JP2006138817A - Method for calculating dynamics characteristics of powder, method for designing reservoir of powder, device for calculating dynamics characteristics of powder, program for calculating dynamics characteristics of powder, and recording medium having recorded dynamics characteristics calculation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for calculating dynamics characteristics or the like for determining the rupture envelope of powder precisely. <P>SOLUTION: The method is used to calculate adhesive force τc and a shear index (n) of powder from normal stress σ and shear stress τ of powder by utilizing a W-S formula expressing the rupture envelope of powder on a σ-τ plane. First, the measurement values of the normal stress σ, the shear stress τ, and tensile breaking stress σt are fitted to the W-S formula, thus acquiring the adhesive force τc and a shear index (n) (S11). Next, it is determined whether the shear stress τ in the W-S formula is larger than that at the upper side of a Mohr's circle passing through (σ, τ)=(0, 0), (-σt, 0) in the normal stress σ=-0.9×σt (S12). When it is determined not to be larger, correction is made to increase the shear index (n), and the corrected shear index (n) and the measured values of the normal stress σ and the shear stress τ are again fitted to the W-S formula, thus the corrected adhesive force τc is acquired (S13). <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention uses a Warren-Spring equation representing a fracture envelope of a powder, and calculates a powder adhesive force and a shear index from the powder normal stress, shear stress, and tensile rupture stress. The present invention relates to a mechanical property calculation method, a powder storage tank design method, a powder mechanical property calculation device, a powder mechanical property calculation program, and a recording medium on which the program is recorded.

  In order to design facilities that handle powder, not only the basic physical properties such as the density, particle size distribution, and liquid content of the powder layer, but also the mechanical properties such as the shear properties and adhesion properties of the powder layer are grasped. There is a need.

  For example, in powder storage equipment such as hoppers and silos, when powders approach each other and external force is applied to them, there may be a problem that the powders cannot be discharged due to clogging near the discharge port. . In many cases, the mechanical properties of the powder layer are deeply involved in the problem.

  Therefore, the designer of the equipment that handles the powder evaluates the mechanical characteristics of the powder layer of the powder that is handled, and based on the evaluation, designs the equipment appropriately so that the above-mentioned problems are unlikely to occur. .

  As a method for evaluating the mechanical properties of the powder layer, an evaluation method based on a shear test is known. The shear test is a test method for evaluating the fracture characteristics of a static powder layer by determining the relationship between the normal stress σ and the shear stress τ acting on the collapse surface when the static powder layer changes to a dynamic state due to collapse. Say. For a powder layer having a predetermined porosity ε, the experiment was performed while changing the vertical stress σ, and the shear stress τ with respect to each vertical stress σ was plotted on the σ-τ plane, whereby a fracture envelope YL as shown in FIG. Can be obtained.

Here, in Non-Patent Document 1, when the powder is a highly adherent powder that easily causes problems such as blockage at the discharge port, the fracture envelope YL may be well matched with the following equation. Are listed.
(Τ / τc) ⁿ = 1 + (σ / σt) (1).
Here, σt is the tensile breaking stress, τc is the adhesive force, and n is the shear index. The above formula is called the Warren-Spring formula or the Farley-Valentin formula. Hereinafter, Formula (1) is referred to as WS formula.

  Further, the relationship between the normal stress σ acting on the collapse surface in the steady state after changing to the dynamic state and the shear stress τ is obtained by a shear test and plotted on the σ-τ plane, as shown in FIG. Such a limit state line CSL can be obtained. The limit state line CSL is a straight line passing through the origin on the σ-τ plane.

  Then, a molding circle MC that passes through the intersection of the fracture envelope YL and the limit state line CSL and is in contact with the fracture envelope YL can be obtained. The tangent line from the origin of this molding circle is an effective destruction envelope EYL as shown in FIG. The inclination angle δ of the effective fracture envelope EYL corresponds to the friction angle of the powder under pressure, and is called the effective internal friction angle (see Non-Patent Document 2).

  As described above, the fracture envelope YL and the limit state line CSL can be obtained by a shear test. From the fracture envelope YL and the limit state line CSL, the tensile breaking stress σt, the adhesive force τc, the shear index n, and the effective internal friction angle Mechanical characteristics such as δ can be obtained.

Non-Patent Document 1 describes a method for obtaining fluidity evaluation and quality control of powder, and the diameter and inclination angle of the discharge port of storage tank equipment using the fracture envelope YL obtained by a shear test. ing.
K. Hirohiro, “Measuring method and utilization of mechanical properties of powder”, Powder and Industry, October 1, 1992, Vol. 24, No. 10, p. 61-74 Powder Equipment / Device Handbook Editorial Committee, “Powder Equipment / Device Handbook”, first edition, Nikkan Kogyo Shimbun, May 30, 1995, p. 63-68

  In order to accurately design facilities for handling powder, it is desired to accurately determine mechanical properties of the powder such as tensile breaking stress σt, adhesive force τc, shear index n, and effective internal friction angle δ. In order to accurately determine the mechanical properties of the powder, it is necessary to accurately determine the fracture envelope YL and the limit state line CSL.

  The present invention has been made in view of the above-described problems, and an object of the present invention is to provide a method for calculating powder mechanical properties and the like that can accurately determine a fracture envelope of the powder.

In order to solve the above problems, the method for calculating the mechanical properties of the powder according to the present invention has a WS formula that represents a fracture envelope of the powder in the σ-τ plane (where τ ≧ 0): (τ / τc) ^A method for calculating the mechanical properties of a powder, wherein ⁿ = 1 + (σ / σt) is used to calculate the adhesive force and shear index of the powder from the normal stress and shear stress of the powder, By fitting the measured values of stress and shear stress to the WS formula, the fitting step for obtaining the adhesive force and the shear index of the powder and the fitting step in the tensile region where the normal stress is negative were performed. In the WS equation, the shear stress in the equation above the Mole circle passing through (σ, τ) = (0,0) and (−σt, 0): τ = (− σ (σ + σt)) ^1/2 Whether it is greater than the shear stress And determining that the shear index obtained in the fitting step is increased, the corrected shear index, the normal stress and the shear stress are A correction step of acquiring a corrected adhesive force by fitting the measured value to the WS formula.

  The fracture envelope of the powder is expected to be in contact with the molding circle even in the tensile region where the normal stress σ is negative. Therefore, it is considered that the condition that the shear stress of the fracture envelope is equal to or greater than the shear stress of the Mole circle at an arbitrary normal stress σ in the tensile region is considered. Further, the Mole circle that is maximum in the tensile region is a Mole circle in a limit state immediately before the tensile fracture, that is, a Mole circle that passes through (σ, τ) = (0, 0) and (−σt, 0).

  Therefore, in the present invention, as in the above-described method, in the tensile region, the shear stress in the WS formula is that of the mole circle that passes through (σ, τ) = (0, 0) and (−σt, 0). When it is not larger than the shear stress in the upper equation, the shear index n is increased and re-fitting is performed to the WS formula. Thereby, since the destruction envelope can be moved in the direction satisfying the above condition, a more accurate destruction envelope can be obtained.

The method for calculating mechanical properties of powder according to the present invention preferably further includes a repetition step of returning to the determination step after the correction step and repeating the determination step and the correction step. By repeating the determination step and the correction step,
A more accurate fracture envelope can be reliably obtained.

  By the way, the fracture envelope and the Mole circle are in contact at (σ, τ) = (0, 0). Therefore, if it is determined whether or not the above condition is satisfied in the vicinity of the vertical stress of −σt (however, greater than −σt), it can be determined whether or not the fracture envelope intersects with the Mole circle. This (near -σt) is preferably greater than -σt and less than or equal to -0.85 × σt, and most preferably −0.9 × σt.

  Further, the shape of the curve of the function including the exponent is sensitive to changes in the exponent. Therefore, it is preferable that the increase in the shear index to be corrected in the correction step is small. Specifically, the increment of the shear index is preferably 0.01 or more and 0.1 or less, and most preferably 0.02.

  Of the mechanical properties included in the WS formula, the tensile breaking stress can be measured using a tensile breaking method. Some shearing test apparatuses that perform an actual shearing test can measure the tensile breaking stress by the above-described tensile breaking method.

  Therefore, the fitting step includes fitting the measured values of the normal stress and the shear stress and the measured values of the tensile rupture stress measured by using the tensile rupture method into a WS formula to thereby determine the adhesive force of the powder. And the correction step is performed by fitting the corrected shear index and the measured values of the normal stress, shear stress, and tensile rupture stress to the Warren Spring equation. It is good also as what acquires acquired adhesive force.

  Further, the fitting step is to obtain the tensile rupture stress, the adhesive force and the shear index of the powder by fitting the measured values of the normal stress and the shear stress to the Warren Spring equation, and the correction step. May obtain the corrected tensile rupture stress and adhesive force by fitting the corrected shear index and the measured values of the normal stress and the shear stress to the WS formula.

  In order to solve the above problems, the powder storage tank design method according to the present invention is determined by a fracture envelope represented by the WS formula obtained by the above-described method for calculating mechanical properties of powder and a shear test. It is characterized in that the diameter and the inclination angle of the outlet in the powder storage tank are obtained using the limit state line and the wall fracture envelope.

  According to the above method, since a more accurate fracture envelope can be used, the powder storage tank can be designed more accurately.

  The above-described powder mechanical property calculation method that calculates the adhesive force and shear index of a powder from the measured values of the normal stress and shear stress of the powder using the above-described mechanical property calculation method of the powder is also described above. The effect of this can be obtained.

  Further, each step in the above-described powder mechanical property calculation method can be executed on a computer by a powder mechanical property calculation program. Furthermore, by storing the powder mechanical property calculation program in a computer-readable recording medium, the powder mechanical property calculation program can be executed on an arbitrary computer.

  As described above, in the method for calculating the mechanical properties of the powder according to the present invention, in the tensile region, the shear stress in the WS formula is (σ, τ) = (0, 0) and (−σt, 0). If it is not larger than the shear stress in the equation above the passing circle, the shear index n is increased and re-fitting is performed to the WS formula, so that an accurate fracture envelope can be obtained. Play.

  Before describing one embodiment of the present invention, the principle of the powder mechanical property calculation method according to the present invention will be described with reference to FIGS.

  The fracture envelope YL of the powder layer is an envelope of the Mole circle group in a limit stress state, which is a state where the powder layer starts to collapse. As shown in FIG. 5, the stress acting on the inside of the powder layer in the critical stress state can be known by drawing a Mole circle (Mole fracture circle) MC in contact with the fracture envelope YL. Since the center of the Mole circle is on the σ axis, the intersections of the Mole circle and the σ axis are the maximum value and the minimum value of the normal stress σ, which are called the maximum principal stress σ1 and the minimum principal stress σ2, respectively. At this time, the shear stress τ is zero.

  FIG. 6 shows the Mole fracture circle MC and the fracture envelope YL in the tensile region where the normal stress is negative. In the illustrated molding failure circle MC, the maximum principal stress σ1 is zero, and the minimum principal stress σ2 is a negative number (−σt) of the tensile breaking stress σt. That is, the Mole fracture circle shown in the figure indicates the stress acting on the inside of the powder layer at the time of tensile fracture.

As shown in FIG. 6, the Mole fracture circle at the time of tensile fracture is in contact with the fracture envelope YL at (σ, τ) = (− σt, 0). For this reason, the fracture envelope YL needs to satisfy the following conditions. However, τ ≧ 0.
Condition 1: In (σ, τ) = (− σt, 0), the slope of the fracture envelope YL is infinite, which is the same as the slope of the Mole fracture circle at the time of tensile fracture.
Condition 2: -σt <σ <0 (tensile region), the shear stress τ of the fracture envelope YL is larger than the shear stress τ of the Mole fracture circle at the time of tensile fracture.

  Regarding condition 1, it is possible that condition 1 is satisfied by calculating the slope (dτ / dσ) of the WS formula (formula (1)) in (σ, τ) = (− σt, 0). Understandable. Therefore, it can be understood that whether or not the destruction envelope YL is accurate can be determined by the condition 2. Specifically, it is determined whether or not the condition 2 is satisfied with respect to the fracture envelope obtained by fitting the measured values of the normal stress σ and the shear stress τ in the shear test to the WS formula. If there is not, a more accurate fracture envelope can be obtained by correcting the shear index n or the adhesive force τc and performing fitting again.

Incidentally, the molding circle shown in FIG.
τ = (− σ (σ + σt)) ^1/2 (2).
Therefore, from the formulas (1) and (2), the condition 2 is expressed by the following formula in the tensile region.
τc ((σ + σt) / σt) ^{1 / n} > (− σ (σ + σt)) ^1/2 (3)
Here, if the dimensionless parameter k is defined as k≡σ / σt (where -1 <k <0), Equation (3) becomes the following equation.
f (k)> σt / τc (4).
Here, f (k) ≡ (k + 1) ^{1 / n} / (− k (k + 1)) ^1/2 .

  FIG. 7 shows the calculation result of the function f (k) with the shear index n as a parameter. In the figure, k = 0 corresponds to σ = 0, and k = −1 corresponds to σ = −σt. Further, the graphs of the shear index n = 2.5 and 3 are too large as an actual powder, but are described as a reference in order to know the tendency when n> 2.

  Referring to FIG. 7, when the value of the parameter k approaches −1, that is, the normal stress σ approaches −σt, the value of the function f (k) diverges to infinity when n> 2, and n = It can be seen that when 2 is converged to 1, and when n <2, it diverges to negative infinity. Therefore, it can be understood that the above equations (3) and (4) should exclude the case of k = −1, that is, σ = −σt.

  In the actual powder, the value of the shear index n is about 1 to 2, and the value of σt / τc is about 0.1 to about 1 (rarely about 2). Therefore, referring to FIG. 7, if the parameter k is −0.6 or more, the above equations (3) and (4) are unconditionally satisfied, and the above equations (3) and (4) are broken. Even if it is used to correct a line, it is meaningless.

  Then, next, it is examined whether the value of the parameter k is desirable for determining whether or not the above expressions (3) and (4) are satisfied. Now, when fitting to the WS formula is performed, it is assumed that a fracture envelope intersecting with the molding circle is obtained as shown by a broken line in FIG. At this time, a region S surrounded by the destruction envelope YL and the molding circle MC is generated. Next, the adhesive force τc is increased, and the area of the region S and the position of the intersection between the fracture envelope YL and the molding circle MC are examined. As a result, a result as shown in FIG. 9 was obtained.

  Referring to FIG. 9, the area S2 of the region S of k = −0.85 is 1/10 of the area S1 of the region S of k = −0.64, and k = −0.9. It can be understood that the area S3 of the region S is 1/20. Therefore, in determining whether or not the above expressions (3) and (4) are satisfied, it is desirable that the parameter k is in a range greater than −1 and not greater than about −0.85. It can be seen that it is most desirable. That is, it can be understood that the normal stress σ is preferably in the range of greater than −σt and not greater than about (−0.85 × σt), and most preferably about (−0.9 × σt).

Embodiment
Hereinafter, an embodiment of the present invention will be described with reference to FIGS. 1 to 4 and FIGS. 10 to 12. FIG. 2 shows an outline of the powder storage tank design system according to this embodiment. The system 10 includes a shear test device 11, a mechanical property calculation device 12, and a storage tank design device 13. These devices 11 to 13 have the same configuration as a general computer.

  The shear test apparatus 11 measures the normal stress σ and the shear stress τ by a shear test. Further, the shear test apparatus 11 can measure the tensile breaking stress σt by the tensile breaking method. The shear test apparatus 11 outputs the measured normal stress σ, shear stress τ, and tensile rupture stress σt to the mechanical property calculation apparatus 12.

  An example of such a shear test apparatus 11 is POWDER BED TESTER PTHN-13BA manufactured by Sankyo Piotech Co., Ltd., which is a Jenike shear test apparatus. This apparatus measures the shear stress τ by a shear test, can measure the tensile rupture strength (stress) σt by a tensile rupture method, and can measure the porosity ε when measuring the tensile rupture strength σt.

  The mechanical characteristic calculation device 12 uses the measured values of the normal stress σ, the shear stress τ, and the tensile rupture stress σt acquired from the shear test device 11 to obtain the fracture envelope YL, and WS that indicates the fracture envelope YL. The adhesive force τc and the shear index n in the equation are calculated. When the shear test apparatus 11 does not measure the tensile rupture stress σt, the adhesive strength τc and the shear index n are obtained by fitting to the WS formula using the measured values of the normal stress σ and the shear stress τ. At the same time, the tensile breaking stress σt can be calculated.

  Further, the mechanical property calculation device 12 obtains a limit state line CSL by using the measured values of the normal stress σ and the shear stress τ acquired from the shear test device 11, and based on the limit state line CSL and the fracture envelope YL. An effective fracture envelope EYL is obtained, and an effective internal friction angle δ, which is a mechanical characteristic indicating the effective fracture envelope EYL, is calculated.

  Further, the mechanical property calculation device 12 obtains a wall fracture envelope WYL (see FIG. 12) using the measured values of the normal stress σ and the shear stress τ acquired from the shear test device 11, and the wall fracture envelope WYL. The wall friction angle φw indicating is calculated. The wall fracture envelope WYL is obtained by changing the movable plate to the wall material to be designed in the parallel plate type shear test device such as POWDER BED TESTER PTHN-13BA manufactured by Sankyo Piotech Co., Ltd. It can be determined by measuring the shear stress τ.

  Further, the mechanical property calculation device 12 outputs the acquired or calculated mechanical properties, that is, the adhesive force τc, the shear index n, the tensile breaking stress σt, the effective internal friction angle δ, and the wall friction angle φw to the storage tank design device 13.

  The storage tank design device 13 uses the adhesive force τc, the shear index n, the tensile breaking stress σt, the effective internal friction angle δ, and the wall friction angle φw acquired from the mechanical property calculation device 12 to design a storage tank that is unlikely to block. To do.

  In the above devices 11 to 13, any form can be used as the form for outputting information to the outside. For example, the form for printing data on a print medium, the form for recording data on a recording medium, Further, there is a mode in which data is transmitted to an external device via a communication medium. Similarly, any form can be used as a form for acquiring information from the outside. For example, a form for scanning a print medium, a form for reading data from a recording medium, and a communication medium from an external device. The form which receives data via is mentioned.

  Next, the mechanical characteristic calculation device 12 and the storage tank design device 13 will be described in more detail. First, details of the mechanical characteristic calculation device 12 will be described with reference to FIGS.

  FIG. 3 shows a schematic configuration of the mechanical characteristic calculation device 12. As illustrated, the mechanical characteristic calculation device 12 includes an input unit 20, a fracture envelope calculation unit 21, a limit state line calculation unit 22, a wall fracture envelope calculation unit 23, an effective fracture envelope calculation unit 24, and an output unit 25. It is the structure provided with.

  The input unit 20 receives information input from the shear test apparatus 11 using an input device, a scan device, a playback device, a reception device, or the like. Further, the input unit 20 transmits data from the shear test apparatus 11 to the fracture envelope calculation unit 21, the limit state line calculation unit 22, and the wall fracture envelope calculation unit 23.

  Examples of the input device include a keyboard, a numeric keypad, a cursor key, for example, a pointing device such as a mouse, and a touch panel. The playback device plays back data recorded on an external recording medium such as a flexible disk, an optical disk, or a magneto-optical disk. Examples thereof include a flexible disk drive, a CD-ROM drive, a DVD drive, and an MO drive. It is done.

  The fracture envelope calculation unit 21 obtains the fracture envelope YL using the measured values of the normal stress σ, the shear stress τ, and the tensile fracture stress σt obtained from the shear test apparatus 11 via the input unit 20, and obtains the fracture envelope. An adhesive force τc and a shear index n, which are mechanical characteristics in the WS formula showing the line YL, are calculated. The destruction envelope calculation unit 21 sends the obtained destruction envelope YL to the effective destruction envelope calculation unit 24. Further, the fracture envelope calculation unit 21 transmits the calculated values of the adhesive force τc and the shear index n together with the measured value of the tensile fracture stress σt to the output unit 25. Details of the destruction envelope calculation unit 21 will be described later.

  The limit state line calculation unit 22 obtains the limit state line CSL using the measured values of the normal stress σ and the shear stress τ acquired from the shear test apparatus 11 via the input unit 20. The limit state line calculation unit 22 sends the obtained limit state line CSL to the effective fracture envelope calculation unit 24.

  The wall fracture envelope calculation unit 23 obtains the wall fracture envelope WYL using the measured values of the vertical stress σ and the shear stress τ acquired from the shear test apparatus 11 via the input unit 20, and calculates the wall fracture envelope WYL. The wall friction angle φw shown is calculated. The wall fracture envelope calculation unit 23 transmits the calculated value of the wall friction angle φw to the output unit 25.

  The effective destruction envelope calculation unit 24 obtains the effective destruction envelope EYL using the destruction envelope YL acquired from the destruction envelope calculation unit 21 and the limit state line CSL acquired from the limit state line calculation unit 22. The effective internal friction angle δ, which is a mechanical characteristic indicating the effective fracture envelope EYL, is calculated. The effective fracture envelope calculation unit 24 transmits the calculated value of the effective internal friction angle δ to the output unit 25.

  The output unit 25 outputs the mechanical characteristics τc · n · σt · φw · δ received from the fracture envelope calculation unit 21, the wall fracture envelope calculation unit 23, and the effective fracture envelope calculation unit 24, as a print output device and a recording device. Information is output to the storage tank design device 13 using a transmission device or the like.

  Note that the recording device records data on an external recording medium such as a flexible disk, an optical disk, and a magneto-optical disk, and examples thereof include a flexible disk drive, a CD-R drive, and an MO drive.

  Next, details of the fracture envelope calculation unit 21 will be described with reference to FIGS. 1 and 4. FIG. 4 shows a schematic configuration of the fracture envelope calculation unit 21. As illustrated, the fracture envelope calculation unit 21 includes a measurement value acquisition unit 30, a storage unit 31, a fitting unit 32, a determination unit 33, a shear index correction unit 34, and a re-fitting unit 35.

  The measurement value acquisition unit 30 acquires measurement values of the normal stress σ, the shear stress τ, and the tensile rupture stress σt from the shear test apparatus 11 via the input unit 20. The measurement value acquisition unit 30 stores the acquired measurement value in the storage unit 31. The storage unit 31 has a function of storing various types of information, and is configured by, for example, a semiconductor memory or a hard disk.

  The fitting unit 32 fits the measured values of the normal stress σ, the shear stress τ, and the tensile rupture stress σt read from the storage unit 31 to the WS formula, and the adhesive force τc, which is a mechanical characteristic in the WS formula, The shear index n is calculated. The fitting unit 32 transmits the tensile fracture stress σt read from the storage unit 31 and the calculated adhesive force τc and the shear index n to the determination unit 33.

  The determination unit 33 uses the tensile rupture stress σt, the adhesive force τc, and the shear index n received from the fitting unit 32 or the re-fitting unit 35, and when the normal stress σ is −0.9 × σt, W− The shear stress τ (where τ ≧ 0) in the S-formation is a Mole circle that passes through (σ, τ) = (0, 0) and (−σt, 0), that is, a Mole fracture circle in the critical stress state immediately before the tensile fracture. It is determined whether or not the condition that the shear stress τ is greater than τ (where τ ≧ 0) is satisfied.

  When this condition is satisfied, the determination unit 33 outputs the received tensile rupture stress σt, adhesive force τc, and shear index n to another block, assuming that the fracture envelope YL has been obtained. On the other hand, when the above condition is not satisfied, the determination unit 33 transmits the shear index n to the shear index correction unit 34 on the assumption that the fracture envelope YL needs to be corrected.

  The shear index correction unit 34 corrects the shear index n received from the determination unit 33 so as to increase by a predetermined increment (preferably about 0.02). The shear index correction unit 34 transmits the corrected shear index n to the re-fitting unit 35.

  The re-fitting unit 35 calculates the normal stress σ, the shear stress τ, and the tensile rupture stress σt read from the storage unit 31, and the shear index n corrected by the shear index correction unit 34 and received from the shear index correction unit 34. , The fitting force τc, which is a mechanical characteristic in the WS equation, is calculated by re-fitting to the WS equation. The re-fitting unit 35 transmits the tensile fracture stress σt read from the storage unit 31, the shear index n received from the shear index correction unit 34, and the calculated adhesive force τc to the determination unit 33. Thereby, the determination operation in the determination unit 33 is repeated.

  FIG. 1 shows a processing operation in the destruction envelope calculation unit 21 having the above configuration. As shown in the figure, first, the measurement value acquisition unit 30 acquires measurement values of the normal stress σ, the shear stress τ, and the tensile rupture stress σt (step S10 (hereinafter sometimes abbreviated as “S10”). The same applies to the steps))).

  Next, using the measured values of the obtained normal stress σ, shear stress τ, and tensile rupture stress σt, the fitting unit 32 performs fitting to the WS formula, thereby obtaining the adhesive force τc and the shear index n. . Next, the determination unit 33 determines that the shear stress τ when the vertical stress σ is −0.9 × σt is greater in the fitted WS formula than the Mole fracture circle in the tensile region at τ ≧ 0. It is determined whether or not the condition that is large is satisfied (S12).

  When the above condition is not satisfied (NO in S12), the shear index correction unit 34 increases the shear index n by a predetermined increment, and increases the shear index n, the normal stress σ, the shear stress τ, and the tension. Using the measured value of the breaking stress σt, the re-fitting unit 35 performs the fitting to the WS formula again, thereby obtaining the adhesive force τc (S13). Then, it returns to step S12 and repeats the said processing operation.

  Note that if the increase in the shear index n is too large, the shape of the fracture envelope may change abruptly and the accuracy may deteriorate, whereas if it is too small, the determination processing and re-fitting processing will increase. The processing time becomes longer. Therefore, the increment of the shear index n is desirably about 0.01 or more and about 0.1 or less, and particularly desirably about 0.02.

  On the other hand, if the above condition is satisfied (YES in S12), the determination unit 33 determines that the fracture envelope YL has been obtained, and the determination unit 33 sets the acquired tensile rupture stress σt, adhesive force τc, and shear index n to other blocks. Output. Thereafter, the processing operation in the destruction envelope calculation unit 21 is terminated.

  Next, details of the storage tank design device 13 will be described with reference to FIGS. Now, as shown in FIG. 10, consider a case where a storage tank 40 is designed in which the lower part is tapered and the lowermost part is a powder outlet. Further, the minimum discharge port diameter at which blockage is unlikely to occur is defined as the minimum diameter B, and the angle formed between the vertical direction and the tapered surface is defined as the inclination angle α.

  11 and 12 show the processing operation for obtaining the minimum aperture B and the inclination angle α. In this processing operation, mechanical characteristics σt · τc · n of the fracture envelope YL regarding the powder to be designed, mechanical characteristics δ of the effective fracture envelope EYL, and mechanical characteristics φw of the wall fracture envelope WYL are obtained as a mechanical characteristic calculation device. It starts by acquiring from 12.

  First, as shown in FIG. 13, the fracture strength fc, which is the principal stress of the larger Mole fracture circle passing through the origin, is obtained from the fracture envelope YL (S40). Further, as shown in FIG. 13, the Mole fracture circle in contact with the destruction envelope YL and the effective destruction envelope EYL passes through the intersection of the destruction envelope YL and the limit state line CSL and is in contact with the destruction envelope YL. Since it is a circle, the larger principal stress of the Mole fracture circle is the maximum principal stress σ1. Therefore, the maximum principal stress σ1 is obtained from the fracture envelope YL and the effective fracture envelope EYL (S42).

  Next, at least three sets (fc, δ, σ1) are obtained by changing the pre-consolidation of the powder and repeating the steps S40 and S42 (S44). Thus, since at least three points can be plotted on the σ 1 -δ plane, the relationship of the effective friction angle δ to the maximum principal stress σ 1 can be represented by a graph (S45).

  Similarly, since at least three points can be plotted on the σ1-fc plane, the relationship of the fracture strength fc to the maximum principal stress σ1 can be represented by a graph (S46). Here, the value of σ 1 / fc represents the fluidity of the powder and is defined as FF (flow function).

  Further, the representative value δ0 of the effective friction angle δ is selected from at least three sets (fc, δ, σ1) obtained in step S44 (S47). An example of the representative value δ0 is an intermediate value of the effective friction angle δ.

  Next, using the representative value δ0 of the effective friction angle selected in step S47 and the wall friction angle φw acquired from the mechanical characteristic calculation device 12, the critical inclination angle αc and the flow factor that serve as the boundary between the funnel flow and the mass flow are used. ff is obtained (S48). The critical inclination angle αc can be obtained by using a flow pattern determination diagram (not shown) showing the boundary line between the funnel flow region and the mass flow region for each effective internal friction angle δ in the α-φw plane.

  Further, the flow factor ff can be obtained from a calculation formula using the representative value δ0 of the effective friction angle, the wall friction angle φw, and the critical inclination angle αc as variables. Alternatively, the flow factor ff can be obtained using a contour map of the flow factor ff in the α-φw plane when the effective friction angle δ is the representative value δ0.

  Here, the flow factor ff represents the fluidity of the flow path, and is ff = σ1 / (bar σ1). The bar σ1 is the maximum principal stress that works along the arch portion in the powder layer. Therefore, the flow factor ff is a straight line passing through the origin on the σ1− (bar σ1) plane.

  Next, the intersection of the graph of the flow function FF on the σ 1 -fc plane and the graph of the flow factor ff on the σ 1-(bar σ 1) plane is obtained, and the maximum principal stress σ 1 at the intersection is obtained (S49). Next, the obtained effective friction angle δ at the maximum principal stress σ1 is obtained using the graph of the effective friction angle δ with respect to the maximum principal stress σ1 expressed in step S45, and this is set as a calculated value δ1 (S50). .

  Next, steps S47 to S50 are repeated with the calculated value δ1 as the representative value δ0 until δ1 = δ0 ± 1.5, that is, until the calculated value δ1 coincides with the representative value δ0 within the allowable range (S51). .

  Next, the maximum principal stress bar σ1 at the intersection of the graph of the flow function FF and the graph of the flow factor ff determined in step S49 is determined (S52), and α = αc−4 (S53). The process of step S53 is an angle narrowed by 4 degrees from the critical inclination angle αc in order to ensure that the entire powder is discharged by its own weight when the cross section of the discharge port of the storage tank is circular. Is the designed inclination angle α. In addition, when the cross section of the discharge port of the storage tank is rectangular, the critical inclination angle αc is set as the designed inclination angle α.

  By the way, in the limit state where the arch portion is held at the opening of the storage tank, the force balance equation γ × B × g = H (α) × (bar σ 1) is established. Here, γ is a bulk density, g is a gravitational acceleration, and H (α) is a correction term in consideration of the inclination angle α at both ends of the arch portion. In the balance type, the left side corresponds to the weight of the arch part, and the right side corresponds to the force necessary to support the arch part. The balance equation is an equation when an SI unit system is used as a unit of force. When a gravity unit system such as gram weight or kilogram weight is used, it is necessary to omit the gravitational acceleration on the left side. .

  Accordingly, in order to obtain the minimum opening diameter B, H (α) is obtained by using α obtained in step S53 (S54), and the obtained H (α) and the obtained from step S52 (bar σ1). Then, B = (bar σ1) × H (α) / (γ × g) is calculated using the bulk density γ obtained from the particle density Dens and the porosity ε (S55).

  Here, H (α) can be obtained from the approximate expression H (α) = 2 + (α / 60) when the discharge part at the lower part of the storage tank has a conical cone shape, and the cross section of the discharge part is rectangular. In this case, the approximate expression H (θ) = 1 + (θ / 180) can be obtained. Alternatively, H (α) can be obtained from a graph showing the relationship between the inclination angle α and H (α).

  Then, the inclination angle α obtained in step S53 and the minimum aperture B obtained in step S55 are output (S56), and the processing operation is terminated.

〔Example〕
Using the powder storage tank design system 10 of the above embodiment, the storage tank was designed from actual powder.

  In this example, fly ash was used as the powder. Regarding the particle size distribution of the powder, the volume-based geometric average diameter was 18 μm, and the geometric standard deviation was 2.0. As the shear test apparatus 11, the above-mentioned POWDER BED TESTER PTHN-13BA manufactured by Sankyo Piotech Co., Ltd. was used.

  Next, when the measured values of the normal stress σ, the shear index n, and the tensile breaking stress σt output from the shear test apparatus 11 are input to the mechanical property calculation apparatus 12, a fracture envelope YL is obtained. The fracture envelope YL has a tensile fracture stress σt = 247 Pa, an adhesive force τc = 282 Pa, and a shear index n = 1.7, and is as shown by a solid line in FIG. And when the said mechanical characteristic from the mechanical characteristic calculation apparatus 12 was input into the storage tank design apparatus 13, it became the minimum diameter B = 110mm of the storage tank. The inclination angle was constant at 23 °.

  Next, as a comparative example of the above example, a storage tank was designed for the same powder by obtaining the fracture envelope YL by a conventional method. At this time, the obtained fracture envelope YL was the tensile fracture stress σt = 247 Pa, the adhesive force τc = 245 Pa, and the shear index n = 1.4, and was as shown by the broken line in FIG. The fracture envelope YL intersected with the mole circle at σ = −0.64 × σt. Moreover, when the storage tank was designed using this fracture envelope YL, the minimum diameter B of the storage tank was 135 mm, which was larger than that of the example. The inclination angle was constant at 23 °.

  Next, 15 types of SUS hoppers with an inclination angle of 23 ° (constant) and a minimum aperture B of 80 mm to 150 mm in 5 mm increments were manufactured, and it was confirmed whether or not the fly ash was actually discharged in its entirety. It was. As a result, when the minimum diameter B was 105 mm or more, the entire amount of fly ash was discharged. From the above results, it can be understood that the present embodiment can design a more accurate storage tank than the conventional one.

  The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. That is, embodiments obtained by combining technical means appropriately changed within the scope of the claims are also included in the technical scope of the present invention.

  For example, in the said embodiment, although the shear test apparatus 11, the dynamic characteristic calculation apparatus 12, and the storage tank design apparatus 13 are comprised separately, any two or all can also be provided integrally.

  In addition, the applicant of the present application constructed a causal relationship between the basic physical properties and mechanical properties of the powder using an NN (neural network) model, and used the constructed NN model to obtain the mechanical properties from the basic physical properties of the powder. It has been proposed to calculate and further design a storage tank (for example, Japanese Patent Application No. 2003-94671). In order to reflect an accurate causal relationship in the NN model, it is necessary to accurately obtain basic physical properties and mechanical properties of the powder. Therefore, when constructing the NN model for the first time, by using the mechanical property calculation device 12 of the above embodiment, the tensile rupture stress σt, the adhesive force τc, and the shear index n, which are the mechanical properties of the WS formula, are accurately determined. Since it can be obtained well, a highly accurate NN model can be constructed.

  Moreover, each structure of the shear test apparatus 11, the dynamic characteristic calculation apparatus 12, and the storage tank design apparatus 13 may be comprised by hardware logic, and may be implement | achieved by software using CPU as follows.

  That is, the shear test apparatus 11, the mechanical property calculation apparatus 12, and the storage tank design apparatus 13 are a CPU (central processing unit) that executes instructions of a control program that realizes each function, and a ROM (read only memory) that stores the program. A RAM (random access memory) for expanding the program, and a storage device (recording medium) such as a memory for storing the program and various data. The object of the present invention is a recording medium in which the program code (execution format program, intermediate code program, source program) of the control program of each of the devices 11 to 13, which is software that implements the functions described above, is recorded in a computer-readable manner. Can also be achieved by reading the program code recorded on the recording medium and executing it by the computer (or CPU or MPU).

  Examples of the recording medium include tape systems such as magnetic tape and cassette tape, disk systems including magnetic disks such as flexible disks / hard disks, and optical disks such as CD-ROM / MO / MD / DVD / CD-R, and IC cards. A card system such as an optical card (including a memory card) or a semiconductor memory system such as a mask ROM / EPROM / EEPROM / flash ROM can be used.

  Moreover, the shear test apparatus 11, the dynamic characteristic calculation apparatus 12, and the storage tank design apparatus 13 may be configured to be connectable to a communication network, and the program code may be supplied via the communication network. The communication network is not particularly limited. For example, the Internet, intranet, extranet, LAN, ISDN, VAN, CATV communication network, virtual private network, telephone line network, mobile communication network, satellite communication. A net or the like is available. Also, the transmission medium constituting the communication network is not particularly limited. For example, even in the case of wired such as IEEE 1394, USB, power line carrier, cable TV line, telephone line, ADSL line, etc., infrared rays such as IrDA and remote control, Bluetooth ( (Registered trademark), 802.11 wireless, HDR, mobile phone network, satellite line, terrestrial digital network, and the like can also be used. The present invention can also be realized in the form of a carrier wave or a data signal sequence in which the program code is embodied by electronic transmission.

  By changing the shear index and re-fitting when the conditions in the tensile region are not met, a more accurate fracture envelope can be obtained, so when there are many powder errors or measured values by the shear test are small Even in this case, the fracture envelope can be obtained with high accuracy.

It is a flowchart which shows the processing operation of the fracture | rupture envelope calculation part in the mechanical property calculation apparatus of the storage tank design system which is one Embodiment of this invention. It is a block diagram which shows schematic structure of the said storage tank design system for powders. It is a block diagram which shows schematic structure of the said dynamic characteristic calculation apparatus. It is a block diagram which shows schematic structure of the said destruction envelope calculation part. It is a graph which shows a destruction envelope and a mole circle. It is a graph which shows the fracture | rupture envelope and a mole circle in a tension | pulling area | region. It is a graph which shows the mode of change with respect to the parameter k of the function f (k). It is a graph which shows the destruction envelope calculated | required in the Example and the comparative example. It is a figure which shows in a tabular form how the area of the area | region enclosed by a destruction envelope and a mole circle will change when adhesive force is changed. It is a schematic diagram which shows the storage tank designed in a storage tank design apparatus. It is a flowchart which shows the processing operation which calculates | requires the minimum diameter and inclination | tilt angle of the said storage tank. It is a flowchart which shows the processing operation which calculates | requires the minimum diameter and inclination | tilt angle of the said storage tank. It is a graph which shows the correspondence of the normal stress obtained by a shear test, and a shear stress.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Powder storage tank design system 11 Shear test apparatus 12 Mechanical property calculation apparatus 13 Storage tank design apparatus 21 Fracture envelope calculation part 30 Measurement value acquisition part 32 Fitting part 33 Judgment part 34 Shear index correction part 35 Refitting part 40 Storage tank YL destruction Envelope MC MC circle B Minimum tank diameter α Inclination angle

Claims (12)

In the σ-τ plane (where σ: normal stress, τ: shear stress, τ ≧ 0), Warren-Spring equation representing the fracture envelope of the powder:
(Τ / τc) ⁿ = 1 + (σ / σt),
(Where σt: tensile rupture stress, τc: adhesive force, n: shear index) and the powder mechanics for calculating the powder adhesive force and shear index from the powder normal stress and shear stress A characteristic calculation method comprising:
Fitting step to obtain the powder adhesion and shear index by fitting the normal and shear stress measurements from the shear test to the Warren Spring equation;
In the tensile region where the normal stress is negative, the shear stress in the Warren-Spring equation fitted in the fitting step is that of the Mole circle passing through (σ, τ) = (0,0) and (−σt, 0). Upper equation:
τ = (− σ (σ + σt)) ^1/2 ,
A determination step for determining whether the shear stress is larger than the shear stress in
If it is determined in the determination step that it is not large, the shear index acquired in the fitting step is corrected so as to increase, and the corrected shear index and the measured values of the normal stress and shear stress are converted into the Warren. A method for calculating the mechanical properties of a powder, comprising: a correction step of obtaining a corrected adhesive force by fitting to a spring equation.   2. The method for calculating mechanical properties of powder according to claim 1, further comprising a repetition step of returning to the determination step after the correction step and repeating the determination step and the correction step.   3. The powder mechanical property according to claim 1, wherein the determining step is a step of determining based on a shear stress when the normal stress is greater than −σt and −0.85 × σt or less. Calculation method.   4. The method for calculating mechanical properties of powder according to claim 3, wherein the determining step is a step of determining based on a shear stress when the normal stress is −0.9 × σt.   The method for calculating the mechanical properties of a powder according to any one of claims 1 to 4, wherein an increase in the shear index to be corrected in the correcting step is 0.01 or more and 0.1 or less.   6. The method for calculating mechanical properties of powder according to claim 5, wherein the increase in the shear index is 0.02. The fitting step includes fitting the measured values of the normal stress and the shear stress and the measured values of the tensile rupture stress measured by using the tensile rupture method to the Warren Spring equation, and thereby the adhesion force of the powder and To obtain the shear index,
The correcting step obtains a corrected adhesive force by fitting the corrected shear index and the measured values of the normal stress, shear stress, and tensile breaking stress to the Warren Spring equation. The method for calculating mechanical properties of a powder according to any one of claims 1 to 6. The fitting step is to obtain the tensile rupture stress, adhesive force, and shear index of the powder by fitting the measured values of the normal stress and shear stress to the Warren Spring equation,
The correcting step is to obtain the corrected tensile breaking stress and adhesive force by fitting the corrected shear index and the measured values of the normal stress and the shear stress to the Warren spring equation. The method for calculating mechanical properties of a powder according to any one of claims 1 to 6, characterized in that:   A fracture envelope expressed by a Warren-Spring equation obtained by the method for calculating mechanical properties of powder according to any one of claims 1 to 8, a limit state line and a wall fracture envelope obtained by a shear test. A method for designing a storage tank for powder, wherein the diameter and the inclination angle of the outlet of the storage tank for powder are obtained.   Using the method for calculating mechanical properties of powder according to any one of claims 1 to 8, calculating the adhesive force and shear index of powder from the measured values of normal stress and shear stress of powder. An apparatus for calculating mechanical properties of powders characterized by the following.   A program for calculating mechanical properties of powder, which causes a computer to execute the method for calculating mechanical properties of powder according to any one of claims 1 to 8.   A computer-readable recording medium on which the program for calculating mechanical properties of powder according to claim 11 is recorded.

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