Magnetic element

Abstract

The present invention relates to a transformer capable of reducing manufacturing costs by removing a portion with low magnetic flux density, the transformer comprising: a lower core having a top surface and a bottom surface, and side surfaces positioned between the top surface and the bottom surface; and an upper core arranged, on the lower core, in the same shape as the lower core, wherein the upper core and / or the lower core includes a recessed portion on the side surface thereof so that a portion having a weak magnetic flux density is removed, and thus it can be expected that manufacturing costs can be reduced and magnetic flux uniformity can be improved.

Description

magnetic elements

[0001] The present invention relates to a magnetic element capable of reducing manufacturing costs by eliminating a portion having low magnetic flux density.

[0002] In general, an electronic device requires a driving power source to operate, and a power supply unit, such as a power supply unit (PSU), is essential to supply this driving power to the electronic device.

[0003] Magnetic elements such as transformers and inductors are widely used in EMI (Electro Magnetic Interference) filters and in DC-DC converters for electric and hybrid vehicles, which are currently undergoing extensive research and development.

[0004] In particular, in display devices such as flat-panel TVs, slimming is required along with larger display sizes, so there is a challenge of reducing thickness while satisfying the increased power consumption of larger displays.

[0005] In a power supply unit (PSU), the transformer takes up a relatively large volume compared to other components, so reducing the thickness of the transformer itself is the biggest challenge in making it slimmer.

[0006] Figure 1 is an exploded perspective view showing an example of a typical transformer configuration.

[0007] Referring to Fig. 1, a typical slim transformer (10) includes a secondary coil (13) and a primary coil (14) between an upper core (11) and a lower core (12). At least one of the primary coil and / or the secondary coil may be a multi-insulated coil. As illustrated in Fig. 1, the secondary coil (13) may be composed of a plurality of conductive metal plates, and the primary coil (14) may have a form in which a conductive wire is wound.

[0008] Fig. 2a is an exemplary diagram showing the magnetic flux density generated in the lower core of the transformer of Fig. 1 in a plan view, Fig. 2b is an exemplary diagram showing the magnetic flux density in a coupled state in the form of a side cross-section, and Fig. 2c is an exemplary diagram showing the magnetic flux density in a coupled state in the form of a perspective view.

[0009] Magnetic flux density refers to the magnetic flux passing through a unit area, and the unit is Gauss (G) or Tesla (T). Magnetic flux density represents the strength of a magnetic field, and the strength of the magnetic flux φ passing perpendicularly through a cross-section with an area S and the magnetic flux density B has the following mathematical equation 1.

[0010]

[0011] When the smallest value of the magnetic flux density is displayed in blue and the largest value is displayed in red, Fig. 2a shows the magnetic flux density information in a state where the coil is placed in the lower core excluding the upper core. As shown in the figure, the magnetic flux density appears high in the area around the middle and near the outer part due to the current flowing in the coil. On the other hand, as shown in Figs. 2b and 2c, it can be seen that the magnetic flux density decreases from the area where the middle parts (CL1, CL2) face each other to the outside of the core. That is, it can be seen that the magnetic flux density of the side part (“A”) of the upper core (11) and the lower core (12) and the corner part (“B”) of the upper core (11) and the lower core (12) is relatively significantly lower than that of other parts. The magnetic flux density of the side part (“A”) of the upper core (11) and the lower core (12) is canceled by the eddy current, so the current density is low.

[0012] The purpose of the present invention is to provide a magnetic element capable of reducing manufacturing costs and improving the uniformity of magnetic flux by removing a portion having a relatively low magnetic flux density.

[0013] According to one embodiment of the present invention for achieving this purpose, a magnetic element comprises a lower core including an upper surface, a lower surface, and a side surface positioned between the upper surface and the lower surface; and an upper core disposed on the lower core with the same shape as the lower core, wherein at least one of the upper core and the lower core is configured to have a concave portion on the side surface.

[0014] Detailed features of a magnetic element according to one embodiment of the present invention are that the lower core includes a first outer leg and a second outer leg spaced apart from each other on the upper surface, and a first middle leg spaced between the first outer leg and the second outer leg, the upper core includes a third outer leg and a fourth outer leg spaced apart from each other on the lower surface, and a second middle leg spaced between the third outer leg and the fourth outer leg, and the concave portion is formed on a side surface adjacent to both longitudinal ends of the first middle leg and / or the second middle leg.

[0015] In a magnetic element according to one embodiment of the present invention, the concave portion may be spaced apart from the first outer group and the second outer group by the same distance, and may be spaced apart from the third outer group and the fourth outer group by the same distance.

[0016] In a magnetic element according to one embodiment of the present invention, the width of the concave portion may have a size corresponding to 20% to 30% of the horizontal length of the upper core and / or the lower core.

[0017] In a magnetic element according to one embodiment of the present invention, the width of the concave portion may be greater than the width of the first intermediate foot and / or the second intermediate foot.

[0018] In a magnetic element according to one embodiment of the present invention, the depth of the concave portion may have a size corresponding to 5% to 10% of the vertical length of the upper core and / or lower core.

[0019] According to another embodiment of the present invention, a magnetic element includes a lower core including an upper surface, a lower surface, and a side surface positioned between the upper surface and the lower surface; and an upper core disposed on the lower core with the same shape as the lower core, wherein at least one of the lower core and the upper core may have a configuration having a chamfered portion with an outer edge portion removed.

[0020] In a magnetic element according to another embodiment of the present invention, the chamfered portion may be formed at both corners of the first lower surface and / or the second upper surface.

[0021] In a magnetic element according to another embodiment of the present invention, it is preferable that the chamfered portion is cut in the direction of the first lower surface and / or the second upper surface at a position lower than 50% of the height of the outer surface of the first outer leg and the second outer leg and / or the third outer leg and the fourth outer leg.

[0022] In a magnetic element according to another embodiment of the present invention, it is preferable that the cutting angle of the chamfered portion forms an acute angle with the first upper surface and / or the second lower surface.

[0023] According to another embodiment of the present invention, a magnetic element includes a lower core including an upper surface, a lower surface, and a side surface positioned between the upper surface and the lower surface; and an upper core disposed on the lower core with the same shape as the lower core, wherein at least one of the lower core and the upper core may have a configuration having a concave portion formed on a side surface and a chamfered portion with an outer edge portion removed.

[0024] The magnetic element according to the present invention can have the effect of reducing manufacturing costs and improving the uniformity of magnetic flux by removing a part with a low magnetic flux density.

[0025] Figure 1 is an exploded perspective view of a typical transformer.

[0026] Figure 2a is an exemplary diagram showing the magnetic flux density generated in the lower core of the transformer of Figure 1 in a plan view.

[0027] Figure 2b is an example diagram showing the magnetic flux density in the form of a cross-section in a coupled state.

[0028] Figure 2c is an example diagram showing the magnetic flux density in a combined state in the form of a perspective view.

[0029] Figure 3 is a perspective view of a transformer according to a first embodiment of the present invention.

[0030] FIG. 4a is a perspective view showing the upper core of a transformer according to the first embodiment of the present invention.

[0031] Figure 4b is a perspective view showing the lower core of a transformer according to the first embodiment of the present invention.

[0032] Figure 4c is a plan view of the lower core of a transformer according to the first embodiment of the present invention.

[0033] FIG. 4d is a side view of the lower core of a transformer according to the first embodiment of the present invention.

[0034] Figure 5 is a perspective view of the lower core of a transformer according to a second embodiment of the present invention.

[0035] Figure 6 is a perspective view of the lower core of a transformer according to a third embodiment of the present invention.

[0036] FIG. 7 is an exemplary diagram showing the magnetic flux density generated in a transformer according to the first embodiment of the present invention in the form of a plan view of the lower core, a side view of the core, and a perspective view of the transformer.

[0037] FIG. 8 is an exemplary diagram showing the magnetic flux density generated in a transformer according to a second embodiment of the present invention in the form of a plan view of the lower core, a side view of the core, and a perspective view of the transformer.

[0038] FIG. 9 is an exemplary diagram showing the magnetic flux density generated in a transformer according to a third embodiment of the present invention in the form of a plan view of the lower core, a side view of the core, and a perspective view of the transformer.

[0039] With respect to the embodiments of the present invention disclosed in the text, specific structural and functional descriptions are merely exemplified for the purpose of explaining the embodiments of the present invention, and the embodiments of the present invention may be implemented in various forms and should not be construed as being limited to the embodiments described in the text.

[0040] The present invention is susceptible to various modifications and takes various forms. Specific embodiments are illustrated in the drawings and described in detail herein. However, this is not intended to limit the present invention to specific disclosed forms, but rather to encompass all modifications, equivalents, and alternatives falling within the spirit and technical scope of the present invention.

[0041] While terms like "first" and "second" may be used to describe various components, these components are not limited by these terms. These terms are used solely to distinguish one component from another. For example, without departing from the scope of the present invention, a first component could be referred to as a "second component," and similarly, a second component could also be referred to as a "first component."

[0042] When a component is referred to as being "connected" or "connected" to another component, it should be understood that it may be directly connected or connected to that other component, but there may also be other components in between. Conversely, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there are no other components in between. Other expressions that describe the relationship between components, such as "between" and "directly between" or "adjacent to" and "directly adjacent to", should be interpreted similarly. Similarly, "disposed on" can mean disposed directly on the surface of another component or disposed above the surface by a distance.

[0043] The terminology used in this application is only used to describe specific embodiments and is not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly indicates otherwise. In this application, it should be understood that the terms "comprises" or "has" indicate the presence of a disclosed feature, number, step, operation, component, part, or combination thereof, but do not preclude the possibility of the presence or addition of one or more other features, numbers, steps, operations, components, parts, or combinations thereof.

[0044] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Terms defined in commonly used dictionaries should be interpreted to have a meaning consistent with their meaning in the context of the relevant technology, and shall not be construed in an idealized or overly formal sense unless explicitly defined herein.

[0045] Meanwhile, if a particular embodiment can be implemented differently, the functions or operations specified within a particular block may occur in a different order than specified in the flowchart. For example, two consecutive blocks may actually be performed substantially simultaneously, or, depending on the related functions or operations, the blocks may be performed in reverse order.

[0046] Hereinafter, transformers according to various embodiments of the present invention will be described with reference to the attached drawings. For convenience of explanation, transformers according to embodiments are described using a Cartesian coordinate system (x, y, z), but may be described using other coordinate systems, and embodiments are not limited thereto. According to the Cartesian coordinate system, the x-axis, y-axis, and z-axis are orthogonal to each other, but embodiments are not limited thereto. That is, the x-axis, y-axis, and z-axis may intersect each other.

[0047] Fig. 3 is a perspective view of a transformer according to a first embodiment of the present invention. Fig. 4a is a perspective view showing an upper core of a transformer according to a first embodiment of the present invention, Fig. 4b is a perspective view showing a lower core of a transformer according to a first embodiment of the present invention, Fig. 4c is a plan view of a lower core of a transformer according to a first embodiment of the present invention, and Fig. 4d is a side view of a lower core of a transformer according to a first embodiment of the present invention.

[0048] A transformer (1000) according to the first embodiment of the present invention is composed of a core portion (100A) and a coil portion (200).

[0049] The above core portion (100A) comprises an upper core (110A) and a lower core (120A) arranged to overlap vertically below the upper core (110A).

[0050] The upper core (110A) includes a first upper surface (111), a first lower surface (112), a first outer leg (OL1) and a second outer leg (OL2) arranged horizontally apart from each other on the first lower surface (112), and a first middle leg (CL1) arranged between the first outer leg (OL1) and the second outer leg (OL2).

[0051] The lower core (120A) disposed below the upper core (110A) includes a second lower surface (121) and a second upper surface (122), a third outer leg (OL3) and a fourth outer leg (OL4) disposed spaced apart from each other along the horizontal direction on the second upper surface (122), and a second middle leg (CL2) disposed between the third outer leg (OL3) and the fourth outer leg (OL4).

[0052] The coil portion (200) is arranged between the upper core (110A) and the lower core (120A), and is arranged to surround the first intermediate leg (CL1) and the second intermediate leg (CL2).

[0053] The upper core (110A) and the lower core (120A) according to the first embodiment each include a concave portion (“C”) and a chamfered portion (“D”).

[0054] For convenience of explanation in the drawings below, the concave portion (“C”) is indicated as an upper core concave portion (117) and a lower core concave portion (127), and the chamfered portion (“D”) is indicated as an upper core chamfered portion (113-2, 114-2) and a lower core chamfered portion (123-2, 124-2).

[0055] The upper core (110A) according to the first embodiment includes a first upper surface (111), a first lower surface (112), a first left surface (113), a first right surface (114), a first side surface (115), and a second side surface (116), as shown in FIG. 4A.

[0056] On the first lower surface (112), a first outer leg (OL1) and a second outer leg (OL2) are arranged horizontally apart from each other. A first intermediate leg (CL1) is arranged on the first lower surface (112) between the first outer leg (OL1) and the second outer leg (OL2). The first outer leg (OL1) and the second outer leg (OL2) protrude from the first lower surface (112) at the same height. The first intermediate leg (CL1) protrudes from the first lower surface (112) at the same height as the first outer leg (OL1) and the second outer leg (OL2). In some cases, the first intermediate leg (CL1) may have a lower height than the first outer leg (OL1) and the second outer leg (OL2).

[0057] The concave portion (117) of the upper core (110A) is formed on each of the first side surface (115) and the second side surface (116). At this time, the concave portion (117) is positioned at the same distance from the outer surface (113-1) of the first left side surface (113) and the outer surface (114-1) of the first right side surface (114). That is, the concave portion (117) of the upper core (110A) is spaced apart from the first outer leg (OL1) and the second outer leg (OL2) by the same distance. For example, by providing the concave portion (117) such that the horizontal distance between the center of the concave portion (117) and the first outer leg (OL1) is the same as the horizontal distance between the center of the concave portion (117) and the second outer leg (OL2), the uniformity of the magnetic flux can be improved. In addition, when a magnetic product using the above-described upper core (110A) and lower core (120A) is implemented as a transformer, core loss and inductance can be improved. An upper core chamfer (113-2, 114-2) can be formed in the portion where the first upper surface (111) is bent to the first left surface (113) and the first right surface (114), respectively.

[0058] The lower core (120A) according to the first embodiment includes a second upper surface (122), a second lower surface (121), a second left surface (123), a second right surface (124), a third side surface (125), and a fourth side surface (126), as illustrated in FIGS. 4b to 4d . On the second upper surface (122), a third outer leg (OL3) and a fourth outer leg (OL4) are arranged to be spaced apart from each other in the horizontal direction. A second intermediate leg (CL2) is formed on the second upper surface (122) between the third outer leg (OL3) and the fourth outer leg (OL4). The third outer leg (OL3) and the fourth outer leg (OL4) protrude from the second upper surface (122) at the same height. The second intermediate leg (CL2) protrudes from the second upper surface (122) at the same height as the third outer leg (OL3) and the fourth outer leg (OL4). In some cases, the second metatarsal (CL2) may have a lower height than the third metatarsal (OL3) and the fourth metatarsal (OL4).

[0059] The concave portion (127) of the lower core (120A) is formed on the third side (125) and the fourth side (126), respectively. At this time, the concave portion (127) of the lower core (120A) is positioned at the same distance from the outer surface (123-1) of the second left side (123) and the outer surface (124-1) of the second right side (124). That is, the concave portion (127) of the lower core (120A) is spaced apart from the third outer leg (OL3) and the fourth outer leg (OL4) by the same distance. Lower core chamfer portions (123-2, 124-2) are formed at the portions that are bent from the first lower surface (121) to the second left side (123) and the second right side (124), respectively.

[0060] As illustrated in Fig. 4c, the width (D1) of the concave portion (127) of the lower core (120A) according to the first embodiment may have a size corresponding to 20% to 30% of the horizontal length (Dt) of the lower core (120A). The horizontal length (Dt) represents the distance from the outer surface (123-1) of the second left side (123) to the outer surface (124-1) of the second right side (124).

[0061] Of course, although not shown, the width of the concave portion (117) of the upper core (110A) may also have a size corresponding to 20% to 30% of the horizontal length of the upper core (110A). When the width of the concave portion (117) is 20% or less of the horizontal length of the upper core (110A), the same performance as the existing magnetic element can be maintained, but the effect of material saving is small, and when the width of the concave portion (117) is 30% or more of the horizontal length of the upper core (110A), the magnetic element may not operate normally. Preferably, the width of the concave portion (117) has a size corresponding to 28% of the horizontal length of the upper core (110A). In addition, the width (D1) of the concave portion (127) of the lower core (120A) may be larger than the width (D5) of the second intermediate leg (CL2). Of course, although not shown, the width of the concave portion (117) of the upper core (110A) may also be greater than the width of the first intermediate leg (CL1). If the width of the concave portion (117) is formed to a size smaller than 20% of the horizontal length, the effect of removing a region with a relatively low magnetic flux density is reduced, and if it is formed to a size larger than 30%, it may become a factor that deteriorates the performance of the transformer.

[0062] The depth (D3) of the concave portion (127) of the lower core (120A) may have a size corresponding to 5% to 10% of the vertical length (D4) of the lower core (120A). Of course, although not shown, the depth of the concave portion (117) of the upper core (110A) may also have a size corresponding to 5% to 10% of the vertical length of the upper core (110A). Preferably, it has 9.5% of the vertical length.

[0063] As illustrated in FIG. 4d, lower core chamfers (123-2, 124-2) are formed at the corners of the third outer leg (OL3) and the fourth outer leg (OL4) on the second lower surface (121) of the lower core (120A) according to the first embodiment. The total height (H3) of the third outer leg (OL3) is equal to the sum of the height (H1) from the second lower surface (121) to the second upper surface (122) and the height (H2) of the portion of the third outer leg (OL3) protruding from the second upper surface (122) toward the upper core (110A).

[0064] The lower core chamfered portions (123-2, 124-2) of the lower core (120A) are cut to form an acute angle (θ) with the second lower surface (121). Similarly, although not shown, the upper core chamfered portions (113-2, 114-2) of the upper core (110A) may also be cut to form an acute angle (θ) with the first upper surface (111).

[0065] The lower core chamfer (123-2, 124-2) cut at an acute angle from the second lower surface (121) is cut to the outer surfaces (123-1, 124-1) of the second left surface (123) and the second right surface (124), respectively. At this time, the height (H4) from the second lower surface (121) to the outer surfaces (123-1, 124-1) cut is cut to a position lower than 50% of the height (H3) of the third outer leg (OL3) and the fourth outer leg (OL4). Preferably, it has a value of 45% of the height (H3) of the third outer leg (OL3) and the fourth outer leg (OL4).

[0066] For example, when the volume of a typical upper core and lower core is 9,583.95 mm3, the volume of the upper core and lower core of a transformer in which concave and chamfered portions are formed as in the first embodiment of the present invention is 9,162.75 mm3. Therefore, the portion in which the concave and chamfered portions are formed uses less material by a volume amounting to approximately 4.39% of the entire core.

[0067] Fig. 5 is a perspective view of the lower core of a transformer according to a second embodiment of the present invention. Unlike the first embodiment, the transformer may have a configuration in which only concave portions are formed on the upper core and the lower core, and no chamfer portions are formed on the first upper surface and / or the second lower surface. Except for this, the transformer according to the second embodiment may be identical to the transformer according to the first embodiment, and thus, a duplicate description will be omitted. Although not illustrated, the upper core of the transformer according to the second embodiment is also configured to be symmetrical, similar to Fig. 5.

[0068] Fig. 6 is a perspective view of the lower core of a transformer according to a third embodiment of the present invention. Unlike the first embodiment, the transformer may have a configuration in which chamfered portions (123-2, 124-2) are formed on the first upper surface and / or the second lower surface of the upper core and the lower core, but no concave portions are formed on the upper core and the lower core. Except for this, the transformer according to the third embodiment may be the same as the transformer according to the first embodiment, and thus, redundant descriptions are omitted. Although not illustrated, the upper core of the transformer according to the third embodiment is also configured to be symmetrical, similarly to Fig. 6.

[0069] Each of (a), (b), and (c) of FIGS. 7 to 9 is an exemplary diagram showing the magnetic flux density generated in the transformer according to the first to third embodiments of the present invention in a plan view of the lower core, a side view of the core, and a perspective view of the transformer, respectively. Unlike the exemplary diagrams of magnetic flux density measurement according to FIGS. 2a to 2c, as shown in FIG. 7 (a), (b), and (c), it can be seen that the portions with low magnetic flux density, such as the concave portions (117, 127) and the chamfer portions (113-2, 124-2, 123-2, 124-2), have been cut off and the portions with low magnetic flux density have disappeared. In addition, in the case of the transformer according to the second embodiment in which only the concave portions (117, 127) are formed while leaving the outer corner portions of the upper and lower cores as they are, the outer corner portions of the upper and lower cores are shown to have relatively low magnetic flux densities, as in FIG. 8. Likewise, in the case of the transformer according to the third embodiment in which chamfers (113-2, 124-2, 123-2, 124-2) are formed on the outer edges of the upper and lower cores without forming concave portions on both sides of the upper and lower cores, as shown in FIG. 3, there still exists a portion with low magnetic flux density on the side of the upper core (the lower core is not shown) in which no concave portions are formed.

[0070] As described above, the transformers in which the concave and chamfered portions are formed together, or in which only the concave or chamfered portions are formed, as in the first to third embodiments, have primary inductance, secondary inductance, coupling coefficient, leakage inductance, and core loss values ​​as shown in [Table 1] below.

[0071] Measurement targetPrimary inductance [μH]Secondary inductance [μH]Coupling coefficientLeakage inductance [μH]Core loss [㎽]General 87.8983862.9219410.9939489.655778049200.519First embodiment 87.9449192.9234180.9939569.654521775199.632Second embodiment 87.9052272.9222500.99293110.43373547199.873Third embodiment 87.9349302.9233030.9939159.686012691200.268

[0072] As explained above, by removing the part with low magnetic flux density, it is possible to reduce the raw materials for manufacturing the transformer.

[0073] Although the present invention has been described above with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various modifications and changes may be made to the present invention without departing from the spirit and scope of the present invention as set forth in the claims below.

[0074] The mode for carrying out the invention has been sufficiently described in the above-mentioned “Best mode for carrying out the invention.”

[0075] The magnetic element according to the embodiment can be used in a power supply unit of an electronic device or a DC converter of an electric or hybrid vehicle.

Claims

1. A lower core including an upper surface and a lower surface, and a side surface located between the upper surface and the lower surface; and It includes an upper core arranged on the lower core with the same shape as the lower core, A magnetic element in which at least one of the upper core and the lower core has a concave portion on a side surface.

2. In paragraph 1, The lower core includes a first outer leg and a second outer leg spaced apart from each other on the upper surface, and a first middle leg arranged between the first outer leg and the second outer leg, The upper core includes a third outer leg and a fourth outer leg spaced apart from each other on the lower surface, and a second middle leg arranged between the third outer leg and the fourth outer leg, The above concave portion is a magnetic element formed on a side surface adjacent to the longitudinal end of at least one of the first or second intermediate legs.

3. In the second paragraph, the concave portion is a magnetic element spaced apart from the first outer group and the second outer group by the same distance, and spaced apart from the third outer group and the fourth outer group by the same distance.

4. In the second paragraph, a magnetic element in which the width of the concave portion is greater than the width of at least one of the first intermediate leg or the second intermediate leg.

5. A magnetic element in the first paragraph, wherein the width of the concave portion has a size corresponding to 20% to 30% of the horizontal length of at least one of the upper core or the lower core.

6. A magnetic element in the fifth paragraph, wherein the depth of the concave portion has a size corresponding to 5% to 10% of the vertical length of at least one of the upper core or the lower core.

7. A lower core including an upper surface and a lower surface, and a side surface located between the upper surface and the lower surface; and It includes an upper core arranged on the lower core with the same shape as the lower core, A magnetic element in which at least one of the lower core and the upper core has a chamfered portion with an outer edge portion removed.

8. In the 7th paragraph, the chamfered portion is a magnetic element formed on at least one of the two corners of the first lower surface or the second upper surface.

9. In the 8th paragraph, the chamfered portion is a magnetic element cut in the first lower surface direction and the second upper surface direction at a position lower than 50% of the outer surface height of the first outer leg, the second outer leg, the third outer leg, and the fourth outer leg.

10. A lower core including an upper surface and a lower surface, and a side surface located between the upper surface and the lower surface; and It includes an upper core arranged on the lower core with the same shape as the lower core, At least one of the lower core and the upper core, a concave formed on the side; and A magnetic element having a chamfered portion with the outer edge portion removed.

Images