Measurement cell for measuring the surface force exerted by a flow of particles

Abstract

The present description relates to a measurement cell (110) comprising a stationary portion (112), a resonator (114) comprising a longitudinal axis (Δ) and a solid movable portion (116) comprising an exposure face (117) to be exposed to the flow of particles. The solid portion is movable with respect to the stationary portion about a single axis of rotation (Ox) perpendicular to a plane formed by the longitudinal axis of the first resonator and a direction normal to the exposure face. The axis of rotation and the longitudinal axis of the resonator are separated in the direction normal to the exposure face by a non-zero distance (dp). A first distance (h) between the axis of rotation and a centre of mass (Cm) of the movable solid portion is less than a second distance (p) between the axis of rotation and a centre of pressure (Cp) of the exposure face.

Description

[0001] “Measuring cell for measuring the surface force exerted by a flow of particles”

[0002] TECHNICAL FIELD OF THE INVENTION

[0003] The present description relates to a measuring cell for the surface force exerted by a flow of particles, neutral and / or charged. In addition, the present description relates to a device for measuring the surface force exerted by a flow of particles comprising such a measuring cell and a method for measuring the surface force exerted by a flow of particles using such a device. The present description relates in particular to the measurement of the surface force exerted by a flow of particles in a rarefied environment, for example the qualification of ground-based satellite thrusters in a rarefied environment (low pressure), in particular the qualification of electric and cold gas thrusters.

[0004] STATE OF THE ART

[0005] The measurement of the surface force exerted by a flow of particles, neutral and / or charged, particularly in a rarefied environment, finds applications, for example, and in a non-limiting manner, in the qualification of satellite thrusters or in the measurement of the pressure of a plasma in a tokamak for the exploration of plasma physics. By rarefied environment, we understand the vacuum or an environment within an enclosure, for example the interior of a box, in which the mean free path of the particles is greater than the dimensions of the enclosure. In particular, a difficult problem associated with satellite propulsion is the qualification and then validation of the ground performance of the thrusters.The parameters that we seek to qualify include in particular the thrust level (magnitude in Newton (N) of the force exerted by the flow of particles ejected by the propellant), the specific impulse (in seconds (s)) and the efficiency of the propellant defined by a figure of merit which compares the kinetic energy of the flow of particles and the energy injected into the propellant.

[0006] In this description, we are interested in measuring the surface force exerted by a flow of particles, for example for ground qualification but also in orbit in the case of satellite thrusters.

[0007] In the case of electric propulsion, for example, electrical energy is used to ionize the atoms of the propellant mass and eject the particles (ionized gas) up to their ejection velocity. In this example, we are therefore interested in measuring the surface force exerted by a flow of charged particles. In the example of a cold gas thruster that uses a gas stored under high pressure which is released into a nozzle, which allows the thrust to be directed, we are seeking to measure the surface force exerted by a flow of neutral particles.

[0008] Measuring the surface force exerted by a particle flow in a rarefied environment requires high resolution, i.e. a minimum surface force value that can be measured as low as possible, and this over large measurement ranges. For example, a resolution better than 10' will be sought. 7 Pa, or 10' 5 pN.crrr 2, that is to say a minimum value of surface force that can be measured less than 10' 7 Pa, or 10' 5 pN.cnr 2 , on measurement ranges between, for example, 10' 7 Pa and 10 2 Pa.

[0009] It is known to use thrust balances (or pendulums) in vacuum chambers, particularly for the qualification of electric thrusters for ground-based satellites. Such thrust balances are described, for example, in Packan et al. [Ref. 1]. The pendulum is attached to the chamber on one side and supports the thruster at the other end. It is possible to determine the surface force indirectly by measuring the deflection of the pendulum. However, such thrust balances are bulky and require gravity to operate, which does not allow, for example, use in orbit.

[0010] More recently, studies have been conducted on the development of probes for measuring plasma impact on a target. The displacement of this target or the stresses it undergoes makes it possible to determine the surface force of the jet. Such a measurement is intrusive in that it can modify the properties of the particle jet. There is therefore a need for a probe of limited size, yet capable of carrying out surface force measurements over measurement ranges ranging from approximately 10-7 Pa to 102 Pa.

[0011] In the article by Chavers et al. [Ref. 2], a target designed for measuring the thrust of a high-power electric thruster is described. More precisely, the measuring device comprises a 5 cm diameter target held by a 22.8 cm long arm, the arm being held by a titanium beam on which strain gauges are fixed. When the plasma impacts the target, the arm transmits the force to the titanium beam, which deforms. The strain gauges measure the deformation of the beam, from which the thrust of the plasma can be determined. However, this device has the disadvantage of having a sensitivity proportional to the length of the arm. As a result, the device is relatively large, which, in addition to the bulk, can induce changes in the behavior of the plasma. The system also requires gravity to operate. It can therefore only be installed by being suspended from the ceiling of a measuring box.

[0012] The device described in Trottenberg et al. [Ref. 3] also aims to measure the thrust of a propellant. The device comprises a 20 mm diameter target held at the end of an 11 cm arm balanced with a weight. When the plasma impacts the target, it is displaced. An active galvanometer compensates for this force to return the pendulum to its initial position. Smaller than a pendulum or the target described in [Ref. 2], the dimensions of the device described in [Ref. 3] are nevertheless large and the device has the disadvantages of the pendulum in which, on the one hand, sensitivity is proportional to the length of the arm, and on the other hand, the system requires gravity to operate.

[0013] In this context, the present description describes measuring cells suitable for measuring the surface force exerted by a flow of neutral and / or charged, compact particles, which do not require gravity to operate.

[0014] SUMMARY OF THE INVENTION

[0015] In this description, the term "include" means the same as "include" or "contain", and is inclusive or open and does not exclude other elements not described or shown.

[0016] Furthermore, in the present description, the term "about" or "substantially" is synonymous with (means the same as) has a margin of 10%, for example 5%, below and / or above the respective value. According to a first aspect, the present description relates to a measuring cell for measuring the surface force exerted by a particle flow comprising:

[0017] - a fixed part configured to be mechanically and electrically connected to a support;

[0018] - at least one first resonator comprising a longitudinal axis, said first resonator having a first end secured to said fixed part;

[0019] - a mobile massive part comprising a face for exposure to the flow of particles, said massive part being such that:

[0020] - said massive part is movable relative to the fixed part along a single axis of rotation perpendicular to a plane formed by the longitudinal axis of the first resonator and a direction normal to the exposure face;

[0021] - the rotation axis and the longitudinal axis of the first resonator are distant in the direction normal to the exposure face by a predetermined non-zero distance;

[0022] - the first resonator has a second end secured to said mobile solid part; and

[0023] - a first distance between the axis of rotation and a center of mass of the mobile massive part is strictly less than a second distance between the axis of rotation and a center of pressure of the exposure face, the first distance and the second distance being distances projected onto a plane parallel to the exposure face.

[0024] The center of mass of the moving massive part is also called the center of inertia. In the case where the moving massive part is homogeneous in mass (all points have the same weight), the center of mass is the same as the barycenter of the moving massive part.

[0025] The center of pressure of the exposure face of the moving massive part is the center of application of the resultant of the pressure forces due to the particle flow, that is to say the point on the exposure face at which, in operation, the moment of the pressure forces of the flow is cancelled. In practice, in the approximation of a uniform particle flow incident on the exposure face of the moving massive part, the center of pressure is substantially coincident with the geometric center, or barycenter, of the exposure face.

[0026] A measuring cell according to the first aspect allows a measurement of the surface force exerted by a particle flow exerted on the movable massive part, also called "proof mass" in the present description. More specifically, a measurement of the force exerted by the particle flow can be obtained by a measurement of a modification of the resonant frequency of the resonator fixed between the fixed part and the proof mass when the first resonator is excited at an initial resonant frequency.

[0027] The test mass is subjected to the force exerted by the particle flow, which, thanks to the original arrangement of the measuring cell according to the first aspect, results in the application of compression or traction to the resonator and consequently, a modification of the resonant frequency. Such a measuring cell is advantageous compared to state-of-the-art measuring devices, not only because its size is reduced, but also because the measurement is made without the need for gravity. Consequently, in the case of application to a satellite thruster for example, this allows measurements of the force exerted by the particle flow ejected by the thruster, even when the satellite is in orbit.

[0028] Because the first distance between the axis of rotation and the center of mass of the moving massive part is strictly less than the second distance between the axis of rotation and the center of pressure of the exposure face, the measurement is not very sensitive to the effects of acceleration. Indeed, in such a configuration, the contribution of the thrust is greater than that of the acceleration.

[0029] In preferred embodiments, the ratio between said first distance and said second distance is less than about 0.1, advantageously less than about 0.01.

[0030] The applicant has shown that the lower the ratio between the first distance and the second distance, the less sensitive the device is to the effects of acceleration. This results in a measurement with very good resolution. The more this ratio decreases, and in particular the closer the center of mass Cm gets to the axis of rotation Ox, the more it is possible to reduce the accelerometric sensitivity during the measurement, by decoupling the measurement of the surface force exerted by the particle flow, and the inertial force (and therefore the acceleration of the measuring cell). For a ratio h / p less than 0.1, the inertial force becomes negligible compared to the surface force. The measurement is therefore considerably improved. For this, the massive mobile part can in particular be configured so as to distribute at least part of its mass on either side of the axis of rotation. This distribution of masses makes it possible to act as a counterweight to reduce the inertial sensitivity.The mobile massive part may be configured so as to comprise a first part located on one side of the axis of rotation, the first part comprising for example its exposure surface, and a second part located on another side of the axis of rotation, the second part comprising for example at least in part the wings described below, according to the main extension plane of the mobile massive part. The first part may have a first mass m1 and have a center of mass Cm1 positioned at a distance r1 relative to the axis of rotation, in projection onto a plane (Oxy) parallel to the exposure face, and in particular in a direction perpendicular to the axis of rotation. The second part may have a second mass m2 and have a center of mass Cm2 positioned at a distance r2 relative to the axis of rotation, in projection onto a plane (Oxy) parallel to the exposure face, and in particular in a direction perpendicular to the axis of rotation.The ratio (m1.r1) / (m2.r2) may be substantially between 0.9 and 1.1, and preferably be substantially equal to 1.

[0031] In exemplary embodiments, the first distance is substantially zero, that is to say that the center of mass of the mobile massive part belongs to a plane defined by the axis of rotation of the mobile massive part and by the direction normal to the exposure face. This condition makes it possible to overcome the effects of acceleration in the direction perpendicular to the exposure face, and to further improve the resolution.

[0032] According to one or more exemplary embodiments, a ratio between a third distance, defined between the axis of rotation and the center of mass of the mobile massive part, and a fourth distance, defined between the axis of rotation and the axis of the first resonator, is strictly less than 1, advantageously strictly less than approximately 0.1, the third distance and the fourth distance being distances projected onto a plane perpendicular to the exposure face. This condition makes it possible to overcome the effects of acceleration in the direction parallel to the longitudinal axis of the resonator. Here again, the resolution is improved.

[0033] According to one or more embodiments, the measuring cell is monolithic, or monobloc, that is to say that the assembly comprising the fixed part, the mobile solid part and the resonator is made in a single piece. For example, the measuring cell is made from a block of quartz. Other materials can be considered for the manufacture of the measuring cell, such as silicon, langatate crystal (LGT), gallium phosphate crystal (GaPCL), or more generally any other piezoelectric material: ferroelectric piezoelectric crystals (LBO, LNO, LTO), zinc oxide (ZnO), gallium nitride (GaN), gallium arsenic (GaAs), etc.

[0034] According to one or more exemplary embodiments, the measuring cell comprises two hinges comprising a common axis of rotation, said common axis of rotation forming the single axis of rotation of said mobile solid part. Two hinges make it possible to ensure that there is a single pivot around a single axis and thus limit the effects that could result from rotations along other axes and affect the measurement. A sufficient distance will be sought between the two hinges, for example a distance of between approximately 2 mm and approximately 5 mm.

[0035] In exemplary embodiments, a projection of the axis of the first resonator in a plane parallel to the exposure face and comprising said common axis of rotation intersects said common axis of rotation at a point located between the two hinges, advantageously at a midpoint located substantially halfway between the two hinges. Such a configuration makes it possible to overcome the effects of possible rotations around an axis perpendicular to the exposure face.

[0036] According to one or more exemplary embodiments, a fifth distance, defined between a projection of the center of mass of the mobile massive part on said common axis of rotation and said midpoint, is strictly less than a sixth distance, defined between said midpoint and each of the hinges. The lower the ratio between said fifth distance and said sixth distance compared to 1, the more the measurement is freed from the effects of possible rotations around an axis perpendicular to the exposure face, even in the presence of two hinges. The cell obtained is more robust. This results in better resolution. In preferred exemplary embodiments, the fifth distance is substantially zero and the projection of the center of mass of the mobile massive part on said common axis of rotation is substantially coincident with said midpoint.

[0037] According to one or more exemplary embodiments, the mobile massive part comprises a target forming the exposure surface and two wings, said target being connected to the two wings, to the two hinges and to the second end of the first resonator.

[0038] Such an arrangement of the measuring cell allows, thanks to the presence of the two wings, to shift the center of mass towards the axis of rotation, which makes it possible to limit the effects of acceleration in a direction perpendicular to the exposure face.

[0039] According to one or more exemplary embodiments, the mobile massive part comprises two arms for connecting said target to each of the two wings, the arms defining an opening. Such an opening makes it possible to limit the impact of particles near or on the resonator, which can, during operation and in the case of charged particles, disturb the measurement.

[0040] According to one or more exemplary embodiments, the fixed part comprises a decoupling frame and an external frame configured to be connected to the support, said decoupling frame having a tuning fork shape connected on the one hand to the external frame, and on the other hand to the two said hinges and to the first end of the first resonator. Such an arrangement is advantageous in that it can make it possible to limit the effects resulting from thermal stresses or external vibrations on the resonator. According to one or more exemplary embodiments, the first resonator comprises at least one vibrating beam, for example a vibrating beam in bending mode.In exemplary embodiments, the first resonator comprises two vibrating beams arranged in parallel to form a double tuning fork, each of the beams being connected at its ends respectively to the same first peduncle and to the same second peduncle, the first peduncle and the second peduncle respectively forming the first end and the second end of the resonator. A double tuning fork can make it possible to obtain better resolution.

[0041] According to one or more exemplary embodiments, at least a portion of the mobile solid part comprises a coating of electrically conductive material. The coating of electrically conductive material is for example made of metal or graphite. In the case of a metal, the coating may be obtained by metallization. In the case of graphite, the coating may be obtained by CVD or PVD deposition (acronyms for "chemical vapor deposition" and "physical vapor deposition" respectively). The metallization or graphite deposition may comprise a metallic or graphite coating of all or part of the surface of the mobile solid part. In other exemplary embodiments, the measuring cell may comprise a metal plate arranged on a portion of the mobile solid part in order to obtain the metallization. The metal may comprise one of the following metals (or an alloy of these metals): titanium, tantalum.In the case of a flow of charged particles (electric thruster or tokamak for example), covering the moving mass part with an electrically conductive material coating at least partially can facilitate charge collection. Covering the moving mass part with an electrically conductive material coating at least partially can also increase thermal conductivity, and thus protect the resonator by limiting possible thermal gradients. In general, covering the moving mass part with an electrically conductive material coating at least partially, in particular a metal or graphite coating, can limit erosion and therefore increase the life of the measuring cell.

[0042] According to a second aspect, the present description relates to a device for measuring the surface force exerted by a flow of particles, comprising:

[0043] - a support;

[0044] - at least one first measuring cell according to the first aspect, said fixed part being mechanically and electrically connected to said support;

[0045] - an electronic circuit configured to excite the first resonator of said at least one first measuring cell at an initial resonant frequency and measure, when the device is subjected to the flow of particles, a measurement resonant frequency;

[0046] - a processing unit configured to determine, from a difference between the measurement resonant frequency and the initial resonant frequency, the surface force exerted by the particle flow.

[0047] According to one or more exemplary embodiments, the device according to the second aspect comprises a second measuring cell, making it possible to make differential measurements and to gain in resolution. The second cell is for example substantially similar to the first measuring cell and comprises for example a fixed part mechanically connected to the support, a resonator and a movable solid part. The fixed part, the resonator and the movable solid part of the second measuring cell are substantially identical respectively to the fixed part, the resonator and the movable solid part of the first measuring cell.However, the positions of the resonator and the rotation axis in the direction normal to the exposure face are reversed between the first measuring cell and the second measuring cell, such that when the exposure face of each of the measuring cells is exposed to the particle flow, one resonator undergoes compression while the other resonator undergoes extension. The processing unit is then, for example, configured to further determine a difference between the measurement resonant frequency measured by means of the first measuring cell and the measurement resonant frequency measured by means of the second measuring cell to determine the surface force exerted by the particle flow. Such a differential measurement makes it possible to dispense with quadratic terms in the dependence of the resonator resonant frequency on the surface force exerted by the particle flow.Such a differential measurement also makes it possible to overcome any possible thermal drift as well as any possible effect of acceleration along an axis perpendicular to a plane comprising the normal to the exposure face and the axis of rotation of the massive mobile part.

[0048] Such a differential measurement can also be carried out with a single measuring cell comprising two resonators.

[0049] Thus, in exemplary embodiments, the measuring cell comprises a second resonator, substantially identical to the first resonator. The projections of the first resonator and the second resonator in a plane perpendicular to the axis of rotation are located on either side of a projection of said axis of rotation on said plane, such that when the exposure face is exposed to the particle flow, one resonator undergoes compression while the other resonator undergoes extension. Here again, with such an arrangement, it is possible to make a differential measurement which will make it possible to cancel out disturbances common to both cells, such as drift induced by thermal flows or vibrations.

[0050] The description relates according to a third aspect to a satellite comprising a thruster with means for ejecting a flow of neutral and / or charged particles and a device for measuring the force exerted by said flow of particles according to the second aspect, the support of the measuring device being mechanically and electrically connected to a body of the stellite by means of an arm.

[0051] The description relates according to a fourth aspect to an enclosure with a rarefied environment configured for the qualification of a flow of neutral and / or charged particles. The enclosure comprises a device for measuring the force exerted by a flow of particles according to the second aspect, the support of the measuring device being mechanically and electrically connected to a body of the enclosure, for example by means of an arm, the measuring device being configured to measure the flow of particles.

[0052] For example, the enclosure is a box with a rarefied environment configured for the qualification of a satellite thruster comprising means for ejecting a flow of neutral and / or charged particles. The measuring device is then configured to measure the flow of particles ejected by the thruster.

[0053] The description relates according to a fifth aspect to a method for measuring the surface force exerted by a flow of particles by means of a device according to the second aspect.

[0054] In exemplary embodiments, the method comprises:

[0055] - an excitation of the first resonator and a measurement of an initial resonant frequency of the resonator, without particle flow;

[0056] - receiving the particle flow by the exposure face of the measuring cell and measuring a measurement resonance frequency of the resonator resulting from the force applied by the particle flow on said exposure face;

[0057] - the determination, from a difference between the measurement resonance frequency and the initial resonance frequency, of the surface force of the particle flow.

[0058] For example, the method according to the fifth aspect allows the measurement of the surface force exerted by a flow of particles ejected by a satellite thruster. The measurement of the initial resonant frequency of the resonator is made for example when the thruster is switched off and then the thruster is switched on for the measurement of the measuring resonant frequency of the resonator resulting from the force applied by the flow of particles ejected by the thruster, on the exposure face of the measuring cell.

[0059] According to one or more exemplary embodiments, the measurement of the surface force exerted by said particle flow is carried out when the thruster is on a satellite in orbit.

[0060] According to one or more exemplary embodiments, the measurement of the surface force exerted by said particle flow is carried out when the propellant is in an enclosure with a rarefied environment on the ground, for example a vacuum chamber.

[0061] According to one or more exemplary embodiments, the measuring method comprises:

[0062] - the successive application of several potential differences between a region comprising a coating of electrically conductive material of the mobile solid part and a facing metal plate, the application of each potential difference resulting in an electrostatic force applied to the mobile solid part;

[0063] - for each potential difference, the measurement of a measurement resonance frequency resulting from said electrostatic force and the determination of the difference between the measurement resonance frequency and the initial resonance frequency.

[0064] These steps allow calibration of the measuring device. We can then know the electrostatic force applied as a function of the voltage. Knowing the measurement resonance frequency (since it is measured), we obtain the calibration curve of the difference between the measurement resonance frequency and the initial resonance frequency as a function of the force applied to the moving solid part.

[0065] BRIEF DESCRIPTION OF THE FIGURES

[0066] Other advantages and characteristics of the invention will appear on reading the description, illustrated by the following figures:

[0067] Figure 1 represents a diagram of a device for measuring the surface force exerted by a flow of particles, according to an exemplary embodiment;

[0068] Figure 2A represents a diagram of a measuring cell according to an exemplary embodiment, according to a first view;

[0069] Figure 2B shows a schematic of the measuring cell illustrated in Fig. 2A, according to a second view;

[0070] Figure 3A represents a diagram of a resonator of a measuring cell, according to an exemplary embodiment, the resonator being formed from a tensile beam; Figure 3B represents a diagram of an arrangement of a resonator as illustrated in Fig. 3A, according to an exemplary embodiment;

[0071] Figure 3C represents a diagram of a resonator of a measuring cell, according to another exemplary embodiment, the resonator being formed of a double beam in tension;

[0072] Figure 4A represents a diagram of a measuring device according to an exemplary embodiment, the device comprising two measuring cells arranged for a differential measurement;

[0073] Figure 4B shows a diagram of an example of a measuring cell in a device according to the present description, the measuring cell comprising two resonators arranged for differential measurement;

[0074] Figure 5 represents a diagram of a measuring cell, as well as a device for calibrating the cell, according to an exemplary embodiment;

[0075] Figure 6A represents a diagram of a monolithic measuring cell according to an exemplary embodiment, according to a first view;

[0076] Figure 6B shows a schematic of the measuring cell illustrated in Fig. 6A, according to a second view;

[0077] Figure 6C shows a schematic of the measuring cell illustrated in Fig. 6A, according to a third view;

[0078] Figure 6D represents a diagram of the measuring cell illustrated in Fig. 6A, and indicates in particular the positions of the centers of pressure Cp, center of mass Cm, relative to the axis of rotation Ox of the mobile massive part;

[0079] Figure 7A represents a diagram of a monolithic measuring cell as illustrated in Fig.6A, arranged on a support, according to an exemplary embodiment and according to a first view;

[0080] Figure 7B shows a schematic of the measuring cell illustrated in Fig. 7A, according to a second view.

[0081] Figure 8 shows a diagram of a satellite equipped with a device for measuring the surface force exerted by a flow of particles according to the present description, configured for measuring the surface force exerted by the flow of particles ejected by the thruster of the satellite.

[0082] Figure 9 represents a diagram of an enclosure for the ground qualification of a satellite thruster, by means of a device for measuring the surface force exerted by a flow of particles according to the present description.

[0083] The attached figures are schematic and are not necessarily to scale; they are intended primarily to illustrate the principles of the invention. From one figure (fig.) to another, identical elements (or parts of elements) are identified, where possible, by the same reference signs.

[0084] DETAILED DESCRIPTION OF THE INVENTION

[0085] Fig. 1 represents a diagram of a device 100 for measuring the surface force exerted by a flow of particles 10, according to an exemplary embodiment.

[0086] The measuring device 100 comprises in this example a measuring cell 110 fixed on a support (not shown). The measuring cell comprises in particular a resonator 114 and a mobile solid part 116, also called a test mass in the present description, which will be described in more detail later. The test mass 116 comprises an exposure face 117 to the particle flow and is mobile about a single axis of rotation (not shown in Fig. 1). An electronic circuit 120 is configured to excite the resonator at an initial resonance frequency frO. The test mass and the resonator are arranged such that in operation, when the device undergoes a surface force Fp exerted by a particle flow 10 incident on the exposure face 117, the test mass undergoes a rotation which causes a tensile force T (or a compression) on the resonator. This results in a change in the resonant frequency of the resonator.The electronic circuit 120 then measures the modified resonant frequency of the resonator, called the measurement resonant frequency and denoted fm in the present description. The measuring device 100 further comprises a processing unit 130 configured to determine, from the difference between the measurement resonant frequency and the initial resonant frequency, the modulus Fp of the surface force Fp exerted by the flow of particles.

[0087] The electronic circuit 120 comprises, for example and in a known manner, an electronic oscillator 122 configured to apply to coupling electrodes (not shown) arranged on the resonator, a voltage Vf such as to excite the resonator at the initial resonant frequency frO. The resonator is, for example, a vibrating beam in traction mechanically excited by piezoelectric effect, as will be described in more detail later. The electronic circuit 120 also comprises an amplifier 124 configured to increase the power of the electrical signal generated by the vibrating beam and a frequency meter 126 allowing the measurement of the frequency of the amplified signal.

[0088] The processing unit 130 may comprise one or more physical entities, and may be gathered in one or more computers. When in the present description, reference is made to calculation or processing steps for the implementation in particular of method steps, it is understood that each calculation or processing step may be implemented by software, hardware, firmware, microcode or any appropriate combination of these technologies. When software is used, each calculation or processing step may be implemented by computer program instructions or software code. These instructions may be stored or transmitted to a storage medium readable by the processing unit and / or be executed by the processing unit in order to implement these calculation or processing steps.

[0089] Fig. 2A and Fig. 2B show two views of an example of a measuring cell 110 of a measuring device according to the present description. The cell is illustrated schematically to explain its operation.

[0090] The measuring cell 110 comprises a fixed part 112 mechanically connected to a support of the device (not shown in the figures). The measuring cell further comprises at least a first resonator 114 comprising a longitudinal axis A and a movable solid part 116, or test mass. The first resonator 114 has a first end secured to the fixed part 112 and a second end secured to the movable solid part (point B). The movable solid part 116 comprises an exposure face

[0091] 117 to the particle flow. The mobile massive part 116 is mobile relative to the fixed part 112 along a single axis of rotation Ox perpendicular to a plane formed by the longitudinal axis A of the first resonator and a direction n normal to the exposure face 117. As illustrated in Fig. 2A, the axis of rotation Ox and the longitudinal axis A of the first resonator 114 are distant in the direction n normal to the exposure face by a predetermined non-zero distance dp.

[0092] As illustrated in Fig. 2B, the measuring cell may comprise two hinges

[0093] 118 comprising a common rotation axis, said common rotation axis forming the single rotation axis Ox of said mobile massive part. Thus, the test mass is connected to the fixed part by the two hinges. This configuration leaves as only degree of freedom to the test mass 116 a rotation around the common rotation axis Ox. Thus, the normal force to the exposure surface 117 of the test mass exerted by the particle flow is transmitted to the resonator 114. In the example of Fig. 2A, the resonator 114 is arranged on the front face of the measuring cell (substantially in the plane of the exposure surface) while the test mass is connected to the fixed part by the two hinges arranged on the rear face (substantially in a plane of the face opposite the exposure surface). This results in a tensile force T applied to the resonator, while the test mass experiences a tensile force -T applied at point B.In other embodiments, the resonator 114 may be arranged on the rear face of the measuring cell (face opposite the exposure surface) while the test mass is connected to the fixed part by the two hinges arranged on the front face (exposure surface). This will result in a compressive force applied to the resonator.

[0094] Advantageously, a projection of the axis A of the first resonator in a plane parallel to the exposure face and comprising said common rotation axis Ox intersects said common rotation axis at a midpoint O located substantially halfway between the two hinges (see Fig. 2B). This arrangement makes it possible to overcome effects resulting from possible rotations along an axis orthogonal to the exposure face (axis Oz).

[0095] The resonator 114 is for example a vibrating beam working in bending, in a plane parallel to the exposure face. Electrodes arranged on the beam make it possible in a known manner to couple the resonator to the oscillating electrical circuit 120 (Fig. 1) and to mechanically excite the beam (by piezoelectric effect) at its resonant frequency. The vibrating beam is for example excited in a fundamental bending mode, that is to say it vibrates in the plane of the cell (xOy plane). Resonators are described in more detail below with reference to Fig. 3A to Fig. 3C. The dimensions of the resonator determine its natural vibration frequency. The natural vibration frequency can vary according to the compression or extension (traction) forces exerted longitudinally on the resonator. The electronic circuit is configured to determine the vibration frequency of the vibrating beam when it is subjected to such forces.From the measurement of the variation in the vibration frequency, the force exerted by the particle flow can be quantified as described below. By convention, the bold notations in this description represent vectors.

[0096] The impact of the particle flow (10, Fig. 1) on the exposure face 117 of the proof mass 116 creates a moment with respect to the axis Ox. The moment is a function of the distance p between the center of application Cp of the resultant of the pressure forces due to the particle flow (or center of pressure) and the axis Ox, the distance p being a distance projected onto a plane parallel to the exposure face. In practice, the center of pressure Cp can be substantially coincident with the geometric center, or barycenter, of the exposure face 117.

[0097] As illustrated in Fig. 2A, the force (in Newton) exerted by the particle flow F p= ~Fp is exerted at the center of pressure Cp at a distance d p z + py from the center O, where dp is the distance between the axis of rotation Ox and the axis A of the first resonator 114, said distance being a distance projected onto a plane Oxz perpendicular to the exposure face 117.

[0098] The moment M0(F p ) of force F p applied in Cp, with respect to the Ox axis, is thus: [Math 1] ^o(fp) = -pF p x

[0099] There is also an M moment o (-T) of the traction force -T applied at point B by the resonator to the test mass, relative to the Ox axis: [Math 2] M0(-T) = d p Tx

[0100] In a quasi-static approximation, the sum of the moments of the forces applied to the test mass with respect to the Ox axis is zero: [Math 3] amplification factor.

[0101] More generally, as will be described in more detail later, the test mass can also be subjected to accelerations along the y and z axes, linked to vibrations. The geometry of the measuring cell can be optimized to reduce these effects.

[0102] The extension force on the resonator modifies its vibration frequency such that: [Math 4]

[0103] Where P is the thrust (or surface force Fp / A, where A is the surface area of ​​the exposure face), f r is the vibration frequency of the resonator when a pressure force is exerted by the particle flow on the test mass, f r0 is the vibration frequency of the unconstrained resonator, S p l is the linear pressure sensitivity and S p 2is the quadratic sensitivity. This equation does not take into account non-linear frequency variations beyond order 2, which are assumed to be negligible. The last term represents the frequency variation due to possible disturbances. Indeed, when measuring the force exerted by the particle flow, the cell may be subjected to stresses resulting from the measurement environment. These stresses may result from vibrations, in particular from vacuum pumps in the box intended to receive the measuring cell, from heating from the particle flow, or from an electrical charge resulting, for example, from a flow of charged particles and capable of generating forces. Thus, when the cell is not exposed to the particle flow, the vibration frequency of the resonator is equal to f rQ Exposure of the measuring cell to the particle flow results in a change in the vibration frequency which becomes f r(P). The frequency difference f r (P) - f r0 allows to determine the surface force exerted by the particle flow F p / A. The measuring device thus described has the advantage of allowing a measurement regardless of the gravity field. Indeed, regardless of the orientation of the measuring cell, if it does not move during the measurement, the effect of gravity is cancelled out in the term f r (P) - f r0 Such a device also allows measurements to be made in microgravity, and in particular in space, for example in the case of satellite thrusters in orbit.

[0104] Fig. 3A represents a diagram of a resonator of a measuring cell, according to an exemplary embodiment. In this example, the resonator 114 is formed of a vibrating beam whose dimensions are a length L (y direction) and widths I and e (respectively in the x and z directions). The width e along the z axis is called the non-vibrating width of the beam and the width I along x is called the vibrating width. As illustrated in Fig. 3B, the vibrating beam is mounted in tension between the fixed part 112 and the test mass 116. It is connected respectively to the fixed part 112 by a first end and to the test mass by a second end.

[0105] For a vibrating beam 114 as illustrated in Fig. 3A, the linear pressure sensitivity S can be determined p , for example using the Rayleigh method, and taking into account the amplification factor = — : dp

[0106] [Math 5] 1.49 x 10“ 3

[0107] Linear pressure sensitivity S p l is expressed in Hz / (pN.cm-2), I and e are the dimensions of the beam in the x and z directions respectively, E is the Young's modulus of the material from which the beam is formed, and p is the density of the material, A is the surface area of ​​the exposure face 117.

[0108] The sensitivity of the measuring cell can thus be modified by adjusting various parameters. Firstly, the choice of material allows the Young's modulus E and its density p to be modified. However, the sensitivity is inversely proportional to the square root of the material properties, and the choice of material therefore has a moderate influence on the sensitivity. The geometry of the test mass also influences the sensitivity. The sensitivity of the cell is in fact proportional to the surface area A of the particles on the test mass. It is also proportional to the amplification factor  p , that is, the distance between the exposure surface and the axis of rotation Ox. Finally, the sensitivity depends on the geometry of the vibrating beam.

[0109] The finer the non-vibrating width e and the vibrating width I, the higher the sensitivity of the cell. These dimensions thus have a significant impact on the sensitivity, which is inversely proportional to the square of the vibrating width. The finer the beam, the greater the sensitivity. However, the reduction in the vibrating and non-vibrating widths is limited by the manufacturing technique and the mechanical strength of the material. A beam that is too thin risks being destroyed during its manufacture, handling and use. The applicant has shown that optimized dimensions for the vibrating beam were between approximately 1 micron and approximately 1 mm for a dimension of the beam section and between approximately 0.1 mm and approximately 10 mm for the length of the beam.

[0110] Other resonators may be used in a measuring cell of a device according to the present description.

[0111] Fig. 3C thus represents a diagram of a resonator of a measuring cell formed from a double beam in tension.

[0112] Instead of a vibrating beam (Fig. 3B), it is possible to use a double tuning fork (Fig. 3C). The resonator then comprises two vibrating beams 321, 322 each attached by a peduncle 311, 312, the peduncle 311 being connected to the fixed part 112 by a fastener 301 and the peduncle 312 being connected to the test mass 116 by a fastener 302. When the beams vibrate, they create waves in phase opposition which cancel each other out in the two peduncles. This makes it possible to prevent waves from propagating in the fixed part 112 (or in the test mass 116), which would constitute a source of energy loss for the device.

[0113] As appears in equation [Math 4], the sensitivity of the measuring cell to the force exerted by the particle flow also implies a sensitivity to other parasitic forces.

[0114] For example, parasitic forces can result from vibrations of the measuring cell that cause dynamic acceleration.

[0115] The point of application of an acceleration undergone by the measuring cell is located at the center of mass Cm of the test mass (Fig. 2A, Fig. 2B), at a distance hy + d g z of the Ox axis of rotation of the proof mass, where h is the distance between the center of mass Cm and the Ox axis, the distance h being a distance projected onto a plane parallel to the exposure face, and d g is the distance between the axis of rotation Ox and the center of mass Cm, said distance being a distance projected onto a plane Oxz perpendicular to the face. The acceleration r = r x % + r y y + r zz experienced by the measuring cell creates a force F= Mr applied to the center of mass, where M is the mass of the test mass.

[0116] The moment of force F, applied to the center of mass Cm, relative to the axis Ox, is:

[0117] M0( ) = hF z - dgFy x

[0118] The moments about the y and z axes are null since the Ox axis is the only axis of rotation of the proof mass.

[0119] In the above equation, we assume that the component F xof the force F does not cause a variation in frequency. This assumes that the distance dmp between a projection of the center of mass Cm of the massive moving part on the common axis of rotation of the hinges (see Fig. 2B) and the midpoint O between the hinges is very small compared to a distance dpc between said midpoint and each of the hinges. In other words, the projection of the center of mass Cm of the test mass on the common axis of rotation is substantially coincident with the midpoint O.

[0120] Assuming the test mass is fixed, then the fundamental principle of dynamics states that the sum of the moments of the forces applied to the center of mass relative to point O is zero:

[0121] [Math 6]

[0122] Similar to [Math 5], we can express the sensitivity in acceleration S a l cc in Hz / g as a function of the amplification factor A^ cc with i=z or y such thatz acc

[0123] [Math 7]

[0124] 1 49

[0125] The sensitivity depends on the beam dimensions (non-vibrating width e and vibrating width I), the material properties (Young's modulus E and density p) and the mass M of the test mass. With the beam dimensions and the material fixed, the acceleration sensitivities are proportional to:

[0126] [Math 8]

[0127] Since in a measuring cell according to the present description h is less than p, the ratio —is less than the amplification factor p= — and the contribution of dp dp acceleration in the measurement is thus less than that of the thrust. Furthermore, it is thus possible to choose the geometry of the test mass of the measuring cell in such a way as to minimize Sf. To do this, the test mass of the measuring cell can be designed in such a way that h is very small compared to dp, for example h approximately equal to 0.

[0128] Furthermore, it is possible to choose the geometry of the test mass of the measuring cell so as to minimize S. For this, the test mass of the measuring cell can be designed so that dg is strictly less than dp, advantageously less than 0.1 dp. For example, in the case where the axis of rotation is the common axis of rotation of two hinges 118, the hinges can no longer be arranged on the rear face of the test mass but in the middle of the thickness of the test mass, to make the distance dg tend towards 0.

[0129] Parasitic forces may also result from the deposition of electrical charges on the test mass in the case of a measurement of a surface force exerted by a flow of charged particles. The applicant has shown that a coating comprising an electrically conductive material on the test mass makes it possible to evacuate these charges. Such a coating may also make it possible to increase the lifetime of the measuring cell. As will be explained with reference to Fig. 5, such a coating, for example metallic, may also be used as an electrode in a calibration procedure of the measuring device.

[0130] Drifts in the measurement of the surface force exerted by the particle flow can also result from temperature rises that can cause thermal expansion. The presence of a metal coating on the test mass can reduce temperature gradients at the ends of the resonator and therefore reduce thermal drifts.

[0131] As shown in equation [Math 4], the frequency variations depend on a quadratic term of the surface force of the particles exerted on the test mass. To gain measurement precision, this quadratic term can be limited by a differential measurement between two sensors.

[0132] Fig. 4A represents a diagram of a measuring device according to an exemplary embodiment, the device comprising two measuring cells 110A, 110B arranged for a differential measurement.

[0133] The first measuring cell 1 10A is similar to the measuring cell described in relation to Fig. 2A and Fig. 2B and comprises a fixed part 1 12A mechanically connected to the support of the device (not shown), a resonator 114A and a mobile massive part or proof mass 1 16A with an exposure face 1 17A. The proof mass is in rotation around a single axis OAX, for example the common rotation axis of hinges 1 18A. We denote CrriA the center of mass and CPA the center of pressure. In operation, the exposure face 1 17A undergoes a surface force F P A exerted by the particle flow. This results in a tensile force TA (OR extension) on the resonator 114A at the connection point BA of the resonator with the test mass. We denote MFA the parasitic force exerted at the center of mass CrriA and resulting from an acceleration along y, for example due to vibrations.

[0134] The second measuring cell 1 10B comprises a fixed part 1 12B mechanically connected to the support, a resonator 1 14B and a mobile massive part or proof mass 1 16B with an exposure face 1 17B. The fixed part, the resonator and the mobile massive part of the second measuring cell are substantially identical respectively to the fixed part, the resonator and the mobile massive part of the first measuring cell. In particular, the proof mass 1 16B is in rotation about a single axis OBX, for example the common axis of rotation of hinges 1 18B. We denote CrriB the center of mass and CPB the center of pressure.

[0135] Compared to the first measuring cell, only the position of the resonator 114B relative to the axis of rotation is reversed. In other words, the distances, along the direction n normal to the exposure face, between the resonator and the axis of rotation are substantially identical in both cells but the positions of the resonator and the axis of rotation are reversed between the first measuring cell and the second measuring cell, such that when the exposure face of each of the measuring cells is exposed to the particle flow, one resonator undergoes compression while the other resonator undergoes extension.

[0136] Thus, in operation, when the exposure face 1 17B undergoes a surface force F PB exerted by the particle flow, this results in a compression force TB on the resonator 1 14B at the connection point BB of the resonator with the test mass. We denote MFB the parasitic force exerted at the center of mass CrriB and resulting from an acceleration along y, for example due to vibrations.

[0137] Thus, in the example shown in Fig. 4A, the resonator 114A of the first measuring cell, for example a vibrating beam, undergoes compression under the effect of a surface force exerted by a flow of particles on the exposure face 117A, while the resonator 114B of the second measuring cell, for example a vibrating beam, undergoes extension. This results in opposite frequency variations of the resonators 114A and 114 B .

[0138] In such a device, the fundamental frequencies f r0 of the two resonators are the same, as is the possible remaining thermal drift f th6), where 0 is the temperature. Since only the acceleration sensitivity along y is non-zero then, if the two cells are close to each other, the accelerations along this axis are similar and the contributions ff cc at the resonator frequency of each resonator that derives from this acceleration are also identical. Thus, the frequency f (P) of the resonator 114A of the first measuring cell 110A and the frequency f r B (P) of the resonator 114B of the first measuring cell 1 10B are written: [Math 9]

[0139] The frequency difference A -(P) between the two resonators then makes it possible to have a measurement of the surface force exerted by the particle flow by cancelling out the effects of residual vibration as well as thermal drifts. This results in an improvement in the accuracy of the measurement.

[0140] In the example of Fig. 4A, the measuring device comprises two measuring cells for performing a differential measurement.

[0141] A differential measurement can also be obtained with a single measuring cell comprising two resonators.

[0142] Fig. 4B thus represents a diagram of an example of a measuring cell in a device according to the present description, the measuring cell comprising two resonators arranged for a differential measurement.

[0143] In this exemplary embodiment, the measuring cell 110 comprises a second resonator 114B, substantially identical to the first resonator 114A, the projections of the first resonator and of the second resonator in a plane perpendicular to the axis of rotation being located on either side of a projection of the axis of rotation Ox on said plane, such that when the exposure face 117 is exposed to the flow of particles, one resonator (in this example the first resonator 114A) undergoes an extension (traction TA) while the other resonator (in this example the second resonator 114B) undergoes a compression TB.

[0144] In this example, the frequency difference Af r (F p ) between the two resonators allows, as in the previous example, to have a measurement of the surface force exerted by the flow of particles by canceling the effects of residual vibration as well as thermal drifts.

[0145] Advantageously, a calibration of the measuring device is carried out before the implementation of the device.

[0146] Several calibration methods can be implemented. For example, known forces applied by contact can be applied to the exposure face.

[0147] A preferred calibration solution is an electrostatic calibration.

[0148] Fig. 5 represents a diagram of a measuring cell 110 of a measuring device according to the present description, as well as a device 510 for calibrating the cell, according to an exemplary embodiment. The calibration device 510 comprises means 514 for applying a potential difference between a metallized region of the measuring cell forming a first electrode 119 and a metal plate forming a second electrode 512, located at a distance d from the first electrode. The first electrode 119 is for example made of tantalum or titanium.

[0149] Placing a metal electrode on the proof mass and a metal plate opposite it creates an electrostatic force FES when there is a potential difference between the two electrodes. The electrostatic force creates a movement of the proof mass around the axis of rotation of the proof mass, for example the common axis of the hinges 118, which creates a stress on the resonator 114. The force applied to the proof mass is: [Math 10]

[0150] With A me the surface of the calibration electrode 119 on the test mass, e0 the permittivity of the vacuum and V the potential difference applied between the two electrodes.

[0151] By reproducing the measurement for several values ​​of potential differences, a calibration can be carried out.

[0152] A calibration as described above has the advantage of being contactless with the measuring cell and easy to implement since it is sufficient to place a metal plate under the test mass. Thus, this calibration can be done in situ, or between two measurements.

[0153] Fig. 6A, Fig. 6B and Fig. 6C represent diagrams of a monolithic measuring cell 110 according to an exemplary embodiment, according to different views.

[0154] The measuring cell 110 is monolithic in that the fixed part, the movable solid part, or test mass, and the resonator 114, for example a vibrating beam, are made from a single block of material, for example quartz.

[0155] In this example, the mobile massive part 116 is mobile around two hinges 618. The test mass comprises a target forming the exposure surface 117 and two wings 612, the target being connected on the one hand to the two wings 612 and on the other hand to the two hinges 618 and to one end of the resonator 114. Such an arrangement of the mobile massive part makes it possible to distribute the mass in such a way that the center of mass is close to the axis of the hinges 618.

[0156] According to one example, the exposure surface 117 is arranged on one side of the axis of rotation Ox, along a main extension plane of the mobile massive part 116. The wings 612 may be arranged at least in part on the other side of the axis of rotation Ox, along this plane, as illustrated for example in FIG. 6D. FIG. 6D illustrates a non-limiting example in which the incorporation of the wings 612 makes it possible to bring the center of mass Cm closer to the axis of rotation Ox, so that the ratio h / p between the distance h and the distance p is less than approximately 0.1, and preferably less than approximately 0.01. In practice, according to one example, the center of mass Cm may be substantially positioned on the axis Ox. It is therefore understood that the wings 612 make it possible to bring the center of mass Cm closer to the axis of rotation Ox.

[0157] More generally, the mobile massive part 116 may have a first part with a center of mass Cm1 arranged on one side of the axis of rotation Ox, with Cm1 at a distance r1 from this axis. The mobile massive part 116 may have a second part with a center of mass Cm2 arranged on another side of the axis of rotation Ox, with Cm2 at a distance r2 from this axis. According to the masses m1 and m2 respectively of the first part and the second part, and the distances r1 and r2, it is understood that the material of the mobile massive part 116 may be distributed so as to bring Cm closer to the axis of rotation Ox.

[0158] Note that the use of wings is not the only configuration allowing this rapprochement. This corresponds to an example of structural implementation. The person skilled in the art is able to identify and produce other structures allowing the center of mass Cm to be brought closer to the axis of rotation Ox, and therefore to reduce the h / p ratio. Other structures can in particular be envisaged to distribute the mass of the mobile massive part on either side of the axis of rotation Ox, according to the main extension plane of the mobile massive part 116. For example, it is possible to play on the symmetry of the mobile massive part with respect to the axis of rotation Ox.

[0159] Furthermore, in this example, the fixed part 112 comprises a decoupling frame 630 and an external frame 620 configured to be connected to the support (not shown). The decoupling frame has a tuning fork shape and is connected on the one hand to the external frame and on the other hand to the hinges 618 and to a second end of the resonator 114.

[0160] As illustrated in Fig. 6B, the target may comprise two lightening pockets 617 on the rear face. This makes it possible to limit the mass of the target and the stresses applied to the hinges 618 and the vibrating beam 614, while guaranteeing a large contact surface with the particles, good mechanical strength of the target, and a distance from the parasitic resonance modes of the operating mode of the vibrating beam.

[0161] In exemplary embodiments, the target 617 is connected to the hinges 618 by two arms 610 so as to create an opening 615 between the target and the beam 114. The opening 615, optional, makes it possible to avoid the collision of particles near the vibrating beam. The arms 610 are connected to the wings 612 which make it possible to position the center of mass of the test mass as close as possible to the axis of the hinges, in the xy plane. The parameter h (fig. 2A) is thus substantially zero. A third arm at the base of the test mass connects the wings 612 to the hinges 618 and to the beam 114. Such a geometry of the test mass is advantageous in that it therefore makes it possible to cancel the effects of parasitic accelerations (vibrations) on the two axes x and z.

[0162] The fixed part 112 comprises the decoupling frame 630 and the external frame 620. The external frame 620 has a mechanical function of holding the test mass, the vibrating beam 114 and the decoupling frame 630. It also allows the test mass to be held during manufacturing and its physical protection.

[0163] The external frame 620 comprises connectors 640 (see Fig. 6B, Fig. 6C), configured to ensure physical contact with the support (not shown), formed for example by a base. The connectors 640 also allow electrical contact with the electronic circuit (120, Fig. 1). The connectors 640 are advantageously made of a material having a thermal behavior close to that of the material of the measuring cell, for example kovar® (iron nickel chromium cobalt alloy). They are glued to the external frame for example by conductive glue.

[0164] The decoupling frame 630 forms a thermal and mechanical filter to protect the beam 114 and the test mass 116 from the effects of the external environment. In this example, the decoupling frame has the shape of a tuning fork connected to the external frame by an end piece 631. The branches of the tuning fork are connected to the hinges 618. The vibrating beam is fixed between a central part of the tuning fork and the third arm of the external frame, in a zone of minimum thermal stress. The thinness of the branches of the tuning fork allows them to deform and prevents the transmission of forces.

[0165] The applicant has shown very satisfactory performance with monolithic measuring cells as illustrated in Fig. 6A, Fig. 6B, Fig. 6C. The cells are for example made of quartz. The external dimensions of the measuring cell are for example between about 10 mm and about 30 mm, with a thickness between about 100 microns and about 500 microns at the edges, for example about 500 microns, the thickness being able to reach less than 50 microns at the hinges and the beam.

[0166] With such a geometry of the measuring cell, the applicant obtained a linear sensitivity of 0.6 Hz / (pN.cm-2) or 60 Hz / Pa for a vibration frequency of 60 kHz.

[0167] The measuring cell produced is particularly compact and is insensitive to gravity.

[0168] Fig. 7A and Fig. 7B represent diagrams according to two views of a monolithic measuring cell 110 as illustrated in Fig. 6A, arranged on a support 201, according to an exemplary embodiment.

[0169] The support 201 is in this example a base which takes the form of an electronic card connected to the measuring cell by the connectors 640. This arrangement makes it possible to have the electronics necessary for vibration as close as possible to the measuring cell. The card 201 can also include electrostatic calibration means, for example in the form of 2 plates placed opposite the wings (see also Fig. 5).

[0170] The measuring device may also comprise, in exemplary embodiments, a plate having dimensions similar to those of the electronic card 201 and placed in front of the cell such that substantially only the target of the test mass is exposed to the flow of particles.

[0171] Such a measuring device can then be placed in any position because it is insensitive to gravity.

[0172] Fig. 8 represents a diagram of a satellite 800 comprising a body 810 equipped with a thruster and solar panels 820. As illustrated in Fig. 8, the satellite is in this example equipped with a device for measuring the surface force exerted by a flow of particles according to the present description. The measuring device comprises a measuring cell 110, for example of the type described with reference to the preceding figures. The fixed part of the measuring cell is connected to a support itself fixed to an arm 850 mechanically and electrically connected to the body 810 of the satellite. The measuring device is configured for measuring the surface force exerted by the flow of particles 10 ejected by the thruster of the satellite. The electronic circuit and the processing unit of the measuring device can be remote or arranged close to the measuring cell.

[0173] Fig. 9 represents a diagram of an enclosure 900 with a rarefied environment, for example a vacuum box, configured for the qualification of a satellite thruster 910 comprising means for ejecting a flow of neutral and / or charged particles. The enclosure comprises a device for measuring the force exerted by the flow of particles 10 ejected by the thruster. The measuring device comprises a measuring cell 110, for example of the type described with reference to the preceding figures. The fixed part of the measuring cell is connected to a support itself fixed to an arm 950 connected for example to a rotation plate. The electronic circuit and the processing unit of the measuring device can be remote or arranged close to the measuring cell.

[0174] Although described through a certain number of exemplary embodiments, the devices and methods for measuring the surface force exerted by a flow of particles according to the present description include different variants, modifications and improvements which will be obvious to those skilled in the art, it being understood that these different variants, modifications and improvements are part of the scope of the invention as defined by the following claims.

[0175] REFERENCES

[0176] [Ref. 1] Denis Packan et al. “Thrust Measurements with the ON ERA Micronewton Balance” Paper IEPC-2007-118 at the 30th International Electric Propulsion Conference, Florence, Italy, 17-20 September 2007. [Ref. 2] DG Chavers and FR Chang-Diaz, “Momentum flux measuring instrument for neutral and charged particle flows” Rev. Sci. Instrum., vol. 73, no. 10, pp. 3500-3507, Oct. 2002, doi: 10.1063 / 1.1505107.

[0177] [Réf. 3] A. Spethmann, T. Trottenberg, and H. Kersten, “Spatially Resolved Momentum Flux Measurements for Thruster Plume Diagnostics" presented at the I EPC, 2013.

Claims

CLAIMS 1. Measuring cell (110) for measuring the surface force exerted by a flow of particles comprising: - a fixed part (112) configured to be mechanically and electrically connected to a support; - at least one first resonator (114, 114A) comprising a longitudinal axis (A), said first resonator having a first end secured to said fixed part; - a mobile massive part (116) comprising an exposure face (117) to the flow of particles, said massive part being such that: - said massive part is movable relative to the fixed part along a single axis of rotation (Ox) perpendicular to a plane formed by the longitudinal axis of the first resonator and a direction (n) normal to the exposure face; - the axis of rotation (Ox) and the longitudinal axis of the first resonator are distant in the direction (n) normal to the exposure face by a predetermined distance (d p ) non-zero; and - the first resonator has a second end (B) integral with said mobile massive part; - a first distance (h) between the axis of rotation (Ox) and a center of mass (Cm) of the mobile massive part is strictly less than a second distance (p) between the axis of rotation (Ox) and a center of pressure (Cp) of the exposure face (117), the first distance and the second distance being distances projected onto a plane (Oxy) parallel to the exposure face, the measuring cell (110 being characterized in that the ratio between said first distance (h) and said second distance (p) is less than approximately 0.

1.

2. A measuring cell according to claim 1, wherein the ratio between said first distance (h) and said second distance (p) is less than approximately 0.

01.

3. A measuring cell according to any preceding claim, wherein a ratio between a third distance (d g ) between the axis of rotation (Ox) and the center of mass (Cm) of the massive mobile part and a fourth distance (d p ) between the axis of rotation (Ox) and the axis (A) of the first resonator is strictly less than 1, advantageously strictly less than approximately 0.1, the third distance and the fourth distance being distances projected onto a plane (Oxz) perpendicular to the exposure face.

4. A measuring cell according to any preceding claim, wherein the measuring cell is monolithic.

5. Measuring cell according to any one of the preceding claims, in which: - the measuring cell comprises two hinges comprising a common rotation axis; - said common axis of rotation forms the single axis of rotation (Ox) of said mobile solid part.

6. Measuring cell according to claim 5, in which a projection of the axis (A) of the first resonator in a plane parallel to the exposure face and comprising said common axis of rotation (Ox) intersects said common axis of rotation at a midpoint located substantially halfway between the two hinges.

7. Measuring cell according to claim 6, in which a distance (dmp) between a projection of the center of mass (Cm) of the mobile massive part on said common axis of rotation and said midpoint is strictly less than a distance (dpc) between said midpoint and each of the hinges.

8. Measuring cell according to any one of claims 5 to 7, in which: - the movable massive part (116) comprises a target forming the exposure surface (117) and two wings (612), said target being connected to the two wings, to the two said hinges and to the second end of the first resonator; - the fixed part comprises a decoupling frame (630) and an external frame (620) configured to be connected to the support, said decoupling frame having a tuning fork shape connected on the one hand to the external frame, and on the other hand to the two said hinges and to the first end of the first resonator.

9. Measuring cell according to any one of the preceding claims, in which the first resonator comprises at least one vibrating beam in bending mode.

10. Measuring cell according to any one of the preceding claims, in which at least part of the movable solid part (116) comprises a coating of electrically conductive material.

11. Device (100) for measuring the surface force exerted by a flow of particles (10), comprising: - a support (201); - at least one first measuring cell (110, 110A) according to any one of the preceding claims, said fixed part (112) being mechanically and electrically connected to said support; - an electronic circuit (120) configured to excite the first resonator of said at least one first measuring cell at an initial resonant frequency and measure, when the device is subjected to the flow of particles, a measurement resonant frequency; - a processing unit (130) configured to determine, from a difference between the measurement resonant frequency and the initial resonant frequency, the surface force exerted by the flow of particles.

12. Measuring device according to claim 11 comprising a second measuring cell (110B), in which: - the second measuring cell comprising a fixed part (112) mechanically connected to the support, a resonator (114B) and a mobile solid part (116B), said fixed part, said resonator and said mobile solid part of the second measuring cell being substantially identical respectively to the fixed part, the resonator and the mobile solid part of the first measuring cell; - the positions of the resonator and the rotation axis along the direction (n) normal to the exposure face are reversed between the first measuring cell and the second measuring cell, such that when the exposure face of each of the measuring cells is exposed to the particle flow, one resonator undergoes compression while the other resonator undergoes extension; - the processing unit (130) is configured to further determine a difference between the measuring resonant frequency measured by means of the first measuring cell and the measuring resonant frequency measured by means of the second measuring cell to determine the surface force exerted by the particle flow.

13. Satellite (800) comprising a thruster with means for ejecting a flow of neutral and / or charged particles (10) and a device for measuring the force exerted by said flow of particles according to any one of claims 11 or 12, the support of the measuring device being mechanically and electrically connected to a body (810) of the satellite by means of an arm (850).

14. Enclosure (900) with rarefied environment configured for the qualification of a flow of neutral and / or charged particles, the enclosure comprising a device for measuring the force exerted by a flow of particles according to any one of claims 11 or 12, the support of the measuring device being mechanically and electrically connected to a body of the enclosure, the measuring device being configured to measure the particle flow (10).

15. A method of measuring the surface force exerted by a flow of particles by means of a device according to any one of claims 11 or 12, the method comprising: - an excitation of the first resonator and a measurement of an initial resonance frequency of the resonator (fro), without particle flow; - receiving the particle flow by the exposure face of the measuring cell and measuring a measurement resonance frequency of the resonator (fr(P)+fro) resulting from the force applied by the particle flow on said exposure face; - the determination, from a difference between the measurement resonance frequency and the initial resonance frequency, of the surface force of the particle flow.

16. Measuring method according to claim 15 comprising an additional calibration step, said calibration step comprising: - the successive application of several potential differences between a region comprising a coating of electrically conductive material of the mobile massive part (116) and a facing metal plate, the application of each potential difference resulting in an electrostatic force applied to the mobile massive part; - for each potential difference, the measurement of a measurement resonance frequency resulting from said electrostatic force and the determination of the difference between the measurement resonance frequency and the initial resonance frequency.

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