LINEAR GROOVE FORMATION METHOD AND METHOD FOR PRODUCING GRAIN-ORIENTED ELECTRICAL STEEL SHEET
20220267872 · 2022-08-25
Assignee
Inventors
- Yoshihisa ICHIHARA (Tokyo, JP)
- Takeshi Omura (Tokyo, JP)
- Hirotaka Inoue (Tokyo, JP)
- Shigehiro Takajo (Tokyo, JP)
Cpc classification
B23K26/0869
PERFORMING OPERATIONS; TRANSPORTING
B23K26/40
PERFORMING OPERATIONS; TRANSPORTING
C22C38/60
CHEMISTRY; METALLURGY
B23K26/0846
PERFORMING OPERATIONS; TRANSPORTING
C21D8/12
CHEMISTRY; METALLURGY
C22C38/12
CHEMISTRY; METALLURGY
B23K2101/16
PERFORMING OPERATIONS; TRANSPORTING
International classification
Abstract
A linear groove formation method including forming a coated resist on a surface of a steel sheet, irradiating two or more laser beams onto the surface of the steel sheet while scanning the laser beams in a direction intersecting the rolling direction of the steel sheet cyclically in a rolling direction of the steel sheet, and forming linear grooves by etching portions of the steel sheet. In the laser irradiating process, the coated resist is removed continuously in a sheet transverse direction of the steel sheet by using the laser beams irradiated from respective ones of two or more laser irradiation devices arranged in the sheet transverse direction, and the laser beams are irradiated by shifting centers of two of the laser beams irradiated from two of the laser two of the laser irradiation devices adjacent to each other in the sheet transverse direction.
Claims
1. A linear groove formation method comprising: forming process of forming a coated resist on a surface of a steel sheet, irradiating two or more laser beams onto the surface of the steel sheet while scanning the two or more laser beams in a direction intersecting an rolling direction of the steel sheet cyclically in the rolling direction of the steel sheet to remove the coated resist from portions irradiated with the two or more laser beams, and forming linear grooves by etching portions of the steel sheet from which the coated resist has been removed, wherein, in the irradiating: the coated resist is removed continuously in a sheet transverse direction of the steel sheet by the two or more laser beams irradiated from respective ones of two or more laser irradiation devices arranged in the sheet transverse direction; and when a spot diameter of the two or more laser beams is defined as Φ, the two or more laser beams are irradiated by shifting centers of two of the two or more laser beams irradiated from two of the two or more laser irradiation devices adjacent to each other in the sheet transverse direction by Φ multiplied by 0.05 or more and 0.95 or less in a direction perpendicular to a laser scanning direction.
2. The linear groove formation method according to claim 1, wherein a length in the laser scanning direction of an overlapped portion of portions irradiated with the two of the two or more laser beams is 50 mm or less.
3. The linear groove formation method according to claim 1, wherein the spot diameter Φ of the two or more laser beams is 1 μm or more and 100 μm or less, and an irradiation energy of the two or more laser beams is 1 Jim or more and 30 J/m or less.
4. A method for producing a grain-oriented electrical steel sheet, the method comprising: forming linear grooves on a surface of a grain-oriented electrical steel sheet by the linear groove formation method according to claim 1.
5. The linear groove formation method according to claim 2, wherein the spot diameter Φ of the two or more laser beams is 1 μm or more and 100 μm or less, and an irradiation energy of the two or more laser beams is 1 Jim or more and 30 J/m or less.
6. A method for producing a grain-oriented electrical steel sheet, the method comprising: forming linear grooves on a surface of a grain-oriented electrical steel sheet by the linear groove formation method according to claim 2.
7. A method for producing a grain-oriented electrical steel sheet, the method comprising: forming linear grooves on a surface of a grain-oriented electrical steel sheet by the linear groove formation method according to claim 3.
8. A method for producing a grain-oriented electrical steel sheet, the method comprising: forming linear grooves on a surface of a grain-oriented electrical steel sheet by the linear groove formation method according to claim 5.
Description
BRIEF DESCRIPTION OF DRAWINGS
[0050]
[0051]
[0052]
[0053]
[0054]
[0055]
[0056]
DESCRIPTION OF EMBODIMENTS
[0057] First, experimental results which have led to the completion of the present disclosure will be described.
[0058] First, investigations were conducted regarding a resist pattern forming method for forming grooves by performing electroetching. By performing electroetching on a resist pattern formed by using each of a resist removing method, a gravure printing method, and an ink-jet printing method, grooves having a discontinuous portion 2 of center lines as illustrated in
[0059] After the linear grooves 1 were formed as described above, the coated resist remaining on the surface was stripped in an alkaline solution, decarburization annealing was performed, an annealing separator containing mainly MgO was coated to the annealed steel strip, and the steel strip was wound into a coil. Thereafter, final annealing was performed. After flattening annealing was performed on the steel strip subjected to the final annealing, a tension coating was formed on the steel strip surface to obtain a final product steel strip. Steel sheets each having a length in the sheet transverse direction of 100 mm and a length in the rolling direction of 280 mm were taken from the obtained steel strip, and magnetic properties were evaluated. For the evaluation of the magnetic properties of the steel sheet, iron loss W.sub.17/50 and magnetic flux density B.sub.8 were used. The expression “W.sub.17/50” denotes iron loss when alternating magnetization of 1.7 T and 50 Hz is performed in the rolling direction of the steel sheet, and the expression “B.sub.8” denotes magnetic flux density when magnetization is performed in the rolling direction with a magnetizing force of 800 A/m.
[0060] Iron loss W.sub.17/50 and B.sub.8 obtained by using each of the resist pattern forming methods are given in Table 1. It was clarified that a resist removing method provided the largest effect of improving iron loss. The reason for this is considered to be as follows. In the case of a resist removing method, since a melted portion as illustrated in
TABLE-US-00001 TABLE 1 Resist Pattern Forming No. Method Iron Loss W.sub.17/50 [W/kg] B.sub.8 [T] 1 Resist Peeling Method 0.690 1.930 2 Ink-jet Printing Method 0.700 1.930 3 Gravure Printing Method 0.710 1.920
[0061] Second, after having formed a coated resist by coating a resist ink across the whole surface of a cold rolled steel strip for a grain-oriented electrical steel sheet, resist patterns were formed by using two laser beams irradiated from two adjacent laser irradiation devices arranged in the strip transverse direction of the cold rolled steel strip. At this time, centers of the two adjacent laser beams having a laser spot diameter of Φ were shifted with each other in a direction perpendicular to the laser scanning direction. A coated resist was removed with various distances in the direction perpendicular to the laser scanning direction between the centers of the two laser beams (hereinafter, also referred to as “light path shifting distance d” (refer to
[0062] After having performed decarburization annealing on a cold rolled steel strip for a grain-oriented electrical steel sheet subjected to the formation of linear grooves as described above followed by stripping of the coated resist remaining on the surface in an alkaline solution, a final product steel strip was obtained by performing the processes described above. Steel sheets each having a certain SST size, that is, a length in the sheet transverse direction of 100 mm and a length in the rolling direction of 280 mm, were taken from the obtained steel strip, and W.sub.17/50 and B.sub.8 were evaluated. The results are given in
[0063] On the other hand, it was clarified that there was a tendency for deteriorating magnetic flux density (BO when the light path shift ratio was more than 0.95. This is considered to be because the volume removed by performing etching increases due to an increase in light path shift distance d and the magnetic permeability of the steel sheet decreases.
[0064] From the results described above, the appropriate range of the light path shift ratio is set to be 0.05 or more and 0.95 or less. That is, when the laser spot diameter is defined as Φ, the shift distance in a direction perpendicular to the laser scanning direction between the centers of two laser beams emitted from the two laser irradiation devices adjacent to each other in the sheet transverse direction is set to be Φ multiplied by 0.05 or more and 0.95 or less. It is more preferable that the light path distance ratio described above is 0.10 or more. In addition, it is more preferable that the light path shift ratio is 0.90 or less.
[0065] Third, while each of the laser spot diameter Φ, the light path shift distance d, and the groove depth was set to have a constant value, final product steel strip having various light path overlap lengths c were manufactured by performing the same processes as described above. Steel sheets each having the same size as described above were taken from each the obtained steel strip, and magnetic properties were investigated. The results are given in
[0066] Fourth, appropriate conditions for laser beam irradiation were investigated. A resist ink was coated across the whole surface of a cold rolled steel sheet for a grain-oriented electrical steel sheet whose weight had been measured, a linear resist pattern was formed by using one laser beam irradiated from one laser irradiation device, and electroetching was performed. At this time, electrolytic conditions were controlled so that the depth of the linear grooves formed by the electroetching had a constant value. After having stripped the coated resist remaining on the steel sheet subjected to electroetching, the weight of the steel sheet was measured, and a decrease in the weight of the steel sheet due to electroetching (weight loss) was calculated. By using a value obtained by dividing this weight loss by the weight calculated from the groove width, the groove depth, and the number of linear grooves, that is, a weight loss ratio as an index, appropriate conditions for the laser irradiation were investigated. Here, when the weight loss ratio approaches to 1.0, there is a decrease in the degree of groove shape defects such as groove breaks and white spots. Laser irradiation was performed (1) under the conditions of a spot diameter Φ of 100 μm and an irradiation energy of 0.5 J/m to 35 J/m and (2) under the conditions of an irradiation energy of 20 J/m and a spot diameter Φ of 0.5 μm to 120 μm. Here, the irradiation energy was expressed in units of energy per unit scanning length ((laser power (W))/(scanning speed (m/sec))).
[0067] The results of (1) are given in
[0068] Next, the results of (2) are given in
[0069] Hereafter, preferable embodiments of the present application will be described in detail. However, the present disclosure is not limited to the constitutions disclosed in the embodiments, and the present disclosure may be performed by making various alterations within a range in accordance with the intent of the present application.
[0070] [Grain-Oriented Electrical Steel Sheet]
[0071] The basic constituents, inhibitor constituents, optional constituents, and manufacturing processes of the steel material (slab) for the grain-oriented electrical steel sheet to which the present disclosed embodiments is applied will be described in detail.
[0072] (Basic Constituents)
[0073] C: 0.08 mass % or less
[0074] Although C is added to improve the microstructure of a hot rolled steel sheet, in the case that the C content is more than 0.08 mass %, it is difficult to decrease the C content through decarburization to a C content of 50 mass ppm or less, with which magnetic aging does not occur in manufacturing processes. Therefore, it is preferable that the C content is 0.08 mass % or less. In addition, since secondary recrystallization occurs even in a steel material which does not contain C, there is no particular limitation on the lower limit of the C content.
[0075] Si: 2.0 mass % to 8.0 mass %
[0076] Si is an element effective for improving iron loss by increasing the electrical resistance of steel. However, in the case that the Si content is less than 2.0 mass %, it is not possible to sufficiently realize such an effect of improvement. On the other hand, in the case that the Si content is more than 8.0 mass %, there is a marked deterioration in workability and sheet passage, and there is a decrease in magnetic flux density. Therefore, it is preferable that the Si content is 2.0 mass % to 8.0 mass %.
[0077] Mn: 0.005 mass % to 1.0 mass %
[0078] Mn is an element necessary to improve hot workability. However, in the case that the Mn content is less than 0.005 mass %, it is not possible to sufficiently realize such an effect. On the other hand, in the case that the Mn content is more than 1.0 mass %, there is a deterioration in magnetic flux density. Therefore, it is preferable that the Mn content is 0.005 mass % to 1.0 mass %.
[0079] (Inhibitor Constituents)
[0080] In the present disclosed embodiments, it is sufficient that a slab for a grain-oriented electrical steel sheet has a chemical composition with which secondary recrystallization occurs. In the case that an inhibitor is used to allow secondary recrystallization to occur, for example, it is sufficient that Al and N are appropriately added when an AlN-based inhibitor is used and that Mn and Se and/or S are appropriately added when a MnS—MnSe-based inhibitor is used. It is needless to say that both kinds of inhibitors may be used. In this case, the preferable content of each of Al, N, S, and Se is as follows.
Al: 0.010 mass % to 0.065 mass %
N: 0.0050 mass % to 0.0120 mass %
S: 0.005 mass % to 0.030 mass %
Se: 0.005 mass % to 0.030 mass %
[0081] Moreover, the present disclosed embodiments may be applied to a grain-oriented electrical steel sheet that does not use an inhibitor where the content of Al, N, S, or Se is limited. In this case, it is preferable that the content of each of Al, N, S, and Se be limited as follows.
Al: 0.010 mass % or less
N: 0.0050 mass % or less
S: 0.0050 mass % or less
Se: 0.0050 mass % or less
[0082] In addition to the basic constituents and the inhibitor constituents, the optional constituents described below, which are known to be effective for improving magnetic properties, may be appropriately added.
[0083] One or more selected from Ni: 0.03 mass % to 1.50 mass %,
Sn: 0.01 mass % to 1.50 mass %,
Sb: 0.005 mass % to 1.50 mass %,
Cu: 0.03 mass % to 3.0 mass %,
P: 0.03 mass % to 0.50 mass %,
Mo: 0.005 mass % to 0.10 mass %, and
Cr: 0.03 mass % to 1.50 mass %
[0084] Ni is an element effective for improving magnetic properties by improving the microstructure of a hot rolled steel sheet. However, in the case that the Ni content is less than 0.03 mass %, contribution to an improvement in magnetic properties is small. On the other hand, in the case that the Ni content is more than 1.50 mass %, since secondary recrystallization is unstable, there is a deterioration in magnetic properties. Therefore, it is preferable that the Ni content is 0.03 mass % to 1.50 mass %.
[0085] In addition, Sn, Sb, Cu, P, Mo, and Cr are also elements that improve magnetic properties. However, in the case that the content of each of such elements is less than the corresponding lower limit described above, such an effect is insufficient. In addition, in the case that the content of each of such elements is more than the corresponding upper limit described above, since grain growth in secondary recrystallization is suppressed, there is a deterioration in magnetic properties. Therefore, it is preferable that the content of each of such elements is within the range described above.
[0086] In addition, the remainder which is different from the constituents described above is Fe and incidental impurities. Here, in a product steel sheet, the contents of the basic constituents and the optional constituents other than C in a steel material (slab) are maintained. On the other hand, there is a decrease in the C content due to decarburization annealing. In addition, since there is a decrease in the contents of the inhibitor constituents in final annealing described below, the contents of the inhibitor constituents in a product steel sheet are at a level of incidental impurities.
[0087] After having performed hot rolling on a steel material (slab) for a grain-oriented electrical steel sheet having the chemical composition described above, hot-rolled-sheet annealing is performed. Subsequently, cold rolling is performed once, optionally twice or more with intermediate annealing between periods that cold rolling is performed, to obtain a steel strip having the final thickness.
[0088] Subsequently, after having performed decarburization annealing on the steel strip, coating of an annealing separator containing mainly MgO to the annealed steel strip, the steel strip is wound into a coil. Thereafter, a final annealing is performed for the purpose of the secondary recrystallization and the formation of a forsterite coating film. After having performed flattening annealing on the steel strip that had been subjected to final annealing, a magnesium phosphate-based tension coating is formed to obtain a product steel strip.
[0089] In the present disclosed embodiments, in an appropriately selected process after cold rolling and before an annealing separator coating, linear grooves are formed on the surface of a grain-oriented electrical steel sheet (steel strip).
[0090] [Groove Dimensions]
[0091] Hereafter, preferable groove dimensions of the grooves formed according to the present disclosed embodiments will be described. Here, the meaning of the expression “groove dimensions” includes not only a groove width and a groove depth but also a groove interval between grooves formed cyclically in the rolling direction of a grain-oriented electrical steel sheet (steel strip) and an angle formed by the longitudinal direction of the linear grooves and the sheet transverse direction.
[0092] Groove width: 1 μm to 100 μm
[0093] The groove width of the linear grooves corresponds to the width in the rolling direction of a portion from which a coated resist has been removed (portion which has been irradiated with a laser beam) in a resist pattern. In addition, the width of the portion from which a coated resist has been removed corresponds to the spot diameter of the laser beam used for removing the coated resist. Therefore, the groove width is about 1 μm to 100 μm.
[0094] Groove depth: 4% to 25% of sheet thickness
[0095] The effect of improving iron loss due to formation of grooves increases with an increase in the surface area of the side walls of the grooves, that is, an increase in the formed depth of the groove (groove depth). Therefore, it is preferable that a groove having a depth of 4% or more of the sheet thickness is formed. On the other hand, it is needless to say that, in the case that there is an increase in groove depth, there is an increase in groove volume, which results in a deterioration in magnetic permeability. Moreover, there is a risk of the groove becoming a starting point at which fracturing occurs at the time of sheet passage. Therefore, it is preferable that the upper limit of the groove depth is 25% of the sheet thickness.
[0096] Linear groove forming interval: 1.5 mm to 10 mm
[0097] As described above, since the effect of improving iron loss increases with an increase in the surface area of the side walls of grooves, the effect increases with a decrease in the linear groove forming interval. However, in the case that there is a decrease in the linear groove forming interval, since there is an increase in the volume fraction of grooves with respect to steel sheet volume, there is a deterioration in magnetic permeability. Further, there is an increased risk of fracturing occurring in operation. Therefore, it is preferable that the linear groove forming interval is 1.5 mm to 10 mm. Here, the expression “linear groove forming interval” denotes the distance in the rolling direction between linear grooves.
[0098] Angle formed by longitudinal direction of linear grooves and sheet transverse direction: within a range of ±30°
[0099] In the case that there is an increase in the absolute value of an angle formed by the longitudinal direction of linear grooves and the sheet transverse direction, since there is an increase in the groove volume, there is a tendency for magnetic permeability to be deteriorated. Therefore, it is preferable that the angle formed by the longitudinal direction of linear grooves and the sheet transverse direction is within a range of ±30°.
[0100] [Laser Spot Diameter Φ ]
[0101] The expression “laser spot diameter Φ ” denotes the full-width at half maximum in a strength profile obtained by using a slit method with a slit having a width of 30 μm.
EXAMPLES
[0102] Hereafter, the present disclosure will be described in detail in accordance with examples. The examples below are preferable examples of the present disclosure, and the present disclosure is not limited to the examples at all. The present disclosure may be performed by appropriately making alterations within a range in accordance with the intent of the present disclosure, and working examples performed in such a way are all within the technical scope of the present disclosure.
[0103] After having performed hot rolling on each of the steel materials (slabs) for grain-oriented electrical steel sheets having the chemical compositions given in Table 2 with Fe and incidental impurities, hot-rolled-sheet annealing was performed. Subsequently, cold rolling was performed twice with intermediate annealing between the periods that cold rolling was performed to obtain a cold rolled steel strip having a thickness of 0.23 mm. After having formed a coated resist by coating a resist ink across the whole surface of such a cold rolled steel strip, removal of the coated resist was performed by using two laser beams irradiated from two laser irradiation devices arranged in the strip transverse direction. At this time, as illustrated in
TABLE-US-00002 TABLE 2 Chemical Composition (mass %) C Si Mn Al N Se S O 0.08 3.0 0.1 0.0260 0.007 0.0110 0.003 0.0025
[0104] Samples having an RD length of 280 mm and a TD length of 100 mm were taken from the obtained steel strip such that each linear groove 1 contained one discontinuous portion of center lines, that is, such that each of the samples contains discontinuous portion of center lines. Further, W.sub.17/50 and B.sub.8 were determined by using a single sheet test (SST) method. Here, “RD” denotes the steel sheet rolling direction, and “TD” denotes the sheet transverse direction.
[0105] In addition, for comparison, samples were prepared by performing the same processes as described above with the exception that a resist pattern was formed by using a gravure printing method or an ink-jet printing method, and W.sub.17/50 and B.sub.8 were determined. Here, the width of the grooves formed by using a gravure printing method or an ink-jet printing method was 50 μm.
[0106] The results are collectively given in Table 3. It was clarified that, in the case that the light path shift ratio was within the range of the present disclosed embodiments, it was possible to realize a larger effect of improving iron loss than in the case that the same resist pattern was formed by using other methods. In addition, it was clarified that, in the case that the light path overlap length c was 50 mm or less, it was possible to realize an even larger effect of improving iron loss. Moreover, it was clarified that, in the case that the conditions applied for laser irradiation was within the preferable ranges, it was possible to realize an even much larger effect of improving iron loss.
TABLE-US-00003 TABLE 3 Light Light Path Iron Path Overlap Spot Irradiation Loss Shift Length Diameter Energy Resist Pattern W.sub.17/50 No. Ratio c [mm] Φ [μm] [J/m] Forming Method [W/kg] B.sub.8 [T] Note 1 0 0 50 20 Resist Peeling Method 0.710 1.930 Comparative Example 2 0.05 0 50 20 Resist Peeling Method 0.690 1.930 Example 3 0.1 0 50 20 Resist Peeling Method 0.685 1.930 Example 4 0.5 0 50 20 Resist Peeling Method 0.685 1.930 Example 5 0.9 0 50 20 Resist Peeling Method 0.685 1.930 Example 6 0.95 0 50 20 Resist Peeling Method 0.690 1.930 Example 7 1.0 0 50 20 Resist Peeling Method 0.690 1.920 Comparative Example 8 0 0.1 50 20 Resist Peeling Method 0.700 1.930 Comparative Example 9 0.05 0.1 50 20 Resist Peeling Method 0.685 1.930 Example 10 0.1 0.1 50 20 Resist Peeling Method 0.680 1.930 Example 11 0.5 0.1 50 20 Resist Peeling Method 0.680 1.930 Example 12 0.9 0.1 50 20 Resist Peeling Method 0.680 1.930 Example 13 0.95 0.1 50 20 Resist Peeling Method 0.685 1.930 Example 14 1.0 0.1 50 20 Resist Peeling Method 0.685 1.920 Comparative Example 15 0 10 50 20 Resist Peeling Method 0.700 1.930 Comparative Example 16 0.05 10 50 20 Resist Peeling Method 0.685 1.930 Example 17 0.1 10 50 20 Resist Peeling Method 0.680 1.930 Example 18 0.5 10 50 20 Resist Peeling Method 0.680 1.930 Example 19 0.9 10 50 20 Resist Peeling Method 0.680 1.930 Example 20 0.95 10 50 20 Resist Peeling Method 0.685 1.930 Example 21 1.0 10 50 20 Resist Peeling Method 0.685 1.920 Comparative Example 22 0 40 50 20 Resist Peeling Method 0.700 1.930 Comparative Example 23 0.05 40 50 20 Resist Peeling Method 0.685 1.930 Example 24 0.1 40 50 20 Resist Peeling Method 0.680 1.930 Example 25 0.5 40 50 20 Resist Peeling Method 0.680 1.930 Example 26 0.9 40 50 20 Resist Peeling Method 0.680 1.930 Example 27 0.95 40 50 20 Resist Peeling Method 0.685 1.930 Example 28 1.0 40 50 20 Resist Peeling Method 0.685 1.920 Comparative Example 29 0 50 50 20 Resist Peeling Method 0.710 1.930 Comparative Example 30 0.05 50 50 20 Resist Peeling Method 0.690 1.930 Example 31 0.1 50 50 20 Resist Peeling Method 0.685 1.930 Example 32 0.5 50 50 20 Resist Peeling Method 0.685 1.930 Example 33 0.9 50 50 20 Resist Peeling Method 0.685 1.930 Example 34 0.95 50 50 20 Resist Peeling Method 0.690 1.930 Example 35 1.0 50 50 20 Resist Peeling Method 0.690 1.920 Comparative Example 36 0 60 50 20 Resist Peeling Method 0.710 1.925 Comparative Example 37 0.05 60 50 20 Resist Peeling Method 0.695 1.925 Example 38 0.1 60 50 20 Resist Peeling Method 0.690 1.925 Example 39 0.5 60 50 20 Resist Peeling Method 0.690 1.925 Example 40 0.9 60 50 20 Resist Peeling Method 0.690 1.925 Example 41 0.95 60 50 20 Resist Peeling Method 0.695 1.925 Example 42 1.0 60 50 20 Resist Peeling Method 0.695 1.910 Comparative Example 43 0.1 10 0.5 20 Resist Peeling Method 0.690 1.925 Example 44 0.5 10 110 20 Resist Peeling Method 0.690 1.930 Example 45 0.1 10 50 0.5 Resist Peeling Method 0.690 1.930 Example 46 0.5 10 50 35 Resist Peeling Method 0.690 1.925 Example 47 0.1*.sup.1 10*.sup.2 — — Gravure Printing Method 0.710 1.920 Comparative Example 48 0.5*.sup.1 10*.sup.2 — — Gravure Printing Method 0.710 1.920 Comparative Example 49 0.1*.sup.1 10*.sup.2 — — Ink-jet Printing Method 0.700 1.930 Comparative Example 50 0.5*.sup.1 10*.sup.2 — — Ink-jet Printing Method 0.700 1.930 Comparative Example Underlined items indicate items out of the ranges of the present disclosed embodiments. *.sup.1(shift distance between the center lines in the discontinuous portion of center lines of the formed grooves)/(groove width), which corresponds to the light path shift ratio *.sup.2the length of the discontinuous portion of center lines of the formed grooves, which corresponds to the light path overlap length c