Process

Abstract

The invention relates to a method for determining the concentration of a component in a fluid, such as a cooling lubricant or an HFC fluid, according to the transmitted light principle by means of a laser (22) of a measuring device using a refractometry, the method comprises at least the following method steps: predetermining a peak for the laser light received by refraction on the photodiode array (46) using a fluid to be uniformly transparent, and using an evaluation device (59) to adjust the duty cycle of the laser (22) and / or the current intensity for the laser (22) and / or the sensitivity of the photodiode array (46) such that the peak value remains constant despite the occurrence of an interference variable.

Description

Technical Field

[0001] The invention relates to a method for determining the concentration of a component in a fluid, such as a cooling lubricant or an HFC fluid, using refractometry. Background Art

[0002] DE 10 2010 028 319 A1 discloses a method for controlling the concentration of a cooling lubricant mixed with water for a machine tool, together with an associated device, which is used to measure both the refractive index of the cooling lubricant mixed with water and the electrical conductivity of the cooling lubricant mixed with water by refractometry and to combine the two measured values ​​obtained into a control variable, and to replenish water and / or cooling lubricant when the control variable differs from the setpoint value. In order to determine the refractive index of the cooling lubricant mixed with water, a digital refractometry method is used in the device, which has an LED as a light source and a CCD sensor as a detector. Summary of the invention

[0004] Starting from this prior art, the object of the present invention is to provide a relatively improved measuring method with which a plurality of disturbance variables which may occur during the measurement can be compensated.

[0005] This object is achieved in its entirety by a measuring method having the features of claim 1 .

[0006] The method according to the invention uses a laser of a measuring device for refractometry, which operates according to the transmission principle, and implements at least the following method steps:

[0007] - predetermining the peak value for the laser light received by refraction on the photodiode array by using a fluid to be uniformly transparent, and

[0008] - When using an evaluation device, by matching

[0009] - the duty cycle of the laser and / or

[0010] - the current intensity used for the laser and / or

[0011] - The sensitivity of the photodiode array

[0012] This results in the peak value being kept constant despite the presence of disturbance variables.

[0013] In this way, the concentration in the fluid can be determined more reliably even when different interference variables occur during the measurement. The laser used allows collimation, i.e. parallel orientation of the otherwise divergent laser beam, which results in improved measurement value resolution in the sensor device, which usually consists of a photodiode array, also known in the professional terminology as a "DiodeArray".

[0014] Within the scope of the method according to the invention, such interferences can be caused by turbidity of the fluid, which leads to a loss of intensity of the peak value of the received laser light on the photodiode array. Other possible interference variables are caused by finely dispersed particulate contamination, which is formed on the photodiode array by laser scattering to cause a broad intensity increase that is fanned out. Other interference variables are caused by larger particles or bubbles, which move with the fluid to be measured and cause a brief peak value of the measured value on the photodiode array, the measured value of which is smaller than the peak value measured when refracted through a homogeneous fluid.

[0015] A further interfering variable is formed by contamination on a laser-transmissive wall of the sample chamber, the method being carried out using said wall and along which a fluid flows, said wall and said contamination being passed through together by the laser light, said contamination being detected by the photodiode array by a displacement deviation relative to an adjusted peak at normal refraction.

[0016] Independently of the disturbance variables that occur in each case, these can be reliably detected with the measuring method according to the invention and compensated for by carrying out the method as described above.

[0017] In another preferred embodiment of the method according to the invention, it is provided that for a measurement run with the measuring device, the measuring device is calibrated to a predeterminable refractive index value using a reference fluid. Preferably, a reference fluid, such as water, is used for calibration, the refractive index properties of which are known.

[0018] In another preferred embodiment of the method according to the invention, it is provided that during the cleaning operation of the measuring device, the sample chamber is cleaned with the reference fluid, a comparison is made between the actual value and the setpoint value of the corresponding refractive index value, and possible deviations in the calibration are taken into account, and an error message is output if the deviation is too large. In this way, the calibration and the cleaning operation of the measuring device can be carried out together.

[0019] In another preferred embodiment of the method according to the invention, it is provided that the measuring device is monitored by a higher-level evaluation device, which preferably also performs control and / or regulation tasks in addition to the measured value detection, and which evaluates the measurement data of an externally connected additional measuring device, such as temperature, pressure, viscosity, conductivity, pH value, etc., and actuates external actuators, such as hydraulic pumps, valves, level switches, etc., as a function of the measured data obtained. In this way, a further automated operation of the measuring method can be achieved and a number of additional monitoring tasks can be included in the actuation of the processing machine as a consumer.

[0020] Preferably, for this purpose, provision is made for the measuring device to be connected to a bypass of a hydraulic supply circuit which supplies fluid to the hydraulic consumer, the measuring device being connected to the supply circuit or separated therefrom by means of a valve actuation system. In this way, the actual measuring method can be separated from the fluid supply of the consumers connected to the supply circuit using the corresponding measuring device, which helps to simplify the implementation of maintenance work.

[0021] In particular, the method according to the invention is advantageously characterized in that, in the absence of concentrate in the fluid, the concentrate is supplied to the supply circuit of the fluid by means of the supply device while monitoring the measuring device. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The method according to the invention is explained in detail below with the aid of an exemplary embodiment including a measuring device. In this case, in the drawings which are shown in principle and not to scale:

[0023] Figure 1 A longitudinal section showing the main components of the measuring device;

[0024] Figures 2 to 5 shows different possibilities for carrying out measurements according to the transmitted light principle;

[0025] Figure 6 , Figure 7 , Figure 8 and Fig.10 illustrating different types of operation of the measuring device with the aid of a flow chart; and

[0026] Fig. 9 Type of hydraulic circuit diagram showing the integration of measuring equipment into the hydraulic measuring and supply circuit. DETAILED DESCRIPTION

[0027] exist Figure 1The measuring device shown in the figure with its main system components is shown in a common operating state. The measuring device is used to determine the concentration of components in a fluid, such as a cooling lubricant or an HFC hydraulic fluid by refractometry. Hydraulic fluids are generally used to transfer energy to a hydraulic system in the form of volume flow and / or pressure within the scope of fluid technology. The relevant hydraulic oil is generally made based on mineral oil with corresponding additives. HFC belongs to hydraulic fluids that can be very flammable and generally has a water glycol and polyethylene glycol solution with a water content of more than 35%. The relevant HFC hydraulic fluid is generally configured for use in hard coal mining and in civil aviation. The hydraulic fluid is also obviously used in military vehicles, such as armored vehicles, which may be subjected to shooting due to hostile effects. Cooling lubricants or cooling lubricating materials reduce friction by lubrication and thus reduce tool wear, workpiece heating and energy requirements in cutting processing. In both cases, the specified concentrations of HFC and cooling lubricants are maintained to ensure functionally reliable operation. In this regard, the measuring device according to the present invention is used to maintain the corresponding concentration.

[0028] The fluid to be measured by means of the measuring device is guided through a sample chamber 10 which is connected to a fluid inlet 12 and a fluid outlet 14. Possible flow directions are Figure 1 The inlet 12 and the outlet 14 are indicated here by arrows. Both the fluid inlet 12 and the fluid outlet 14 are connected to a fluid supply circuit 16 in a conventional manner, as shown in the example of FIG. Fig. 9 Depicted in.

[0029] The original sample chamber 10 defines a rectangular parallelepiped-shaped chamber volume with a flat extended structure and extends toward Figure 1 The sample chamber 10 is bounded from the top by a transparent glass wall 18, which is usually composed of a thin-walled rectangular glass plate, and the sample chamber is bounded by a square sealing ring upward and downward relative to the adjacent housing parts of the measuring device on the outer peripheral side, so as to reliably prevent the fluid from undesirably flowing out of the sample chamber 10 into the surrounding environment. The laser 22 is connected to the sample chamber 10 laterally and is placed in the device housing 20 of the measuring device. The upper laser emission surface of the laser is emitted in the direction of the sample chamber 10 into the inclined channel 24 that guides the fluid. In this way, the beam of the light source (here in the form of a laser 22) traverses the sample chamber 10 with the corresponding fluid, and the relevant beam thereby obtains a first refraction n, which will be explained in detail below. In this regard, the refracted beam is detected by a sensor device 26 outside the sample chamber 10. The sensor device 26 has a photodiode array as a photosensor, which is also called a diode array in professional terms. In this context, CCD sensors can also be used, but also CMOS sensors, which as light-sensitive electronic components are based on internal light effects and are freely available on the market in many embodiments.

[0030] If also from Figure 1 As can be seen, the light source in the form of a laser 22 is statically accommodated at one end in an associated accommodation chamber 28 in the device housing 20, so that before the fluid enters the actual sample chamber 10, an exit cross section for the laser beam is flowed through by the fluid, which flows from a horizontally extending line section 30 into the inclined channel 24 parallel to the longitudinal orientation of the sample chamber 10. The line section is oriented in the direction of Figure 1 The right side of the pipe is closed by a plug 32 when viewed from the right side, and the pipe sections 34 and 36 extending vertically from the bottom otherwise open into the associated horizontal pipe section 30, which is located in the direction of the Figure 1 The horizontal line section 30 continues to extend to the right behind the stopper 32 and leads to a vertical line section 36, to which the fluid outlet 14 is connected. Conversely, the fluid inlet 12 leads from the left into the vertical line section 34 to transport the fluid into the sample chamber 10. The horizontal line section 30 continues to lead to the right via the vertical line section 36 and is closed here by a sensor 38, which can be composed of a measuring device for parameters such as pressure, temperature, viscosity, pH value, conductivity, for example. Here, a sensor 38 that can measure two or more different parameters can also be used. Temperature measurement is necessary for temperature compensation of refractometry.

[0031] If you can also Figure 1 As can be seen from the results, the light emission of the light source in the form of a laser 22 takes place at an angle of inclination of approximately 40° to the horizontally extending fluid flow direction in the sample chamber 10. The rectangular surface extension of the sensor device 26 is selected at least in its position relative to the light source so that the light source is preferably surrounded by the sensor device 26 all the way around, both in the preferred transmitted light method here and also when the light beam is incident at different angles. In order to calibrate the measuring device and in particular to adapt the sensor device 26 to the actual measurement situation within the measuring device, the measuring device is based on Figure 2 The illustration can be arranged both horizontally and vertically relative to the light emission point of the laser 22. For this purpose, it is sufficient to loosen and retighten the screws of the adjustment device 40, to which the sensor device 26 is fixed and by means of which the sensor device can be positioned relative to the fixedly arranged sensor housing 42. In this regard, the sensor housing 42 is connected to the upper side of the device housing 20 as a component of the overall housing. In particular, the plate-shaped sensor device 26 opens into a square sensor cavity 44 of the sensor housing 42, which can be provided with gas and thus fill the spatial distance between the sample chamber 10 with its light-transmissive wall 18 and the exposed sensor surface 46 of the sensor device 26. For a simpler illustration, in Figure 1, laser 22 and a sensor in the form of device 26 and corresponding measuring device 38 are shown without associated wiring. Depending on the wavelength and the range of refractive indices at which sensor device 26 is to be supplied, other working gases, for example in the form of xenon, can also be accommodated in sensor chamber 44 instead of air. Figure 1 As seen in an imaginary vertical projection within the drawing plane of , the light source in the form of a laser 22 is arranged at the beginning of the sample chamber 10 and the starting point of the sensor device 26 is arranged at the end of the sample chamber 10. This results in particularly good measurement value detection in the entire area, and due to the inclined arrangement of the laser 22, a good diffraction pattern or interference pattern is obtained when penetrating the fluid in the sample chamber 10, and in addition, due to the inclined angle of incidence of the laser beam on the sensor surface 46, the installation space for the sensor housing 42 and therefore for the entire measuring device can be kept small, so that the measuring device can be installed even when the space conditions are limited. This also makes it easier to retrofit an already existing installation with a measuring device.

[0032] The channel sections 34, 36 extending between the fluid inlet 12 and the fluid outlet 14 are in this respect at least partially designed as a fluid channel 48 in the supply housing 50. In this way, the overall housing of the device is assembled from individual housing parts, in particular the supply housing 50 comprising a component with the fluid channel 40, the device housing 20 with the light source (here in the form of a laser 22) and the sensor housing 42 with the sensor device 26. In this way, a modular design of the overall housing for the measuring device is obtained, which allows the measuring device to be connected to different machines and device parts by matching the individual components.

[0033] As already mentioned at the beginning, the measuring device is part of a fluid supply circuit 16, and the fluid supply circuit can be connected to a pressure supply device, such as a hydraulic pump P1, via a switchable valve V1. The associated motor-driven hydraulic pump P1 extracts a fluid, such as a cooling lubricant or HFC fluid, from a storage tank CM1 and supplies it hydraulically to a conventional processing machine BM as a consumer. The processing machine BM is connected to the fluid line between the hydraulic pump P1 and the switchable valve V1 via a branch 52 on its input side. The output side of the processing machine BM leads to a return line at a branching point 54, which is connected to the fluid output end in the form of a fluid outlet 14 in the supply housing 50 of the measuring device and leads to the storage tank CM1. A further switchable valve V2 is arranged in the mentioned section of the return line between the fluid outlet 14 in the supply housing 50 and the branching point 54, into which the output side of the processing machine BM leads. Furthermore, a third switching valve V3 and a fourth switching valve V4 are connected to the inflow line to the fluid outlet 12 and the return line from the fluid outlet 14 , respectively, and are used to introduce the cleaning medium DL into or out of another storage tank CM2 .

[0034] A control line 56 for transmitting the measurement data extends between the processing machine BM and a measuring device, the housing of which is located at Fig.10 The control lines are shown in the figure with housing parts 20, 42 and 50, and the control lines can realize a cleaning process according to the machine status and / or the measuring device status. The measured parameter detection at least partially realized by the sensor 38 transmits its measured data via an additional measuring line 56 to a processor control system 59 (not shown in detail) as a higher-level system, such as in Fig.10 In addition to the usual measured values ​​of pressure, temperature and viscosity, there is also the possibility of measuring the pH value of the fluid and its conductivity via sensor 38 or other sensors 1, 2, ... x (not shown). Fig. 9Starting from another control line 60, the measuring device can control another fluid pump P2, which, when necessary, extracts the missing concentrate detected by means of the measuring device from the concentrate container CM3, the liquid level in the concentrate container CM3 being monitored by means of a level switch 62, which is coupled to the processor control system 59 of the measuring device by means of another measuring line 64. If, therefore, it is to be determined within the scope of the refractometry performed with the aid of the measuring device that a lubricant component is missing in the scope of the cooling lubricant supply for the processing machine BM or that HFC is missing in the scope of the HFC hydraulic fluid supply, then the missing component can be introduced into the reserve tank CM1 via the concentrate container CM3 by controlling the supply pump P2, and the correctly enriched cooling lubricant amount or HFC fluid reaches the processing machine BM again, and the refractometry measurement is continued within the scope of the enrichment with the aid of the measuring device. Fig.10 The actuators denoted by external actuators 1 , 2 , . . . y in the drawings are in particular components P1 and P2 and valves V1 , V2 , V3 , V4 etc.

[0035] If dirt occurs, in particular with respect to the sample chamber 10, the supply circuit 16 can be blocked by means of the valves V1, V2 and the sample chamber 10 can be cleaned by introducing a suitable cleaning medium DL, including compressed air, by opening the valves V3 and V4 and thus washing away the particle dirt, which is then received in the storage tank CM2 for further processing or disposal. After the cleaning process has been carried out, the valves V3 and V4 can then be returned to their original positions in a spring-actuated manner. Fig. 9 In the initial position shown in , ie moved into its blocking position and after reopening of valves V1 and V2 , the measuring device is used again for refractometric measurements with the fluid supply circuit 15 connected.

[0036] The measuring device according to the invention is explained in greater detail below with reference to an associated measuring method. Figure 2 Such a measurement based on the transmitted light principle is shown here in principle. Figure 1 The laser 22 shown in FIG. 7 emits a collimated laser beam 70 which undergoes a first refraction n1 at the boundary surface of the sample chamber 10 to the glass wall 28. A second refraction n2 then takes place at the glass wall 28 in the form of a conventional glass plate. Figure 2 The signal curve of the linear array or sensor surface 46 in liquids of different concentrations is described. If a vertical adjustment is to be carried out to change the vertical distance between the sensor surface 46 and the glass wall 28, an adjustment possibility for the sensitivity is obtained. If the sensor surface 46 can be moved horizontally, the measurement value range can be adjusted. Figure 2In the principle diagram of the measured value detection together with the curve shown, a homogeneous fluid in the sample chamber 10 is investigated, but turbid fluids can also be checked. This is possible in principle because laser diodes or lasers 22 with different intensities are controllable on the control and / or regulating device side, which is not shown in detail in the form of a processor control system 59. However, it is preferred that the laser 22 adjusts the intensity autonomously.

[0037] exist Figure 3 1 shows by way of example a measured value curve of the turbidity of the fluid in the sample chamber 10, the thick solid measured value curve showing the initial measured value curve and the thin measured line relating to the intensity loss due to the turbidity of the fluid. In order to re-reach an earlier peak detection despite the intensity loss, according to Figure 3 The thick solid curve shown requires an adaptation of the laser 22, for example within the scope of adapting the duty cycle or the discharge ratio (also known in technical terms as "duty cycle"), or by increasing the current intensity for the laser diode. Another adaptation possibility is to change the image refresh rate or the refresh rate, also known in technical terms as the shutter frequency, at the photodiode array or diode array in the form of the sensor device 26. The relevant adaptation of the laser intensity or the detector sensitivity with respect to the possible turbidity of the fluid present in the sample chamber 10 is shown, for example, in Figure 6 In order to implement the relevant setting cycle, at least as an input prerequisite, a peak value determination is performed as a reference, that is, when using a fluid in the sample chamber 10 that is to be uniformly transparent to light, a peak value for the light received by refraction on the photodiode array (DiodenArray) in the form of the sensor device 26 is predetermined, as in Figure 2 The actual refraction of turbidity in the case of output values ​​is based on Figure 7 The representation of is obtained by measuring the variable detection in terms of the duty cycle and the current intensity for the laser 20, including the determination of the shutter frequency of the diode array of the sensor device 26. In this way, interference variables arising due to turbidity can be compensated within the scope of conventional measurements.

[0038] In addition to the aforementioned turbidity, according to Figure 4 As shown in the illustration, other possible interfering variables in the fluid of the sample chamber 10 may also include contaminants, for example in the form of finely dispersed particles 72, such as may usually occur in emulsions, or in the form of larger particles 74 including bubbles in the moving volume flow within the sample chamber 10. Figure 4The leftmost figure shows how the measured value curve is derived from the broad intensity increase caused by the scattering of the laser light by finely dispersed particles 72 in the fluid flow, and how it is derived from the average peak 78 of the measured value curve with zeros rounded off within the range of the usual refraction n1 by the fluid and the usual refraction n2 by the glass plate. A clear difference is the short-term sharp peaks with different intensities caused by the particles 74 or gas bubbles mentioned, which are derived from the changed refraction. The relevant interfering variables can also be compensated by their separate detection and do not interfere with the determination of the concentration of the fluid used with the measuring device.

[0039] according to Figure 5 The diagram of relates again to different disturbance variables in the context of concentration measurement, wherein transparent planar dirt with a changed refractive index n3 appears on the glass wall 18 with a refractive index n2. Figure 5 The peak curve on the sensor surface 46 (diode array) is shown as a dashed line (without dirt 82), and the right curve shows the evaluation with dirt applied to the glass pane 18. Figure 5 The two peak curves of equal measured value magnitude shown in are shifted horizontally by a value Δx, which can be evaluated and thus allows inferences to be drawn about the degree of contamination 42 on the glass plate 18. In this respect, these interfering variables can also be recalculated within the scope of the fluid concentration determination.

[0040] In the case of all the above-mentioned interfering variables such as the disturbance of the fluid, particle contamination or impurities of the glass wall 108, the above-mentioned Fig. 9 The cleaning process described in Figure 8 Here, the measuring and cleaning process can in principle be carried out as follows:

[0041] AUF = Flow to the measuring device is established by opening valves V1 and V2.

[0042] MES = measurement 1 at a defined time (fluid = cooling lubricant or HFC)

[0043] ZU = Stop the inlet flow to the measuring device by closing valves V1 and V2

[0044] SP1 = Start the cleaning process by opening valves V3 and V4

[0045] SPÜ = Clean the sample chamber at a defined time 10

[0046] SP2 = Terminate the cleaning process, valves V3 and V4 remain open

[0047] KAL = measurement at a defined time 2 (fluid = cleaning fluid, water or ventilation)

[0048] AUS = evaluate measurement 2 in KAL and signal (measurement ok, recalibration, maintenance required)

[0049] SP3 = Shut off valves V3 and V4

[0050] The refractometer described above for measuring the concentration of a coolant or HFC fluid or a concentrate of another fluid whose component concentration is to be monitored performs individual discrete measurements for determining the refractive index between 0 and 25% Brix (refractive index value) for the concentration of the coolant and for determining the refractive index between 30% Brix and 50% Brix for the concentration of the HFC. Within the scope of self-diagnosis, there is the possibility of regularly performing an internal check of the sensor device 26 with regard to the validity of the measured data. If, for example, no peak (hot spot) can be detected on the diode array or the sensor surface 46 due to excessive turbidity in the fluid, the sensor device 26 should no longer emit measured values ​​and this should be displayed via the condition of the sensor device 26.

[0051] Furthermore, the measuring device enables so-called online calibration. After cleaning the sample chamber 10 or the measuring cell, a reference measurement is carried out in water or air. If deviations from the expected values ​​for the cleaning fluid are measured, the sensor device 26 is automatically recalibrated. For this purpose, the measured value with the cleaning fluid is used as the new zero point. In addition, a warning "clean the refractometer" or the like is issued. By evaluating the deviations from the initial values ​​at startup, it is also possible to calibrate the sensor device 26 according to the method described in the previous section. Figures 2 to 5 The embodiment of the invention foresees the replacement of the laser 22 and / or the glass wall 18 in the form of damage to the glass sheet. This therefore has no counterpart in the prior art.

Claims

1. A method for determining the concentration of a component in a fluid, such as a cooling lubricant or HFC fluid, by means of a laser (22) of a measuring device according to the transmitted light principle using refractometry, the method comprising at least the following method steps: - when using a fluid that is uniformly transparent to light, a peak value for the laser light received by refraction on the photodiode array (46) is predetermined, and - by matching when using the evaluation device (59) - the duty cycle of the laser (22) and / or - the current intensity used for the laser (22) and / or - Sensitivity of the photodiode array (46) This results in the peak value being kept constant despite the presence of disturbance variables.

2. The method according to claim 1, characterized in that The interference variable is formed by the turbidity of the fluid, which leads to a loss of intensity of the received laser light peak at the photodiode array (46).

3. The method according to claim 1 or 2, characterized in that: The interference variable is formed by finely dispersed particle dirt, which is formed by laser light scattering on the photodiode array (46) to cause a broad intensity increase.

4. The method according to any one of the preceding claims, characterized in that The interference variable is formed by relatively large particles (74) or bubbles which move together with the fluid to be measured and cause a brief peak in the measured value on the photodiode array (46), the measured value of which is smaller than the peak measured when refracted through a homogeneous fluid.

5. The method according to any one of the preceding claims, characterized in that The interference variable is formed by contamination on the laser-transmissive wall (18) of the sample chamber (10), along which the fluid flows, the wall and the contamination being penetrated together by the laser light, the contamination being detected by the photodiode array (46) by a displacement deviation (Δx) relative to an adjusted peak value at normal refraction.

6. The method according to any one of the preceding claims, characterized in that For a measurement operation with the measuring device, the measuring device is calibrated to a predeterminable refractive index value (Brix) using a reference fluid.

7. The method according to any one of the preceding claims, characterized in that In a cleaning operation of the measuring device, the sample chamber (10) is cleaned with the reference fluid, a comparison is made between the actual value and the setpoint value of the corresponding refractive index value (Brix), possible deviations in the calibration are taken into account, and an error message is output if the deviation is too great.

8. The method according to any one of the preceding claims, characterized in that The measuring device is monitored by an upper-level evaluation device (59), which evaluates the measurement data of the externally connected additional measuring device (38), such as temperature, pressure, viscosity, conductivity, pH value, etc., and controls external actuators such as hydraulic pumps (P1, P2), valves (V1, V2, V3, V4), liquid level switches (62), etc. based on the obtained measurement data.

9. The method according to any one of the preceding claims, characterized in that The measuring device is connected to a bypass of a hydraulic supply circuit (16) which supplies a hydraulic consumer (BM) with fluid and is connected to or separated from the supply circuit (16) by means of a valve actuation system (V1, V2).

10. The method according to any one of the preceding claims, characterized in that In the absence of concentrate in the fluid, the concentrate is introduced into the fluid supply circuit (16) by means of a supply device (P2, CM3).

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