DESCRIPTION

Field of application

The present invention relates to positive-displacement piston pumps. More specifically, the invention regards a radial piston pump including a housing, a cylinder block in that housing, a plurality of cylinders radially arranged in the cylinder block, a corresponding plurality of pistons, each piston being slidable in the respective cylinder of the plurality of cylinders, and a fluid distributor, which is associated with the cylinder block. Prior art

As it is well known in this specific technical field, a positive-displacement piston pump generally comprises a plurality of pistons housed in a corresponding plurality of rotating cylinders. The pistons, sliding inside the rotating cylinders, cause a suction with an increase of volume in a pumping chamber inside the cylinder when a suction port is open, creating a slight drop in pressure that allows a fluid to be drawn into the pumping chamber. Alternatively, those pistons cause a compression with a decrease of volume in the pumping chamber when a delivery port is open, i.e. when their motion is reversed. In the radial piston pumps, the pistons are arranged in a radial pattern in a cylinder block that rotates within a fixed ring, which is circular and positioned with a certain eccentricity that can be adjusted in the variable flow rate configurations.

The main problem that the piston pump manufacturers must deal with is the noisiness of the pumps themselves. In fact, there are two fundamental causes of noise in piston pumps, namely the noise generated in the fluid (also called "fluidborne noise") and the structure noise (also called "structureborne noise").

The fluidborne noise is mainly due to irregularities, or "ripples" during fluid transfer. In particular, the fluidborne noise is due to the structure of the pumps themselves, which transfer the fluid irregularly and discontinuously, that irregularity being called ripple.

The ripple is caused both by the fluid transfer law (and therefore by the system geometry, in this case it is referred to as primary ripple) and by the irregularities of the switching between delivery and suction (in this case it is referred to as secondary ripple), this latter phenomenon also being related to the fluid compressibility. In general, the ripple induces an operating noise caused by fluctuations of the instantaneous flow rate over time. The fluctuations of the instantaneous flow rate over time generate a pulsating wave which is transmitted through the fluid to the surrounding environment and in particular to the pump walls, to the pipes and to the delivery ducts. The induced noise can reach unpredictable levels, particularly if the foregoing members resonate with the oscillation frequency. The fluid compressibility exerts influence upon the sudden opening of the piston pumping chamber at the delivery port causing a sudden compression of the fluid, which leads to a consequential fluctuation of the instantaneous flow rate over time. Generally, a pressure of 150 bar causes a reduction in volume of approximately 1-2% of the fluid, generally oil, if devoid of entrapped air, but also a double reduction of volume even if there is a small amount of entrapped air.

The switching between delivery and suction occurring when the pump flow rate (i.e. the linear velocity of the piston) is other than zero, renders the compensation of the foregoing fluid compressibility phenomenon with the change in velocity impossible, particularly when said switching takes place in a phase in which the acceleration of the pistons is at its maximum, causing considerable irregularities in the flow rate itself.

The structureborne noise originates from the imbalance and from the fluctuation of the forces acting in the pump during the movement of the pistons, causing structural vibrations. In particular, that source of noise is inherent to the structure of the pump and has its origin both in the delivery irregularities and in the pulsating frictional forces acting within the pump, such as for example the force of friction acting between the pistons and the fixed ring. In the past, some radial piston pump solutions were proposed, aimed to resolve the foregoing issues, in particular the issue of eliminating the causes of structureborne noise.

For example, the German patent application published with number DE 195 13 767 in the name of Leutner provides a radial piston pump, shown in figure 1A. The pump, indicated with 1 , comprises a star-shaped rotating cylinder block 2 that houses a plurality of radially arranged pistons 3. The pistons of the plurality of pistons 3 are coupled to a corresponding plurality of hydrostatic slipper pads 4 arranged externally to said cylinders on the inner wall of a fixed housing 5 having a cylindrical shape and being positioned with a certain eccentricity. In this way, the pistons of the plurality of pistons 3 slide along the inner wall of the fixed housing 5 through the plurality of hydrostatic slipper pads 4.

The presence of the hydrostatic slipper pads 4 is advantageous for the reduction of the friction between the plurality of pistons 3 and the fixed housing 5 and therefore for the reduction of the wear and tear of the pump 1.

The eccentric position of the fixed housing 5 with respect to the rotating cylinder block 2 can be adjusted or modified by means of the combined action of two control pistons 6 and 7 that act outside the fixed housing 5.

Furthermore, a central fluid distributor 8, coaxial to the rotating cylinder block 2, is provided, the suction and delivery ports being located on that central distributor.

Such a scheme is adopted by the US company Moog in the manufacture of its radial piston pump, indicated by the commercial name RKP, where the hydrostatic slipper pads 4 are guided on the fixed housing 5 by two retaining rings and slide over the inner wall of the fixed housing 5 and maintain contact therewith thanks to the centrifugal force and to the fluid pressure. Though advantageous under various aspects, this first solution has various drawbacks, in particular due to the presence of the hydrostatic slipper pads, which on one hand are necessary to reduce the friction and the wear and tear, but on the other hand lead to a sinusoidal-type law of motion of the pistons, causing a non-constant instantaneous flow rate and therefore a ripple.

The hydrostatic slipper pads 4 slide in fact with circular motion over a cylinder positioned with a certain eccentricity, those hydrostatic slipper pads requiring a support whose contour does vary with rotation and requiring a minimum and constant opening (meatus) between themselves and the bearing surface. The motion of the slipper pads in any case leads to a disadvantageous substantially sinusoidal-type law of motion of the pistons, causing the foregoing ripple. With reference to figure IB, a dimensionless graph of the instantaneous velocity of a single piston (i.e. the instantaneous flow rate of a single piston) is shown in the suction phase and in the delivery phase, as a function of the angle of rotation (expressed in radians) of a piston pump manufactured according to the prior art. In that figure, the suction phase corresponds to the negative portion of the graph and the delivery phase corresponds to the positive portion of the graph.

Considering, in general, a positive-displacement pump comprising a plurality of pistons, said velocity law does not allow a constant sum of the piston velocities (and therefore a constant flow rate) to be obtained for any angular phase shift of the pistons and therefore it causes ripple.

The ripple tends to zero as the number of pistons approaches infinity, however said increase of the number of the pistons obviously leads to an increase of the cost, to an increase of the opening and closing noises of the suction and delivery ports, and also to the increase of the volumetric losses.

In the known designs, the ripple also leads to harmful cusps and discontinuities that also reflect in an irregularity in the torque absorbed by the pump.

Furthermore, the substantially sinusoidal trend of the piston motion law entails a high noise due to the switching between the suction and delivery phase, the switching taking place in the phase of maximum acceleration of the pistons and with a non-zero velocity of the pistons (and therefore of the fluid), this velocity being equal to zero only in one point, as it can be seen in figure IB.

Furthermore, the German patent application published with number DE 197 26 572 to Eisenbacher et al. discloses a piston pump wherein three pistons, which are radially arranged and angularly shifted by 120°, are set in motion by an eccentric portion of a drive shaft that moves an object having an approximately triangular shape, which abuts on the pistons with minimum lateral scraping.

This known design is generally adopted in the manufacturing of high- pressure pumps employed in combustion engines, for example. Even though serving its purpose, this solution has drawbacks since the radial forces are not balanced, one piston being in the delivery phase, one in the suction phase, and another that can be both in the suction phase and in the delivery phase, generating a resulting force that rotates with the driving shaft. The technical problem of the present invention is to provide a radial piston pump, having structural and functional characteristics so as to allow to overcome the limits and the difficulties that still afflict the radial piston pumps according to the prior art, in particular eliminating the most important causes of fluidborne noise and of structureborne noise. The purpose of the present invention is to devise a radial piston pump that can provide a constant flow rate and therefore a null ripple.

Another purpose of the present invention is to devise a radial piston pump able to reduce the effect of the switching irregularity between the delivery phase and the suction phase and to reduce the fluid-compressibility effect. Another purpose of the present invention is to devise a radial piston pump featuring a mechanical design having balanced forces to eliminate vibrations and featuring a mechanical system apt to minimize friction and wear and tear.

Summary of the invention The solution idea at the basis of the present invention is to provide a radial piston pump whose law of motion is determined by a cam profile on which the pistons slide without friction, providing a constant flow rate, reducing the effect of the switching irregularity and guaranteeing a proper mechanical operation.

Based on this solution idea, the foregoing technical problem is solved by a radial piston pump including a housing, a cylinder block in the housing, a plurality of cylinders radially arranged in the cylinder block, a corresponding plurality of pistons, each piston being slidable in the respective cylinder of the plurality of cylinders, a fluid distributor, which is associated with said cylinder block, and a cam profile including a plurality of cam lobes, each lobe comprising a delivery ramp and a suction ramp, characterized in that at least two pistons of the plurality of pistons have an end portion that protrudes from the respective cylinder and is a follower simultaneously engaging with a same type of ramp of a relative lobe of the plurality of cam lobes. It is noted that the follower, engaging with the cam profile, may comprise a rolling member associated with the end portion of each piston of the plurality of pistons, such a rolling member being selected among a roller or a sphere.

Moreover, a support bearing can be interposed between each piston of the plurality of pistons and the respective rolling member.

In particular, the support bearing can be a hydrostatic support bearing or a hydrodynamic support bearing.

Preferably, the support bearing can be a hydrostatic support bearing having a hydrodynamic component being less than 50% of the total support.

Advantageously, the fluid distributor may comprise delivery ports and a plurality of pre-injection holes that are interposed between those delivery ports, the plurality of pre-injection holes being apt to put in communication the cylinders of the plurality of cylinders in advance with the delivery ports of the fluid distributor.

It is also noted that the plurality of cylinders and respective pistons may be arranged on at least one first level and one second level, those first and second levels being parallel to each other and being arranged perpendicularly to a longitudinal axis of the housing.

According to an aspect of the present invention, the first level and the second level may comprise six pistons each, those pistons being arranged at equally spaced angles, the cam profile being formed on an inner wall of the housing and including three cam lobes equidistant from each other, each of them occupying a portion of the inner wall corresponding to an angle of 120°, the cam profile being fixed and the cylinder block being rotating. Suitably, the cylinders of the plurality of cylinders and the respective pistons of the plurality of pistons can be substantially arranged in an angular configuration that is radially symmetrical with respect to an axis of rotation of the radial piston pump.

According to another aspect of the present invention, a piston can be angularly shifted from another piston, with respect to the start of a same type of ramp of a relative lobe with which they are simultaneously engaged, by an angle that corresponds to half of an active angular extension of the delivery (or suction) portions of the cam profile.

In particular, the pistons of the first level can be angularly shifted from the pistons of the second level by an angle equal to 30°, corresponding to half of the active angular extension of the delivery (or suction) portions of the cam profile.

It is also observed that the cam profile can be a central cam profile with respect to the housing and can be an external profile, the fluid distributor being fixed and integral with the housing. More in particular, the central cam profile can be rotating.

Moreover, the cam profile may be apt to impose to said at least two pistons, having the respective followers simultaneously engaging with a same type of ramp of a relative lobe, a law of motion such that the sum of the velocities of those at least two pistons is substantially constant for each angle of rotation of the radial piston pump.

Suitably, the law of motion may provide, in the function describing the velocity νί(φ) of those at least two pistons, a horizontal inflection point between a suction phase and a delivery phase, with null velocity and null acceleration for those at least two pistons during the switching between the suction phase and the delivery phase. Advantageously, the law of motion can be substantially described by the integral of the function νί(φ) = C * (1 + οοβ(φ)), where φ is the angle of rotation of the pump or a linear function of the angle of rotation of the pump and C is a proportionality factor.

It is also observed that the law of motion can be an even function when the motion of the at least two pistons is considered only along the delivery ramp or only along the suction ramp of a lobe of the plurality of cam lobes, as well as the law of motion can be an odd function when the motion of the at least two pistons can considered along an entire lobe of the plurality of cam lobes. Finally, the law of motion can be changed based on the fluid compressibility.

The present invention also refers to method for manufacturing a radial piston pump including a housing, a cylinder block in the housing, a plurality of cylinders radially arranged in the cylinder block, a corresponding plurality of pistons, each piston being slidable in the respective cylinder of the plurality of cylinders, and a fluid distributor, which is associated with the cylinder block, wherein a cam profile is provided in the radial piston pump, such a cam profile including a plurality of cam lobes, each lobe comprising a delivery ramp and a suction ramp, at least two pistons of the plurality of pistons having an end portion that protrudes from the respective cylinder and is follower simultaneously engaging with a same type of ramp of a relative lobe of the plurality of cam lobes.

Suitably, the cam profile is shaped so as to transmit to each piston of the plurality of pistons a law of motion that provides, in the function describing the velocity νι(φ) of each piston of the plurality of pistons, a horizontal inflection point between a suction phase and a delivery phase, the sum of the velocities of the at least two pistons being substantially constant for each angle of rotation of the radial piston pump. Moreover, the law of motion can be substantially described by the integral of the function νί(φ) = C * (1 + οοβ(φ)), where φ is the angle of rotation of the pump or a linear function of the angle of rotation of the pump and C is a proportionality factor. The features and advantages of the radial piston pump according to the invention will become apparent from the following description of an embodiment thereof, given by way of non-limiting example with reference to the accompanying drawings.

Brief description of the drawings In those drawings: figure 1A shows a schematic sectional view of a radial piston pump according to the prior art;

- figure IB shows a graph of the instantaneous velocity of a single piston as a function of the angle of rotation of a piston pump according to the prior art, in the delivery phase and in the suction phase; figure 2 shows a schematic sectional view of a radial piston pump in accordance with the present invention;

- figure 3 A shows a two-dimensional plane development view of a central fluid distributor of t he radial piston pump of figure 2; - figure 3B schematically shows a portion of the plane development view of t he central fluid distributor of figure 3A; figure 4 shows a schematic sectional view of a portion of the radial piston pump of figure 2;

- figure 5A shows a graph of a function describing the velocity of a piston of the piston pump according to the present invention;

- figure 5B shows a graph of a superimposition of two functions equal to the function represented in figure 5A but phase-shifted by π; figure 6 shows a graph of a function describing the velocity of a piston of the piston pump in accordance with the present invention between -π and +π;

- figure 7 A shows a graph of the law of motion of a single piston as a function of the angle of rotation of a piston pump according to the present invention, in the delivery phase and in the suction phase; - figure 7B shows a graph of the instantaneous velocity of a single piston as a function of the angle of rotation of a piston pump in accordance with the present invention, in the delivery phase and in the suction phase;

- figure 8 shows a detail of the graph of the instantaneous velocity of a single piston of figure 7B as a function of the angle of rotation of a piston pump in accordance with the present invention; figure 9 shows a schematic sectional view of a radial piston pump in accordance with an alternative embodiment of the present invention; and

- figure 10 shows a schematic sectional view of a radial piston pump in accordance with a further alternative embodiment of the present invention.

Detailed description

With reference to those figures, and in particular to figure 2, a positive- displacement radial piston pump manufactured according to the present invention is globally and schematically indicated with 10. It is worth noting that the figures represent schematic views and are not drawn to scale, but instead they are drawn so as to emphasize the important features of the invention. Moreover, in the figures, the different elements are depicted in a schematic manner, their shape varying depending on the application desired. Finally, it is noted that in the figures the same reference numbers refer to elements that are identical in shape or function.

The radial piston pump 10 includes a fixed housing 1 1 , a rotating cylinder block 12 in the fixed housing 1 1 , a plurality of cylinders 13 radially arranged in the rotating cylinder block 12, a corresponding plurality of pistons 14, each piston being slidable in the respective cylinder of the plurality of cylinders 13, and a central fluid distributor 15, which is associated with said rotating cylinder block 12, that central fluid distributor 15 being integral with said fixed housing 1 1. The central fluid distributor 15 houses suction ports and delivery ports similarly with that described in the prior art section. In the radial piston pump 10 according to the present invention, the cylinders 13 and the respective pistons 14 are substantially arranged in an angular configuration that is radially symmetrical with respect to an axis of rotation of the rotating cylinder block 12 (or with respect to an axis of rotation of the radial piston pump). Advantageously according to the invention, each piston of the plurality of pistons 14 has an end portion 16, which protrudes from the respective cylinder and is a follower 17 engaging with a cam profile 18.

In particular, the engagement with the cam profile 18 is a rolling engagement, the rolling engagement comprising a rolling member 17' that supports the end portion 16 of each piston of the plurality of pistons 14.

The follower 17 therefore comprises a rolling member 17', associated with the end portion 16 of each piston of the plurality of pistons 14, the rolling member 17' preferably being selected from a roller or a sphere.

In particular, it's preferable to adopt a single roller as rolling member 17', since a roller allows simpler mechanical machining, is more inexpensive, more reliable, and causes less Hertzian pressure and therefore less stress on the cam profile 18.

Furthermore, a support bearing 19 is interposed between each piston of the plurality of pistons 14 and the respective rolling member 17'. In this way, in accordance with the invention, the rolling member 17' on one hand rolls without scraping on the cam profile 18 and on the other hand is supported by the support bearing 19, preventing a scraping contact with its housing in the respective piston. Consequentially, the frictions between the follower 17, the plurality of pistons 14, and the cam profile 18 are minimized, thus minimizing the noise and the wear of the radial piston pump 10.

If a roller is adopted as the rolling member 17', the support bearing 19 can be more easily built.

The support bearing 19 can be a hydrostatic support bearing or a hydrodynamic support bearing, for example. The use of a hydrodynamic support bearing 19 entails on one hand a lower loading capacity, but on the other hand less volumetric loss.

It is also possible to use a support bearing 19 with a predominantly hydrostatic component and with a smaller hydrodynamic component, preferably less than 50% of the total support.

In the embodiment shown in figure 2, provided as a non-limiting example of the present invention, the rotating cylinder block 12 is a star-shaped rotating cylinder block (i.e. is in the form of a disk with radially arranged holes). As previously illustrated, the radial piston pump 10 is substantially radially symmetric with respect to its axis of rotation and maintains this symmetry during the rotation. The pistons of the plurality of pistons 14 are radially arranged and slide inside the cylinders of the plurality of cylinders 13 of the rotating cylinder block 12, that rotating cylinder block 12 rotating within the fixed housing 1 1 , which has preferably a cylindrical shape.

Whereas the delivery phase is caused by the contact between the cam profile 18 and the follower 17 of the pistons 14, the suction phase is caused by the centrifugal force generated by the rotation of the rotating cylinder block 12 that allows the follower 17 adhering to the cam profile 18, suction and delivery ports being arranged on the central fluid distributor 15. The suction phase is therefore substantially guaranteed by the centrifugal force generated by the rotation of the rotating cylinder block 12.

Furthermore, to ensure the operation even at low velocities of rotation of the radial piston pump 10, a desmodromic control (not shown in figure 2), acting on a portion of the end portion 16 of each piston of the plurality of pistons 14, is provided. The desmodromic control may be a cam counter- profile with a profile conjugated to the cam profile 18. In particular, the desmodromic control can be in engagement with a portion of the end portion 16 located closer to the centre of rotation of the pump. Alternatively, it is certainly possible to use, instead of the above described desmodromic control, other methods to control the suction phase, for example control methods based on springs.

As previously mentioned, in the radial piston pump 10 in accordance with the present invention, suction ports and delivery ports are created and suitably arranged in the central fluid distributor 15, as shown with greater detail in figure 3A, which schematically shows a two-dimensional plane development view of that central fluid distributor 15, where 23 indicates a plurality of suction ports and 24 a plurality of delivery ports, where the circular dashed lines represent the traced profiles of the pistons of the plurality of pistons 14 that face the central fluid distributor 15.

As better shown in figure 3B, which represents a portion of the central fluid distributor 15 of figure 3A, a plurality of small pre-injection holes 25, properly calibrated, is interposed between the delivery ports 24 of the central fluid distributor 15, the plurality of small pre-injection holes 25 being apt to put in communication the cylinders of the plurality of cylinders 13 in advance with respect to the delivery ports 24 of the central fluid distributor 15.

Advantageously, the foregoing configuration allows to reduce the fluidborne noise, which noise is due to the sudden opening of the piston pumping chamber, situated inside cylinder, at the delivery ports 24, the plurality of small pre-injection holes 25 anticipating in a gradual and controlled manner a miniscule passage of fluid that is used to compensate the compressibility thereof in the piston pumping chamber.

Furthermore, in the embodiment of the radial piston pump 10 of figure 2, the law of motion of the pistons of the plurality of pistons 14 is determined by the cam profile 18, which is realized on at least one inner portion of the fixed housing 1 1.

Furthermore, in the radial piston pump 10, the plurality of cylinders 13 and respective pistons 14 are arranged on at least one first level 21 and at least one second level 22, those levels 21 and 22 being parallel to each other and being arranged perpendicularly with respect to a longitudinal axis of the fixed housing 1 1 (for example the axis of rotation of the radial piston pump). In particular, the inner portion of the fixed housing 1 1 affected by the cam profile 18 occupies an area of the inner wall of the fixed housing 1 1 corresponding to levels 21 and 22.

Such a configuration is not to be meant as limiting the scope of the present invention, since the plurality of cylinders 13 and respective pistons 14 can be arranged also on a single level, as well as on more than two levels.

The cam profile 18 of the radial piston pump 10 in accordance with the present invention comprises a plurality of cam lobes 20, each lobe comprising a delivery ramp Ri and a suction ramp I¾, as shown in figure 4, which shows a schematic sectional view of a portion of the radial piston pump of figure 2, in particular a single lobe of the plurality of cam lobes 20 is shown. Obviously a piston is in the delivery phase when its follower 17 is engaged with the delivery ramp Ri, whereas said piston is in the suction phase when the follower 17 is engaged with the suction ramp R2, in accordance with the direction of rotation of the pump as indicated in the figures.

Conveniently, at least two pistons of the plurality of pistons 14 have the respective followers 17 engaging simultaneously with a same type of ramp of a relative lobe of the plurality of cam lobes 20. Clearly, the at least two pistons may have the respective followers 17 engaging simultaneously with a same lobe of the plurality of cam lobes 20. But it can be provided also a configuration in which at least two pistons, also belonging to different levels, are respectively engaging with different lobes, but in any case engaging with the same type of ramp and having an appropriate relative angular shift with respect to the start of the respective ramp, said ramp thus possibly belonging to different lobes and said shift being such as to guarantee the constancy in the sum of the flow rates of the pistons, as it will be specified below. In others words, the invention provides that there are at least two pistons 14 with followers 17 simultaneously engaging with a cam profile 18 in a same active phase (i.e. engaging with the same type of ramp) and with an angular shift (or angular distance) so as to guarantee a substantially constant sum of the overall pump flow rate. In this way, as it will be clearly evident from the following description, it is possible to produce the radial piston pump 10 in which the at least two pistons of the plurality of pistons 14 follow a law of motion such that the sum of their velocities is substantially constant, and therefore such that the instantaneous flow rate is substantially constant, the change of instantaneous flow rate of a piston in the delivery phase (or suction phase) being substantially compensated by the change of the instantaneous flow rate of the other piston in the delivery phase (or suction phase), the followers 17 of these at least two pistons engaging simultaneously with the same type of ramp of a relative lobe of the plurality of cam lobes 20.

The at least two pistons of the plurality of pistons 14, having the respective followers 17 engaging simultaneously with the same type of ramp of the relative lobe of the plurality of cam lobes 20, are angularly shifted by a suitable angle a with respect to the start of the delivery ramp Ri or suction ramp I¾ of the relative lobe with which the respective follower 17 is engaged, so as to guarantee the constancy of the sum of the velocities of the pistons 14.

In particular, if two pistons of those pistons having the respective followers 17 engaging simultaneously with the same type of ramp of a relative lobe of the plurality of cam lobes 20 are considered, the angle a necessary to guarantee the constancy of the sum of their velocities corresponds to half of the active angular extension of the delivery (or suction) portions of the cam profile 18.

For the case in which at least two pistons are engaging with a same type of ramp of a same lobe of the plurality of cam lobes, the angle a, which in this case is the angular shift between two adjacent pistons, corresponds to the ratio between the active angular extension of the delivery (or suction) portions of the cam profile 18 and the total number of pistons of the plurality of pistons 14 having the respective followers 17 engaging simultaneously with the same type of ramp (i.e. always a delivery or suction ramp) of the same lobe of the plurality of cam lobes 20.

Here and hereinafter, the term "active angular extension" of the delivery (or suction) portions of the cam profile 18 means the angle of rotation of the pump necessary for a single piston of the plurality of pistons 14 to carry out a full stroke (i.e. the complete delivery phase or suction phase) and hereafter it will be indicated with e _c . The number of lobes of the plurality of cam lobes 20 determines the number of complete strokes of each piston of the plurality of pistons 14 for every complete revolution of the cylinder block 12 and therefore determines the value of the active angular extension e _c .

In the embodiment of figure 2, the radial piston pump 10 comprises a first level 21 and a second level 22, each level having six pistons that lie in the same plane and are spaced apart by equal angles, i.e. they are separated from each other by an angle of 60° (the pistons drawn with dashed lines in figure 2 are the six pistons of the second level 22, which, in the local reference system of figure 2, are arranged below the pistons of the first level 21). The radial piston pump 10 also includes a fixed housing 1 1 with a cam profile 18, formed in the inner wall of the fixed housing 1 1 , the cam profile comprising a plurality of cam lobes 20. In the example shown in figure 2, provided only as a non-limiting example, the cam profile 18 comprises three cam lobes made on the inner wall of the fixed housing 1 1 at the same distance from each other, each of them extending over 120°, and therefore the cam profile 18 has an active angular extension equal to 60°.

The two levels 21 and 22 are angularly shifted from each other by 30°. In this way the pistons of the first and second level 21 and 22 having the respective followers 17 engaging simultaneously with the same type of ramp of a relative lobe of the plurality of cam lobes 20 are angularly shifted by an angle a = 30° with respect to the start of the delivery ramp Ri or suction ramp R2 of the relative lobe with which they are engaged, in such a way that for each first-level piston engaging with a cam lobe in the delivery phase (or suction phase), there is a corresponding second-level piston engaging with the same type of ramp of a relative cam lobe in the delivery phase (or suction phase), i.e. in the same active phase, and angularly shifted by 30° with respect to the start of the ramp. Consequentially, for this pair of pistons, the angular shift of a = 30° corresponds to e _c /2, and therefore is capable of guaranteeing constancy in the sum of the velocities, as described above. Note that the number of pistons of the plurality of pistons 14, the value of the active angular extension e _c of the delivery (or suction) portions of the cam profile 18, the number of the lobes of the plurality of cam lobes 20 of the cam profile 18, as well as the number of levels, may vary according to specific needs and/ or circumstances, the figure 2 being provided only as an example and not limiting the scope of the present invention.

Advantageously according to the present invention, the radial piston pump 10 of figure 2 allows a radial balancing of the forces since there is always a same number of pistons in the suction phase and in the delivery phase, those pistons being at equally spaced angles.

In this way, the constraints on the equilibrium of the forces are respected at every moment, the resultant of the forces being substantially null for every angle of rotation of the pump, and frictions and wear of the radial piston pump 10 are minimized. As a consequence, the most important causes of structureborne noise are eliminated in the radial piston pump 10.

As previously mentioned, advantageously according to the present invention, at least two pistons of the plurality of pistons 14 have the respective followers 17 engaging simultaneously with the same type of ramp (delivery ramp Ri or suction ramp I¾) of a relative lobe of the plurality of cam lobes 20, those pistons following a law of motion and having a relative angular shift such that the sum of their velocities is substantially constant for each angle of rotation of the pump.

As a consequence, it is possible to realize a radial piston pump in which the sum of the velocities of all the pistons whose followers are engaging with the delivery ramp Ri, as well as the sum of the velocities of all the pistons whose followers are engaging with the suction ramp R2, is substantially constant for each angle of rotation of the pump, thus resulting in a substantially constant instantaneous flow rate and eliminating the ripple. As previously mentioned, in the known designs of the radial piston pumps, the presence of hydrostatic slipper pads leads to a disadvantageous, substantially sinusoidal-type, law of motion of the pistons. Advantageously, the radial piston pump 10 in accordance with the present invention allows a free selection of the law of motion of the pistons of the plurality of pistons 14 through the selection of the geometry of the cam profile 18. It is therefore possible to select an appropriate shape for the cam profile 18 so that the instantaneous flow rate of the radial piston pump 10 is substantially constant.

It is in fact known that the instantaneous flow rate Q(t) at time t of a positive-displacement piston pump is defined as:

Q(t) =∑iQi(t) =∑iAiVi(t) where the index i moves from 1 to n, n being the total number of pistons simultaneously involved in the delivery (or suction), A being the cross- sectional area of the i ^th piston, and Vi(t) being the instantaneous velocity of the i ^th piston.

As a consequence, in order to obtain a constant instantaneous flow rate and therefore in order to eliminate the ripple, ∑iVi(t) must be constant, i.e. invariant with t, and therefore∑iVi(t) = k must hold, where k is a constant.

In order to relate the above formula with the radial piston pump 10 that is physically manufactured, the instantaneous velocity Vi(t) of the i ^th piston will be linked to the angle of rotation φ of the radial piston pump 10, by calling βί(φ) the spatial coordinate of the i ^th piston as a function of the angle φ and by setting:

Vi(t) = 5si(t)/5t = δβί(φ)/δφ * δφ/δΐ = δβί(φ)/δφ * _ω = νΐ(φ) * ω where ω is the rotational velocity of the pump (ω = δφ/δΐ), which is considered to be constant, any changes thereof being irrelevant. The analysis thus switched from the time t domain to the angle of rotation of the pump φ domain, and therefore the condition for achieving a null ripple is written as:

Σΐνΐ(φ) = Σίδ φΚδφ = k

As previously illustrated, in the known designs of the radial piston pumps, the condition expressed by the above equation (∑ίνί(φ) = ∑ίδβί(φ)/δφ = k) is never met. This happens because the known designs involve a sinusoidal or sinusoidal-like law of motion of the piston, such a law being imposed by the fact of having the pistons supported by a pad in circular motion on a cylinder positioned with a certain eccentricity. Such a law of motion, for a single i ^th piston, may be expressed by the following equation: leading to: νΐ(φ) = δβί(φ)/δφ = k * οοβ(φ)

As already observed with reference to figure IB, considering a pump comprising a plurality of pistons, the trend of the pistons velocity as a function of the angle of rotation of the pump does not allow to achieve a constant sum of the velocities for any angular shift of the pistons and therefore it causes ripple.

Furthermore, again referring to figure IB, it is observed that the switching between delivery and suction takes place in the moment of maximum acceleration of the pistons and that the point at which their velocity is equal to zero is only a single time instant having a null angular width.

Alternatively, advantageously according to the present invention, the movement of the pistons of the radial piston pump 10 inside the cylinders is determined by the cam profile 18, which is shaped so as to impose upon every i ^th piston of the plurality of pistons 14 a law of velocity as a function of the angle of rotation of the pump of the following kind: such a function νι(φ) being defined between -π and +π, where the angle of rotation of the pump φ = -π corresponds to the start of the piston stroke and the angle φ = +π corresponds to the end of the piston stroke. In this way, suitably, νι(φ) = 0 at the start of the piston stroke (φ = -π), there is a maximum at φ = 0, and finally νί(φ) = 0 at the end of the piston stroke (φ = +π); in fact, it is impossible to start a motion with velocity other than zero and, upon termination of the motion, the velocity must return to zero. The angular interval [-π, +π] therefore corresponds to the individual delivery or suction phase. Figure 5A illustrates the function νι(φ) = 1 + οοβ(φ) for a single piston, whereas figure 5B illustrates the superposition of two functions νί(φ) = 1 + οοβ(φ) that are phase shifted by an angle φ = π, the sum S of these two functions being constant for every angle φ, therefore demonstrating the possibility of cancelling the ripple in the case of two pistons engaging simultaneously with the cam profile 18 with an appropriate phase shift of their respective laws of motion, said phase shift corresponding to the angular shift between said pistons with respect to the start of the relative delivery ramp Ri or suction ramp I¾.

The angle of rotation φ of the pump is therefore the argument of the function that describes the velocity. Alternatively, the argument of the function that describes the velocity may be a linear function of the angle of rotation of the pump, in such a way that the angular interval [-π, +π] corresponds to a rotation of the pump corresponding to the delivery or suction phase.

Conveniently, the function νί(φ) is an even function for the individual delivery phase (or suction phase) when the reference is in the middle of said phase. As shown in figure 6, which shows the graph of the function νί(φ) = 1 + οοβ(φ) between -π and +π, if a horizontal line passing through the average value of said function is drawn, the motion of the piston during the delivery phase (or suction phase) is divided into four sections Xi, X2, X3 and X ₄ . The first section Xi is substantially a mirror image of section X3, as well as the section X2 is substantially a mirror image of the first section X ₄ .

Note that also other laws of motion that satisfy the equation ∑ίνί(φ) = ∑ίδβί(φ)/δφ = k may be used, as well as small deviations from the above law cause small ripple effects.

Furthermore, advantageously in accordance with the present invention, the function νί(φ) = 1 + οοβ(φ) is continuous and is differentiable infinite times and therefore has derivatives with small jerk, snap, crackle and pop values, guaranteeing the continuity and a particularly smooth variation of the forces acting within the radial piston pump 10.

The total active angular extension of the cam profile 18 is now defined as 2ec, therefore taking into account both the suction phase and the delivery phase of an individual piston, and said total active angular extension will now be linked to the round angle 2π. In the case of the cam profile 18 comprising the plurality of lobes 20, by calling L the total number of lobes, the total active angular extension is parameterized to the round angle by setting 2ec = 2 fL. This indicates that the law of motion for a single piston will be repeated L- times on the round angle 2π. Consequentially, ec = π/L represents the active angular extension of the delivery (or suction) portions of the cam profile.

Furthermore, since the angle of rotation φ, or a linear function thereof such that the rotational angular interval [-π, +π] corresponds to the delivery phase (or suction phase), is the argument of the function that describes the velocity, the law of the velocity νι(φ) is rewritten as: so that when φ = ± βο/2, the argument of the cosine is equal to ± π. The parameter C is a proportionality factor necessary to generalize said law of velocity. The integration of the previous equation with respect to the angle φ yields the lift law βί(φ) of the cam profile 18 for each piston of the plurality of pistons 14 of the radial piston pump 10:

Φ) = ί νί(φ)άφ = Κ + 0 * φ + 0 * (e _c /27i) * where K is the integration constant. The term "lift law βί(φ)" of the cam profile 18 here and hereafter indicates the law of motion of a single piston of the plurality of pistons 14, in the delivery phase and in the suction phase.

As a consequence, the law of motion of each piston of the plurality of pistons 14 is substantially described by the integral of the function νι(φ) = C * ( 1 + cosfo)).

Remembering that 2ec = 2 fL, the law of motion of a single piston may also be rewritten as a function of L as:

¾(φ) = ί νί(φ)άφ = Κ + 0 * φ + 0 * (1 /2Ι * sin(2(|>L)

It is preferable to keep e _c as variable instead of L when βί(φ) describes the lift law for angular extensions of the cam profile 18 that do not correspond to the exact division of the round angle by the total number of cam lobes L.

The constants C and K are derived by imposing the boundary conditions on the lift law βί(φ) of the cam profile 18. In particular, in a first phase of the motion of the pistons, from a minimum lift to a maximum lift, it is imposed that: if φ = -ec/2 (start of the piston stroke), β(φ) = 0 (i.e. minimum lift); if φ = +ec/2 (end of the piston stroke), β(φ) = A (i.e. maximum lift), A being the total travel distance (stroke) of each piston of the plurality of pistons 14.

Alternatively, in a second phase of the piston motion from a maximum lift to a minim lift, i.e. in the switching between delivery and suction (or between suction and delivery), the sign of the piston velocity is inverted and the law of motion is rewritten as:

¾(φ) = ί νί(φ)άφ = Ki + C^ + Ci * (l /2L) * sin(2(|>L) under the following conditions: if φ = +ec/2, β(φ) = A, i.e. maximum lift; - if φ = +3ec/2, β(φ) = 0, i.e. minimum lift.

Such conditions lead to:

• during the phase of the motion from minimum lift to maximum lift:

C = A/ e _c ⁼ A*L/ π;

K = A/2; · in phase of the motion from maximum lift to minimum lift (i.e. after the inversion of the sign of the piston velocity) :

Ci = -A/e _c = -A*L/ π;

Hereinafter, the phase from minimum lift to maximum lift indicates the delivery phase, whereas the phase from maximum lift to minimum lift indicates the suction phase. Such law can be further slightly modified to take into account the fluid compressibility phenomenon or also dynamic delays in the fluid behaviour. In particular, with the purpose of eliminating or at least reducing the fluidborne noise induced by the sudden opening of the piston cylinder at the delivery port, said law may be modified by the amount by which the fluid is compressed during the first communication of the cylinders of the plurality of cylinders 13, full of uncompressed fluid, with the delivery, so as to gradually regulate its compression. Given that the fluid is generally compressed on the order of 1-2% every 150 bar, the modification to said law shall be substantially modest and in line with this small compressibility.

The lift law βί(φ) of the cam profile 18 as defined according to the above equations, apart from the small corrections related to the fluid compressibility, is represented in figure 7A as a function of the angle of rotation (expressed in degrees) of the radial piston pump 10 of figure 2. In the figure 7A, provided as a nonlimiting example of the present invention, each piston of the plurality of pistons 14 has a total stroke A and the cam profile 18 comprises three equally spaced cam lobes, with a total active angular extension 2e _c equal to 120°. The graph of figure 7A is thus defined over the entire total active angular extension 2e _c = 120°. In particular, the graph is defined between -30° and 90° and therefore the switching between delivery and suction takes place at the angle φ = 30°. In this example, the delivery phase is characterized by an increase of βί(φ) and is represented in the left portion of the graph in figure 7A, whereas the suction phase is characterized by a decrease of βί(φ) and is represented in the right portion of the graph in figure 7A.

Again with reference to figure 7A, advantageously according to the present invention, the sections characterizing the start and the end of the lift are extremely smooth and can be assimilated to sections with null flow rate, which is very advantageous in the design and in the proportioning of the central fluid distributor 15.

The lift law βί(φ) defined in accordance with the above equations leads to a law for the velocity νί(φ) of a single piston of the plurality of pistons 14 that is illustrated in figure 7B as a function of the angle of rotation (expressed in degrees) of the radial piston pump 10, said figure representing again, as a non-limiting example, the law of velocity of a piston in the suction and delivery phases in the case of a cam profile comprising three cam lobes with total active angular extension 2e _c = 120°. In the example considered, the negative portion of the graph corresponds to the suction phase whereas the positive portion corresponds to the delivery phase.

Advantageously in accordance with the present invention, as it is clearly evident in figure 7B, the above discussed lift law of the cam profile 18 provides, in the function that describes the velocity νί(φ) of each piston of the plurality of pistons 14, a horizontal inflection point (i.e. with δβί(φ)/δφ = 0 e δ¾(φ)/δφ ² = 0) between the suction phase and the delivery phase, i.e. the pistons of the plurality of pistons 14 have null velocity and null acceleration during the switching between suction and delivery, i.e. when their motion is inverted.

Furthermore, the function νί(φ) is an even function for the individual delivery and suction phases, whereas it is an odd function when the reference is taken in the middle of the total active angular extension (corresponding to the point of connection between the delivery ramp Ri and the suction ramp In others words, the law of motion is an even function whenever the motion of the piston is considered only along the delivery ramp Ri or only along the suction ramp R ₂ of a lobe of the plurality of cam lobes 20, whereas it is an odd function whenever the motion of the piston is considered along an entire lobe of the plurality of cam lobes 20, i.e. along the entire total active angular extension 2e _c .

Such features of the function νί(φ) are indispensable to ensure that when at least two pistons of the plurality of pistons 14 have the respective followers 17 engaging simultaneously with the same type of ramp of a relative lobe of the plurality of cam lobes 20 (i.e. in the same active phase of the cam), they have a constant sum of their velocities and therefore the ripple is null. To understand the trend of the sum of the velocities of two pistons, it is convenient to imagine the advancement of the pistons on the cam profile 18 (or vice versa) by superimposing two curves as the one shown in figure 7B, such curves being appropriately phase shifted, where the phase shift between one curve and the other corresponds to the angular shift between the two pistons with respect to the start of the relative delivery ramp Ri or suction ramp I¾ with which the pistons are engaged. Obviously, for appropriate phase shifts between the two curves, the sum of the instantaneous flow rates is null, eliminating the ripple. As previously indicated, in the case of two pistons with respective followers 17 engaging simultaneously with the same type of ramp of a relative lobe of the plurality of cam lobes 20, in order to eliminate the ripple they must have an angular shift, with respect to the start of the respective ramp, equal to ec/2, as it can be easily seen in figure 8. A portion of the law of velocity of fig. 7B (the delivery phase, in particular) is shown in that figure. In particular, the number 26 indicates a portion of the area of the graph that corresponds to the flow rate of a first piston and the number 27 indicates a portion of the area of the graph that corresponds to the flow rate of a second piston, the follower of which is engaging with a same type of ramp (and therefore in a same active phase of the cam profile 18), the second piston being angularly shifted by ec/2 (30° in the example of figure 8) with respect to the first piston. It is evident that the curve in delivery phase tends to flatten in the center, as well as it flattens at the ends. Consequentially, if the two pistons are angularly shifted by ec/2, the sum of their flow rates is constant for every angle φ, since the decrease in flow rate of the second piston is perfectly compensated by the increase in flow rate of the first piston.

The velocity of the first piston being defined as νι(φ) and the velocity of the second piston being defined as V2((t> + e _c /2), the following equation is therefore obtained thanks to the law of the velocity as represented in figure 7B: for each angle φ, k being a constant, in such a way that as the velocity (i.e. the instantaneous flow rate) of the first piston increases, the velocity of the second piston decreases by the same amount, the first piston starting to slide on a ramp when the second piston begins to surpass the mid-point of said ramp, thus guaranteeing the constancy of the sum of the velocities.

Based on the foregoing submissions, it is therefore clear that whenever the foregoing function νί(φ), or any other trigonometric function similar thereto, is used, the argument of the trigonometric functions describing the velocity of two pistons simultaneously engaging with a same type of ramp of a relative lobe will be phase shifted by π, said phase shift by π therefore corresponding to the angular shift by e _c /2=30° of figure 8. Suitably, in the radial piston pump 10, the pistons of the first and second level 21 and 22 having the respective followers 17 engaging simultaneously with the same type of ramp of a relative lobe of the plurality of cam lobes 20 are angularly shifted by an angle a = 30° with respect to the start of the relative ramp on which they are engaged, which corresponds to an angular shift of e _c / 2, therefore guaranteeing the constancy of the sum of the velocities.

Furthermore, the inflection point between the suction phase and the delivery phase implies the fact that the switching between the suction phase and the delivery phase takes place advantageously with null velocity and with null acceleration, the velocity also remaining substantially null in a significant neighbourhood of the inflection point, causing said switching to occur in a longer time interval than that occurring in the known solutions and thus reducing the pump noise.

This is a considerable advantage with respect to the known solutions, where, as shown in figure IB, the velocity of the piston is null only at one instant, the moment of the switching between suction and delivery being the moment of maximum acceleration for the piston, the fast switching therefore thwarting any attempt of dampen the fluid compressibility phenomenon. In the known designs, the switching therefore takes place at a velocity other than zero, the velocity being null only at one point, while the switching is a phenomenon that should occur within a time interval (or angular interval) having appreciable width (few degrees), and therefore greater than zero.

For example, from the above lift law βί(φ), given a piston of the plurality of pistons 14 with a maximum lift A= 10 mm, for an angle of rotation of the pump equal to φ = 1,5° before and after the switching, Si(±1.5°) = +0.001 mm results, where the starting radius of the cam profile 18 is of the order of 70 mm, and consequentially such a deviation from the null value is negligible with respect to the machining tolerances.

As previously observed, the radial piston pump preferably comprises a first level and a second level of six pistons each, which pistons are arranged at equally spaced angles. The radial piston pump also includes a fixed housing with a cam profile, formed in the inner wall of the fixed housing and comprising three cam lobes equidistant from each other on the inner wall of the fixed housing, said cam profile therefore having an active angular extension e _c equal to 60°.

According to a second embodiment of the present invention (not illustrated in the figures), the same result can also be achieved by a radial piston pump comprising three cam lobes equidistant from each other on inner wall of the fixed housing and four levels (or orders) of pistons rather than two, so that each level comprises three pistons, those levels being shifted from each other by one fourth of the angular extension e _c of the cam profile (i.e. e _c /4). Alternatively, according to a third embodiment of the present invention (not illustrated in the figures), the radial piston pump may comprise a cam profile including three cam lobes and a first and second level of nine pistons each, wherein the total angular extension of the cam profile spans only 80° of the 120° available. According to a fourth embodiment of the present invention (not illustrated in the figures), the radial piston pump may comprise a cam profile including two cam lobes and a first and a second level having four or six pistons each.

According to a fifth embodiment of the present invention (not illustrated in the figures), the radial piston pump may comprise a cam profile including four cam lobes and a first and a second level having eight or twelve pistons each.

Obviously, as the number of cam lobes (and therefore the number of pistons) increases, the costs and the volumetric losses increase too.

In a further alternative embodiment not shown in the figures, the pistons may be tilted by an average value of the pressure angle of the cam profile, so as to reduce the stresses between the piston and cylinder body induced by lateral forces acting on the follower of the piston, such a solution being advantageous for high pressures though implying the non-symmetry and non reversibility of the pump itself.

Two additional embodiments that may be defined as dual with respect to the preferred embodiment are described below with reference to figures 9 and 10. In these two embodiments, a cam that is central with respect to the external housing of the pump is provided, but the considerations and the theoretical discussion of the operation previously made are applicable also to these two embodiments.

In the embodiment shown in figure 9, a radial piston pump is globally indicated with 30, the law of motion of a plurality of pistons 31 of the pump being determined by a central cam 32 having an external profile, the central cam 32 being fixed and integral with the pump body. A fluid distributor 33 is also fixed and integral with the pump body. The motion of the pistons of the plurality of pistons 31 is provided by a cylinder block 34 that is apt to rotate inside a fixed housing 35, as indicated by the arrow in figure 9.

Moreover, in a further alternative embodiment shown in figure 10, a radial piston pump is globally indicated with 40, the law of motion of a plurality of pistons 41 of the pump being determined by a central cam 42 having an external profile, the cam being rotating as indicated by the arrow in the figure 10, while a cylinder block 43, housing the pistons, is fixed and integral with the pump body. A fluid distributor 44 is also fixed and integral with the pump body, the distributor housing a plurality of check valves 45, in particular two check valves for each piston of the plurality of pistons 41 , one valve for the delivery and the other valve for the suction.

Now a method for manufacturing a positive-displacement radial piston pump 10 is described, wherein each piston of a plurality of pistons 14 is structured with an end portion 16 protruding from a respective cylinder until it engages with a cam profile 18 as a follower 17. As previously mentioned, the cam profile 18 includes a plurality of cam lobes 20, each lobe comprising a delivery ramp Ri and a suction ramp I¾, at least two pistons of the plurality of pistons 14 having the respective followers 17 simultaneously engaging with a same type of ramp of a relative lobe of the plurality of cam lobes 20.

Such a method allows eliminating the ripple in a radial piston pump and simultaneously to reduce the noise occurring during the switching between the delivery and suction phases.

In particular, the method provides for the realization of a cam profile (i.e. the cam profile 18), the shape of which allows to apply a law of motion to the pistons such that:

- the start and the end of the delivery phase, as well as the start and the end of the suction phase, have null velocity and null acceleration;

- with respect to the vertical axis passing through its maximum, the function that describes the velocity in the delivery phase is an even function, as well as with respect to the vertical axis passing through its minimum, the function that describes the velocity in the suction phase is even;

- the overall function that describes the velocity of a single piston both in suction and in delivery phase exhibits a horizontal inflection point that connects the two phases; this inflection point, where velocity and acceleration are null, ensures that even in a large neighborhood thereof the velocity and the acceleration are so low such that they can be considered null; - it is substantially described by the integral of the function νι(φ) = C * ( 1 +

- the pistons of the plurality of pistons 14 having the respective followers 17 engaging simultaneously with a same type of ramp of a relative lobe of the plurality of cam lobes 20 are angularly shifted in such a way that, with reference to figure 6, whereas one piston starts to travel along a portion of a ramp corresponding to the section Xi, the second piston starts to travel along a portion of a same type of ramp corresponding to the section X3; in this way, whenever the foregoing function νί(φ) or any other trigonometric function similar thereto is used, the argument of the trigonometric functions of two pistons simultaneously engaging with the same type of ramp of a relative lobe is phase shifted by π. The foregoing method therefore allows manufacturing a radial piston pump in which the sum of the velocities of the pistons involved in the delivery phase (or suction phase) is constant.

In conclusion, the radial piston pump according to the present invention comprises a cam profile including a plurality of cam lobes, each lobe comprising a delivery ramp and a suction ramp, at least two pistons of the plurality of pistons having an end portion that protrudes from the respective cylinder and is a follower simultaneously engaging with a same type of ramp of a relative lobe of the plurality of cam lobes. Therefore, the hydrostatic slipper pads that characterize the positive-displacement piston pumps in accordance with the prior art are no longer used, and the pump configuration in accordance with the invention is such that the sum of the velocities of all the pistons is always constant for every angle of rotation of the pump.

The cam profile is suitably shaped in such a way that the lift law of the cam profile is substantially described by:

¾(φ) = ί Vi((())d(t> = K + C * ((> + C * ( 1 /2L) * sin(2((>L) during the phase of the piston motion from minimum lift to maximum lift and,

¾(φ) = ί νί(φ)άφ = Κι + Οι * φ + Οι * ( 1 /2Ι * sin^L) during the phase of the piston motion from maximum lift to minimum lift, the constants C, K, Ci and Ki being defined as above.

Advantageously, the foregoing cam profile allows to obtain a law of velocity for each piston of the plurality of pistons of the radial piston pump capable of providing, on one hand, a constant pump flow rate and of allowing, on the other, a proper mechanical operation of the pump itself, that is meeting the following conditions from a mathematical point of view:

- providing a constant instantaneous flow rate (∑iVi(t) = k);

- the function βί(φ) being continuous; - the function νί(φ) being continuous;

- the function cceleration) being continuous;

- the function erk) being continuous;

- the function (snap) being continuous; - the function (crackle) being continuous; and

- the function pop) being continuous.

Particularly advantageously according to the present invention, in addition to the shape of the cam profile imposing the above law of motion, the pistons are suitably angularly shifted so that the sum of their velocities is substantially constant.

Furthermore, advantageously the radial piston pump features a mechanical design with balanced forces, since there is always a corresponding number of pistons in the suction phase and in the delivery phase, such pistons being angularly equally spaced. In this way, the resultant of the forces is substantially null for each angle of rotation, so that all that remains is a resistant torque that, the instantaneous flow rate being constant, is also constant; in this way, the pump supports are subject to much less stress, vibrations are practically absent or much smaller, and there are no damaging fluctuations of forces and torque; furthermore, the smoothness of the switching due to inflection point eliminates most of the vibrations due thereto.

Advantageously, the radial piston pump in accordance with the present invention is symmetric and in this case there is no obligatory direction of rotation of the rotating cylinder block and a "four-quadrants" configuration may be achieved, where the radial piston pump is reversible and may also act as a motor.

Obviously, a person skilled in the art, in order to meet particular needs and specifications, can carry out several changes and modifications to the radial piston pump described above, all included in the protection scope of the invention as defined by the following claims.