the equations, to facilitate manufacturing of the pumps, and to reduce their cost, it can be advantageous to select some geometrical simplification conditions. For example, as illustrated in Figure 2(f), the circumferential tracks of all the radial cams can have a same peripheral rim profile, such that ri(z) = r(z) Vi e [l, m], which considerably simplifies the equations.

[0044] An alternative example of geometrical simplification condition can consist of giving the same constant dimensions to all the radial cams, thus defining that Rlni = Rlnl, Rlbi = Rlbl, and bi = bl, Vi e [l, m] This geometrical simplification condition can also simplify the equations.

[0045] Another geometrical simplification condition can consist of designing radial cams to have two-by-two flow complementary geometries (i.e., radial cams coupled in pairs to yield a constant flow rate). The radius, Rli(a), of the peripheral rim of every second cam (3i) (i.e., the index i is an even natural number) is computed from the radius, Rl(i-l)(a), of the previous cam (3(i-l)) (j.e., the index i is an odd natural number) by the equation:

with D ₀ = D^C ^ Rl i) = DiO&i. Rlbi)

[0046] The foregoing geometrical simplification conditions, and other geometrical simplification conditions can be combined or applied individually.

Design of a Pair of Complementary Cams

[0047] In order to illustrate how a pair of complementary radial cams can be designed, we consider the specific case of a pump comprising two radial cams (31, 32) only. The first radial cam (31) which is defined as the reference cam, must first be characterized by defining values for the constant dimensions Rlnl, Rlbl, bl, and by defining the variation laws Rll(a) and rl(z). Care should be taken when defining Rlnl, Rlbl, and Rll(a), that at any one point of the curve thus defined, the normal to the tangent to the curve at said any one point preferably does not form an angle of more than a predefined value with the radius joining said any one point to the rotation axis, Zl. In case of a vane having a sharp leading edge, the predefined value is preferably 30°. In case the leading edge of the vane has a rounded profile, the predefined value can be higher, of the order of up to 45°. This angle corresponds to the so-called pressure angle formed between the vane, which is oriented radially, and the circumferential track. A large value of the pressure angle generates high levels of stress between the vane and the radial cam. As discussed supra, an example of smooth function can be Ui(a) = ½ (1 - cos(p · a)), characterizing the radius Rll (a) of (the left side of) the first radial cam as Rl^ (a) = RZn- _L - (Rlri - Rlb- ) . ½(1— cos(p . a)). The derivative (tangent) of the curve can be calculated and the pressure angle determined, thus defining the ranges of values of Rlnl and Rlbl satisfying the predefined conditions on the pressure angle..

[0048] The volumetric displacement, D 1 , of the first radial cam (31) is defined by Equation (3), as,

[0049] The overall volumetric displacement, DO = Dl + D2 = constant (cf. Equation (2)).

Since the volumetric displacements, Dl, D2, of each of the first and second radial cams (31, 32) vary between zero (when a nose intercepts the downstream plane, Pi,) and a maximum value (when a belly intercepts the downstream plane), the overall volumetric displacement, DO, can be expressed when D2 = 0 and Dl is maximum as follows:

[0050] Now that the reference cam is defined, it remains to define the geometry of the second, complementary cam (32) satisfying Equation (2), which can be expressed as - D2 + DO -Dl = 0, and expressing D2 as defined in Equation (2):

[0051] To solve this quadratic equation for Rl2(a), values of Rln2 and of b2 must be predefined. Alternatively, b2 can be arrived at by predefining a value of Rlb2 and expressing b2 as a function of Rlb2. The former option (i.e., predefined values of Rln2 and b2) is straightforward and the equation can be solved easily. The latter option (i.e., predefined values of Rln2 and Rlb2) can be carried out as follows. As discussed with respect to Equation (4a), DO, can be expressed when Dl = 0 (i.e., Rll (a) = Rlnl) and D2 is maximum (i.e., Rl2(a) = Rlb2) as follows,

[0052] The value of b2 can thus be determined from the predefined values of Rln2 and Rlb2. The design of a pair of complementary cams has been discussed supra. The same method can be used for the specific case discussed supra of a series of m cams complementary two-by-two. In the next section, an alternative manner of designing m complementary cams, with m > 2, is described using a set of (m - 1) reference cams.

Design of a Complementary Cams with Respect to a Set of Reference Cams (m > 2)

[0053] Another preferred option is to design a set of m radial cams (m > 2) with geometries that are flow complementary by determining the geometry of the m ^th cam on the basis of the predefined geometries of the (m - 1) first cams which are used as reference cams. This can be achieved as described supra for a pair of complementary cams, simply by considering the (m - 1) first cams as one“aggregate” reference cam forming the reference cam as described supra. The geometry of the m ^th cam can be determined using Equation (4b) as described supra, taking the aggregate reference cam as the first cam defined in the preceding section.

Design of Identical Complementary Cams

[0054] The method for designing a pair of complementary cams presented above can generate complementary cams that are identical only in very specific cases, which can be complex to determine and which probability to arrive at by trials and errors is very low. Designing a pump with all radial cams having the same geometry is, of course, very advantageous in terms of manufacturing, production cost, and management of spare parts for maintenance and repair. A method is presented in continuation for designing a pair of complementary cams which have the same geometry.

[0055] When rotating a radial cam (3i) in a direction, the corresponding vane (5i) translates radially away from the axis of rotation when a leading edge of the vane follows the corresponding circumferential track from a belly to an adjacent nose of the cam - the vane rises — , and translates towards the axis of rotation, Zl, when the vane travels from the nose to a next belly - the vane descends. In the field of cams, the person of ordinary skill in the art refers to the sections of a cam making the vane rise as the“ rising ramp” and the sections of the cam making the vane descend, the“ descending ramp A cam having a periodicity of p, has p rising ramps and p descending ramps. If the direction of rotation of the cam is reversed, then the ascending ramps become descending ramps and, accordingly, the descending ramps become rising ramps. The notions of rising and descending ramps are therefore tightly linked to the direction of rotation of a cam.

[0056] A pair of identical complementary cams (same Rlni, Rlbi, bi, Ui(a), and ri(z)) can be designed by first designing a pair of complementary cams as described above, by defining a reference cam and determining the geometry of the second, complementary cam using Equation (4b), and with the sole condition that the reference cam and complementary cams thus designed share same values of the breadth, bi, and of the nose radius, Rln, i.e., bl = b2 and Rlnl = Rln2. The resulting complementary cam will most probably have a different geometry than the reference cam. A pair of complementary cams having same geometry can be obtained quite easily from the thus obtained pair of complementary, albeit differing cams as follows.

[0057] As shown in Figure 6, a pair of identical complementary cams (31 = 32) can be designed from a pair of complementary and dissimilar radial cams sharing same breadth, bl = b2, and nose radius, Rlnl = Rln2, by using the rising ramp definition of the reference cam (31) for both cams and the descending ramp definition of the complementary cam (32) computed with Equation (4b) for both cams

[0058] This way, a pair of identical complementary cams is obtained, greatly simplifying manufacturing and spare parts management. By definition, however, the pair of identical complementary cams thus obtained are not symmetrical, in that the smooth function Ui(a) is not an even function and Ui(-a) ¹ Ui(a). This means that reversibility of such pair of identical complementary cams can be problematic depending on the geometries thereof. It would be advantageous to design a pair of identical complementary cams which are also symmetrical so that reversibility of the pump can be enhanced.

Design of Identical Complementary Cams which are Symmetrical (Approximation)

[0059] A pair of identical quasi-complementary cams which are symmetric can easily be designed from a pair of symmetric and differing complementary cams defined by bl = b2 and Rlnl = Rln2, by taking the quadratic mean of Rlil and Rli2by as defined in Equation (5),

[0060] This approximation allows symmetric identical cams to be designed which are quasi-complementary, in that a small (theoretical) flowrate fluctuation, dQ / dt, of not more than 0.1%, preferably not more than 0.05% is generated. By comparison, pumps of the prior art (e.g., US2717555) designed on the basis of a constant overall cross-sectional area, år=i = const., generate flowrate fluctuations, dQ / dt, of the order of 4 to 4.5%, i.e., one to two orders of magnitude higher than the highest fluctuation obtained with a pump according to the present invention. [0061] Methods for designing m complementary cams have been described supra. Pumps according to the present invention can now be designed with a multitude of configurations.

Embodiments of Pumping Systems with Various Geometries and Values of m, r, s, p,

Da,

[0062] As shown in Figure l(a)-(j), pumps according to the present invention can have various configurations. For examples,

• Pumps comprising m = 2 radial cams are illustrated in. Figure 1(a)- 1(f), and a pump with m = 3 radial cams is illustrated in Figure l(j),

• Pumps comprising m = 2 pumping systems formed by m / k = 1 radial cam divided into k = 2 cam portions as shown in Figure l(g and l(i), or comprising m = 4 pumping systems formed by m / k = 2 radial cams, each radial cam being divided into k = 2 cam portions as shown in Figure 1(h). When a pump comprises cams divided into several cam portions (i.e., k > 1 cam portion per cam), each cam preferably comprises a number p of noses greater than 2k (ifk > 1, p > 2k). For example, in the embodiments of Figure 1(g) and l(i), if m / k = 1 radial cam divided into k = 2 cam portions, the cam preferably comprises at least p = 4 noses (p > 2k = 4), with p = 5 noses in Figure 1(g) and l(i). Similarly, referring to Figure 1(h), if m / k = 2 radial cams, each divided into k = 2 cam portions per cam, the number p of noses of each cam is preferably at least 2k = 4 (p > 2k = 4), with p = 4 noses in the embodiment of Figure 1(h).

• The radial cams can be external cams (cf. Figure 1(a) - 1 (d), 1 (i), and l(j)) or internal cams (cf. Figure l(e)-(h)).

• The complementary cams can be offset with respect to one another by an angle Da = p / p (i.e., the respective noses and bellies of the complementary cams are not located at the same azimuthal angles), and the downstream ends of the corresponding liners are flush, i.e., Pl = P2, as shown in Figure 1(b)- 1(e) and l(j),

• The complementary cams can be flush (i.e., the respective noses and bellies of the complementary cams are aligned along the transverse direction parallel to the axis Zl) and the downstream ends of the corresponding liners are offset by an angle Da = p / p, i.e. Pl ¹ P2.

• The periodicity, p > 1, can vary from p = 2 as shown in Figure l(c)-(e) and l(j), to higher values, such as p = 3 (cf. Figure 1(a), 1(b)), or p = 4 or 5 (cf. Figure 1(f), 1(g), and l(i)).

• The cams can be symmetrical, as identified by the label‘(S)’ in Figure l((a), l((d), 1(f), 1(g), and l(j), yielding dV / dt(a)-curves which are symmetrical and allowing the cams to rotate in both directions with identical stress on the vanes, or asymmetrical, as identified by the label‘(NS)’ in Figure 1(b), 1(c), 1(e), 1(h), and l(i).

• Two radial cams of a pair of complementary cams can be identical as identified by the label‘31 = 32’ in Figure l(b)-l(f), or different as identified by the label‘31 ¹ 32’ in Figure 1(a) and l(j).

[0063] The graphs plotting the flowrate, dV / dt as a function of the azimuthal angle, a , clearly show that each cam individually yields strong flowrate fluctuations (cf. short- and long-dashed lines), but by the complementarity of their geometries, the individual fluctuations of each cam is compensated by the remaining cams, yielding an overall constant flowrate,

[0064] As shown in Figure l(a)-(i), with m = 2 cams, the second cam (32) has a geometry fully determined by the geometry of the first cam (31) such that the respective flowrates produced by the rotation of one cam has fluctuations that complement the fluctuations of the other cam to yield a total flowrate which is constant (i.e., with no fluctuation). Similarly, and as illustrated in Figure l(j), when m = 3, the flowrate produced by the rotation of the third cam (33) must be the complementary of the sum of flowrates produced by the rotations of the first and second cams (31-32) which, together form an aggregate reference cam, to yield a total flowrate which is constant (i.e., with no fluctuation).

[0065] According to a preferred embodiment of the present invention, the chamber comprises first, and second lateral walls separated by a joining wall of breadth, B, and the volumetric pump comprises m radial cams consisting of r consecutive external cams or of s consecutive internal cams, all radial cams being rigidly coupled to one another and rotatably mounted on the axis of rotation, Zl, (i.e., m = r or m = s , and m, r, and s are natural numbers, with m > 1). If a set of radial cams comprises external cams only, then s = 0. Inversely, if a set of radial cams comprises internal cams only, then r = 0.

[0066] In an alternative embodiment, illustrated in Figures 1(g) to l(i), the same chamber of breadth, B, encloses m volumetric pumps formed by r external cams or s internal cams, each cam being divided into k portions. Each portion of cam forms a pumping system, thus forming in total m = r k or m = s k volumetric pumps. This embodiment is advantageous in that it allows pumps of small dimensions and/or with less parts to be produced, as it may be formed of a single radial cam (r or s = 1) mounted on the axis of rotation, Zl, with m = k = 2 cam portions only. The k portions of a same radial cam are physically separated from one another by k vanes (portions) and appropriate separation walls, preferably forming an integral part of the liners. Each radial cam (k = 1) or cam portion (k > 1) belongs to a corresponding pumping system, and the r or s radial cams form together, m = k · r or k · s pumping systems. Since the inlet volume must be separated from the outlet volume by the m pumping systems enclosed in the chamber, the m pumping systems must extend over substantially the whole chamber breadth, B, measured parallel to the axis of rotation, Zl . If a cam is divided into k >l cam portions, it is preferred that the cam comprises p > 2k noses, e.g.,a pump comprising r = m / k = 1 eternal radial cam, divided into k = 2 cam portions by k = 2 vanes, the radial cam of the pump preferably comprises at least p > 2k = 4 noses. This ensures that two noses of the cam are at all times present in each pumping system, thus clearly separating a transfer volume defined between two noses from the inlet and outlet of a corresponding pumping system. It is possible to have p = k noses (e.g., r = m/k = 1 radial cam divided into k = 2 cam portions and having p = 2 noses) but sealing problems may occur at the level of the contact points between the cam and the vanes. Sealing can be ensured at the cost of a cam geometry comprising a longer dwell zone, wherein a dwell zone is defined as a circular portion of the cam contour, with Rl(a) = const. = Rn or Rb. A longer dwell zone inevitably reduces the capacity of the transfer volumes and therefore reduces the output of the pump. Furthermore, the area of friction between the dwell regions and corresponding liners increases with the length of the dwell region, thus increasing abrasion rate.

[0067] The periodicity p is given herein the usually accepted meaning in mathematics of the pulsation of a periodic function. A periodic function is a function that repeats its values in regular intervals or periods of 2p / p radian. The most important examples are the trigonometric functions, which repeat over intervals of 2p radians. In other words, the period, T = 2p / p, of a function is the smallest amount it can be shifted while remaining the same function. Intuitively, the period is a measure of a function "repeating" itself. A function/is said to be periodic with a period T or a periodicity p (T and p being nonzero constants) if we have fix + n · T) =flx), V.r

& VneN.

Components of the Pump

[0068] As shown in Figure 2(a)-(f), each of the m radial cams comprises a circumferential track (3t) comprising p track noses, defined as the portions of the circumferential track (3t) comprised between the segments of central angle, a _n on the 2 peripheral rims corresponding to a nose defined by radii Rlni & Rmi. The segments correspond to single points, and the corresponding track nose corresponds to a line, in case the radius, Rli = Rlni at a single value of the central angle, a _n , as shown e.g., in Figure 2(a), wherein a nose is formed by the apex of the smooth curve U(a). Alternatively, the track nose can be a surface defining an area in case the segments corresponding to a peripheral rim nose extend over a range of values of the central angle, a _n , as illustrated e.g., in Figures 2(b) and 7. Such track noses forming a surface having an area are called dwell regions (3id), which are circular portions of the circumferential track. Radial cams comprising dwell regions may be advantageous for sealing at the level of the liners by a close fit with no contact to limit wear and energy losses by increasing the sealing area. The liners are described more in details below.

[0069] As can clearly be seen in Figure 7, the peripheral dwell regions (3id) are circular, defined by a left peripheral rim section of radius Rlni and a right peripheral rim section of radius, Rmi (not shown in Figure 7). Peripheral dwell regions (3id) defining track nose surfaces must be accompanied by corresponding circular belly regions defined by a left peripheral rim section of radius Rlbi and a right peripheral rim section of radius, Rrbi (not shown in Figure 7), of same central angle as the dwell region for the following reason. The overall flowrate of a two-cam pump is equal to the sum of the flowrates associated with the individual first and second cams, Q = Ql + Q2. As a track nose surface of the first radial cam is level with the downstream end of the corresponding first liner, the corresponding flowrate, Ql, associated with said first cam is zero. At the same time, a belly region of the second radial cam is level with the corresponding second liner, and the overall flowrate is equal to Q2: Q= Q2. Since the overall flowrate of the pump must be constant, the flowrate associated with the second radial cam must be constant too over the whole azimuthal angle range over which the dwell region extends. These circular belly regions are quite visible in the examples illustrated in Figure 7(a) and (b).

[0070] The circumferential tracks of each of the r consecutive external cams and or of the s consecutive internal cams are separated from one another by (r - 1) or (s - 1) dividing walls (3wi), each dividing wall being normal to the axis of rotation, Zl, and comprising at least a circular ring of outer radius equal to the largest of the nose radii, Rmi, Rln(i+l), and of inner radius equal to or smaller than the smallest of the belly radii, Rrbi, Rlb(i+l), of two adjacent radial cams (3i, 3(i+l)) separated by said dividing wall.

[0071] The first and second outer circumferential tracks are defined as the circumferential tracks which are adjacent to a single neighbouring circumferential tracks; In other words, they are the circumferential tracks which are adjacent to the first and second lateral walls of the chamber. As illustrated in Figure 2(f), the first and/or the second outer circumferential tracks can optionally be provided with an outer dividing wall (3owl, 3ow2) separating the outer circumferential tracks from the first or second lateral walls of the chamber. The outer dividing walls (3owl, 3ow2) are not essential but help enhancing the fluid tightness between a radial cam and a lateral wall of the chamber with cost effective dimensions tolerances.

[0072] The pump must comprise m vanes (5i) or vane portions (5i), each one associated with one circumferential track. Two vane portions can be combined for forming a single element. For example, two vane portions can be combined to form a single element in a pump comprising a single internal cam shared by two pumping systems, with the two corresponding vane portions being diametrically opposed to each other and optionally joined together by a section that can deform elastically (cf. Figure 1(g)). Each vane (5i) or vane portion comprises a leading edge and is mounted in the chamber so as to translate linearly back and forth along a vane radial plane including the axis of rotation, Zl, as the corresponding cam (portion) (3i) rotates and the leading edge of the vane (portion) keeps permanent contact with the rotating circumferential track (3ti). Together with the radial cams, the vanes (portions) must fluidly separate the inlet volume from the outlet volume. To achieve this goal, the leading edge of each vane must have a geometry mating the geometry of the corresponding circumferential track profile. For external cams, the leading edge is furthest from the axis of rotation when contacting the circumferential track at peripheral nose surface (i.e., at a nose of the cam) as illustrated in Figure 3(a) and is closest thereto when contacting the circumferential track at a belly as illustrated in Figure 3(b). For internal cams it is the opposite. A sealed contact can thus be maintained during the rotation of the radial cams relative to the chamber, and the inlet volume is thus fluidly separated from the outlet volume at any time. As shown in Figure 3, if the axis of rotation, Zl, comprises r radial cams which are separated by (r - 1) dividing walls (3wi), the r corresponding vanes can be separated by separators rigidly fixed to the chamber and each facing a dividing wall so as to seal the gap formed between two adjacent vanes, the dividing wall. In order to maintain a fluid separation at any time between the inlet and outlet volumes, it is clear that each vane or vane portion must have a height, di, measured radially at least equal to the absolute value of the difference between the nose radius Rlni and the belly radius Rlbi, of the corresponding radial cam (di > |Rlni - Rlbi|).

[0073] The concave circumferential tracks in some embodiments of the present invention, allow using cylindrical vanes with a round end tip (ball end). This presents the advantage of better cleanability and higher resistance to abrasion by presenting no sharp edges, and increased sealing efficiency around the vanes at casing interface (plunger/piston type of sealing).

[0074] Many systems can be applied to drive the translation of the vanes (portions) ensuring a permanent contact of the leading edges thereof with the corresponding circumferential tracks. For example, resilient means, such as a spring, can be coupled to the vanes with a bias pressing the leading edge against the corresponding circumferential track. Alternatively, a synchronized positive drive (electromagnet or swing) can be used, or the like. The present invention is not limited by a choice of any of such methods, as long as the leading edges of the vanes keep contact with the corresponding circumferential track.

[0075] The liners define with the circumferential tracks transfer volumes reaching the outlet volume in a synchronized fashion summing up in a constant flowrate. To this effect, m liners (7i) and/or liner portions (7i), each one being associated with a circumferential track are rigidly coupled to the chamber and have the following geometry. Each liner has a geometry of revolution, about the axis of rotation, Zl, and, in a direction parallel to the axis of rotation, Zl, is defined by a liner profile mating the circumferential track profile at the level of a track nose of the corresponding radial cam or cam portion, such that the corresponding radial cam can rotate about the axis of rotation with respect to the liner, with substantially no clearing (= sealing tolerance) between the liner and the circumferential track at the level of the track nose, and with an increasingly large clearing at any other level, with a maximum clearing at the level of the bellies. The expression,“the liner profile mates the circumferential track profile” is meant that both profiles share the same function, Ri(a, z), of the distance to axis of rotation, Zl, with the radius of the liner being slightly larger than the radius of the circumferential track, within tolerances, to allow rotation of the cam relative to the corresponding liner. Figure 2(d)-(f) show some examples of simple circumferential track geometries which circumferential track profiles are mated by the geometries of the corresponding liners (7i). Figure 2(d) shows a flat circumferential track, Figure 2(e) shows a convex circumferential track, and Figure 2(f) shows a concave circumferential track, all mated by the corresponding liners (7i).

[0076] The peripheral length of each liner is equal to or larger than the length of a circular arc comprised between two consecutive noses of the corresponding radial cam. In case of radial cams devoid of any dwell region, each liner must have a peripheral length of at least (2p x Rni(z)) / p, wherein Rni(z) = Rlni + ri(z), is the radius of a nose at any point of the circumferential track along the direction of the longitudinal axis, Zl . In case of a radial cam comprising dwell regions of central angle, an, each liner must have a peripheral length of at least (2p / p - an) Rni(z). [0077] Each radial cam is flanked on either side thereof by a side wall. The side wall can be a dividing wall (3wi), an outer lateral wall (3owi), or a lateral wall of the chamber. When a first nose of a radial cam (3i) reaches the upstream end of a liner, an incipient open transport chamber (6i) forms and fills with fluid present in the inlet volume. As the cam rotates and the first nose and an adjacent nose of the radial cam with a belly therebetween are comprised within the peripheral length of the liner (7i), a closed transport chamber is formed defined as the volume comprised between the circumferential track and the liner and flanked on either side by a side wall. At this stage, the closed transport chamber is fluidly separated from both inlet and outlet volumes. Upon further rotation of the cam, the first nose reaches the downstream end of the liner, and the transport chamber opens onto the outlet volume. The transport chamber is therefore never in fluid communication with both inlet and outlet volumes simultaneously. The cross-sectional opening, Ai, is formed by the intersection of a transport chamber with the downstream radial plane (which intersects the downstream end of the liner).

[0078] The cross-sectional openings have an area, Ai, on the downstream plane, Pi, defined as the radial plane comprising the axis of rotation, Zl, and passing by a point of the downstream edge of the corresponding liner and/or liner portion which is located furthest away from the outlet. Said cross-sectional opening is bounded, on the one hand,

• between the cross-sections of the corresponding liner and/or liner portion, and of the corresponding circumferential track and, on the other hand;

• between the cross-sections of two adjacent dividing walls or, for the outer circumferential tracks, between a dividing wall and either an outer dividing wall or the first or second lateral walls.

[0079] In the present document, when two corresponding elements of a pumping system which are movable with respect to one another are said to have the same dimension, it is clear that this expression encompasses a tolerance, d, required for allowing said relative movement to happen. For example, a liner has the nose radius, Rn, of the external cam it is associated with, it means that the value, Rn(liner), of the liner is slightly larger by a tolerance, d, than the value, Rn(cam), of the external cam, such that the external cam and liner can rotate relative to one another. The tolerance, d, should be sufficiently large for allowing the relative movement of the two corresponding elements without excessive friction, and sufficiently small to form a seal conferring a sufficient fluid tightness to the contact area between the two elements.

[0080] The relative positions of the downstream end of the liners with respect to a set of complementary cams and the distances separating the downstream end of the liners from the corresponding vanes are key to obtain the synchronized effect of complementary sum of flowrates. The relative positions of the upstream ends of the liners in the inlet volume, though not essential to the present invention, can also be optimized to sum up to an overall constant flowrate filling the transfer volumes of each pumping system in a synchronized manner to prevent any fluctuation in the inlet volume before transportation of the fluid towards the outlet volume. This can reduce the stress on the piping system connected to the inlet. Furthermore, a reversible pump must have liners of same peripheral length to offer the same complementary sum of flowrates in both directions of rotation. The azimuthal distance separating the downstream end of a liner from the corresponding vane or vane portion must be equal for all pumping systems

[0081] The relative positions of the liners with respect to the corresponding radial cams required to achieve the effect sought in the present invention can follow different patterns. Two main patterns are described herein, can either be,

• m radial cams are offset two by two by a central angle, Da = p / p, and the m liners have their downstream ends (7d) flush with one another, or

• m radial cams are flush with one another and the m liners have their downstream ends (7d) offset two by two by a central angle, Da = p / p, or

• m radial cams are each divided into k portions and their corresponding k liners have their downstream ends (7d) successively offset by a central angleof 2p / k.

Pump characterized by an offset Da = p / p or Da = 0 between radial cams

[0082] In a first embodiment illustrated in Figures 1(b)- 1(e), l(j), 4(a), and 5(a), the pump of the present invention can comprise m = 2 or 3 (or more) radial cams offset two-by-two by an angle Da = p / p. In particular, the volumetric pump comprises,

• r = m external cams or s = m internal cams, wherein all the r or s radial cams are rigidly coupled to one another along the axis of rotation, Zl, with an azimuthal offset of Da = p / p measured at the axis of rotation, Zl, and wherein p is preferably comprised between 2 and 4, more preferably p = 2 or 3, and

• m liners (7i) or liner portions (7i), wherein the downstream ends of the liners are azimuthally flush and

[0083] In a second embodiment illustrated in Figures 1(a), 1(f), and 4(b), the pump of the present invention can comprise m = 2 or 3 (or more) radial cams flush two-by-two, i.e., with their respective noses and bellies located at the same azimuthal angles, a. In particular, the volumetric pump comprises,

• r = m external radial cams or s = m internal cams, wherein all the r or s radial cams are rigidly coupled to one another along the axis of rotation, Zl, with no azimuthal offset, and wherein p is preferably comprised between 2 and 4, more preferably p = 2 or 3, and

• m liners (7i) or liner portions (7i), wherein the downstream ends of the m liners are offset two-by-two by an azimuthal angle of Da = p / p, and

Pump characterized by s internal cams

[0084] When numerous pumps are available on the market comprising external cams (e.g. lobe pumps), internal cams are more seldom used. An internal cam defines an inner cavity wherein the peripheral edge is an inner edge of the internal radial cam of depth, W, and is centred on the axis of rotation, Zl, of radius varying p-periodically from a lowest value corresponding to the nose radius, Rn, to a highest value corresponding to the belly radius, Rb.

[0085] A pump according to the present invention comprising internal cams is illustrated in Figures l(e)& 1(f). The pumps illustrated in said Figures comprise m = 2 inner cams of periodicity, p = 2 to 4 (and can be higher), rotatably mounted relative to the chamber about the axis of rotation, Zl . Two vanes (51, 52) contact the first and second circumferential tracks to fluidly separate the inlet volume from the outlet volume. First and second liners (71, 72) centred on the axis of rotation, Zl, contact within a tolerance, d, the peripheral nose surfaces of the first and second circumferential tracks. The circumferential tracks (3 lt, 32t) of the first and second internal cams (31, 32) form with the corresponding liners (71, 72) a transport chambers (61, 62) which, upon rotation of the internal cams, transports fluid from the inlet volume towards the outlet volume

[0086] Figure 1(f) illustrates an embodiment wherein the two internal cams are mounted without any azimuthal offset, Da = 0. The liners are mounted such that their respective downstream ends are offset with an azimuthal offset, Da = tt / r. Figure 1(e), by contrast, illustrates an embodiment wherein the two internal cams are mounted with an azimuthal offset, Da = p / p. The liners are mounted such that their respective downstream ends are flush (i.e., Da = 0). Pump characterized by s internal cams each divided into k portions

[0087] Figures l(g)&l(h) show embodiments of an alternative pump comprising a s = 1 or 2 internal cams each divided into k portions (k = 2). The internal cams in these Figures have a periodicity, p = 4 or 5, but it is clear that the same design can be applied with any value of p > 1 , preferably p > 2k. The internal cavity defined by the internal cam is fluidly divided in two halves-cavities by two translating vane portions (51, 52) radially and coaxially aligned. Each half-cavity is provided with an inlet volume including an inlet (lu) and an outlet volume including an outlet (ld) and by two liners (71, 72) which geometry mating the circumferential tracks of the internal cam fluidly separates the inlet volume from the outlet volume. The liners are mounted such that their respective downstream ends are offset with an azimuthal offset, Da = 2p / k (k = 2 and Da = tt). Fluid enters each half-cavity by the corresponding inlet and enters into the transport chambers (61, 62) formed between the circumferential tracks and the corresponding liners. As the internal cam rotates, the fluid is transported to the outlet volume whence it exits the outlet volume through the outlet. Each of the two half cavities is provided by its own pumping system formed by a liner and one half of the internal cam, defined by the vane portions. The flowrate out of the pumping system associated with a first half-cavity is complementary with the flowrate out of the pumping system associated with a second half-cavity, yielding a constant overall flowrate.

Mixing pump characterized by more than one inlets

[0088] The volumetric pump of the present invention can also be used for mixing two or more fluids (Fl, F2, ...) with highly accurate mixing ratios and homogeneity. In a first embodiment illustrated in Figure 5(a) for a pump characterized by m = r = 2 external cams of periodicity, p = 3, with an offset of azimuthal angle, 2p / p = p / 3 rad (= 60°), the inlet volume can be provided with more than one inlets, each in fluid communication with a source of fluid, Fl, F2, to be mixed and transferred to the outlet.

[0089] In a preferred embodiment illustrated in Figure 5(b), a pump arrangement comprises q axes, with q > 1 (in Figure 5(b) q = 3), wherein q pumping systems are arranged in parallel for mixing q fluids (Fl, F2, ...) at same or different mixing ratios for transferring a mixture of the q fluids to an outlet volume provided with an outlet (ld) for evacuating the mixture of q fluids. The pump comprises q inlets (1 lu, 2lu, 3 lu), each inlet being in fluid communication with a corresponding inlet volume, the q inlet volumes being fluidly separated from one another. The outlet volumes of the q pumping systems form a single outlet volume. Because the q pumping systems can deliver fluids at an accurately controlled flowrate, a homogeneous mixture having the desired mixing ratio reaches the outlet volume and the outlet (3d). Mixing ratios can be controlled by varying the width, W, of the q inlet volumes and cams of the q pumping systems. Alternatively, or concomitantly, the rotation rate of the q pumping systems can be varied relative to one another.

Design alternatives

[0090] The volumetric pump of the present invention can also comprise several outlets and/or an outlet can be in fluid communication with a manifold comprising more than one outlets. This embodiment can be advantageous in case of printing or depositing a paste following several parallel lines which can be curvilinear in coating applications or in the food industry, or for filling phials with a controlled volume of fluid, e.g., in the pharmaceutical or cosmetic industries, and the like.

[0091] The principle of radial cam rotary-type positive displacement pumps according to the present invention is based on the rotation of a number of radial cams relative to the chamber and liners. For example, the m radial cams can rotate about their respective axis of rotation, and the chamber can be static. Alternatively, the m radial cams can be static, and the chamber can rotate about an axis of rotation, together with the corresponding vanes or vane portions, and liners or liner portions. Alternatively, both radial cams and chamber can rotate at different rotation rates, in same or different directions of rotation. Having both radial cams and chamber rotating in the same rotating direction allows an accurate control of very low values of flowrates.

[0092] The one or more inlets and/or the one or more outlets can be oriented normal to the axis of rotation, Zl, opening at the joining wall of the chamber as shown in Figures 1, 4, and 5. Alternatively, they can be oriented parallel to the axis of rotation, Zl, opening at a lateral wall of the chamber as shown in Figure 5(b).

Examples

[0093] Table 1 lists a number of examples of pumps, characterized by the parameters, m, r, s, and p.

Table 1: Examples of volumetric pumps according to the present invention.

Applications

[0094] The volumetric pump of the present invention is particularly adapted for applications where shear stresses on the transported fluid should be as low as possible. Low shear stresses preserve shear-sensitive fluids and preserve the internal components of the pump against the aggression of abrasive fluids or solid particles suspended in the fluid. The pump minimizes generation of shear stresses to the fluid by excluding rotors interacting in contra-rotation, and by presenting no sharp angle normal to the flow of the fluid. Furthermore, by reducing pulsations on the outflow, and possibly also the inflow, the stresses the flowing fluid is exposed to are reduced at the interfaces and in the piping system too.

[0095] The volumetric pump of the present invention is also particularly adapted for applications where cleaning is critical, like sanitary applications or with fast setting/curing materials which could block the moving parts if not removed quickly when the pump is stopped. By having no dead volumes and by having the exposed surfaces of the rotors swept by the vanes, the pump can be designed to be Clean In Place (CIP) or Steam In Place (SIP). The simple mechanical design with one axis of rotation only per pumping subsystem makes it fast and easy to disassemble for cleaning its components or replacing them.

[0096] With little to no pulsations generated in the outflow this volumetric pump is ideal for dosing and specially controlled extrusion applications such as 3D printing of fluids and pastes.

[0097] The volumetric pump according the present invention can be used in anyone of the following applications.

(a) In the food & beverage industry, for transfers and fillings. The low shearing will preserve fragile products or (semi-)solids contained in fluids such as fruit chunks in yogurts. This pump design also reduces cavitation allowing for the transfer of fragile liquids such as wine. The good cleanability makes it easy to respect any sanitary requirements.

(b) In Pharmaceutics and bio-medical applications in general.

(c) 3D printing by extrusion of food pastes and liquids. (d) Bio-printing, such as the 3D printing of stem-cells.

(e) 3D printing by extrusion of concrete, mortar and cement in the construction industry.

(f) 3D printing by extrusion of clays and ceramics.

(g) Cosmetics.

(h) In flow chemistry.

(i) Transfer of paints and other non-Newtonian industrial fluids.

(j) In the paper industry where the pulps filled with fibres are highly shear sensitive and the coatings present high viscosities that can vary with stress.

(k) In site deposition of adhesives and gaskets, like in the automotive industry.