Bearing analysis device, bearing analysis method, program, and program storage medium

Abstract

To easily identify multiple natural frequencies of a bearing on the basis of vibration data of a rotary apparatus without referring to specifications of the bearing or using man-hours for the disassembly investigation of the bearing.SOLUTION: A bearing analysis device for deriving the natural frequencies of a bearing of a rotary apparatus comprises: a vibration signal acquisition unit which acquires vibration signals from a vibration sensor installed near the bearing; a frequency analysis unit which performs frequency analysis on the acquired vibration signals using multiple methods; a peak frequency list generation unit which integrates multiple peak frequencies obtained by the frequency analysis unit to generate a peak frequency list; a natural frequency list acquisition unit which acquires a natural frequency list for the multiple bearings; an error calculation unit which compares the peak frequency list with the natural frequency list to calculate errors; and a natural frequency derivation unit which derives the natural frequencies of the bearing on the basis of the error calculation results.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a bearing analysis device, a bearing analysis method, a program, and a storage medium for deriving the natural frequency of a bearing of a rotating device. [Background technology]

[0002] As a conventional technique for diagnosing a rotating machine, a method for diagnosing a rotating machine using a spectrum intensity at a natural frequency of the rotating machine as an evaluation index is known.

[0003] For example, in Patent Document 1, paragraph 0039 states, "FIGS. 4 to 6 are diagrams showing examples of frequency analysis results (frequency spectrum) of sound data acquired using acoustic sensors 32, 34A, and 34B under specific motor rotation speed conditions (n ​​[rpm] in FIG. 4, 2n [rpm] in FIG. 5, and 4n [rpm] in FIG. 6)." and paragraph 0072 states, "Then, based on the amplitude of the peak frequency (natural frequency) component of the diagnosis target part (e.g., gear 4) in the frequency analysis result (frequency spectrum) of the diagnostic sound data, an abnormality determination is made for the sound source (i.e., the diagnosis target part) (steps S206 to S208). Here, the peak frequency (natural frequency) of the diagnosis target part is identified in the above-mentioned peak frequency identification step (step S108) and sound source information acquisition step (step S114)."

[0004] In this way, in Patent Document 1, sound data is acquired using multiple acoustic sensors, the natural frequency of the part to be diagnosed is identified from the peak frequency common to the sound data, and the spectrum of the sound data is used to determine abnormality in the part to be diagnosed. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 7077426 Summary of the Invention [Problem to be solved by the invention]

[0006] As described above, in Patent Document 1, the natural frequency of a mechanical component such as a motor or gear is derived from a common peak frequency in the spectrum of multiple sound data. However, when the mechanical component to be diagnosed is a bearing consisting of a cage, an inner ring, an outer ring, and rolling elements, not only does it have multiple natural frequencies such as the cage frequency, the outer ring rolling element passing frequency, the inner ring rolling element passing frequency, and the rolling element rotation frequency, but the signal levels of these frequencies are different, so the technology in Patent Document 1 cannot identify each natural frequency from the common peak frequency.

[0007] As a method for determining the natural frequency of a bearing, if specifications or blueprints are available, one can calculate the natural frequency of the bearing based on the dimensions of each part listed therein. If specifications or blueprints are not available, another method can be considered: disassembling the bearing, measuring the dimensions of each part, and then calculating the natural frequency of the bearing based on the measured dimensions.

[0008] However, these methods also have issues in terms of maintaining equipment availability, such as the large amount of work required to individually calculate the natural frequency of each bearing in an environment where there are many different types of bearings with different specifications, resulting in enormous investigation costs. In addition, when it is necessary to disassemble and investigate each bearing without being able to refer to specifications, it is necessary to stop operation of the rotating machinery for a corresponding period of time.

[0009] Therefore, an object of the present invention is to easily identify multiple natural frequencies of a bearing based on vibration data of a rotating device, without having to refer to bearing specifications or spend time on disassembling and inspecting the bearing. [Means for solving the problem]

[0010] In order to solve the above problems, the bearing analysis device of the present invention is a bearing analysis device that derives the natural frequency of a bearing of a rotating equipment, and includes a vibration signal acquisition unit that acquires a vibration signal from a vibration sensor installed in the vicinity of the bearing, a frequency analysis unit that performs frequency analysis of the acquired vibration signal using a plurality of methods, a peak frequency list generation unit that integrates a plurality of peak frequencies obtained by the frequency analysis unit to generate a peak frequency list, a natural frequency list acquisition unit that acquires a natural frequency list of a plurality of bearings, an error calculation unit that compares the peak frequency list with the natural frequency list to calculate an error, and a natural frequency derivation unit that derives the natural frequency of the bearing based on the error calculation result. Effect of the Invention

[0011] According to the present invention, it is possible to easily identify a plurality of natural frequencies of a bearing based on vibration data of a rotating device, without referring to specifications of the bearing or spending man-hours on disassembling and inspecting the bearing. [Brief description of the drawings]

[0012] [Figure 1] FIG. 2 is a block diagram of the bearing analyzer of the first embodiment. [Diagram 2] 4 is a processing flowchart of a bearing analysis according to the first embodiment. [Diagram 3] FIG. 4 is a spectrum diagram showing an example of analysis by frequency analysis A1 in the first embodiment. [Figure 4] FIG. 4 is a spectrum diagram showing an example of analysis by frequency analysis A2 in the first embodiment. [Diagram 5] FIG. 4 is a spectrum diagram showing an example of analysis by frequency analysis A3 in the first embodiment. [Figure 6] FIG. 4 is a diagram showing an example of an intermediate product of a peak frequency list generating unit in the first embodiment. [Figure 7] FIG. 4 is a diagram showing an example of a peak frequency list L1 according to the first embodiment. [Figure 8] FIG. 13 is a diagram showing an example of a standard natural frequency list L2 according to the first embodiment. [Figure 9] FIG. 13 is a diagram showing an example of a natural frequency list L3 according to the first embodiment. [Figure 10]FIG. 4 is a diagram showing an example of an error calculation result by an error calculation unit according to the first embodiment. [Figure 11] FIG. 11 is a block diagram of a bearing analyzer according to a second embodiment. [Figure 12] 10 is a processing flowchart of a bearing analysis according to the second embodiment. [Figure 13] 13 is an example of a determination result obtained by the bearing analyzer of the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] Hereinafter, a bearing analysis device of the present invention that derives the natural frequency of a bearing from vibration data of a rotating device will be described with reference to the drawings. EXAMPLES

[0014] First, a bearing analyzer 1 according to a first embodiment of the present invention will be described with reference to FIGS.

[0015] 1 is a functional block diagram showing the configuration of a bearing analysis device 1 of this embodiment and a rotating device 2 that is the diagnosis target of the bearing analysis device 1. The rotating device 2 and the bearing analysis device 1 will be described below in order.

[0016] <Rotating equipment 2> The rotating device 2 is an electric motor or a generator equipped with at least a bearing 21, a vibration sensor 22, and a rotation speed sensor .

[0017] The bearing 21 is a bearing consisting of a cage, an inner ring, an outer ring, and rolling elements, and supports the rotating shaft of the rotating device 2. Since the bearing 21 is composed of the above-mentioned multiple elements, it has multiple natural frequencies such as the cage frequency f1, the outer ring rolling element passing frequency f2, the inner ring rolling element passing frequency f3, and the rolling element rotation frequency f4. In the following, these frequencies are collectively referred to as the natural frequency f n This natural frequency f n Since is a value determined according to the specifications of the bearing 21, the natural frequency f n If this can be determined, the specifications of the bearing 21 can be estimated.

[0018] The vibration sensor 22 is a sensor that detects vibrations that occur when the rotating device 2 is driven, and specifically is an acceleration sensor, an ultrasonic sensor, an AE (Acoustic Emission) sensor, an acoustic microphone, or the like, that is installed near the bearing 21.

[0019] The rotation speed sensor 23 is a sensor that detects the rotation speed n of the rotating shaft of the rotating device 2, and specifically is a magnetic rotation angle sensor or the like.

[0020] <Bearing analysis device 1> The bearing analysis device 1 is a computer including an arithmetic unit 11 , a main memory unit 12 , an auxiliary memory unit 13 , an input interface 14 , and an output interface 15 .

[0021] The arithmetic device 11 is a processor such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit).

[0022] The main storage device 12 is a volatile storage device such as a semiconductor memory, and holds a vibration signal acquisition unit 12a, a rotation speed signal acquisition unit 12b, a frequency analysis unit 12c, a peak frequency list generation unit 12d, a natural frequency list acquisition unit 12e, an error calculation unit 12f, and a natural frequency derivation unit 12g. These will be described in detail later.

[0023] The auxiliary storage device 13 is a non-volatile storage device such as a hard disk drive (HDD) or a solid state drive (SSD), and stores a program source 13a, a standard natural frequency list 13b, and a derivation result 13c. Details of these will be described later.

[0024] The input interface 14 is an interface for receiving information from the outside, and includes an interface for connecting an input device operated by a user (such as a mouse, keyboard, or touch panel (not shown)), an interface for receiving a vibration signal from the vibration sensor 22, and an interface for receiving a rotation speed signal from the rotation speed sensor 23.

[0025] The output interface 15 is an interface for transmitting information to the outside, and is an interface for connecting to an output device (not shown, such as a display) that presents information to a user, and is an interface for connecting to an output device (not shown, such as a display) that presents information to a user. n It includes an interface for transmitting the derivation result 13c to an external system, etc.

[0026] In addition, in Fig. 1, each functional unit such as the vibration signal acquisition unit 12a is illustrated in the main memory device 12, but this is a convenient representation, and in reality, the desired functional unit illustrated in the figure is realized in the main memory device 12 by the arithmetic device 11 executing a desired program in the program source 13a read from the auxiliary memory device 13 and deployed in the main memory device 12. For example, the vibration signal acquisition unit 12a is realized by the arithmetic device 11 executing a vibration signal acquisition program included in the program source 13a. However, since this mechanism is a well-known technique in the computer field, the above-mentioned explanation will be omitted hereinafter as appropriate.

[0027] <Flowchart> FIG. 2 shows the natural frequency f n 13 is a flowchart showing an example of a derivation process of

[0028] In step S1, the vibration signal acquisition unit 12a acquires a vibration signal of the bearing 21 from the vibration sensor 22 via the input interface 14. The vibration signal acquired here is a time waveform of a voltage value.

[0029] In step S2, the rotation speed signal acquisition unit 12b acquires a rotation speed signal from the rotation speed sensor 23 via the input interface 14. The rotation speed signal acquired here is the number of rotations n per minute of the rotating shaft of the rotating device 2 (i.e., of the bearing 21 supporting the rotating shaft), and is, for example, 1200 rpm.

[0030] In steps S3 to S5, the frequency analysis unit 12c performs frequency analysis in parallel using a plurality of methods on the vibration signal acquired in step S1.

[0031] The frequency analysis A1 in step S3 is, for example, an analysis method in which the vibration signal is transformed into the frequency domain by Fourier transform. An example of the analysis result is shown in FIG.

[0032] The frequency analysis A2 in step S4 is, for example, an analysis method in which the vibration signal is envelope-processed and then converted into the frequency domain by Fourier transform. An example of the analysis result is shown in FIG.

[0033] The frequency analysis A3 in step S5 is, for example, an analysis method in which the vibration signal is filtered using a band-pass filter, then envelope processed and transformed into the frequency domain using Fourier transform. An example of the analysis result is shown in FIG.

[0034] In step S6, the peak frequency list generating unit 12d extracts peaks from the multiple frequency analysis results (see FIGS. 3 to 5) obtained in steps S3 to S5, and generates a peak frequency list L1 by integrating the extracted peaks.

[0035] Here, an example of the peak extraction result by the peak frequency list generating unit 12d is shown with reference to Fig. 6. Data strings C1, C2, and C3 in Fig. 6 are data strings in which peaks are extracted from the frequency analysis results of Fig. 3, Fig. 4, and Fig. 5 obtained in steps S3 to S5, respectively. Note that for convenience in Fig. 6, the number of data in each data string is the same, but since the number of data in each string actually depends on the number of peaks in each frequency analysis result, the number of data in each string is usually different.

[0036] Fig. 7 is an example of a peak frequency list L1 generated by the peak frequency list generating unit 12d by integrating the data strings C1 to C3 of Fig. 6. The integration of peaks executed here is specifically a process of finding the logical sum of the data strings C1 to C3, and as a result, the peak frequency list L1 illustrated in Fig. 7 is derived.

[0037] In step S7, the natural frequency list acquisition unit 12e reads out the standard natural frequency list L2 from the auxiliary storage device 13 and corrects this list based on the rotation speed n obtained by the rotation speed signal acquisition unit 12b to acquire a natural frequency list L3 corresponding to the current rotation speed n. Note that, if the current rotation speed n is the standard rotation speed, the standard natural frequency list L2 can be used as the natural frequency list L3 as it is.

[0038] FIG. 8 is an example of the standard natural frequency list L2 when the standard rotation speed is 1200 rpm. As shown here, the standard natural frequency list L2 lists the natural frequency f n This natural frequency f n Specifically, these are the cage frequency f1, which is the natural frequency of the cage, the inner ring rolling element passing frequency f2, which is the natural frequency of the inner ring, the outer ring rolling element passing frequency f3, which is the natural frequency of the outer ring, and the rolling element rotation frequency f4, which is the natural frequency of the rolling elements. Note that bearing # is an ID that identifies the specifications of the bearing.

[0039] Here, the natural frequency f n is proportional to the rotation speed, so to obtain the natural frequency list L3 corresponding to the current rotation speed n, each vibration value in the standard natural frequency list L2 can be multiplied by the ratio between the current rotation speed n and the standard rotation speed assumed in the standard natural frequency list L2.

[0040] Fig. 9 shows an example of the natural frequency list L3 acquired in this step when the current rotation speed n acquired in step S2 is 2400 rpm. In this example, since the ratio of the current rotation speed n (2400 rpm) to the standard rotation speed (1200 rpm) is 2:1, the natural frequency list acquisition unit 12e calculates each numerical value in the natural frequency list L3 in Fig. 9 by doubling the value of each natural frequency in the standard natural frequency list L2 in Fig. 8.

[0041] In step S8, the error calculation unit 12f calculates an error from the peak frequency list L1 (see FIG. 7) generated in step S6 and the natural frequency of each bearing in the natural frequency list L3 (standard natural frequency list L2 at the standard rotation speed) acquired in step S7.

[0042] Fig. 10 shows an example of the error calculated by the error calculation unit 12f using the standard natural frequency list L2 (Fig. 8) when the current rotation speed n acquired in step S2 is the standard rotation speed (1200 rpm). If the current rotation speed n is not the standard rotation speed (1200 rpm), the error can be calculated in a similar manner using the natural frequency list L3 (Fig. 9) corrected according to the current rotation speed n.

[0043] As shown in Figure 10, the error calculation results include, for each bearing #, an error d1 for the cage frequency f1, an error d2 for the inner ring rolling element passing frequency f2, an error d3 for the outer ring rolling element passing frequency f3, an error d4 for the rolling element rotation frequency f4, and a bearing error Δ, which is the sum of errors d1 to d4.

[0044] The error is derived for each bearing. For example, the error between the value "32.0" in the peak frequency list L1, which is closest to the cage frequency f1 "28.1" of bearing #1 in FIG. 8, is calculated. The error is calculated, for example, as follows: (closest value included in peak frequency list L1 - cage frequency f1) / cage frequency f1 x 100. In the case of the previous example, the error d1 for the cage frequency f1 is (32.0-28.1) / 28.1 x 100 ≈ 13.8.

[0045] Similarly, the error d2 for the inner rolling element passing frequency f2 is calculated to be 0.7, the error d3 for the outer rolling element passing frequency f3 is calculated to be 0.7, and the error d4 for the rolling element rotation frequency f4 is calculated to be 2.2. In this manner, the error calculation unit 12f calculates the natural frequency f of each bearing from the peak frequency list L1 and the natural frequency list L3. n The error is calculated from the above to generate a calculation result of the error for each bearing.

[0046] In step S9, the natural frequency derivation unit 12g calculates the natural frequency f of the bearing from the calculation result of the error Δ of each bearing generated in step S8. n and stores the result as derivation result 13c in the auxiliary storage device 13. If necessary, the derivation result is displayed on a monitor via the output interface 15, and the analyzed device state is output to an external diagnostic system.

[0047] The natural frequency f of bearing 21 at the current rotation speed n is derived, for example, as follows. In FIG. 10, the bearing # with the smallest error Δ is #6 with an error Δ of "6.5", so the bearing 21 to be diagnosed is most likely to be a bearing with specifications of #6, and the natural frequency f n By extracting the natural frequency f of bearing 21 at the current rotation speed (1200 rpm), n can be derived.

[0048] In this way, the bearing analysis device 1 according to the present embodiment acquires the vibration and rotation speed of the bearing 21, derives the peak frequency list L1 from a plurality of frequency analysis results for the vibration, calculates the error for each bearing from the peak frequency list L1 and the natural frequency list L3 (the standard natural frequency list L2 at the time of the standard rotation speed), and calculates the natural frequency f n This method derives the natural frequency f of the bearing 21 of the rotating equipment 2 without referring to the specifications of the bearing or spending man-hours on disassembling and inspecting the bearing. n Since it is possible to derive the above, it is possible to reduce the cost of the man-hours that were previously required to refer to the specifications of the bearing, or to disassemble and inspect the bearing.

[0049] In FIG. 2, step S1 is executed first and then step S2 is executed. However, as long as step S1 of acquiring a vibration signal precedes steps S3 to S5 of performing frequency analysis and step S2 of acquiring a rotation speed signal precedes step S8 of calculating an error, steps S1 and S2 may be executed at timings different from those shown in the flowchart of FIG. 2. EXAMPLES

[0050] Second Embodiment Next, a bearing analyzer 1 according to a second embodiment of the present invention will be described with reference to Figures 11 to 13. Note that a duplicated description of points common to the first embodiment will be omitted.

[0051] Fig. 11 is a functional block diagram of the bearing analysis device 1 of this embodiment. Whereas the bearing analysis device 1 of embodiment 1 merely derives the natural frequency of the bearing 21, the bearing analysis device 1 of this embodiment also has a function of diagnosing the bearing 21 using the derived natural frequency. For that reason, in this embodiment, the following configuration is added to the bearing analysis device 1 of embodiment 1. That is, a feature amount extraction unit 12h, a judgment criterion acquisition unit 12i, and an apparatus state judgment unit 12j are added to the main memory device 12, and judgment criteria 13d and judgment results 13e are added to the auxiliary memory device 13. The following will focus on the functions of the added configuration.

[0052] FIG. 12 is a flowchart showing an example of the device state estimation process performed by the bearing analyzer 1.

[0053] Step S11 corresponds to the process shown in FIG. 2 of the first embodiment, and is a process for calculating the natural frequency f n It should be noted that this step is a process that needs to be executed only once before the rotating device 2 is actually operated, and the following steps S12 to S15 are basically processes that are executed all the time while the rotating device 2 is actually operated.

[0054] In step S12, the vibration signal acquisition unit 12a acquires a vibration signal from the vibration sensor 22 via the input interface .

[0055] In step S13, the frequency analysis unit 12c performs frequency analysis on the vibration signal acquired in step S12, and the feature extraction unit 12h extracts the results of the frequency analysis corresponding to a plurality of bands centered on the plurality of natural frequencies derived in step S11 as features. Note that the frequency analysis executed here is, for example, a method of performing envelope processing on the vibration signal data and then mapping it to the frequency domain by Fourier transform, and the band is defined as ±5% of the derived natural frequency.

[0056] In step S14, the device state determination unit 12j uses the determination criterion 13d acquired by the determination criterion acquisition unit 12i from the auxiliary storage device 13 to determine the device state for each of the feature quantities extracted in each band, and stores the determination result as a determination result 13e in the auxiliary storage device 13. The determination criterion 13d has a normal value for each band and three categories for each band. The three categories are a category of less than 2, a category of 2 to less than 5, and a category of 5 or more. The maximum value in each band is divided by the normal value, and if it is less than 2, the determination result is set to 0, if it is 2 to less than 5, the determination result is set to 1, and if it is 5 or more, the determination result is set to 2.

[0057] Fig. 13 shows an example of the judgment result for each band. The judgment result shown here indicates that the cage and outer ring of the bearing 21 are normal (judgment result = 0), but minor damage has occurred in the rolling elements (judgment result = 1), and there is a possibility that major damage has occurred in the inner ring (judgment result = 2). In this case, the judgment result for the bearing as a whole is judgment result = 2, indicating the possibility of major damage.

[0058] Finally, in step S15, the device state determination unit 12j determines whether an instruction to end the determination has been issued. If the requirements are met, the process of FIG. 12 ends, and if the requirements are not met, the process returns to step S12 to continue monitoring the rotating device 2.

[0059] Thus, according to this embodiment, by outputting the judgment result 13e illustrated in FIG. 13 to an external display or the like via the output interface 15, a manager, inspector, etc. can easily know the condition (problem area) of the bearing 21 of the rotating equipment 2, thereby making it possible to reduce the costs associated with maintenance inspection, etc. [Explanation of symbols]

[0060] 1 Bearing analysis equipment 11 Arithmetic unit 12 Main storage 12a Vibration signal acquisition section 12b Rotational speed signal acquisition section 12c Frequency Analysis Section 12d Peak frequency list generator 12e Natural frequency list acquisition section 12f Error calculation section 12g Natural frequency derivation part 12h Feature extraction section 12i Judgment criteria acquisition part 12j Equipment status determination unit 13 Auxiliary storage device 13a Program Source 13b Standard Natural Frequency List 13c Derivation result 13d Judgment Criteria 13e Judgment result 14 Input Interface 15 Output Interface 2 Rotating Equipment 21 Bearings 22 Vibration Sensor 23 Rotational speed sensor L1 Peak Frequency List L2 Standard Natural Frequency List L3 Natural Frequency List

Claims

1. A bearing analysis device that derives a natural frequency of a bearing of a rotating device, comprising: a vibration signal acquisition unit that acquires a vibration signal from a vibration sensor installed in the vicinity of the bearing; a frequency analysis unit that performs frequency analysis on the acquired vibration signal using a plurality of methods; a peak frequency list generating unit that generates a peak frequency list by integrating the plurality of peak frequencies obtained by the frequency analysis unit; a natural frequency list acquisition unit that acquires a list of natural frequencies of a plurality of bearings; an error calculation unit that compares the peak frequency list with the natural frequency list to calculate an error; a natural frequency deriving unit that derives a natural frequency of the bearing based on a result of the error calculation; A bearing analysis device comprising:

2. 2. The bearing analysis device according to claim 1, a rotation speed signal acquisition unit that acquires a rotation speed signal from a rotation speed sensor of the rotating device, the natural frequency list acquisition unit acquires a standard natural frequency list prepared in advance based on a ratio of the rotation speed acquired by the rotation speed signal acquisition unit to a standard rotation speed, thereby acquiring the natural frequency list.

3. 2. The bearing analysis device according to claim 1, The bearing is a bearing including a cage, an inner ring, an outer ring, and rolling elements, the error calculated by the error calculation unit is a sum of an error from a cage frequency indicated in the natural frequency list, an error between the cage frequency indicated in the natural frequency list and an outer ring rolling element passing frequency, an error between the cage frequency indicated in the natural frequency list and an inner ring rolling element passing frequency, and an error between the cage frequency indicated in the natural frequency list and a rolling element rotation frequency, The bearing analysis device according to claim 1, wherein the natural frequency derivation unit extracts, from the natural frequency list, the natural frequency of a bearing having specifications for which the sum of the errors is minimum.

4. 2. The bearing analysis device according to claim 1, A feature extraction unit that extracts features of the acquired vibration signal; an apparatus state determination unit that determines a state of the rotating device by using a predetermined determination criterion and the feature amount; A bearing analysis device comprising:

5. A bearing analysis method for deriving a natural frequency of a bearing of a rotating device, comprising the steps of: a vibration signal acquiring step of acquiring a vibration signal from a vibration sensor installed in the vicinity of the bearing; A frequency analysis step of performing frequency analysis on the acquired vibration signal using a plurality of methods; a peak frequency list generating step of generating a peak frequency list by integrating the plurality of peak frequencies obtained in the frequency analysis step; A natural frequency list acquisition step of acquiring a natural frequency list of a plurality of bearings; an error calculation step of comparing the peak frequency list with the natural frequency list to calculate an error; a natural frequency deriving step of deriving a natural frequency of the bearing based on a result of the error calculation; A bearing analysis method comprising:

6. A program for causing a computing device to execute the bearing analysis method according to claim 5.

7. A program storage medium storing the program according to claim 6.

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