A Thermal Runaway Simulation Method and Medium for a Lithium-Ion Battery System

Abstract

The present invention discloses a method and medium for simulating thermal propagation of a lithium-ion battery system. The simulation method includes: obtaining thermal runaway test data of battery cells, establishing a geometric model of the battery system and performing mesh division on the geometric model to obtain a mesh model of the battery system, importing the mesh model into ANSYS Fluent software, setting basic parameters for completing simulation calculations in ANSYS Fluent software, writing a heat source expression for the heating sheet and a heat source expression for each battery cell, recording an initial log file for controlling calculations in ANSYS Fluent software, writing a first log file corresponding to each battery cell based on the initial log file, and applying ANSYS Fluent software to perform simulation calculations to obtain the simulation results of thermal propagation of the lithium-ion battery system; the present invention performs simulation of thermal propagation of the battery system based on thermal runaway test data without the need to activate the thermal runaway model inside ANSYS Fluent software.

Description

Technical Field

[0001] The present invention belongs to the field of lithium-ion batteries, and more specifically, relates to a method and medium for simulating thermal propagation of a lithium-ion battery system. Background Art

[0002] During the use of the battery cell, phenomena such as increased internal resistance and lithium metal deposition may occur inside. With the accumulation of time, the risk of thermal runaway will gradually increase; in addition to the influencing factors generated during the use of the battery cell, other factors such as water immersion, thermal shock, vibration, overcharging and over-discharging may also become the causes of triggering thermal runaway. In a battery system, when one battery cell experiences thermal runaway, due to the heat transfer phenomenon, the thermal runaway may spread to other battery cells.

[0003] Performing simulation calculation and analysis on a lithium-ion battery system can provide technical support during the R & D and design stages of a battery module and a battery pack, estimate and judge risk items, and make targeted modifications according to the simulation results. After obtaining a safe result from the simulation data, conduct actual measurement verification. Avoid wasting manpower, material resources and financial resources caused by multiple tests. The ANSYS Fluent software provides special simulation models for thermal runaway: the 1-equation thermal runaway model and the 4-equation thermal runaway model. However, these two simulation models have the problem that it is difficult to obtain the parameters of the battery thermal runaway model, which may lead to the problem that data fitting may fail.

[0004] Therefore, it is expected to invent a method for simulating thermal propagation of a lithium-ion battery system, which can solve the problem of data fitting failure caused by the ANSYS Fluent software in the prior art. Summary of the Invention

[0005] The object of the present invention is a method for simulating thermal propagation of a lithium-ion battery system,

[0006] To achieve the above object, the present invention provides a method for simulating thermal propagation of a lithium-ion battery system. The battery system includes a plurality of battery cells, and is characterized in that the simulation method includes:

[0007] Obtaining thermal runaway test data of the battery cells;

[0008] Establishing a geometric model of the battery system and performing mesh division on the geometric model to obtain a mesh model of the battery system;

[0009] Importing the mesh model into the ANSYS Fluent software and setting basic parameters for completing simulation calculation in the ANSYS Fluent software;

[0010] Based on the thermal runaway test data of the battery cells and the mesh model, writing a heat source expression for a heating sheet and a heat source expression for each battery cell;

[0011] Record an initial log file for controlling the calculation in the ANSYS Fluent software, and write a first log file corresponding to each of the battery cells based on the initial log file;

[0012] Based on the basic parameters, the heat source expression of the heating sheet, the heat source expression of each battery cell, and the first log file corresponding to each battery cell, apply the ANSYS Fluent software to perform simulation calculations to obtain the thermal runaway simulation results of the lithium-ion battery system.

[0013] Optionally, obtaining the thermal runaway test data of the battery cell includes:

[0014] Perform an adiabatic thermal runaway test on one of the battery cells to obtain the temperature-time curve of the battery cell;

[0015] Based on the temperature-time curve, obtain the thermal runaway test data of the battery cell.

[0016] Optionally, the thermal runaway test data of the battery cell includes the trigger temperature, end temperature, and thermal runaway time of the battery cell thermal runaway.

[0017] Optionally, according to the size, shape of the battery and the layout of the battery system, use finite element preprocessing software to establish the geometric model of the battery system.

[0018] Optionally, the simulation method further includes: after obtaining the mesh model of the battery system, establish a calculation domain corresponding to each battery cell in the mesh model.

[0019] Optionally, the simulation method further includes:

[0020] After writing the heat source expression of the heating sheet and the heat source expression of each battery cell, select the heat source expression of the battery cell in the calculation domain corresponding to each battery cell.

[0021] Optionally, the heat source expression of the heating sheet is: at the beginning of the calculation, the heating sheet heats the battery cell at a constant power, and when the battery cell reaches the thermal runaway trigger temperature, heat generation stops;

[0022] The heat source expression of each battery cell is: when the temperature of the battery cell reaches the thermal runaway trigger temperature, start generating heat at the volumetric average heat generation power of the battery cell, and the volumetric average heat generation power is P = C bat ·m bat ·(T3 - T2) / ((t3 - t2)·V bat )), where C bat is the specific heat capacity of the battery cell, m bat is the mass of the battery cell, V batwhere \(V\) is the volume of the battery cell, \(T_2\) is the thermal runaway triggering temperature, \(T_3\) is the thermal runaway end temperature, \(t_2\) is the time at the start of thermal runaway, and \(t_3\) is the time at the end of thermal runaway.

[0023] Optionally, the simulation method further includes: after writing the first log file corresponding to each battery cell based on the initial log file, writing a second log file;

[0024] The first log file is used to modify the heat source parameters corresponding to each battery cell. The content of the first log file includes: at a predetermined position in the ANSYS Fluent software, changing the heat source of the battery cell from the corresponding heat source expression to a constant 0;

[0025] The second log file is used to command each battery cell. The content of the second log file includes: comparing whether the average temperature of the battery cell reaches the thermal runaway end temperature. If the judgment result is yes, execute the initial log file.

[0026] Optionally, the basic parameters include a calculation model, material parameters, boundary conditions, a solution method, and variable monitoring.

[0027] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the thermal runaway simulation method of the lithium-ion battery system is implemented.

[0028] The beneficial effects of the present invention are as follows:

[0029] The thermal runaway simulation method of the lithium-ion battery system of the present invention includes: obtaining thermal runaway test data of battery cells, establishing a geometric model of the battery system and performing mesh division on the geometric model to obtain a mesh model of the battery system, importing the mesh model into the ANSYS Fluent software, and setting basic parameters for completing simulation calculations in the ANSYS Fluent software. Based on the thermal runaway test data of the battery cells and the mesh model, writing a heat source expression for the heating sheet and a heat source expression for each battery cell, recording an initial log file for controlling the calculation in the ANSYS Fluent software, and writing a first log file corresponding to each battery cell based on the initial log file. Based on the basic parameters, the heat source expression of the heating sheet, the heat source expression of each battery cell, and the first log file corresponding to each battery cell, applying the ANSYS Fluent software to perform simulation calculations to obtain the thermal runaway simulation result of the lithium-ion battery system. The thermal runaway simulation method of the lithium-ion battery system of the present invention is based on the ANSYS Fluent software and thermal runaway test data, and performs thermal runaway simulation of the battery system based on the thermal runaway test data, without the need to activate the thermal runaway model inside the ANSYS Fluent software, solving the problem of data fitting failure caused by the difficulty in obtaining a large number of battery thermal runaway parameters in the prior art.

[0030] Other features and advantages of the present invention will be described in detail in the following detailed implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] By describing the exemplary embodiments of the present invention in more detail in conjunction with the accompanying drawings, the above and other objects, features, and advantages of the present invention will become more apparent, wherein, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0032] Figure 1 The flowchart of a method for simulating thermal runaway of a lithium-ion battery system according to an embodiment of the present invention is shown.

[0033] Figure 2 The temperature-time curve of the battery cell obtained from the single-cell thermal runaway test of a method for simulating thermal runaway of a lithium-ion battery system according to an embodiment of the present invention is shown.

[0034] Figure 3 The geometric model diagram of the battery system of a method for simulating thermal runaway of a lithium-ion battery system according to an embodiment of the present invention is shown.

[0035] Figure 4 The temperature-time curves of multiple battery cells in the battery system of a method for simulating thermal runaway of a lithium-ion battery system according to an embodiment of the present invention are shown. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0037] According to a method for simulating thermal runaway of a lithium-ion battery system of the present invention, the battery system includes a plurality of battery cells, and is characterized in that the simulation method includes:

[0038] Obtaining the thermal runaway test data of the battery cell;

[0039] Establishing a geometric model of the battery system and performing mesh division on the geometric model to obtain a mesh model of the battery system;

[0040] Importing the mesh model into ANSYS Fluent software and setting the basic parameters for completing the simulation calculation in ANSYS Fluent software;

[0041] Based on the thermal runaway test data of the battery cells and the mesh model, write the heat source expressions for the heating sheet and each battery cell.

[0042] Record the initial log file for controlling the calculation in ANSYS Fluent software, and write the first log file corresponding to each battery cell based on the initial log file.

[0043] Based on the basic parameters, the heat source expressions for the heating sheet and each battery cell, and the first log file corresponding to each battery cell, apply ANSYS Fluent software to perform simulation calculations to obtain the thermal propagation simulation results of the lithium-ion battery system.

[0044] Specifically, the thermal propagation simulation method for the lithium-ion battery system of the present invention includes: obtaining the thermal runaway test data of the battery cells, establishing the geometric model of the battery system and performing mesh division on the geometric model to obtain the mesh model of the battery system, importing the mesh model into ANSYS Fluent software, and setting the basic parameters for completing the simulation calculations in ANSYS Fluent software. Based on the thermal runaway test data of the battery cells and the mesh model, write the heat source expressions for the heating sheet and each battery cell. Record the initial log file for controlling the calculation in ANSYS Fluent software, and write the first log file corresponding to each battery cell based on the initial log file. Based on the basic parameters, the heat source expressions for the heating sheet and each battery cell, and the first log file corresponding to each battery cell, apply ANSYS Fluent software to perform simulation calculations to obtain the thermal propagation simulation results of the lithium-ion battery system. The thermal propagation simulation method for the lithium-ion battery system of the present invention is based on ANSYS Fluent software and thermal runaway test data, and performs thermal propagation simulation of the battery system based on the thermal runaway test data without the need to turn on the thermal runaway model inside ANSYS Fluent software, solving the problem of data fitting failure caused by the difficulty in obtaining a large number of battery thermal runaway parameters in the prior art.

[0045] Furthermore, when using the thermal propagation simulation method for the lithium-ion battery system of the present invention, only the basic parameters of each component material, such as density, specific heat capacity, and thermal conductivity, need to be provided, which are easy to obtain; and the simulation parameters are all set based on the measured data, and the single-cell temperature rise and thermal runaway time in the simulation results no longer need to be verified for accuracy, and the safety of the battery system can be estimated and judged conveniently, quickly, and accurately.

[0046] Furthermore, after importing the mesh model into ANSYS Fluent software and setting the basic parameters for completing the simulation calculations in ANSYS Fluent software, an initialization operation needs to be performed on ANSYS Fluent software.

[0047] In one example, obtaining the thermal runaway test data of the battery cell includes:

[0048] Performing an adiabatic thermal runaway test on a battery cell to obtain the temperature-time curve of the battery cell;

[0049] Based on the temperature-time curve, obtaining the thermal runaway test data of the battery cell.

[0050] Specifically, performing an adiabatic thermal runaway test on a battery cell to obtain the temperature-time curve of the battery cell during the test, analyzing the obtained temperature-time curve, the point where the temperature rise rate suddenly increases significantly is the starting point of the thermal runaway process of the battery cell, record the temperature at this moment as the trigger temperature T2, the time as t2, the temperature peak is the end point of the thermal runaway process of the battery cell, record the temperature at this moment as the end temperature T3, and the time as t3.

[0051] In one example, the thermal runaway test data of the battery cell includes the trigger temperature, end temperature, and thermal runaway time of the battery cell's thermal runaway.

[0052] In one example, according to the size and shape of the battery and the layout of the battery system, a geometric model of the battery system is established using finite element preprocessing software.

[0053] In one example, the simulation method further includes: after obtaining the mesh model of the battery system, establishing a calculation domain corresponding to each battery cell in the mesh model.

[0054] In one example, the simulation method further includes:

[0055] After writing the heat source expression of the heating sheet and the heat source expression of each battery cell, select the heat source expression of the battery cell in the calculation domain corresponding to each battery cell.

[0056] In one example, the heat source expression of the heating sheet is: at the beginning of the calculation, the heating sheet heats the battery cell at a constant power, and when the battery cell reaches the thermal runaway trigger temperature, the heat generation stops;

[0057] The heat source expression of each battery cell is: when the temperature of the battery cell reaches the thermal runaway trigger temperature, start generating heat at the volumetric average heat generation power of the battery cell, and the volumetric average heat generation power is P = C bat ·m bat ·(T3 - T2) / ((t3 - t2)·V bat ), where C bat is the specific heat capacity of the battery cell, m bat is the mass of the battery cell, V bat is the volume of the battery cell, T2 is the thermal runaway trigger temperature, T3 is the thermal runaway end temperature, t2 is the time at the start of thermal runaway, and t3 is the time at the end of thermal runaway.

[0058] In one example, the simulation method further includes: after writing the first log file corresponding to each battery cell based on the initial log file, writing a second log file;

[0059] The first log file is used to modify the heat source parameters corresponding to each battery cell. The content of the first log file includes: at a predetermined position in the ANSYS Fluent software, changing the heat source of the battery cell from the corresponding heat source expression to a constant 0;

[0060] The second log file is used to command each battery cell. The content of the second log file includes: comparing whether the average temperature of the battery cell reaches the end temperature of thermal runaway. If the judgment result is yes, execute the initial log file.

[0061] Specifically, the predetermined position in the ANSYS Fluent software is cell zone condition. In the cell zone condition, change the heat source of the battery cell from the corresponding heat source expression to a constant 0.

[0062] In one example, the basic parameters include a calculation model, material parameters, boundary conditions, a solution method, and variable monitoring.

[0063] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the thermal runaway simulation method of the lithium-ion battery system described above.

[0064] Embodiment 1

[0065] As Figure 1 shown, the thermal runaway simulation method of the lithium-ion battery system includes:

[0066] Step 1: Obtain the thermal runaway test data of the battery cell;

[0067] Among them, obtaining the thermal runaway test data of the battery cell includes:

[0068] Conduct an adiabatic thermal runaway test on a battery cell to obtain the temperature-time curve of the battery cell;

[0069] Based on the temperature-time curve, obtain the thermal runaway test data of the battery cell.

[0070] Among them, the thermal runaway test data of the battery cell includes the trigger temperature, end temperature, and thermal runaway time of the battery cell's thermal runaway.

[0071] Specifically, as Figure 2As shown in the figure, four temperature points T1 - T4 are marked in the figure. T1 represents the temperature at the start of the test, and T4 represents the temperature at the end of the test. It can be seen that there are also two temperature turning points in the temperature - time curve. The position where the temperature change rate suddenly increases is denoted as T2, which is the temperature at the start of thermal runaway, and the time at this moment is recorded as T2. The peak position of the temperature curve is denoted as T3, which is the temperature at the end of thermal runaway, and the time at this moment is recorded as T3.

[0072] Step 2: Establish a geometric model of the battery system and perform mesh division on the geometric model to obtain the mesh model of the battery system;

[0073] Among them, according to the size, shape of the battery and the layout of the battery system, a geometric model of the battery system is established using finite element pre - processing software.

[0074] Specifically, as Figure 3 shown, according to the shape and size of the battery and the layout of the system, a geometric model is established using 3D drawing software (such as SolidWorks). The model ignores the components and detailed features that have little impact on the calculation. In this embodiment, the foam, thermal conductive pads, and liquid - cooling plates that have a greater impact on the heat transfer of the battery cells are retained.

[0075] Among them, the simulation method also includes: after obtaining the mesh model of the battery system, a calculation domain corresponding to each battery cell is established in the mesh model.

[0076] Step 3: Import the mesh model into ANSYS Fluent software and set the basic parameters for completing the simulation calculation in ANSYS Fluent software;

[0077] Among them, the basic parameters include calculation model, material parameters, boundary conditions, solution method, and variable monitoring.

[0078] Specifically, import the mesh model into ANSYS Fluent software and complete all other settings except the heat source parameters, including calculation model, material parameters, boundary conditions, calculation method, variable monitoring, etc. The interface between the battery cell and the air domain considers convective heat transfer and radiative heat transfer.

[0079] Step 4: Based on the thermal runaway test data of the battery cell and the mesh model, write the heat source expression of the heating sheet and the heat source expression of each battery cell;

[0080] Among them, the simulation method also includes: after writing the heat source expression of the heating sheet and the heat source expression of each battery cell, select the heat source expression of the battery cell in the calculation domain corresponding to each battery cell.

[0081] Among them, the heat source expression of the heating sheet is: at the beginning of the calculation, the heating sheet heats the battery cell at a constant power, and when the battery cell reaches the thermal runaway trigger temperature, heat generation stops;

[0082] The heat source expression for each battery cell is: when the temperature of the battery cell reaches the thermal runaway trigger temperature, heat generation starts at the volumetric average heat generation power of the battery cell, and the volumetric average heat generation power is P = C bat ·m bat ·(T3 - T2) / ((t3 - t2)·V bat ), where C bat is the specific heat capacity of the battery cell, m bat is the mass of the battery cell, V bat is the volume of the battery cell, T2 is the thermal runaway trigger temperature, T3 is the thermal runaway end temperature, t2 is the time at the start of thermal runaway, and t3 is the time at the end of thermal runaway.

[0083] Specifically, after writing the heat source expression of the heating sheet and the heat source expression of each battery cell, save the mesh model as example.cas and example.dat.

[0084] Step 5: Record the initial log file for controlling the calculation in ANSYS Fluent software, and write the first log file corresponding to each battery cell based on the initial log file;

[0085] Among them, the simulation method further includes: after writing the first log file corresponding to each battery cell based on the initial log file, write the second log file;

[0086] The first log file is used to modify the heat source parameters corresponding to each battery cell. The content of the first log file includes: at a predetermined position in ANSYS Fluent software, change the heat source of the battery cell from the corresponding heat source expression to the constant 0;

[0087] The second log file is used to command each battery cell. The content of the second log file includes: compare whether the average temperature of the battery cell reaches the thermal runaway end temperature. If the judgment result is yes, execute the initial log file.

[0088] Specifically, the format of the initial log file and the first log file is bat - 11.jou, and the format of the second log file is check.jou. The second log file uses the Scheme language and writes a command for each battery cell, with the content: compare whether the average temperature of the battery cell reaches the thermal runaway end temperature. If the judgment result is yes, execute the initial log file.

[0089] Step 6: Based on the basic parameters, the heat source expression of the heating sheet, the heat source expression of each battery cell, and the first log file corresponding to each battery cell, apply ANSYS Fluent software to perform simulation calculations to obtain the thermal propagation simulation results of the lithium - ion battery system.

[0090] Specifically, re-read the example.cas and example.dat files, write commands in the execute commands, and require the software to execute the check.jou file after each time step calculation to determine the status of each battery cell; initialize and calculate. In the initial stage of the calculation, the heating sheet is in the heating stage for the battery cells, and the time step can be set to 1 s; when any one of the battery cells reaches the thermal runaway state, the time step can be adjusted to a smaller value, such as 0.1 s. The temperature-time curves of multiple battery cells obtained from the simulation calculation are as Figure 4 shown. Select 8 battery cells and label them as 1.1 - 1.8.

[0091] Embodiment 2

[0092] The present invention discloses a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned thermal propagation simulation method for a lithium-ion battery system is implemented.

[0093] According to the computer-readable storage medium of the present disclosure, non-temporary computer-readable instructions are stored thereon. When the non-temporary computer-readable instructions are run by a processor, all or part of the steps of the methods of the various embodiments of the present disclosure described above are executed.

[0094] The above-mentioned computer-readable storage medium includes but is not limited to: optical storage media (such as CD-ROMs and DVDs), magneto-optical storage media (such as MOs), magnetic storage media (such as magnetic tapes or external hard drives), media with built-in rewritable non-volatile memories (such as memory cards), and media with built-in ROMs (such as ROM cartridges).

[0095] The various embodiments of the present invention have been described above. The above description is exemplary and not exhaustive, and is also not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art in the technical field without departing from the scope and spirit of the described embodiments.

Claims

1. A method for simulating thermal propagation of a lithium-ion battery system, the battery system comprising a plurality of battery cells, characterized in that, The simulation method includes: Obtaining the thermal runaway test data of the battery cell; Establishing a geometric model of the battery system and performing mesh division on the geometric model to obtain a mesh model of the battery system; Importing the mesh model into ANSYS Fluent software and setting basic parameters for completing simulation calculations in the ANSYS Fluent software; Based on the thermal runaway test data of the battery cell and the mesh model, writing a heat source expression for the heating sheet and a heat source expression for each battery cell; Recording an initial log file for controlling calculations in the ANSYS Fluent software and writing a first log file corresponding to each battery cell based on the initial log file; Based on the basic parameters, the heat source expression of the heating sheet, the heat source expressions of each battery cell, and the first log file corresponding to each battery cell, applying the ANSYS Fluent software to perform simulation calculations to obtain the thermal propagation simulation results of the lithium-ion battery system.

2. The system thermal spread simulation method according to claim 1, wherein The obtaining the thermal runaway test data of the battery cell includes: Performing an adiabatic thermal runaway test on one battery cell to obtain a temperature-time curve of the battery cell; Based on the temperature-time curve, obtaining the thermal runaway test data of the battery cell.

3. The system thermal spread simulation method according to claim 2, wherein The thermal runaway test data of the battery cell includes the trigger temperature, end temperature, and thermal runaway time of the battery cell thermal runaway.

4. The system thermal spread simulation method according to claim 1, wherein According to the size, shape of the battery and the arrangement of the battery system, applying finite element preprocessing software to establish a geometric model of the battery system.

5. The system thermal spread simulation method according to claim 1, characterized in that It also includes: After obtaining the mesh model of the battery system, establishing a calculation domain corresponding to each battery cell in the mesh model.

6. The system thermal spread simulation method according to claim 5, wherein It also includes: After writing the heat source expression for the heating sheet and the heat source expressions for each battery cell, selecting the heat source expression of the battery cell in the calculation domain corresponding to each battery cell.

7. The system thermal spread simulation method according to claim 1, wherein The heat source expression of the heating sheet is: at the beginning of the calculation, the heating sheet heats the battery cell at a constant power, and when the battery cell reaches the thermal runaway trigger temperature, heat generation stops; The heat source expression of each of the battery cells is: when the temperature of the battery cell reaches the thermal runaway trigger temperature, heat generation starts at the volumetric average heat generation power of the battery cell, and the volumetric average heat generation power is P = C bat ·m bat ·(T3 - T2) / ((t3 - t2)·V bat ), where C bat is the specific heat capacity of the battery cell, m bat is the mass of the battery cell, V bat is the volume of the battery cell, T2 is the thermal runaway trigger temperature, T3 is the thermal runaway end temperature, t2 is the time at the start of thermal runaway, and t3 is the time at the end of thermal runaway.

8. The system thermal spread simulation method according to claim 1, wherein It also includes: After writing the first log file corresponding to each battery cell based on the initial log file, writing a second log file; The first log file is used to modify the heat source parameters corresponding to each battery cell, and the content of the first log file includes: at a predetermined position in the ANSYS Fluent software, changing the heat source of the battery cell from the corresponding heat source expression to a constant 0; The second log file is used to command each battery cell, and the content of the second log file includes: comparing whether the average temperature of the battery cell reaches the thermal runaway end temperature, and if the judgment result is yes, executing the initial log file.

9. The system thermal spread simulation method according to claim 1, wherein The basic parameters include a calculation model, material parameters, boundary conditions, a solution method, and variable monitoring.

10. A computer-readable storage medium, characterized in that, This computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the thermal propagation simulation method of the lithium-ion battery system according to any one of claims 1-9.

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