IONIZER AND METHOD FOR NEUTRALIZING CHARGES ON SURFACES

Description

[0001] The present invention relates to an ionizer for neutralizing charges on surfaces, in particular an ionizer based on alternating voltage. According to a further aspect, the invention relates to a method for neutralizing charges on surfaces, in particular using alternating voltage.

[0002] The charging and discharging of bodies with static electricity is a phenomenon that can occur in all industrial sectors. Electrostatic charging occurs in particular through the sudden separation of two boundary layers, allowing electrons to jump from one body to the other. When two atoms collide with their shells, for example, briefly touching and then quickly separating, electrons jump from one atom to the other. This process, known as charging, upsets the neutral state of the atoms. Negatively or positively charged surfaces can result. Atoms with an excess of positive or negative charges always try to return to their neutral state, e.g., by repelling the excess charge in a process also known as "discharging."

[0003] Spontaneous and uncontrolled discharges can cause significant problems. For example, they can disrupt manufacturing processes, especially if material webs accidentally stick together due to the electrostatic charge. There are even more serious consequences: electrical devices can be damaged if the discharge occurs through them. Finally, uncontrolled discharges can lead to fires, especially when processing highly flammable materials.

[0004] To avoid the problems mentioned above, controlled discharge must be ensured. Discharge devices for the contactless reduction of electrostatic charges on electrically insulating materials are well known and used in many production processes.

[0005] For example, the document DE 19 710 984 C1 relates to an active ionizer which ionizes the surrounding air by applying high voltage to emission electrodes, whereby the free electrons and gas ions thus generated are attracted by the electric field of the charged material, so that they contribute to its neutralization.

[0006] US 4271451 A, DE 3324589 A1 and DE 1589781 A1 each disclose an ionizer according to the preamble of independent claim 1.

[0007] In the prior art arrangements, the ionization of the air by the electrode usually occurs independently of the degree and / or polarity of the material charge on the surface to be treated. Accordingly, it is not possible, or not readily possible, to achieve surfaces with residual charges of + / -10V with the prior art arrangements.

[0008] Based on the above-mentioned problem, the present invention is based on the object of specifying an ionizer and a method for neutralizing charges on surfaces with which particularly low residual charges, in particular below + / - 10V, can be achieved without increasing the manufacturing costs.

[0009] This object is achieved according to the invention by the subject matter of the independent patent claims 1 and 10, wherein advantageous developments of the invention are specified in the corresponding dependent patent claims.

[0010] Accordingly, the invention relates to an ionizer for neutralizing charges on surfaces, wherein the ionizer has an alternating voltage source comprising an output that outputs a waveform with a positive half-wave and a negative half-wave. The ionizer further comprises a transformer with a primary side and a secondary side, wherein the primary side is electrically connected or connectable to the output of the alternating voltage source. The ionizer has a discharge device that is electrically connected or connectable to the secondary side of the transformer, and a control device for adjusting the waveform. The control device is designed to control the waveform such that the positive and negative half-waves are asymmetrical to one another.

[0011] By asymmetrically adjusting the waveform on the primary side of the transformer, the number of ions generated at the electrode can be easily adapted to the surface to be treated. In particular, the asymmetric design of the waveform allows a higher number of positive ions or negative ions to be generated, depending on the surface charge. Accordingly, the amount of positive and negative ions generated by the waveform at the at least one electrode can be adapted to the static charges of the surface to be neutralized. For example, if there is an excess of positive static charge on the surface, the waveform can be modified such that more negative ions are released at the discharge electrode to compensate for the excess of positive static charges on the surface.The opposite is the case when an excess of negative charges on the surface needs to be compensated.

[0012] By providing an asymmetric waveform on the primary side of the transformer, hardware waveform adjustment on the secondary side of the transformer is eliminated. This eliminates the need for additional hardware. Furthermore, there are no hardware limitations for optimizing the ion balance on the surface being treated.

[0013] Overall, the ionizer according to the invention enables a particularly efficient, active neutralization of surface charges, so that residual charges in the range of less than + / -10 volts can be achieved.

[0014] According to a further embodiment, the control device is designed to reduce an amplitude of the positive half-wave and / or the negative half-wave provided by the alternating voltage source. Such a change in the amplitude of the positive or negative half-wave is a particularly effective way to control the ions generated at the electrode. This is particularly the case because ions are typically generated at an electrode above a certain voltage value, for example 4 kV, as will be explained in more detail later. Accordingly, the control device can be designed to reduce the amplitude of the positive half-wave when there is an excess of positive charges on the surface. The same applies to reducing the amplitude of the negative half-wave.This can be reduced if a smaller number of negative ions is required, for example if the surface to be treated has an excess of negative charge carriers.

[0015] According to a further embodiment, the control device is designed to flatten a voltage rise during the positive and / or negative half-wave, at least in some regions. In other words, the control device can be designed to lengthen or shorten one of the two half-waves compared to the other. By means of such a steeper or flatter voltage rise, it can be easily achieved that the amplitude of the positive and negative half-waves is different. The electrical work performed during the positive and negative half-waves remains unchanged despite the different amplitudes.

[0016] According to the invention, the AC voltage source comprises an inverter connected to the primary side of the transformer. The control device is designed to control the waveform by controlling the inverter. In an alternative embodiment not part of the invention, however, the control device can be designed to directly control an AC voltage source designed as a power supply, so that an asymmetrical waveform is output.

[0017] According to a further embodiment, the control device is configured to receive surface charge data indicative of the electrical charges present on a surface to be treated. The control device is further configured to control the waveform based on the surface charge data. According to this embodiment, the ionizer is dynamically adaptable to the electrical charges present on the surface to be treated. For example, if there is an excess of positive charges on the surface to be treated, the waveform can be changed such that a plurality of negative ions are generated at the electrode.

[0018] The surface charge data may include one or more of the following data: Positive ion data indicates a quantity of positive charges on the surface to be treated; negative ion data indicates a quantity of negative charges on a surface to be treated.

[0019] The positive ion data can be determined by a measuring device located on the secondary side of the transformer for measuring the amount of positive electricity and transmitted to the control device. The negative ion data can be determined by a corresponding measuring device located on the secondary side of the transformer and designed to determine the amount of electricity of negative charges.

[0020] According to a further embodiment, the control device is designed to: Determining a number of positive charges on the surface to be treated based on the positive ion data; determining a number of negative charges on the surface to be treated based on the negative ion data; determining a difference between the number of positive and negative charges on the surface to be treated; checking the waveform based on the difference between positive and negative charges.

[0021] According to this embodiment, the waveform for generating the ions can be precisely adapted to the number of positive and negative charges on the surface to be treated, so that a particularly low residual charge value can be achieved.

[0022] According to a further embodiment, the control device is designed to: Comparing the difference between the number of positive and negative charges on the surface to be treated with a first threshold value; reducing the amplitude of the positive half-waves of the waveform if the difference exceeds the first threshold value.

[0023] According to a further embodiment, the control device is designed to: Comparing the difference between the number of positive and negative charges on the surface to be treated with a second threshold value; reducing the amplitude of the negative half-waves of the waveform if the difference is below the second threshold value.

[0024] According to the above-mentioned embodiments, the negative or positive half-wave of the waveform is only changed if the difference between the positive and negative charges on the surface to be treated exceeds / falls below a certain limit. Thus, an adjustment of the waveform is only necessary when significant charge differences on the surface occur, which can lead to more gentle use of the electrode.

[0025] In another aspect, the present invention relates to a method for neutralizing charges on surfaces, the method comprising: Providing an alternating voltage having a waveform with a positive half-wave and a negative half-wave; changing the provided alternating voltage into an input voltage using an inverter such that the input voltage has a positive and a negative half-wave that are asymmetrical to one another; converting the input voltage into an output voltage using a transformer; applying the output voltage to a discharge device.

[0026] According to a further embodiment, changing the provided AC voltage comprises reducing the amplitude of the provided positive half-wave and / or the negative half-wave.

[0027] According to a further embodiment, changing the provided alternating voltage, at least in some areas, comprises flattening a voltage increase during the positive and / or negative half-wave.

[0028] According to a further embodiment, the method further comprises: Receiving surface charge data indicative of the electrical charges present on a surface to be treated; modifying the provided waveform based on the surface charge data.

[0029] According to a further embodiment, the method further comprises: Determining a number of positive charges on the surface to be treated based on the positive ion data; determining a number of negative charges on the surface to be treated based on the negative ion data; determining a difference between the number of positive and negative charges on the surface to be treated; changing the provided waveform based on the difference between positive and negative charges.

[0030] According to a further embodiment, the method further comprises: Comparing the difference between the number of positive and negative charges on the surface to be treated with a first limit value and / or a second limit value; reducing the amplitude of the positive half-waves of the waveform if the difference exceeds the first limit value or reducing the amplitude of the negative half-waves of the waveform if the difference is below the second limit value.

[0031] Exemplary embodiments of the ionizer according to the invention and of the method according to the invention are described in more detail below with reference to the accompanying drawings.

[0032] They show: FIG. 1 shows a schematic view of a discharge device and a surface to be treated; FIG. 2 shows a schematic view of a substantially symmetrical waveform; FIG. 3 shows a schematic view of an embodiment of the ionizer according to the present invention; FIG. 4 shows a schematic view of a first waveform in which the amplitude of the positive half-wave has been reduced; and FIG. 5 shows a schematic view of a waveform in which the amplitude of the negative half-wave has been reduced.

[0033] Identical reference numerals refer to identical or similarly designed elements or features in the FIGS shown here.

[0034] FIG. 1 shows a schematic view of a discharge device 18 and a surface 10 to be treated. The surface 10 to be treated can, for example, be a material web that is wound up and unwound in rolls (not shown here). When winding up and unwinding material webs from such rolls, a separation of thin material layers from one another occurs, which can lead to a charging of the surface 10. In the embodiment shown here FIG. 1 As a result, positive charges 12 and negative charges 14 have accumulated on the material web 10.

[0035] As already mentioned above, the charges present on the surface 10 can cause disruptions to the manufacturing process and even fires. To prevent such discharges, FIG. 1 a discharge device 18 is shown, which can be part of an ionizer (not shown in full). The discharge device 18 is rod-shaped and has a plurality of discharge electrodes 20. Each of these discharge electrodes 20 is supplied with high voltage, so that a strong electric field is created at the tip-shaped electrode 20, through which positive or negative ions can be released. Ions released in this way are discharged onto the material web as an ion cloud in order to neutralize the charges 12, 14. The surface 10 shown as a material web can move, for example, in the direction of arrow 22 relative to the stationary discharge device 18.

[0036] The invention is not limited to a specific number of discharge electrodes or discharge devices. Rather, the ionizer of the present invention may comprise any number of discharge electrodes. In other embodiments, the discharge device comprises, instead of or in addition to the discharge electrodes, blowing heads or rotating nozzles connected to the ionizer's AC voltage source.

[0037] As the FIG. 1 As can also be seen, there is an imbalance of positive and negative charges 12, 14 on the surface 10 of the material web. In particular, the exemplary embodiment shown here shows an excess of positive charge carriers. To detect the positive and negative charges 12, 14, these can be measured, in particular, before the ionizer is put into operation. This embodiment is based on the consideration that the proportion of positive and negative charges changes only insignificantly in an established manufacturing process and thus a one-time calibration upon commissioning of the ionizer is generally sufficient.

[0038] Alternatively, a sensor device (not shown) can be provided, which continuously or at predetermined times detects the surface charge and communicates this to a blocking device. For this purpose, "field mill sensors" or "piezoelectric field sensors" can be used, which are aligned with respect to the surface 10 to be discharged in such a way that a measurement of the electrostatic field of the surface 10 is possible via the physical effect of "charging by induction."

[0039] According to the present invention, the type and amount of positive and negative ions emitted by the discharge device 18 can be quickly and easily changed. Accordingly, the ionizer of the present invention can be adapted to an excess of positive and / or negative charges 12, 14.

[0040] At the FIG. 1 The discharge device shown is a discharge device which is preferably supplied with an alternating voltage. A waveform 30 of an alternating voltage known from the prior art, which can be used to supply the discharge device 18, is shown in FIG. 2 shown. Waveform 30 from FIG. 2 is a symmetrical waveform, meaning the positive half-waves 32, 34, 36 are axially symmetrical with the negative half-waves 38, 40. Of course, a shift of π / 2 between the positive and negative half-waves 32, 34, 36, 38, 40 must be taken into account. Accordingly, in this description, the term "symmetrical" means that the positive and negative half-waves have essentially identical amplitude, width, and slope.

[0041] The FIG. 2 The positive half-waves 32, 34, 36 of the waveform 30 shown have an amplitude 42 of approximately 7 kV. The negative half-waves 38, 40 of the waveform 30 have an amplitude 44 of approximately -7 kV. If such a waveform 30 is applied to a discharge device 18 according to FIG. 1 applied, there is a substantially uniform production of negative and positive ions at the discharge device 18. Although an active discharge of the surface to be treated can be achieved with such a waveform 30, which is more effective than the discharge by passive discharge devices, particularly low residual charges of less than + / - 10 V cannot generally be achieved by such control.

[0042] FIG. 3 shows a schematic view of an embodiment of an ionizer according to the present invention. The ionizer 40 has an AC voltage source 42. The AC voltage source 42 has an output 41 that outputs a waveform with a positive half-wave and a negative half-wave. A transformer 44 has a primary side 43 that is or can be electrically connected to the output of the AC voltage source. The transformer 44 further has a secondary side 45 that is connected to an electrode 46 (such as one of the electrodes 20 in FIG. 1 ) is electrically connected or connectable.

[0043] The ionizer 40 further comprises a control device 48 for adjusting the waveform. In particular, the control device is designed to control the waveform on the primary side of the transformer. In the embodiment according to FIG. 3 For this purpose, the control device is connected to the AC voltage source 42. Accordingly, the control device 48 directly determines the waveform provided at the output of the AC voltage source.

[0044] In one embodiment, the AC voltage source 42 may include an inverter that is controllable by the control device 48.

[0045] The inverter can convert a DC voltage (not shown) provided to operate the AC voltage source 42 into an AC voltage with various waveforms. The control device 48 is configured to control which waveform is generated by the inverter.

[0046] In an alternative embodiment, which is not part of the present invention, the AC voltage source can be a power supply that is operated with an AC voltage, wherein the control device 48 is then designed to control the power supply such that a modification of the AC voltage applied to the input of the AC voltage source 42 is controllable. Thus, in this alternative, which is not part of the invention, the waveform provided at the output 41 of the AC voltage source 42 can also be adjusted by the control device 48.

[0047] According to the present invention, the control device is configured to control the waveform such that the positive and negative half-waves are asymmetrical to each other. In particular, the control device 48 can be configured to change the amplitude and / or the rise / fall of the positive and negative half-waves so that an asymmetrical waveform is formed. Examples of such modified, asymmetrical waveforms are FIGs. 4 and 5 can be found.

[0048] The control device 48 is designed to control the waveform at the output of the AC voltage source 42 based on the surface charge data. In particular, the control device can control a waveform according to Figur 4 If surface charge measurements indicate an excess of positive charge carriers on the surface, the control device 48 can set a waveform in the sense of Figur 5 set.

[0049] The control device 48 can be configured to determine a difference in the number of positive and negative charges on the surface based on surface charge data. For example, the difference can be a positive value if an excess of positive charge carriers is present. Accordingly, a negative difference value can indicate an excess of negative charge carriers on the surface. A difference value of essentially zero indicates a substantially neutrally charged surface.

[0050] The control device can control the waveform based on this difference. In this case, the control device 48 can be designed to compare the difference in the charge carriers on the surface to be treated with one or more limit values. In a first example, the control device 48 can be designed to compare the difference value with a first limit value. The first limit value can be a positive limit value. If the difference is positive (excess of positive charge carriers) and lies above the limit value, the control device 48 can reduce the amplitude of the positive half-wave of the waveform, as is the case, for example, in Fig. 4 is shown.

[0051] The control device 48 can be configured to compare the difference value with a second limit value. The second limit value can be a negative limit value. If the difference value is negative (excess negative charge carriers) and lies below the second limit value, the control device 48 can reduce the amplitude of the negative half-wave of the waveform, as is the case, for example, in Fig. 5 is shown.

[0052] Comparing the difference of charge carriers on the surface to be treated with one or more threshold values has the advantage that a change in the ions released by the ionizer electrode (i.e. a change in the waveform) is only made when significant charge differences on the surface have been detected.

[0053] FIG. 4 shows an example of a waveform 130, such as may be output according to the present invention on the secondary side 45 of the transformer 44. It should be noted that according to the embodiment in FIG. 3 The waveform is already provided at the output of the AC voltage source in the form shown here. Only the amplitude of waveform 130 is increased by transformer 44 compared to the signal provided at the output of the AC voltage source, as is well known.

[0054] The waveform 130 of the FIG. 4 is a waveform in which the positive half-waves 132, 134, 136 have been reduced in amplitude compared to the negative half-waves 138, 140. This can be particularly the case if the charges on the surface to be treated have an excess of positive charges. Compared to the FIG. 2 In the symmetrical waveform 30 shown, the negative half-waves 138, 140 are essentially unchanged. They still have an amplitude 144 of approximately 7 kV. Only the amplitude of the positive half-waves 132, 134, 136 of waveform 130 is reduced compared to the amplitude 44 of waveform 30. In particular, the positive amplitude 142 of waveform 130 is reduced to approximately 5.5 kV, whereby fewer positive ions are produced at the electrodes of the ionizer compared to the negative ions. This is the case because ions are typically only produced at the tip-shaped electrodes of the discharge device above a threshold voltage.

[0055] In the example according to the FIG. 4 An exemplary limit voltage of 4 kV is represented by the hatched discharge voltage ranges 150, 152, 154 on the positive half-waves 132, 134, 136 as well as the discharge voltage ranges 156, 158 of the negative half-waves 138, 140. Of course, the limit voltage also depends in particular on the arrangement of the discharge electrodes and can therefore vary considerably. As can be seen directly, the areas of the discharge regions 150, 152, 154 of the positive half-waves 132, 134, 136 are significantly smaller than the areas of the discharge regions 156, 158 of the negative half-waves 138, 140. In other words, a larger proportion of the electrical work generated by the negative half-waves 138, 140 is used to produce negative ions than is the case with the positive half-waves 132, 134, 136.

[0056] An adjustment of the amplitude, in particular a reduction of the amplitude, of the positive half-waves 132, 134, 136 is carried out according to the FIG. 4 by flattening the slope of the positive half-waves 132, 134, 136. In other words, the voltage rise in the positive half-waves 132, 134, 136 of the waveform 130 is slower than it is in the negative half-waves 138, 140. Thus, although the electrical work performed by the positive and negative half-waves is essentially identical, the slower rise and the associated broadening / lengthening of the positive half-waves 132, 134, 136 results in a reduction in the amplitude 142 of the positive half-waves 132, 134, 136.

[0057] Another embodiment of a waveform according to the present invention is shown in FIG. 5 The waveform 230 in FIG. 5 essentially corresponds to the FIG. 4 shown waveform 130, but mirrored about the zero axis. Accordingly, the waveform 230 is also FIG. 5 asymmetric. In contrast to the waveform 130 from FIG. 4 is the waveform 230 of the FIG. 5 not the amplitude 242 of the positive half-waves 232, 234, 236 is reduced. Rather, in waveform 230, the amplitude 244 of the negative half-waves 238, 240 is now reduced.

[0058] Similar to the waveform according to FIG. 4 the reduction of the amplitude 244 of the negative half-waves 238, 240 is carried out according to the FIG. 5 by reducing the slope of the negative half-waves 238, 240. The resulting amplitude 244 of the negative half-waves 238, 240 can have a value of approximately -5.5 kV, with the positive amplitude 242 of the positive half-waves 232, 234, 236 having a value of approximately 7 kV.

[0059] As already mentioned with regard to the FIG. 4As described above, the discharge voltage ranges 250, 252, 254 of the positive half-waves 232, 234, 236 also have a correspondingly larger area than is the case with the discharge voltage ranges 256, 258 of the negative half-waves 238, 240. It follows that a waveform 230 with negative half-waves of reduced amplitude is used in particular for the treatment of surfaces on which an excess of negative charge carriers is detected.

[0060] The invention is not limited to the embodiments shown in the drawings, but results from a combination of all features disclosed herein.

Claims

1. An ionizer (40) for neutralizing charges on surfaces, wherein the ionizer (40) comprises the following: • an AC voltage source (42) comprising an output which outputs a waveform (130, 230) having a positive half-wave (132, 134, 136, 232, 234, 236) and having a negative half-wave (138, 140, 238, 240); • a transformer (44) having a primary side (43) and a secondary side (45), wherein the primary side (43) is electrically connected to the output of the AC voltage source (42); • a discharging device (18) that is electrically connected to the secondary side (45) of the transformer; • a control means (48) for adjusting the waveform (130, 230), wherein the control means (48) is configured in order to control the waveform (130, 230) in such a way that the positive and negative half-waves (132, 134, 136, 138, 140, 232, 234, 236, 238, 240) are asymmetrical to one another, characterized in that the AC voltage source (42) comprises an inverter connected to the primary side (43) of the transformer, wherein the control means (48) is configured in order to control the waveform (130, 230) by driving the inverter.

2. The ionizer (40) according to claim 1, wherein the control means (48) is configured in order to reduce an amplitude of the positive half-wave (132, 134, 136, 232, 234, 236) and / or the negative half-wave (138, 140, 238, 240) provided by the AC voltage source (42).

3. The ionizer (40) according to claim 1 or 2, wherein the control means (48) is configured in order to flatten a voltage increase at least in regions during the positive and / or the negative half-wave (132, 134, 136, 138, 140, 232, 234, 236, 238, 240).

4. The ionizer (40) according to any one of claims 1 to 3, wherein the control means (48) is configured in order to: • receive surface charge data indicative of the electrical charges (12, 14) located on a surface (10) to be treated; • control the waveform (130, 230) based on the surface charge data.

5. The ionizer (40) according to claim 4, wherein the surface charge data comprises one or more of the following data: • positive ion data indicative of an amount of positive charges on the surface to be treated; • negative ion data indicative of an amount of negative charges on the surface to be treated.

6. The ionizer (40) according to claim 5, wherein the control means (48) is configured in order to: • determine a number of positive charges on the surface to be treated based on the positive ion data; • determine a number of negative charges on the surface to be treated based on the negative ion data; • determine a difference between the number of positive and negative charges on the surface to be treated; • control the waveform (130, 230) based on the difference between positive and negative charges.

7. The ionizer (40) according to claim 6, wherein the control means (48) is configured in order to: • compare the difference between the number of positive and negative charges on the surface to be treated with a first threshold value; • reduce the amplitude of the positive half-wave (132, 134, 136, 232, 234, 236) of the waveform (130, 230) when the difference exceeds the first threshold value.

8. The ionizer (40) according to claim 6 or 7, wherein the control means (48) is configured in order to: • compare the difference between the number of positive and negative charges on the surface to be treated with a second threshold value; • reduce the amplitude of the negative half-wave (138, 140, 238, 240) of the waveform (130, 230) when the difference falls below the second threshold value.

9. A method for neutralizing charges on surfaces, wherein the method comprises the following: • provision of an AC voltage having a waveform (130, 230) with a positive half-wave (132, 134, 136, 232, 234, 236) and a negative half-wave (138, 140, 238, 240); • change of the supplied AC voltage into an input voltage with the aid of an inverter such that the input voltage has a positive and a negative half-wave (132, 134, 136, 138, 140, 232, 234, 236, 238, 240) that are asymmetrical to one another; • conversion of the input voltage into an output voltage by means of a transformer; • application of the output voltage to a discharging device.

10. The method according to claim 9, wherein the change of the supplied AC voltage comprises a reduction of the amplitude of the supplied positive half-wave and / or the negative half-wave.

11. The method according to claim 9 or 10, wherein the change of the supplied AC voltage comprises, at least in regions, a flattening of a voltage increase during the positive and / or negative half-wave (132, 134, 136, 138, 140, 232, 234, 236, 238, 240).

12. The method according to claims 9 to 11, wherein the method further comprises: • receiving surface charge data indicative of the electrical charges located on a surface to be treated; • change of the supplied waveform (130, 230) based on the surface charge data.

13. The method according to claims 9 to 12, wherein the method further comprises: • determination of a number of positive charges (12) on the surface to be treated based on the positive ion data; • determination of a number of negative charges (14) on the surface to be treated based on the negative ion data; • determination of a difference between the number of positive and negative charges on the surface to be treated; • change of the supplied waveform (130, 230) based on the difference between positive and negative charges.

14. The method according to claim 13, wherein the method further comprises: • comparison of the difference between the number of positive and negative charges on the surface to be treated with a first threshold value and / or a second threshold value; • reduction of the amplitude of the positive half-waves of the waveform (130, 230) when the difference exceeds the first threshold value or reduction of the amplitude of the negative half-waves of the waveform (130, 230) when the difference falls below the second threshold value.