CN114458429A

CN114458429A - Calibration method for enhancing passive regeneration of particle catcher, calibration module and readable storage medium

Info

Publication number: CN114458429A
Application number: CN202011238599.4A
Authority: CN
Inventors: 吴淑梅
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 2020-11-09
Filing date: 2020-11-09
Publication date: 2022-05-10

Abstract

The present application relates to a calibration method for enhancing passive regeneration of a DPF (48) of an exhaust aftertreatment system, the system comprising a close-coupled aftertreatment system (20) having a first SCR (24) and an underground aftertreatment system (40) comprising the DPF (48) and a second SCR (44) located downstream of the DPF (48), the method comprising: based on NO in exhaust gas upstream from DPF (48)₂And concentration ratio of soot (R)_NO2/Soot) Soot level (L) inside DPF (48)_S) An upstream exhaust temperature (T) of the DPF (48)_48UP) A first step (S1) of determining a calibration factor (F) by querying a calibration factor table or curve; applying a calibration factor (F) to a first metered urea injection quantity (M) to be injected into exhaust gas upstream of the first SCR (24)_25ini) Thereby obtaining a first urea calibration injection quantity (M)_25cor) The second step (S2). The application also relates to a calibration module comprising a processor and a memory storing executable instructions, and a storage medium readable by the executable instructions, which when executed, cause a machine to perform the above calibration method.

Description

Calibration method for enhancing passive regeneration of particle catcher, calibration module and readable storage medium

Technical Field

The present application relates to the field of vehicle exhaust aftertreatment, and more particularly to a calibration method to enhance passive regeneration of a particulate trap (hereinafter, DPF) of an exhaust aftertreatment system (hereinafter, ATS for short). The application also relates to a calibration module and a readable storage medium for performing the method.

Background

To meet the increasingly stringent vehicle exhaust requirements of countries throughout the world, a variety of exhaust aftertreatment systems have been developed to reduce the NO emitted into the atmosphere by vehicles, particularly diesel vehicles_XAnd the amount of particulate matter.

To reduce to the maximum extentLittle NO emitted to the atmosphere_XThe exhaust aftertreatment system may include a cryogenic or Close coupled aftertreatment system (Close Couple ATS or cc-ATS) and a subterranean aftertreatment system (Under Floor ATS or uf-ATS), the cc-ATS being located upstream of the uf-ATS. The exhaust gas from the engine first enters the cc-ATS, and NO in the exhaust gas is reduced and eliminated by a first selective catalytic reduction device (SCR for short in the text) in the cc-ATS_XA fraction of the content. Wherein NO_XThe reduced exhaust then enters the uf-ATS where it is reduced by a second SCR to eliminate residual NO in the exhaust_XAnother or second fraction of the amount. The exhaust gas after the exhaust from the uf-ATS is directly discharged to the atmosphere, when the residual NO in the exhaust gas is present_XThe levels need to meet a specific level threshold corresponding to a specific emission requirement.

In addition to including the second SCR, the uf-ATS also includes a DPF for trapping, and thus removing, at least some or all of the particulates in the exhaust. It is well known that DPFs require removal of accumulated particulates by way of regeneration in order to ensure the ability or efficiency of the particulate trap to adsorb or trap particulates. Active regeneration of a DPF requires fuel injection into the exhaust gas and combustion of particulates with the aid of the fuel.

Currently, the amount of reductant-urea injected to the first SCR and the second SCR is typically based on NO in the exhaust entering cc-ATS and uf-ATS, respectively_XThe content is determined without taking into account the factors of DPF regeneration. It is desirable to be able to enhance passive regeneration of a DPF to reduce the need for active regeneration.

Disclosure of Invention

It is an object of the present application to enhance or promote passive regeneration of a DPF to reduce the need for active regeneration, saving fuel.

According to a first aspect of the present application, a calibration method for enhancing passive regeneration of a DPF of an exhaust aftertreatment system is provided, wherein the exhaust aftertreatment system comprises a close-coupled aftertreatment system having a first SCR and an underground aftertreatment system comprising the DPF and a second SCR located downstream of the DPF, the method comprising the steps of:

based on NO in exhaust gas upstream from DPF₂Concentration ratio of soot to soot, soot in DPFA first step of determining a calibration factor by looking up a calibration factor table or curve for the dust level, the upstream exhaust temperature of the DPF;

a second step of applying the calibration factor to a first urea metered injection quantity to be injected into exhaust gas upstream of the first SCR, resulting in a first urea calibration injection quantity;

a third step of obtaining an efficiency of the close-coupled aftertreatment system or a NOx content in the exhaust upstream of the underground aftertreatment system based on the first urea calibration injection amount;

a fourth step of determining a second metered injection amount of urea to be injected into the exhaust upstream of a second SCR of the underground aftertreatment system based on the efficiency or NOx content in the exhaust upstream of the underground aftertreatment system and an allowable NOx content threshold corresponding to a particular emission requirement;

a fifth step of determining whether the final NOx content in the exhaust gas emitted from the underground aftertreatment system is within an allowable NOx content threshold;

a sixth ending step when said final NOx content is less than or equal to an allowable NOx content threshold.

According to a second aspect of the present application, there is provided a calibration module comprising:

a processor; and

a memory storing executable instructions that, when executed, cause the processor to perform the calibration method described above.

According to a third aspect of the present application, there is provided a readable storage medium having stored thereon executable instructions that, when executed, cause a machine to perform the above-described calibration method.

As described above, according to the present application, NO that is reduced or removed by a selective reduction catalyst of a close-coupled aftertreatment system of the aftertreatment system is enabled by reducing a first urea injection amount_XReduced amount of NO in the exhaust gas entering the underground aftertreatment system_XThe amount is increased to facilitate passive regeneration of the particle trap, correspondingly reducing the number of active regenerations necessary or enabling active regeneration of the particle trapThe interval is lengthened, the fuel quantity required by auxiliary active regeneration is reduced, and the purpose of saving fuel is achieved.

Drawings

The above and other features and advantages of the present application will become apparent from the following detailed description, which proceeds with reference to the accompanying drawings.

FIG. 1 is a schematic simplified block diagram of a vehicle exhaust aftertreatment system of the present application;

FIG. 2 is a flow chart of a calibration method for enhancing passive regeneration of a particle trap of a subterranean aftertreatment system of a vehicle aftertreatment system according to an embodiment of the present application;

FIG. 3 schematically illustrates a schematic diagram of a calibration algorithm of the calibration method of FIG. 2;

fig. 4a and 4b are examples of a first sub-calibration factor table and a second sub-calibration factor table, respectively;

fig. 5 schematically shows a diagram of a calibration module for performing the method of fig. 2.

Detailed Description

The principles of the present invention are described in detail below with reference to the embodiments shown in the drawings. It will be understood by those skilled in the art that these examples are illustrative only and are not intended to limit the present invention in any way.

The present application is directed to an exhaust aftertreatment system including a low temperature or close coupled aftertreatment system (cc-ATS)20 and a subterranean aftertreatment system (uf-ATS) 40.

FIG. 1 shows a schematic simplified block diagram of an exhaust aftertreatment system according to an embodiment of the application. The figure shows a vehicle engine 10, with exhaust gases from the engine 10 flowing in a flow direction D in an exhaust pipe 15. The exhaust pipe 15 is provided with the exhaust gas post-treatment system. Herein, the direction in which the exhaust gas from the engine 10 flows in the exhaust pipe 15 is denoted by D (solid arrow), and the terms "upstream" and "downstream" used herein are both with respect to the direction D in which the exhaust gas flows in the exhaust pipe 15. For example, the arrangement of a first component upstream of a second component or a second component downstream of the first component in the exhaust aftertreatment system of the present application means that exhaust gas from the engine 10 enters the first component before entering the second component. In addition, it will be understood by those within the art that the terms "comprises" or "comprising" have an inclusive meaning that it may include additional unlisted items in addition to those that follow the term.

As shown in FIG. 1, the exhaust aftertreatment system of the present application includes a cc-ATS 20 having a first selective catalytic reduction device (SCR)24 and a uf-ATS 40 having a second selective catalytic reduction device (SCR) 44. The lower temperature exhaust gas produced at the initial start of the engine 10 is primarily treated by the cc-ATS 20, while the higher temperature exhaust gas produced at the normal operation of the engine is primarily treated by the uf-ATS 40. However, typically, the cc-ATS 20 and the uf-ATS 40 are active simultaneously, and the exhaust from the engine 10 first enters the cc-ATS 20 for partial NO by its first SCR 24_XThen, the exhaust gas from the cc-ATS 20, in which part of the NOx is reduced, re-enters the uf-ATS 40 for reduction of the remaining NOx by its second SCR 44, and finally the exhaust gas from the uf-ATS 40 is directly discharged to the atmosphere.

As shown in FIG. 1, in addition to including a first SCR 24, the cc-ATS 20 may also include a first oxidation catalyst (DOC) 22 located upstream of the first SCR 24 and a first Ammonia Slip Catalyst (ASC) 26 located downstream of the first SCR 24. In addition to including the second SCR 44, the uf-ATS 40 may also include a second oxidation catalyst (DOC) 42 and a diesel particulate trap (DPF) 48 located upstream of the second SCR 44 and a second Ammonia Slip Catalyst (ASC) 46 located downstream of the second SCR 44. The first DOC 22 and the second DOC 42 are respectively configured to convert carbon monoxide (CO), Hydrocarbon (HC), and nitrogen monoxide (NO) in exhaust gas flowing therethrough into harmless water (H) through oxidation reactions₂0) Carbon dioxide (CO)₂) And nitrogen dioxide (NO)₂). First and

second ASCs

26 and 46 are disposed downstream of first and

second SCRs

24 and 44, respectively, for reducing ammonia (NH) slip in the exhaust downstream of the SCRs via catalytic oxidation₃). The DPF 48 of the uf-ATS 40 is disposed between the second DOC 42 and the second SCR 44 for adsorbing and removing particulates from the exhaust gas flowing therethrough.

In the post-processing system of figure 1,further comprising injecting a reductant, such as urea, with NO in the exhaust upstream of the first SCR 24 of the cc-ATS 20_XChemical reaction occurs in the first SCR 24 to remove NO_XAnd injecting reductant upstream of the second SCR 44 of the uf-ATS 40 with NO in the exhaust_XChemical reaction occurs in the second SCR 44 to remove NO_XAnd a second urea metering and injection device 45. The first and second urea metering and

injection devices

25, 45 may be or include metering valves.

Although not shown in FIG. 1, those skilled in the art will appreciate that the exhaust aftertreatment system of the present application further includes one or more sensors for measurement purposes, including, for example and without limitation, one or more temperature sensors for measuring the temperature of the exhaust gas at one or more locations in the exhaust pipe 15, measuring NO in the exhaust gas at one or more locations in the exhaust pipe 15_XConcentration of one or more NO_XConcentration sensors, etc. In one embodiment, the exhaust aftertreatment system may include measuring the temperature and NO of the exhaust as it exits engine 10_XTemperature sensor of concentration and NO_XA concentration sensor; temperature and NO of exhaust gas discharged from cc-ATS 20_XTemperature sensor of concentration and NO_XA concentration sensor; and NO when the exhaust is ultimately exhausted from the aftertreatment system of the present application to the atmosphere, i.e., out of the uf-ATS 40_XA concentration NOx concentration sensor. Of course, it may also be provided to measure the temperature, O, of the exhaust gas entering and exiting any component (first DOC 22, first SCR 24, first ASC 26, second DOC 24, second SCR 44, second ASC 46, DPF 48, etc.) as desired₂Concentration or NOx concentration, ammonia concentration, particulates, etc.

The present application takes into account the effect of NOx content in the exhaust gas on passive regeneration of the DPF 48 provides a novel calibration method to enhance the passive regeneration of the DPF 48 of the uf-ATS 40 and thus reduce the active regeneration process by varying the amount of urea injected by the first urea dosing and injection device 25 into the exhaust gas upstream of the first SCR 24 of the cc-ATS 20. Specifically, the present application assigns a calibration factor F to the urea injection amount determined by the first urea dosing and injection device 25. Fig. 2 shows a flow chart of the calibration method, and fig. 3 schematically shows a schematic diagram of a calibration algorithm of the calibration method of the present application. The calibration method of the present application for enhancing the passive regeneration of the DPF 48 of the uf-ATS 40 is described below in conjunction with FIGS. 2 and 3.

The calibration method of the present application basically includes the step S1 of determining a calibration factor F and applying the calibration factor F to the first urea metered injection quantity M_25iniTo correct it at step S2. Here, the first urea metered injection quantity M_25iniThe determination may be based on: NO in the exhaust upstream of cc-ATS 20_XContent N_20UP(ii) a Temperature T of exhaust gas upstream of first SCR 24_24UP(ii) a And other parameters including the amount FL of exhaust gas discharged from the engine 10. Herein, exhaust upstream of a component refers to exhaust entering the component; exhaust downstream of a component refers to exhaust emitted from the component.

Step S1, in which the calibration factor F is determined, is based on NO in the exhaust gas upstream from the DPF 48₂And the content ratio R of smoke_NO2/SootSoot level L inside DPF 48_SAnd the upstream exhaust temperature T of the DPF 48_48UPObtained by looking up a calibration table or calibration curve.

Wherein the soot level L in the DPF_SRefers to the amount of soot that has accumulated within the DPF. Firstly, obtaining the total Soot level or amount discharged by an engine by inquiring a calibration table or a curve based on the rotating speed of the engine and the amount of fuel injected into the engine; engine-based exhaust gas quantity FL and exhaust gas temperature T upstream of second DOC 42_42UPThe first Soot amount consumed by the passive regeneration of the DPF 48 is obtained through a lookup table calibration table or a curve according to the equal parameters; o in the exhaust upstream based on DPF 48₂Concentration, engine exhaust gas quantity FL and upstream exhaust gas temperature T of DPF 48_48UPThe second Soot amount consumed by the DPF 48 in the active regeneration is obtained by inquiring a calibration table or curve according to the equal parameters, and then the first Soot amount and the second Soot amount consumed by the DPF 48 are subtracted from the total Soot level or amount to obtain the Soot level L in the DPF 48_S。

Wherein, the calibration table or calibration curve is obtained by recording and summarizing according to experiments and preparing a calibration factor table or curve.

As described above, the calibration factor F is based on R_NO2/Soot、L_SAnd T_48UPThree parameters are determined, and therefore, the calibration table or calibration curve may be a three-dimensional table or curve based on the three parameters.

Alternatively, for easier illustration and operation, two-dimensional tables may be used, i.e., a first factor F1 is obtained based on two of the three parameters, a second factor F2 is obtained based on two different parameters of the three parameters, and then a calibration factor F, e.g., a calibration factor F equal to the product of the first factor F1 and the second factor F2, is obtained by the first factor F1 and the second factor F2. Both the first factor F1 and the second factor F2 are in the range of 0 and 1, so the calibration factor F is a value not less than 0 and not more than 1.

FIGS. 4a and 4b show soot levels L based on the inside of the DPF 48_SAnd exhaust temperature T upstream of DPF 48_48UPAn exemplary first sub-calibration factor table of calibrated first factors F1, and based on R_NO2/SootAnd exhaust temperature T upstream of DPF 48_48UPAn exemplary second sub-calibration factor table of calibrated second factors F2. For example, when the soot level L in the DPF 48_S20g, exhaust temperature T upstream of DPF 48_48UPA first factor F1 of 0.14 at 300 ℃; when R is_NO2/Soot50, exhaust temperature T upstream of DPF 48_48UPThe second factor F2 was 0.07 at 300 deg.C, at which time the calibration factor F was 0.0098.

At this time, the step S1 of determining the calibration factor F includes:

step S11, obtaining soot level L in DPF 48_SAnd exhaust temperature T upstream of DPF 48_48UPAnd consults the first sub-calibration factor table of FIG. 4a to determine a first factor F1;

step S12, obtaining the R_NO2/SootAnd exhaust temperature T upstream of DPF 48_48UPAnd consults the second sub-calibration factor table of FIG. 4b to determine a second factor F2; and

in step S13, the first factor F1 is multiplied by the second factor F2 to obtain the calibration factor F.

After the calibration factor F is obtained, in step S2, the first urea metered injection quantity M determined by the first urea metering and injection device 25 is obtained_25iniAnd multiplying the first urea calibration injection quantity by the calibration factor F to obtain a first urea calibration injection quantity M_25cor。

Since the calibration factor F is a value less than or equal to 1 in the range of 0-1, the first urea calibration injection quantity M_25corIs generally less than or equal to the first metered urea injection quantity M_25iniI.e., the amount of urea injected into the exhaust gas upstream of the first SCR 24 of the cc-ATS 20, is reduced. Thus, the first SCR 24 of the cc-ATS 20 is capable of removing NO by reduction_XReduced amount of NOx content N in the exhaust gas exiting the cc-ATS 20 into the uf-ATS 40_40upAnd (4) increasing. The exhaust gas NOx content increases, facilitating passive regeneration of the DPF 48 of the uf-ATS 40.

The calibration method of the present application further includes determining a first urea calibration injection quantity M in step S2_25corAnd then:

step S3, calibrating injection quantity M based on the first urea_25corObtaining the efficiency eta of cc-ATS 20₂₀Or the NOx content in the exhaust upstream of the uf-ATS 40, which is the NOx content N in the exhaust entering the uf-ATS 40_40up；

Step S4, efficiency η based on cc-ATS 20₂₀Or the NOx content N in the exhaust upstream of the uf-ATS 40_40upAnd a threshold allowable NOx content T corresponding to a particular emission requirement_thresholdDetermining a second urea metered injection quantity M required for the uf-ATS 40₄₅；

In step S5, the NOx content N in the exhaust gas discharged from the uf-ATS 40, specifically, the second ASC 46 is judged_finalWhether a specific emission requirement is met, i.e. whether a threshold value N of the allowable NOx content is present_thresholdWithin. If N is present_finalIs less than or equal to N_thresholdThen the specific emission requirement is met and step S6 is executed to end the method flow. Otherwise, if N_finalExceeds or exceeds N_thresholdThen step S7 is executed.

In the step ofIn S7, based on N_finalAnd N_thresholdUpdating the urea quantity M determined by the first urea metering and injection device 25_25iniIn particular increased. The method flowchart of fig. 2 is then repeatedly executed from step S1.

According to the calibration method of the present application, a calibration factor in the range of 0-1 is provided for modifying, in particular reducing, the amount of urea injected into the exhaust gas upstream of the first SCR of the close-coupled aftertreatment system, reducing the amount of NOx that the first SCR is capable of reductively removing, based on some real-time parameters of the engine and the exhaust gas emitted from the engine. In this way, the exhaust gas entering the DPF of an underground aftertreatment system located downstream of the close-coupled aftertreatment system has an increased NOx content, facilitating passive regeneration of the DPF. The increase in passive regeneration reduces the need for active regeneration, and correspondingly saves the amount of fuel required for active regeneration.

At least some of the steps of the methods of the present invention may be implemented using hardware and software, as well as a combination of both. When the method of the invention is implemented or partly implemented in software, the software may be used for performing the steps of the method of the invention. The required software and data may be stored in a memory and executed by an appropriate instruction execution system, apparatus, or device (e.g., a single or multi-core processor or microprocessor or processor system). The software may comprise an ordered listing of executable instructions for implementing logical functions, which can be embodied in any "processor-readable medium" for use by an instruction execution system, apparatus, or device. These systems may access these instructions and execute them.

Some or all of the steps of the above method may be performed by a calibration module 50 as shown in fig. 5, which calibration module 50 may be integrated into an Electronic Control Unit (ECU) of the vehicle, i.e. the above method may be performed by an electronic control unit of the vehicle.

It should be understood that the calibration module 50 may also be provided separately from the electronic control unit of the vehicle, for example, the control module 50 may be a single chip microcomputer. The control module 50 may include a processor 52 and a memory 54 storing executable instructions and algorithms for the various computational steps.

The calibration module 50 may communicate directly with the respective sensors to obtain the parameters required for each step, or may obtain the parameters from a vehicle Electronic Control Unit (ECU) communicatively coupled to the respective sensors. When the executable instructions in the memory 54 of the calibration module 50 are executed, the processor 52 obtains the parameters required for the calculation from the various sensors or vehicle ECU and retrieves the associated algorithms from the memory 54 to perform the calibration method shown in fig. 2 and 3 in turn.

The present invention has been described in detail with reference to the specific embodiments. It is to be understood that both the foregoing description and the embodiments shown in the drawings are to be considered exemplary and not restrictive of the invention. It will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit of the invention, and these changes and modifications do not depart from the scope of the invention.

Claims

1. A calibration method for enhancing passive regeneration of a DPF (48) of an exhaust aftertreatment system, wherein the exhaust aftertreatment system comprises a close-coupled aftertreatment system (20) having a first SCR (24) and an underground aftertreatment system (40) including the DPF (48) and a second SCR (44) downstream of the DPF (48), the method comprising the steps of:

based on NO in exhaust gas upstream from DPF (48)₂And concentration ratio of soot (R)_NO2/Soot) Soot level (L) inside DPF (48)_S) An upstream exhaust temperature (T) of the DPF (48)_48UP) A first step (S1) of determining a calibration factor (F) by querying a calibration factor table or curve;

applying the calibration factor (F) to a first metered urea injection quantity (M) to be injected into exhaust gas upstream of the first SCR (24)_25ini) Thereby obtaining a first urea calibration injection quantity (M)_25cor) The second step (S2);

calibrating an injection quantity (M) based on the first urea_25cor) Obtaining an efficiency (η) of the close-coupled post-processing system (20)₂₀) Or the NOx content (N) in the exhaust gas upstream of the underground aftertreatment system (40)_40up) Third step of(S3)；

Based on the efficiency (η)₂₀) Or the NOx content (N) in the exhaust gas upstream of the underground aftertreatment system (40)_40up) And a threshold allowable NOx content (T) corresponding to a particular emission requirement_threshold) Determining a second metered injection amount (M) of urea to be injected into exhaust gas upstream of a second SCR (44) of the subterranean aftertreatment system (40)₄₅) The fourth step (S4);

determining a final NOx content (N) in exhaust gas emitted from the subterranean aftertreatment system (40)_final) Whether or not it is at the allowable NOx content threshold (N)_threshold) A fifth step (S5);

at said final NOx content (N)_final) Less than or equal to a threshold allowable NOx content (N)_threshold) And a sixth end step (S6).

2. Calibration method according to claim 1, further comprising at the final NOx content (N)_final) Greater than or exceeding a threshold allowable NOx content (N)_threshold) Based on the final NOx content (N)_final) And allowable NOx content threshold (N)_threshold) Renewing the first urea metered injection quantity (M)_25ini) The seventh step (S7).

3. The calibration method according to claim 2, further comprising dosing the quantity (M) with the updated first urea dose_25ini) The first step (S1) to the fifth step (S5) are repeatedly performed.

4. The calibration method according to any one of claims 1-3, wherein the first step (S1) includes:

based on soot level (L) within the DPF (48)_S) And exhaust temperature (T) upstream of DPF (48)_48UP) A first sub-step (S11) of determining a first factor (F1) by means of a first sub-calibration factor table or curve;

based on the content ratio (R)_NO2/Soot) And exhaust temperature (T) upstream of DPF (48)_48UP) A second sub-step (S12) of determining a second factor (F2) by means of the first sub-calibration factor table or curve; and

a third substep (S13) of multiplying the first factor (F1) by the second factor (F2) to obtain the above calibration factor (F).

5. The calibration method according to any one of claims 1-4, wherein the first factor (F1) and the second factor (F2) are both in the range of 0-1, both endpoints being 0 and 1.

6. Calibration method according to any one of claims 1-5, wherein said first urea calibration injection quantity (M)_25cor) By making the calibration factor (F) and the first urea metering injection quantity (M)_25ini) And multiplying the two to obtain the product.

7. Calibration method according to any one of claims 1-6, wherein said first urea metered injection quantity (M) is_25ini) Based on at least the following determinations: NO in the exhaust upstream of the close-coupled aftertreatment system (20)_XContent (N)_20UP) (ii) a Temperature (T) of exhaust gas upstream of first SCR (24)_24UP) (ii) a An amount of exhaust gas (FL) exhausted from an engine of the engine vehicle.

8. The calibration method according to any one of claims 1-6, wherein the close-coupled aftertreatment system (20) and the subterranean aftertreatment system (40) further comprise a first DOC (22) and a second DOC (42) upstream of the first SCR (24) and the second SCR (44), respectively.

9. A calibration module, comprising:

a processor; and

a memory storing executable instructions that, when executed, cause the processor to perform the calibration method of any one of claims 1 to 8.

10. Calibration module according to claim 9, characterized in that it is integrated in or communicatively connected with an electronic control unit of a vehicle.

11. A readable storage medium having stored thereon executable instructions that, when executed, cause a machine to perform a calibration method according to any one of claims 1 to 8.