BACKGROUND [001] A printing system may include a pen or a printhead to apply a print fluid on a print substrate so as to print a plot or an image. The printhead may be in fluid communication with a pump through a print fluid path. The printing system may have a pressure sensor to sense pressure in the print fluid path. The performance of the printing system may depend inter alia on the accuracy in obtaining pressure values of the print fluid path.

BRIEF DESCRIPTION

[002] Various example features will be apparent from the detailed description which follows, taken in conjunction with the accompanying drawings, wherein:

[003] FIG. 1 schematically represents a printing system according to an example of the present disclosure.

[004] FIG. 2 schematically represents a printing system according to an example of the present disclosure.

[005] FIG. 3 schematically represents a pressure sensor according to an example of the present disclosure.

[006] FIG. 4 schematically represents a pressure sensor according to an example of the present disclosure. [007] FIG. 5 schematically represents a printing system according to an example of the present disclosure.

[008] FIG. 6 schematically illustrates a non-transitory machine-readable storage medium and a processor for an example printing system, such as those shown in FIG. 1, FIG. 2, or FIG. 5.

[009] FIG. 7 is a block diagram of an example of a method for calibrating an example printing system according to the present disclosure. [0010] FIG. 8 is a block diagram of an example of a method for calibrating an example printing system of the present disclosure.

[0011] FIG. 9 represents a graph showing the relationship between the pressure in a print fluid path and the output of a pressure sensor.

[0012] FIG. 10 is a block diagram of an example of a method for calibrating an example printing system of the present disclosure.

DETAILED DESCRIPTION

[0013] Pressures, or pressure values, of a print fluid path of a printing system may be determined based on a signal, reading or output from a pressure sensor associated with the print fluid path. The output of the pressure sensor may be converted to pressure values, e.g. by a controller or processor, based on a known relationship between the pressure in the print fluid path and the output of the pressure sensor, which is e.g. stored in a memory as a lookup table (LUT), equation, gain and offset values, or the like.

[0014] The properties of a pressure sensor may change over time. The properties of the pressure sensor may be altered, for example, due to mechanical wear or exposure to ambient conditions, i.e., environmental or climate conditions such as temperature or humidity. Aging may also affect the properties.

[0015] For example, in a pressure sensor comprising e.g. a Hall-effect sensor and a magnet which are movable one relative to the other, when the relative position between them varies, the Hall-effect detects a change in the electromagnetic field generated by the magnet. If the relative position varies depending on the pressure in a print fluid path, the output of the Hall-effect sensor varies: such a sensor may therefore be employed to determine the pressure in the print fluid path. However, over time there may be an alteration e.g. of the magnetization of the magnet, for example by exposure to external magnetic fields or to ambient conditions such as an extreme temperature.

[0016] Altered properties of the pressure sensor may cause drifting of the pressure sensor, i.e., a change in the sensor output for the same pressure in the print fluid path: in the above example, the Hall-effect sensor may detect a different value of the electromagnetic field for the same relative position with respect to the magnet, and therefore for the same pressure in the print fluid path.

[0017] A calibration, or a re-calibration, of the printing system may therefore be performed in order to establish and store a new relationship between the pressure in the print fluid path and the output of the pressure sensor, to provide accuracy in the determination of the pressure in the print fluid path. Accurate information about the pressure may be useful, for instance, for increasing the printed image quality and the lifespan of the printheads. Furthermore, accurate determination of the pressure may avoid or reduce malfunctions in the printing system, such as detecting a print fluid supply as full before it is full, or over pressurizing the print fluid path if a completion of the refill is not properly determined by the processor. It may therefore avoid damage of the components of the printing system and economic losses to the user.

[0018] With reference to the attached drawings, various examples of printing systems comprising a pressure sensor in a print fluid path, and of methods for calibrating such printing systems, will now be described. Example printing systems and calibration methods disclosed herein enable accurate readings of the pressure in a print fluid path of a printing system in a cost- effective way.

[0019] For clarity reasons, not all the elements of the example printing systems are illustrated in the drawings. Furthermore, the drawings are schematic and generally not to scale, and do not define the precise proportions of the illustrated elements. In the drawings, data connections or electrical connections between elements are represented using dashed lines.

[0020] Examples of printing apparatus which may comprise printing systems and/or may implement calibration methods according to examples disclosed herein may be, amongst others, printers using thermal or piezoelectric inkjet technology, or others; inkjet printers with printheads on a reciprocating carriage or page-wide-array printers with printheads on a print bar spanning the whole width of the print media; 3D printers with nozzles to release agents on a build material. Printing fluids may include latex printing fluids, solvent- based printing fluids or others, as well as fusing agents and other substances used in 3D printing, such as binding agents, detailing agents, or others.

[0021] FIG. 1 schematically represents a printing system according to an example of the present disclosure. The printing system may comprise: a nozzle 60 to eject a drop of print fluid 110 on a print substrate 120; a pump 30 in fluid communication with the nozzle 60 through a print fluid path 50; a pressure sensor 40 to sense a pressure in the print fluid path 50; and a processor 10. In FIG. 2, an example printing system 100 is similar to that of FIG. 1 and comprises a print fluid supply 20 in fluid communication with the pump 30 and with the nozzle 60 through the print fluid path 50. In some examples, the printing system 100 may comprise a plurality of print fluid supplies 20 fluidly communicated with nozzles 60 through corresponding fluid paths 50, e.g. a print fluid path 50 for each different colour of the print fluid. In examples, the nozzle 60 may be provided in a printhead with a printhead chamber containing the print fluid 110. In examples, the print fluid supply 20 may be a cartridge, a tank, a reservoir, a container, or a vessel.

[0022] In some examples, the processor 10 may vary the pressure in the print fluid path 50, e.g. increase the pressure, by operating the pump 30. The processor 10 may also decrease the pressure in the print fluid path 50, e.g. by causing the printhead to eject print fluid through the nozzle 60 while the pump 30 is not operating, or while print fluid in the print fluid path 50 is decreasing because the print fluid supply 20 is running out.

[0023] In example printing systems 100 as in FIG. 1 and FIG 2, the processor 10 is to calibrate the printing system 100, i.e., to establish a relationship between an output of the pressure sensor 40 and a pressure in the print fluid path 50. For instance, a calibration may be performed based on associating a first output value of the pressure sensor 40 with a first known pressure value of the print fluid path and a second output value of the pressure sensor 40 to a second known pressure value of the print fluid path.

[0024] In examples, the first and second output values of the pressure sensor 40 are obtained by the processor 10 operating the pump and/or the nozzle to vary the pressure in the print fluid path 50 until the output of the pressure sensor stabilizes, and a corresponding first output value of the pressure sensor 40 is obtained as this stabilized first output value, and then operating the pump and/or the nozzle to vary the pressure in the print fluid path 50 until the output of the pressure sensor stabilizes again, and a corresponding second output value of the pressure sensor 40 is obtained as this stabilized second output value.

[0025] In some implementations, the processor 10 may operate the nozzle 60, i.e., may cause the nozzle 60 to eject print fluid, to decrease the pressure in the print fluid path 50 until the output of the pressure sensor 40 stabilizes, and thus obtain the first output value of the pressure sensor 40; then the processor 10 may operate the pump 30 to increase the pressure in the print fluid path 50 until the output of the pressure sensor 40 stabilizes, and thus obtain the second output value of the pressure sensor 40. In examples, the processor 10 may operate the nozzle 60 to eject print fluid while the pump 30 is not operating. In examples, the processor 10 may operate the pump 30 while the nozzle 60 is not operating, i.e., is not ejecting print fluid. In some implementations, the order may be varied, i.e., the pressure may first be increased as described, and then decreased as described.

[0026] In examples, an output of the pressure sensor 40 may stabilize while the pressure in the print fluid path 50 decreases or increases, due to the pressure reaching a saturation point, where the pressure is at a lower or at an upper end of an instrument range of the pressure sensor. The printing system is therefore calibrated in a calibration range which corresponds to the instrument range.

[0027] In this case, which will also be disclosed in more detail later on in relation to example calibration methods, when the pressure in the print fluid path 50 decreases and reaches the minimum pressure that the pressure sensor is able to sense, the pressure sensor 40 may saturate at a lower saturation point, and the sensor output may then stabilize at a first saturation output value, or lower saturation point output value, even if the pressure in the print fluid path continues decreasing. Similarly, when the pressure in the print fluid path 50 increases and reaches the maximum pressure that the pressure sensor 40 is able to sense, the pressure sensor 40 may saturate at an upper saturation point, and the sensor output may then stabilize at a second saturation output value, or upper saturation point output value, even if the pressure in the print fluid path continues increasing.

[0028] The maximum and minimum pressure that the pressure sensor is able to sense are the ends of the instrument range of the pressure sensor, and will be referred to herein as upper saturation pressure and lower saturation pressure, respectively. The upper and lower saturation pressures are a characteristic of the pressure sensor and are therefore known, and stable over time. [0029] The first and second known pressure values referred to above may respectively correspond to the lower saturation pressure and the higher saturation pressure, which cause stabilization of the pressure sensor output at respectively the lower and upper saturation output values. [0030] In some examples, an output of the pressure sensor 40 may stabilize after the pressure in the print fluid path 50 increases, or decreases, and stabilizes at a known pressure value, for example because a predetermined event occurs, or because a component of the printing system (e.g. a relief valve) sets a predetermined pressure in the print fluid path 50. In such cases, the printing system may be calibrated in a calibration range which is narrower than the instrument range.

[0031] In examples, the printing system may be calibrated in a calibration range where one of the first or second known pressure values may correspond to a predetermined event, and the other of the first or second known pressure values may correspond to a saturation point of the pressure sensor 40.

[0032] In some examples, stabilized output value of the pressure sensor is to be understood as an output value that remains within a predetermined range over a predetermined time. In some examples, stabilized output of the pressure sensor may be understood as a substantially constant or steady output value. The pressure sensor output values may be e.g. voltage values.

[0033] An example calibrated printing system 100 as disclosed herein may produce a trustworthy knowledge of the pressure in the print fluid path of the printing system, that may be used e.g. to perform accurate diagnosis of the printing system. [0034] In some examples, a calibration of the printing system 100 may be carried out without removing the pressure sensor 40 from the printing system 100, and therefore without emptying the print fluid path 50. Such a calibration may be carried out by a user, instead of trained staff. The calibration process may therefore be done with minimum printing system downtime and user experience may be improved. Furthermore, reducing staff interventions may mean minimizing repair costs. [0035] FIG. 3 and FIG. 4 illustrate example pressure sensors 40 which may be employed in a printing system 100 according to examples disclosed herein. In FIG. 3 and FIG. 4, an example pressure sensor 40 comprises a Hall-effect sensor 41 and a magnet 43. The Hall-effect sensor 41 detects an electromagnetic field generated by a magnet 43, and provides an output depending on the detected electromagnetic field. The magnet 43 is displaceable relative to the Hall-effect sensor 41 , and therefore the detected electromagnetic field and the output of the Hall-effect sensor depend on the position of the magnet 43 with respect to the Hall-effect sensor 41. [0036] The magnet 43 is mounted to vary its position with the pressure in the print fluid path 50, as will be described in detail below, such that a variation in the pressure displaces the magnet 43 towards or away from the Hall-effect sensor 41 : the output of the Hall-effect sensor 41 thus depends on the pressure in the print fluid path 50.

[0037] In the examples of FIG. 3 and FIG. 4, the pressure sensor 40 comprises an enclosure 400 defining a reference fluid chamber 42, e.g. a reference air fluid chamber, and a print fluid chamber 45. The print fluid chamber 45 is in fluid communication with the print fluid path 50, and the print fluid 110 traverses the print fluid chamber 45. In examples, the pressure in the reference fluid chamber 42 may be constant. In examples, the reference fluid chamber 42 may be in fluid communication with atmospheric air.

[0038] The magnet 43 may be attached to a movable support separating the reference fluid chamber 42 from the print fluid chamber 45. In FIG. 3 the movable support may be an elastic membrane 44, e.g. made from an elastic polymer, comprising a portion 48 fixed to the enclosure 400 to separate the two chambers. In FIG. 4 the plunger 47 may slide inside the enclosure 400 and is biased by a spring 46.

[0039] The pressure in the print fluid chamber 45 varies with a variation of the print fluid path 50, thereby changing the pressure differential between the reference fluid chamber 42 and the print fluid chamber 45 and causing a displacement of the movable support, i.e. the elastic membrane 44 or the plunger 47. The displacement of the movable support, in turn, displaces the magnet 43 towards or away from the Hall-effect sensor 41 , varying the electromagnetic field sensed by the Hall-effect sensor 41 . The output of the Hall-effect sensor 41 of the pressure sensor 40, e.g. a voltage reading, changes accordingly. An output of the pressure sensor 40 is therefore associated with a pressure value in the print fluid path 50. In examples, the output of the pressure sensor 40 may be the output of the Hall-effect sensor 41 .

[0040] As illustrated in FIG. 3 and FIG. 4, the displacement of the movable support holding the magnet 43 is limited, e.g. physically limited, for instance by the configured elasticity of the elastic membrane 44, or by stoppers. In examples, one or more stoppers may be walls of the enclosure 400, such as wall 49. For instance, if the pressure in the print fluid path 50 gradually decreases, the pressure in the print fluid chamber 45 decreases, and the movable support and the magnet 43 are displaced towards the wall 49. The output of the Hall-effect sensor 41 varies with the position of the magnet 43 and therefore with the pressure in the print fluid path 50. However, once the movable support reaches the wall 49, the magnet 43 subsequently remains in the same position, and therefore the pressure sensor output remains the same, i.e. it stabilizes, even if the pressure in the print fluid path 50 decreases further. Similarly, if the pressure in the print fluid path 50 gradually increases until the movable support reaches the upper wall of the enclosure 400, the magnet 43 subsequently remains in the same position, and therefore the pressure sensor output is stabilized, even if the pressure in the print fluid path 50 increases further.

[0041] The limitation of the displacement of the movable support and the magnet 43 therefore results in two saturation pressures of the pressure sensor 40, in which the pressure sensor output stabilizes and in which the pressure in the print fluid path is known, because it is a characteristic of the pressure sensor (e.g. it may be calibrated during the production of the pressure sensor), and is stable over time. The lower and upper saturation pressures define an instrument range of the pressure sensor 40 and may be used to calibrate the printing system such as disclosed in more detail below.

[0042] In some implementations of printing systems as disclosed herein, other kinds of pressure sensors may be employed, different from Hall-effect sensors. In some examples, pressure sensors employed in printing systems disclosed herein may have saturation pressures fixed by physical limits different from mechanical stoppers.

[0043] The pressure sensor output may depend linearly or non-linearly on the pressure in the print fluid path. In examples, the pressure sensor output may decrease when the pressure increases, and consequently the output of the pressure sensor may be higher at the lower saturation point and lower at the upper saturation point. In other examples, the relationship between the pressure in the print fluid path and the sensor output may depend linearly or non-linearly on the pressure in the print fluid path, and may increase when the pressure increases, and consequently the output of the pressure sensor may be lower at the lower saturation point and higher at the upper saturation point.

[0044] In examples, the first output value and the second output value at which the output of the pressure sensor stabilize during calibration as disclosed herein, for instance as discussed above in relation with the example printing systems of FIG. 1 or FIG. 2, may be respectively associated with the upper and lower saturation pressures of a pressure sensor 40.

[0045] FIG. 5 illustrates examples of a printing system 100 which is similar to the example of FIG. 2 and may be calibrated as disclosed herein, and in which the print fluid path 50 may comprise a pressure relief valve 70, in this example a bypass relief valve. The pressure relief valve 70 opens when the pressure in the print fluid in the print fluid path 50 reaches a cracking pressure, which is a characteristic of the pressure relief valve 70. The pressure relief valve 70 thus establishes a limit to the pressure in the print fluid path 50, and this may be employed to calibrate the printing system, as further discussed later on. Implementations of a printing system 100 may comprise two or more pressure relief valves 70, with different pressure characteristics, e.g. each bypassing the pump 30.

[0046] Example printing systems as disclosed herein may be calibrated after a pressure sensor is installed in the printing system and/or during the lifespan of the printing system, e.g. with a certain frequency. The calibration allows compensating potential errors caused by variations in the pressure sensor properties, and maintains accurate readings of the pressure in the print fluid path overtime. It may also avoid or reduce preventive replacements of the sensor, reducing cost and downtimes.

[0047] Furthermore, a calibration may be performed e.g. if the pressure sensor 40 has been exposed to extreme conditions that may alter its properties, for instance during transport or storage of a printing system. The pressure sensor may therefore employ a cost-effective magnet, instead of a high-cost magnet designed to withstand extreme conditions, and transport or storage may be carried out with minimized restrictions related to environmental conditions. Extreme conditions may comprise for example environmental conditions, e.g. beyond a predetermined temperature. [0048] Examples of methods according to the present disclosure are described below. In some implementations, such example methods may be carried out in any example printing system according to this disclosure, e.g. under the control of processor 10 referred to above, that executes sequences of machine-readable instructions contained in a non-transitory machine- readable storage medium 11, such as a memory, connected to the processor 10, as shown in FIG. 6.

[0049] The non-transitory machine-readable storage medium 11 may include any electronic, magnetic, optical, or other physical storage device that stores executable instructions. The non-transitory machine-readable storage medium 11 may be, for example, Random Access Memory (RAM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), a storage drive, an optical disk, and others. In some examples, the processor 10 is an application specific processor, for example a processor to control the printing system 100. The processor 10 may also be a central processing unit.

[0050] Example methods are described in the following, with reference to FIG. 7 to FIG. 10, for calibrating a printing system. The example methods may be employed for instance to calibrate a printing system 100 comprising a pressure sensor 40, according to any of the examples herein disclosed.

[0051] FIG. 7 is a block diagram of an implementation of a method 200 for calibrating a printing system, e.g. a printing system 100 according to examples disclosed herein, comprising a print fluid path 50 between a pump 30 and a nozzle 60, the print fluid path 50 comprising a pressure sensor 40, as in any of the above examples.

[0052] With reference to FIG. 7, the example method 200 comprises: at 210, varying a pressure in the print fluid path 50, until an output of the pressure sensor 40 stabilizes at a first output value; at 220, varying the pressure in the print fluid path 50 until the output of the pressure sensor 40 stabilizes at a second output value; at 230, establishing a relationship between the output of the pressure sensor 40 and a pressure in the print fluid path 50, based on associating the first output value with a first known pressure value and the second output value to a second known pressure value.

[0053] In implementations of example method 200, the pressure in the print fluid path may be varied, e.g. increased or decreased as convenient, by operating the pump 30 and/or the nozzle 60 as disclosed above with reference to FIG. 1 and FIG. 2.

[0054] In implementations of a printing system 100 and a method 200, the relationship between the output of the pressure sensor 40 and a pressure in the print fluid path 50 may be a linear relationship. It may be a positive or negative linear relationship, e.g. depending on the characteristics of the pressure sensor 40 and/or on its installation in the printing system 100.

[0055] Some implementations of calibration methods will be described in the following with reference to FIG. 8, which is a block diagram of an example method 300 for calibrating a printing system 100, and FIG. 9, which shows a graph of a relationship between the output of a pressure sensor 40 and the pressure in the print fluid path 50, which may be obtained by calibration method 300. The pressure on the print fluid path 50 in plotted on the abscissa axis, in PSI (pound-force per square inch) and the output of the pressure sensor 40, in mV (millivolt), is plotted on the ordinate axis. In the example, the zero pressure in the graph represents atmospheric pressure.

[0056] Method 300 may comprise, at 310 of FIG. 8, decreasing the pressure in the print fluid path 50 below a lower saturation pressure Psi (see FIG. 9) of an instrument range of the pressure sensor 40. This causes saturation of the pressure sensor 40 at a lower saturation point LS: as a consequence of this saturation, the pressure sensor output stabilizes at a first output value Vsi, as explained above e.g. with reference to FIG. 3 and FIG. 4.

[0057] In other words, as the pressure in the print fluid path decreases, the output or reading of the pressure sensor 40 varies: however, at a certain point during the pressure decrease, the output of the pressure sensor 40 stabilizes, even if the pressure in the print fluid path 50 continues descending; the pressure after which the output stabilizes is the lower saturation pressure Psi of the pressure sensor 40. The stabilization of the pressure sensor output may be detected by the processor 10, which may then record the first output value Vsi.

[0058] Similarly, method 300 may comprise, at 320 of FIG. 8, increasing the pressure in the print fluid path 50 above an upper saturation pressure Ps2 (see FIG. 9) of the instrument range of the pressure sensor 40. This causes saturation of the pressure sensor 40 at an upper saturation point US: as a consequence of this saturation, the pressure sensor output stabilizes at a second output value Vs2.

[0059] As the pressure in the print fluid path rises, the output or reading of the pressure sensor 40 varies: however, at a certain point during the pressure increase, the output of the pressure sensor 40 stabilizes even if the pressure in the print fluid path 50 continues increasing; the pressure after which the output stabilizes is the upper saturation pressure Ps2 of the pressure sensor 40. The stabilization of the pressure sensor output may be detected by the processor 10, which may then record the second output value Vs2.

[0060] The lower saturation pressure Psi and the upper saturation pressure Ps2, are the ends of the instrument range of the pressure sensor 40, i.e., the maximum pressure and the minimum pressure that the pressure sensor 40 is able to sense. Pressures Psi and Ps2 are characteristics of the pressure sensor 40 and are therefore a first known pressure value and a second known pressure value. They may be determined e.g. during manufacture of the pressure sensor 40, before the pressure sensor 40 is installed in a printing system 100, etc.

[0061] Once the first output value Vsi and the second output value Vs2 are obtained at 310 and 320, the example method 300 comprises at 330 establishing a relationship between the output of the pressure sensor and the pressure in the print fluid path, based on the information obtained at 310 and 320, i.e. the output values provided by the pressure sensor at the lower saturation point LS and at the upper saturation point US. That is, the relationship is established based on associating the first output value Vsi _, provided by the pressure sensor at 310, with the lower saturation pressure Psi, and the second output value Vs2 _, provided by the pressure sensor at 320, with the upper saturation pressure Ps2.

[0062] In the example of FIG. 9, the lower saturation pressure of the pressure sensor is Psi = -0.6 PSI (-4.1 kPa), and the upper saturation pressure of the pressure sensor is Ps2 = 2.5 PSI (172.4 kPa), so the pressure sensor instrument range is from -0.6 to 2.5 PSI (-4.1 to 172.4 kPa). At the lower saturation pressure of -0.6 PSI (-4.1 kPa), the pressure sensor gives an output Vsi = 2400 mV, and at the upper saturation pressure of 2.5 PSI (172.4 kPa), the sensor gives an output Vs2 = 1450 mV. In this example the relationship between the pressure and the sensor output is therefore a negative linear relationship; in other examples, e.g. with other pressure sensors, the relationship may be a positive linear relationship. In some examples, both the upper and the lower saturation pressure may be positive pressure values, and in some examples they may both be negative pressure values.

[0063] As disclosed earlier on, the pressure in the print fluid path 50 of the printing system 100 in examples above may be increased e.g. by operating the pump 30, and it may be decreased by e.g. causing the nozzle 60 to eject print fluid while there is a limited amount of print fluid in the print fluid path 50, e.g. because the pump 30 is not operating and/or because a print fluid supply 20 is running out of print fluid.

[0064] In summary, in an example calibration method 300, the processor 10 may gradually decrease, or gradually increase, the pressure in the print fluid path 50 to induce saturation of the pressure sensor 40, in order to obtain, respectively, point LS (pressure Psi, sensor output Vsi) or point US (pressure Ps2, sensor output Vs2) of the graph of FIG. 9, from which the relationship between the pressure in the print fluid path 50 and the output of the pressure sensor 40, e.g. a linear relationship, may be determined by the processor 10. In some implementations of a printing system the relationship between the pressure in the print fluid path and the output of the pressure sensor may be non-linear.

[0065] An example printing system 100 may therefore be calibrated with implementations of methods 200 or 300, and calibration parameters may be stored in the memory 11 of the printing system 100. Calibration parameters to be stored may be the values of the pressure and of the sensor output at the two calibration points, e.g. the lower and upper saturation points in the case of method 300: first and second output values (e.g. Vsi, Vs2 in the above example), associated with their corresponding first and second known pressure values (e.g. Psi, Ps2 in the above example). In some examples, calibration parameters to be stored may be other parameters representing the relationship between the pressure in the print fluid path and the pressure sensor output, such as a look-up table, an equation, the gain and offset of the pressure sensor, or other, which may be determined by the processor 10 based on the first and second output values and the associated first and second known pressure values obtained in the calibration method.

[0066] The stored calibration parameters may be employed by the processor 10 during subsequent operation of the printing system to accurately determine the pressure in the print fluid path 50 from the output of the pressure sensor 40.

[0067] Implementations of methods 200 or 300 may be performed in the order presented in FIG. 7 and FIG. 8, or in the opposite order, that is, 220 before 210, or 320 before 310. On the other hand, the operations at 210 and 220, or the operations at 310 and 320, may be performed one substantially immediately after the other, or they may be separated by a time span, an event of the printing system, or other.

[0068] In implementations of example method 200 or example method 300, the pressure in the print fluid path may be varied, e.g. increased, while the nozzle 60 of the printing system 100 is not ejecting print fluid, i.e., when the printhead comprising the nozzle is not operating. When the printhead is not operating, the pressure in the print fluid path 50 may increase rapidly, and to a higher pressure value.

[0069] In some implementations of a method 200 for calibrating a printing system 100, as described above in relation with FIG. 7, may be performed without saturating the pressure sensor, using a narrower calibration range. In such implementations, at least one of the first and the second known pressure values may be associated with e.g. one of: an event that occurs in the printing system 100 that causes a stabilization of the pressure in the print fluid path 50 to a known pressure value; the operation of a component of the printing system 100 that causes such a stabilization of the pressure in the print fluid path 50 to a known pressure value; or an action performed on the printing system 100 that causes such a stabilization of the pressure in the print fluid path 50 to a known pressure value.

[0070] For example, a pressure relief valve 70 as shown in FIG. 5, associated with the print fluid path 50, may be disabled during normal printing operations, but may be enabled to carry out a calibration process. If the pressure in the print fluid path 5 is then gradually increased by operating the pump 30, the pressure in the print fluid path 50 will stabilize when it reaches a known pressure value, which is a characteristic of the relief valve, as the relief valve will then open and print fluid will recirculate through the relief valve 70 and the pump. The output of the pressure sensor 40 will stabilize accordingly. The relief valve 70 may be enabled or disabled e.g. by opening or closing an on/off valve (not shown) in series with the relief valve 70.

[0071] In examples, two or more of such pressure relief valves 70, with different pressure characteristics, for instance each bypassing the pump 30 as shown in FIG. 5, may each provide a different calibration point for the pressure sensor, i.e., a point where the pressure in the print fluid path is known and a stabilized sensor output may be obtained. Each such pressure relief valve 70 may be connected in parallel with the pump 30 as shown in FIG. 5, and an on/off valve may be provided in series with each pressure relief valve, allowing one of the pressure relief valves to be enabled at a given time to obtain a corresponding calibration point.

[0072] In some implementations, both the first and the second known pressure values may be associated with predetermined events, operation of components, or actions that cause a stabilization of the pressure in the print fluid path 50 to a known pressure value.

[0073] The determination that a calibration is to be performed may be made e.g. by the processor 10 of the above examples of printing systems 100. As already mentioned, a printing system may be calibrated or re-calibrated, for example, with a certain frequency, or based on other conditions.

[0074] Once the processor 10 determines that a calibration is to be performed, the calibration method itself, e.g. as disclosed herein, may be started straight away, or e.g. programmed at a predetermined time; however, in some examples the processor 10 may activate a flag to signal calibration is to be performed, and calibration may be subsequently carried out when it is detected that e.g. a predetermined event occurs in the printing system. This may e.g. avoid or reduce downtimes, print fluid consumption, disruptions of the user work, etc.

[0075] For example, if the printing system is a so-called cold swap printing system, calibration may be performed at the time of a print fluid refill of a print fluid supply, such as e.g. print fluid supply 20 in FIG. 2 or FIG. 5 above. Cold swap printing system is to be understood as a printing system wherein the print fluid path has no buffer or intermediate tank of print fluid, and stops printing when a print fluid source is running out of print fluid, i.e. when the processor detects an "out-of-ink" (OOI) event or, more generally, an "out-of-print-fluid" event. The print fluid supply is then refilled, before printing is resumed. In the following, "OOI" will be used to indicate an event of "out-of-print-fluid" in general.

[0076] FIG. 10 illustrates an implementation of a calibration method 400 of a printing system, including for instance method 300 as disclosed above, which may be performed when an OOI event occurs and a refill operation is performed in a printing system 100 as disclosed herein, for example as described with reference to FIG. 2 or FIG. 5. [0077] In FIG. 10, method 400 may be triggered at 410, when a calibration flag is activated, e.g. by the processor 10. At 420, checks are performed until an OOI event is detected. Once the OOI event is detected, the process described above at 310 (FIG. 8) is carried out: the pressure is decreased until the pressure sensor output stabilizes at a first output value. The pressure in the print fluid path may be decreased, for instance, by allowing the nozzle to continue ejecting print fluid after the OOI event: since the print fluid supply 20 is running out of print fluid, the amount of print fluid in the print fluid path will gradually decrease, and the pressure will similarly decrease. In some examples, the pump is not operated after the OOI is detected, whereby the decrease in the pressure may be faster.

[0078] At 430, this first output value, i.e., the output value Vsi of the lower saturation point, is then saved, and at 440 the process performs checks until the installation of a new print fluid supply is detected. Once the new print fluid supply is detected, the process described above at 320 (FIG. 8) is carried out: the pressure is increased until the pressure sensor output stabilizes at a second output value. For instance, the pump 30 may be operated to increase the pressure in the print fluid path 50. In some examples, no print fluid is ejected from the nozzle after the new print fluid supply is detected and the pump is operated, whereby the increase in the pressure may be faster.

[0079] At 450, this second output value, i.e., the output value Vs2 of the upper saturation point, is saved. The process described above at 330 (FIG. 8) is finally carried out, wherein the first output value Vsi is associated with the known lower saturation pressure Psi of the pressure sensor, and the second output value Vs2 is associated with the known upper saturation pressure Ps2 of the pressure sensor, to characterize the new relationship between the pressure in the print fluid path 50 and the output of the pressure sensor 40, and the printing system is therefore recalibrated. In some examples, the gain and offset of the pressure sensor 40 may be obtained and stored in the memory 11 of the printing system 100.

[0080] In implementations of a printing system 100 as disclosed herein, examples of method 400 may be carried out by processor 10, wherein the processor:

- detects an out-of-print-fluid event, at 420; - decreases the pressure in the print fluid path until the pressure sensor output stabilizes at a first output value, at 310;

- saves the first output value, associated with a lower saturation pressure of the pressure sensor, at 430;

- detects a print fluid supply, at 440;

- increases the pressure in the print fluid path until the pressure sensor output stabilizes at a second output value, at 320; and

- saves the second output value, associated with a lower saturation pressure of the pressure sensor, at 450.

[0081] In some implementations, the processor then determines, based on the data saved at 430 and 450, the printing system calibration parameters to characterize the relationship between the pressure in the print fluid path and the output of the pressure sensor.

[0082] Implementations of calibration methods performed in occasion of a refill of the print fluid, such as example method 400, profit from a downtime that is already familiar to the user, without adding further disruptions. Furthermore, when a refill is triggered by an OOI, the pressure in the print fluid path is already low, as the print fluid is running out, and therefore the lower saturation pressure may be rapidly reached. Similarly, once a new print fluid supply is provided, the print fluid path is pressurized as in any other refill, and almost no additional time is involved in obtaining the upper calibration point. The calibration may therefore be performed without a significant effect for the user.

[0083] When a calibration method such as 300, 400 described above is employed, the printing system may comprise a pressure limiting device in order to protect the components of the printing system when the pressure is increased, e.g. at 320 of methods 300 or 400. In this case, a cracking pressure of the pressure limiting device may be above the upper saturation pressure Ps2 of the pressure sensor 40, but below a pressure that may cause damages to components of the printing system.

[0084] In some implementations, the calibration method may be carried out in occasion of a refill, as described in relation with example method 400 and FIG. 10, but with operations such as performed at 210, 220, 230 of method 200 of FIG. 7 in place of operations 310, 320, 330. That is, the pressure is varied without reaching the saturation pressures, and the first output value and the second output value may correspond to first and second known pressure values that are not saturation pressures, but known pressures in between the lower and the upper saturation pressures, which as mentioned above may be associated with events, actions or operation of components of the printing system 100 (e.g. relief valve 70). The calibration range in such an example method is narrower than the pressure sensor instrument range, i.e., the two calibration points employed in this case are between points LS and US on the graph of FIG. 9.

[0085] In some implementations, more than two known pressure values and corresponding calibration points, e.g. three or more, may be employed in example methods for calibrating the printing system disclosed herein. By using more than two calibration points, non-linear relationships between the pressure in the print fluid path and the sensor output may be accurately calibrated.

[0086] For instance, one or more calibration points may be saturation points of the pressure sensor, and one or more calibration points may be based on events occurring in the printing system, operation of components of the printing system, or actions performed on the printing system, for which the pressure in the print fluid path is known, such as for example enablement of a pressure relief valve as described above. In examples, calibration of the printing system may be carried out employing an upper and a lower saturation points, and one or more intermediate points based on other events, operation of components, or actions, including any of the examples referred to above.

[0087] In some examples, the pressure sensor drift over time may be monitored using the data from successive re-calibrations. If the pressure sensor drift for example reaches a predetermined threshold, a replacement of the pressure sensor 40 may be flagged by the processor 10.

[0088] The present disclosure also presents a non-transitory machine-readable storage medium, encoded with instructions executable by a processor, the machine-readable storage medium comprising: instructions to vary a pressure in a print fluid path between a pump and a nozzle, the print fluid path comprising a pressure sensor, until an output of the pressure sensor stabilizes at a first output value; instructions to vary the pressure in the print fluid path until the output of the pressure sensor stabilizes at a second output value; and instructions to calibrate the printing system based on associating the first output value with a first known pressure value and the second output value to a second known pressure value.

[0089] The present description illustrates and describes certain examples. Different sets of examples have been described; these may be applied individually or in combination, sometimes with a synergetic effect. This description is not intended to be exhaustive or to limit these principles to any precise form disclosed. Many modifications and variations are possible in light of the above teachings. Any feature described in relation to any one example may be used in combination with a part of the other features described in the example, and/or in combination with any features of any other of the examples.

[0090] For reasons of completeness, various aspects of the invention are set out in the following numbered clauses:

Clause 1. A method for calibrating a printing system, comprising:

- varying a pressure in a print fluid path between a pump and a nozzle, the print fluid path comprising a pressure sensor, the pressure being varied until an output of the pressure sensor stabilizes at a first output value;

- varying the pressure in the print fluid path until the output of the pressure sensor stabilizes at a second output value; and

- establishing a relationship between the output of the pressure sensor and the pressure in the print fluid path, based on associating the first output value with a first known pressure value and the second output value to a second known pressure value.

Clause 2. The method of clause 1, wherein varying the pressure in the print fluid path comprises decreasing the pressure in the print fluid path below a lower saturation pressure of an instrument range of the pressure sensor, causing saturation of the pressure sensor, and causing the pressure sensor to provide a stabilized first output value, and wherein the first known pressure value corresponds to the lower saturation pressure of the pressure sensor. Clause 3. The method of any of clauses 1 or 2, wherein varying the pressure in the print fluid path comprises increasing the pressure in the print fluid path above an upper saturation pressure of an instrument range of the pressure sensor, causing saturation of the pressure sensor, and causing the pressure sensor to provide a stabilized second output value, and wherein the second known pressure value corresponds to the upper saturation pressure of the pressure sensor.

Clause 4. The method of any of the preceding clauses, wherein establishing the relationship between the output of the pressure sensor and the pressure in the print fluid path comprises establishing a linear relationship between the output of the pressure sensor and the pressure in the print fluid path.

Clause 5. The method of any of the preceding clauses, wherein the pressure is varied in the print fluid path after it is detected that a predetermined event occurs in the printing system.

Clause 6. The method of any of the preceding clauses, wherein varying the pressure in the print fluid path comprises, after an out-of-print-fluid event is detected, decreasing the pressure in the print fluid path until saturation of the pressure sensor at a lower saturation pressure, and saving a first output value corresponding to the lower saturation pressure.

Clause 7. The method of any of the preceding clauses, wherein varying the pressure in the print fluid path comprises, after a print fluid supply is detected, increasing the pressure in the print fluid path until saturation of the pressure sensor at an upper saturation pressure, and saving a second output value corresponding to the upper saturation pressure.

Clause 8. The method of any of the preceding clauses, wherein at least one of the first and the second known pressure values is associated with one of:

- an event that occurs in the printing system causing stabilization of the pressure in the print fluid path to a known pressure value;

- operation of a component of the printing system causing stabilization of the pressure in the print fluid path to a known pressure value; and

- an action performed on the printing system causes stabilization of the pressure in the print fluid path to a known pressure value.

Clause 9. The method of any of the preceding clauses, wherein varying the pressure in the print fluid path comprises increasing the pressure until a pressure relief valve associated with the print fluid path opens, print fluid recirculates through the relief valve and the pump, and the pressure in the print fluid path stabilizes at a characteristic pressure value of the relief valve, the first or second known pressure value being the characteristic pressure value of the pressure relief valve.

Clause 10. A printing system comprising: a nozzle to eject a drop of print fluid on a print substrate; a pump in fluid communication with the nozzle through a print fluid path; a pressure sensor to sense a pressure in the print fluid path; a processor to operate the pump and/or the nozzle to vary the pressure in the print fluid path until a stabilized first output value of the pressor sensor is obtained, and to operate the pump and/or the nozzle to vary the pressure in the print fluid path until a stabilized second output value of the pressor sensor is obtained, and to calibrate the printing system by associating the first output value of the pressure sensor with a first known pressure value of the print fluid path and a second output value of the pressure sensor to a second known pressure value of the print fluid path.

Clause 11. The printing system of clause 10, wherein the processor is to: operate the nozzle causing the nozzle to eject print fluid to decrease the pressure in the print fluid path until the stabilized first output value of the pressor sensor is obtained, and operate the pump to increase the pressure in the print fluid path until the stabilized second output value of the pressor sensor is obtained.

Clause 12. The printing system of any of clauses 10 or 11 , wherein the processor is to:

- detect an out-of-print-fluid event,

- decrease the pressure in the print fluid path until the pressure sensor output stabilizes at a first output value;

- save the first output value, associated with a lower saturation pressure of the pressure sensor;

- detect a print fluid supply;

- increase the pressure in the print fluid path until the pressure sensor output stabilizes at a second output value;

- save the second output value, associated with a lower saturation pressure of the pressure sensor.

Clause 13. The printing system of clause 12, wherein the processor is to determine calibration parameters to characterize the relationship between the pressure in the print fluid path and the output of the pressure sensor, based on the saved first output value associated with the lower saturation pressure and the saved second output value associated with the upper saturation pressure. Clause 14. The printing system of any of clauses 10 to 13, wherein the pressure sensor comprises a Hall-effect sensor and a magnet, the relative position between the magnet and the Hall-effect sensor varying with the pressure in the print fluid path. Clause 15. A non-transitory machine-readable storage medium encoded with instructions executable by a processor, the machine-readable storage medium comprising:

- instructions to vary a pressure in a print fluid path between a pump and a nozzle, the print fluid path comprising a pressure sensor, until an output of the pressure sensor stabilizes at a first output value;

- instructions to vary the pressure in the print fluid path until the output of the pressure sensor stabilizes at a second output value; and

- instructions to calibrate the printing system based on associating the first output value with a first known pressure value and the second output value to a second known pressure value.