Patent Publication Number: US-9837796-B2

Title: Spark plug

Description:
This application claims the benefit of Japanese Patent Applications No. 2014-134328, filed Jun. 30, 2014, which is incorporated by reference in its entities herein. 
     FIELD OF THE INVENTION 
     The present invention relates to an electrode of a spark plug. 
     BACKGROUND OF THE INVENTION 
     Conventionally, there is a technique to provide an electrode tip made of a noble metal at a ground electrode of a spark plug (see International Publication No. WO 2012/167972). In this conventional technique, the electrode tip is welded to an electrode base material forming the ground electrode. That is, the electrode tip is joined to the electrode base material via a melt portion which is formed by a portion of the electrode tip and a portion of the electrode base material being melted in welding. 
     Problems to be Solved by the Invention 
     In recent years, due to trend of high compression and high supercharging of an internal combustion engine, the ground electrode of a spark plug is exposed to a higher temperature than before. Thus, the difference between the temperature of the ground electrode during combustion of fuel and the temperature of the ground electrode between combustion and combustion is made greater than before. As a result, due to the difference between the thermal expansion coefficient of the electrode tip and the thermal expansion coefficient of the melt portion, a crack is likely to occur between the electrode tip and the melt portion. Due to the crack, oxide scale is likely to grow. Thus, it is difficult to ensure a high service life of the spark plug. 
     Means for Solving the Problems 
     The present invention has been made to solve the above-described problem, and can be embodied in the following modes. 
     SUMMARY OF THE INVENTION 
     (1) According to one mode of the present invention, a spark plug is provided. The spark plug includes a ground electrode including: 
     a tip having a columnar portion at one end side and containing a noble metal as a principal component; and 
     an electrode base material, at least a portion of another end side of the tip being joined to the electrode base material via a melt portion formed by the tip and the electrode base material being melted together. In the spark plug, in a cross section passing through a central axis of the columnar portion, both a first point and a second point are located at a position whose distance to the central axis in a direction perpendicular to the central axis is shorter than ⅔ of a length from the central axis to an outer surface of the columnar portion, where the first point is located on the melt portion at one side with respect to the central axis and is farthest from a surface of the tip at the one end side in a direction of the central axis; and the second point is located on the melt portion at another side with respect to the central axis and is farthest from the surface of the tip at the one end side in the direction of the central axis. In the cross section, when a line connecting a third point and a fourth point is defined as a reference line, the spark plug satisfies a relationship of: C 1 ≧D 1  and C 2 ≧D 2 , where, the third point is located on the melt portion at the one side with respect to the central axis and is farthest from the central axis and the fourth point is located on the melt portion at the other side with respect to the central axis and is farthest from the central axis. 
     A distance between the reference line and a fifth point is defined as C 1 , where the fifth point is located on the melt portion at the one side with respect to the central axis and is closest to the surface of the tip at the one end side in the direction of the central axis. A distance between the reference line and a sixth point is defined as C 2 , where the sixth point is located on the melt portion at the other side with respect to the central axis and is closest to the surface of the tip at the one end side in the direction of the central axis. A distance between the first point and the reference line is defined as D 1 . A distance between the second point and the reference line is defined as D 2 . 
     In such a mode, the amount of a component of the tip in the melt portion can be increased as compared to a mode where C 1 &lt;D 1  or C 2 &lt;D 2  is satisfied. As a result, the difference in thermal expansion at an interface between the melt portion and the tip can be decreased, and thus occurrence of a crack and growth of oxide scale at the interface between the melt portion and the tip can be suppressed. 
     The phrase “both a first point and a second point are located at a position whose distance to the central axis in the direction perpendicular to the central axis is shorter than ⅔ of the length from the central axis to an outer surface of the columnar portion” means that (i) the length (distance) from the central axis to the first point is shorter than ⅔ of the length (distance) from the central axis to an outer surface at the same side as the first point, of two outer surfaces of an end portion; and (ii) the length (distance) from the central axis to the second point is shorter than ⅔ of the length (distance) from the central axis to the outer surface at the same side as the second point, of the two outer surfaces of the end portion. 
     (2) The spark plug of the above mode may satisfy a relationship of:
 
 C 1/ D 1≧1.2 and  C 2/ D 2≧1.2.
 
     In such a mode, the amount of the component of the tip in the melt portion can be increased as compared to a mode where C 1 /D 1 &lt;1.2 or C 2 /D 2 &lt;1.2 is satisfied. As a result, the difference in thermal expansion at the interface between the melt portion and the tip can be decreased, and thus occurrence of a crack and growth of oxide scale at the interface between the melt portion and the tip can be suppressed. 
     (3) In the spark plug of the above mode, the other end side of the tip may be not in direct contact with the electrode base material and may be joined to the electrode base material via the melt portion. 
     In such a mode, the tip and the base material having different thermal expansion coefficients are disposed with the melt portion, which has an intermediate thermal expansion coefficient between these thermal expansion coefficients, being interposed therebetween. Thus, occurrence of a crack at the joined portion between the tip and the ground electrode can be suppressed. 
     The present invention can be embodied in various forms other than the spark plug. For example, the present invention can be embodied in forms such as a ground electrode, a method for welding a ground electrode, a method for manufacturing a ground electrode, and a method for manufacturing a spark plug. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features and advantages of the present invention will become more readily appreciated when considered in connection with the following detailed description and appended drawings, wherein like designations denote like elements in the various views, and wherein: 
         FIG. 1  is an explanatory view showing a partial cross section of a spark plug  10 . 
         FIG. 2  is a cross-sectional view and plan view showing a structure around an electrode tip  450  provided at a ground electrode  400  of the spark plug  10 . 
         FIG. 3  is a cross-sectional view showing another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . 
         FIG. 4  is a cross-sectional view showing still another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . 
         FIG. 5  is a cross-sectional view showing still another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . 
         FIG. 6  is a cross-sectional view showing still another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . 
         FIG. 7  is a table showing results of a peeling resistance test. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A. First Embodiment 
     A1. Overall Structure of Spark Plug 
       FIG. 1  is an explanatory view showing a partial cross section of a spark plug  10 . In  FIG. 1 , with an axis CA, which is the axis of the spark plug  10 , as a boundary, the external shape of the spark plug  10  is shown at the left side of the axis CA in the sheet of  FIG. 1 , and the cross-sectional shape of the spark plug  10  is shown at the right side of the axis CA in the sheet of  FIG. 1 . In the description of the present embodiment, in the spark plug  10 , the lower side in the sheet of  FIG. 1  is referred to as “front side”, and the upper side in the sheet of  FIG. 1  is referred to as “rear side”. 
     The spark plug  10  includes a center electrode  100 , an insulator  200 , a metallic shell  300 , and a ground electrode  400 . In the present embodiment, the axis CA of the spark plug  10  is also the axis of each of the center electrode  100 , the insulator  200 , and the metallic shell  300 . 
     The spark plug  10  has, at the front side thereof, a gap SG formed between the center electrode  100  and the ground electrode  400 . The gap SG of the spark plug  10  is referred to also as “spark gap”. The spark plug  10  is configured to be mountable to an internal combustion engine  90  in a state where the front side thereof at which the gap SG is formed projects from an inner wall  910  of a combustion chamber  920 . When a high voltage (e.g., 10 thousand to 30 thousand volts) is applied to the center electrode  100  in a state where the spark plug  10  is mounted on the internal combustion engine  90 , spark discharge occurs in the gap SG. The spark discharge which has occurred in the gap SG ignites an air-fuel mixture in the combustion chamber  920 . 
       FIG. 1  shows X, Y, and Z axes which are orthogonal to each other. The X, Y, and Z axes in  FIG. 1  correspond to X, Y, and Z axes in other drawings described later. 
     Of the X, Y, and Z axes in  FIG. 1 , the X axis is an axis orthogonal to the Y axis and the Z axis. In the X axis direction along the X axis, a +X axis direction is a direction from the depth side of the sheet of  FIG. 1  toward the near side thereof, and a −X axis direction is a direction opposite to the +X axis direction. 
     Of the X, Y, and Z axes in  FIG. 1 , the Y axis is an axis orthogonal to the X axis and the Z axis. In the Y axis direction along the Y axis, a +Y axis direction is a direction from the right side of the sheet of  FIG. 1  toward the left side thereof, and a −Y axis direction is a direction opposite to the +Y axis direction. 
     Of the X, Y, and Z axes in  FIG. 1 , the Z axis is an axis along the axis CA. In the Z axis direction along the Z axis (an axial direction), a +Z axis direction is a direction from the rear side of the spark plug  10  toward the front side thereof, and a −Z axis direction is a direction opposite to the +Z axis direction. 
     The center electrode  100  of the spark plug  10  is an electrode having electrical conductivity. The center electrode  100  has a bar shape extending with the axis CA as a center. In the present embodiment, the center electrode  100  is formed from a nickel alloy (e.g., INCONEL 601 (“INCONEL” is a registered trademark)) containing nickel (Ni) as a principal component. In the description of the present specification, the term “principal component” means a component contained in a largest amount when each component contained in the element is compared in mass %. The front side of the center electrode  100  projects from the front side of the insulator  200 . The center electrode  100  is electrically connected to a metal terminal  190 . 
     The insulator  200  of the spark plug  10  is an insulator having an electrical insulation property. The insulator  200  has a tubular shape extending with the axis CA as a center. In the present embodiment, the insulator  200  is produced by baking an insulating ceramic material (e.g., alumina). The insulator  200  has an axial bore  290  which is a through hole extending with the axis CA as a center. The center electrode  100  is held in the axial bore  290  of the insulator  200  and on the axis CA in a state where the center electrode  100  projects from the front side of the insulator  200 . 
     The metallic shell  300  of the spark plug  10  is a metallic body having electrical conductivity. The metallic shell  300  has a tubular shape extending with the axis CA as a center. In the present embodiment, the metallic shell  300  is a member in which low-carbon steel formed into a tubular shape is subjected to nickel plating. In another embodiment, the metallic shell  300  may be a member subjected to zin plating, or may be a member not subjected to plating (unplated). The metallic shell  300  is fixed to the outer surface of the insulator  200  by means of crimping in a state of being electrically insulated from the center electrode  100 . The metallic shell  300  has an end surface  310  formed at the front side thereof. The insulator  200  projects together with the center electrode  100  from the center of the end surface  310  in the +Z axis direction. The ground electrode  400  is joined to the end surface  310 . 
     The ground electrode  400  of the spark plug  10  is an electrode having electrical conductivity. The ground electrode  400  includes an electrode base material  410  and an electrode tip  450 . The electrode base material  410  has a shape in which the electrode base material  410  extends from the end surface  310  of the metallic shell  300  in the +Z axis direction and then bends toward the axis CA. The rear side of the electrode base material  410  is joined to the metallic shell  300 . The electrode tip  450  is joined to the front side of the electrode base material  410 . The electrode tip  450  forms the gap SG between the center electrode  100  and the electrode tip  450 . 
     In the present embodiment, the material of the electrode base material  410  is a nickel alloy containing nickel (Ni) as a principal component, similarly to the center electrode  100 . In the present embodiment, the material of the electrode tip  450  is an alloy containing platinum (Pt) as a principal component and 10 mass % of nickel (Ni). In another embodiment, the material of the electrode tip  450  may be any material which is more excellent in durability than the electrode base material  410 , may be a pure noble metal (e.g., platinum (Pt), iridium (Ir), ruthenium (Ru), rhodium (Rh), etc.), or may be another alloy containing one of these noble metals as a principal component. 
     A2. Structure Around Electrode Tip of Ground Electrode 
       FIG. 2  is a cross-sectional view and a plan view showing a structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . The electrode tip  450  has a substantially cylindrical shape. The electrode tip  450  is disposed at the ground electrode  400  such that the axis CA of the spark plug  10  coincides with the central axis of the cylinder of the electrode tip  450 . 
     The following process is performed in providing the electrode tip  450  at the ground electrode  400 . First, the electrode tip  450  is placed at a predetermined position on the electrode base material  410 . Then, the electrode tip  450  and the electrode base material  410  are resistance-welded to each other. As a result, the electrode tip  450  and the electrode base material  410  are temporarily fixed to each other. Thereafter, a laser beam is applied to a site where the electrode tip  450  and the electrode base material  410  are in contact with each other, from around the electrode tip  450 , so that the electrode tip  450  and the electrode base material  410  are laser-welded to each other. For the laser welding, any laser such as a gas laser, a solid-state laser, and a semiconductor laser can be used. 
     In laser welding, the laser beam is applied in a direction from the outer periphery of the electrode tip  450  toward the axis CA of the electrode tip  450  which is a direction from the electrode tip  450  side toward the electrode base material  410  side. The application of the laser beam is performed from around the electrode tip  450  toward the electrode tip  450  and the electrode base material  410  at  10  to  20  locations which are located at substantially equal angular positions with respect to the axis CA. 
     As a result, a portion of the electrode tip  450  and a portion of the electrode base material  410  are melted together to form a melt portion  455 . When the melt portion  455  is cooled and solidified, an end portion  454  at a side opposite in the axial direction to an end surface  453  at an exposed side, of the electrode tip  450 , and the electrode base material  410  are joined to each other via the melt portion  455 . Of the electrode tip  450  that has not been melted, an end portion  450   p  at a side opposite to the electrode base material  410  has a cylindrical shape. Therefore, the end surface  453  is circular. The cross-sectional view at the upper part of  FIG. 2  is a cross-sectional view on an A-A cross section RP passing through the axis CA and including a direction in which the ground electrode  400  extends toward the axis CA (see the lower part of  FIG. 2 ). In the present embodiment, the cross section RP is a surface which does not include a portion WPL melted last by the applied laser beam, of the melt portion  455 . 
     In the present specification, when a state after the melt portion  455  is formed is described, a portion that has not been melted, of the electrode tip  450  that is prepared initially together with the electrode base material  410 , is referred to as “electrode tip  450 ”. In addition, when a state after the melt portion  455  is formed is described, a portion that has not been melted, of the electrode base material  410  that is prepared initially together with the electrode tip  450 , is referred to as “electrode base material  410 ”. 
     As a result of laser welding, the formed melt portion  455  has a shape described below in a cross section passing through the axis CA. A reference character denoting each portion of the electrode tip  450  is defined as follows. 
       451 : an outer surface of the cylindrical portion  450   p  of the electrode tip  450  at one side (the right side in  FIG. 2 ) with respect to the axis CA. 
       452 : an outer surface of the cylindrical portion  450   p  of the electrode tip  450  at the other side (the left side in  FIG. 2 ) with respect to the axis CA. 
       453 : an end surface of the electrode tip  450  at a side opposite in the axial direction to the side at which the electrode base material  410  is located. 
     A reference character denoting each portion of the melt portion  455  is defined as follows. 
     Pa 1 : a point farthest from the end surface  453  in the axial direction, on the melt portion  455  at the one side (the right side in  FIG. 2 ) with respect to the axis CA. 
     Pa 2 : a point farthest from the end surface  453  in the axial direction, on the melt portion  455  at the other side (the left side in  FIG. 2 ) with respect to the axis CA. 
     Pa 3 : a point farthest from the axis CA, on the melt portion  455  at the one side with respect to the axis CA. 
     Pa 4 : a point farthest from the axis CA, on the melt portion  455  at the other side with respect to the axis CA. 
     Pa 5 : a point closest to the end surface  453  in the axial direction, on the melt portion  455  at the one side with respect to the axis CA. 
     Pa 6 : a point closest to the end surface  453  in the axial direction, on the melt portion  455  at the other side with respect to the axis CA. 
     Pa 7 : an end point of an interface ISO between the electrode tip  450  and the electrode base material  410  at the one side with respect to the axis CA. 
     Pa 8 : an end point of the interface ISO between the electrode tip  450  and the electrode base material  410  at the other side with respect to the axis CA. 
     RL: a reference line which is a straight line passing through the point Pa 3  and the point Pa 4 . 
     A reference character denoting a dimension of the electrode tip  450  is defined as follows. 
     W: a width of the electrode tip  450  at an end at a side opposite in the axial direction to the side at which the electrode base material  410  is located (in the present embodiment, the diameter of the cylinder of the cylindrical portion  450   p ). 
     A reference character denoting a dimension of each portion of the electrode tip  450  and the melt portion  455  at the one side with respect to the axis CA is defined as follows. 
     A 1 : a distance between the outer surface  451  of the cylindrical portion  450   p  of the electrode tip  450  and the point Pa 7 . 
     B 1 : a distance between the outer surface  451  of the cylindrical portion  450   p  of the electrode tip  450  and the point Pa 3 . 
     C 1 : a distance between the reference line RL and the point Pa 5 . 
     D 1 : a distance between the reference line RL and the point Pa 1 . 
     E 1 : a distance between the axis CA and the point Pa 1 . 
     In the present specification, a distance between a straight line and a point is defined as the length of a perpendicular extending from the point to the straight line. 
     A reference character denoting a dimension of each portion of the electrode tip  450  and the melt portion  455  at the other side with respect to the axis CA is defined as follows. 
     A 2 : a distance between the outer surface  452  of the cylindrical portion  450   p  of the electrode tip  450  and the point Pa 8 . 
     B 2 : a distance between the outer surface  452  of the cylindrical portion  450   p  of the electrode tip  450  and the point Pa 4 . 
     C 2 : a distance between the reference line RL and the point Pa 6 . 
     D 2 : a distance between the reference line RL and the point Pa 2 . 
     E 2 : a distance between the axis CA and the point Pa 2 . 
     In the present embodiment, the melt portion  455  has a shape which satisfies the following condition, in the cross section passing through the axis CA:
 
 C 1≧ D 1  (1), and
 
 C 2≧ D 2  (2).
 
     The satisfaction of the above formulas (1) and (2) means that as compared to a mode where the above formulas (1) and (2) are not satisfied, a more amount of the electrode tip  450  is melted to form the melt portion  455 . That is, in such a mode, as compared to the mode where the above formulas (1) and (2) are not satisfied, the proportion of the material of the electrode tip  450  in the material of the melt portion  455  can be increased. As a result, the thermal expansion coefficient (linear expansion coefficient) of the melt portion  455  can be close to the thermal expansion coefficient of the electrode tip  450 . Thus, a possibility can be reduced that when the spark plug  10  is mounted to an engine and the engine is operated so that a combustion cycle is executed, a crack occurs and grows at interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450  due to the difference in thermal expansion coefficient between the melt portion  455  and the electrode tip  450 . In addition, as a result, a possibility can also be reduced that oxide scale grows at the crack portion. 
     Melting a more amount of the electrode tip  450  to increase the proportion of the material of the electrode tip  450  in the material of the melt portion  455  means that the proportion of the material of the electrode base material  410  in the material of the melt portion  455  is relatively decreased. As a result, the difference between the thermal expansion coefficient of the melt portion  455  and the thermal expansion coefficient of the electrode base material  410  increases. Thus, strain at interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410  also relatively increases. 
     However, the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410  are located farther from the spark gap SG than the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450  (see  FIG. 1 ). Thus, the temperatures of the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410  does not become high as compared to the temperatures of the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 . That is, amounts of variation in the dimensions of the interfaces IS 3  and IS 4  at high temperature and at low temperature are small as compared to the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 . Thus, even when the proportion of the material of the electrode tip  450  in the material of the melt portion  455  is increased to such a degree that the above mode exerts an advantageous effect, a possibility that a crack occurs at the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410  is relatively low. 
     The above formulas (1) and (2) are preferably satisfied in any cross section passing through the axis CA. However, normally, a tip of a ground electrode in a spark plug is ideally provided so as to have rotational symmetry. Thus, it can be considered that if the above formulas (1) and (2) are satisfied in a predetermined cross section, the above advantageous effects of the present embodiment are obtained. Thus, whether the above formulas (1) and (2) are satisfied is determined in a plane RP which passes through the axis of the electrode tip  450  and includes the direction in which the ground electrode  400  extends (see the lower part of  FIG. 2 ). Hereinafter, in determining the cross-sectional shape of the melt portion  455 , the cross section RP is used as a reference. In the present embodiment, the cross section RP is a surface which does not include the portion WPL melted last by the applied laser beam in laser welding (see the lower part of  FIG. 2 ). 
     Meanwhile, in the present embodiment, at the one side (the right side in  FIG. 2 ) with respect to the axis CA, the point Pa 1  farthest from the end surface  453 , on the melt portion  455 , is located at a position whose distance to the axis CA in a direction perpendicular to the axis CA is shorter than ⅔ of the length (W/2) from the axis CA to the outer surface  451  of the cylindrical portion  450   p . In addition, at the other side (the left side in  FIG. 2 ) with respect to the axis CA, the point Pa 2  farthest from the end surface  453 , on the melt portion  455 , is located at a position whose distance to the axis CA in the direction perpendicular to the axis CA is shorter than ⅔ of the length (W/2) from the axis CA to the outer surface  451  of the cylindrical portion  450   p . That is, the melt portion  455  has a shape which satisfies the following condition, in the cross section passing through the axis CA:
 
 E 1&lt; W/ 3  (3), and
 
 E 2&lt; W/ 3  (4).
 
     In such a mode, the melt portion  455  and the electrode tip  450  are in contact with each other at wider interfaces IS 1  and IS 2  as compared to a mode where the above formulas (3) and (4) are not satisfied. In addition, the melt portion  455  and the electrode base material  410  are also in contact with each other at wider interfaces IS 3  and IS 4  as compared to the mode where the above formulas (3) and (4) are not satisfied. Thus, the electrode tip  450  is firmly joined to the electrode base material  410  via the melt portion  455 . 
     The melt portion  455  of the present embodiment also satisfies the following condition.
 
 A 1+ A 2&gt; B 1+ B 2
 
     The satisfaction of the above formula means that an amount (A 1 +A 2 ) by which the melt portion  455  extends inward (toward the axis CA side) from the outer surfaces  451  and  452  is larger than an amount (B 1 +B 2 ) by which the melt portion  455  extends outward from the outer surfaces  451  and  452 . In such a mode, an amount of the melt portion  455  flowing outward of the outer surfaces  451  and  452  of the melt portion  455  is small, and a more amount of the electrode tip  450  melts at the inner side of the outer surfaces  451  and  452  of the melt portion  455 , to form an interface with the melt portion  455 . As a result, the end portion  454  of the melt portion  455  at the electrode base material  410  side can be firmly joined to the melt portion  455  in a wider area. 
     A3. Another Structure Around Electrode Tip of Ground Electrode 
       FIG. 3  is a cross-sectional view showing another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . In the mode of  FIG. 2 , the shape of the melt portion  455  is asymmetrical about the axis CA in the cross section RP. On the other hand, in the mode shown in  FIG. 3 , the shape of the melt portion  455  is substantially symmetrical about the axis CA in the cross section RP. Regarding the other points, the shape of the melt portion  455  in  FIG. 3  is the same as the shape of the melt portion  455  in  FIG. 2 . In the present specification, the phrase “substantially symmetrical about a line” means that when one of two figures is inverted about the line, a portion having an area which is 90% or more of the area of the figure overlaps the other figure. 
     The melt portion  455  in the mode of  FIG. 3  can be formed by a method in which, for example, as compared to the formation of the melt portion  455  in the mode of  FIG. 2 , the quality in each direction from the axis CA of the electrode tip  450  and the electrode base material  410  is made more uniform, or output of the laser beam in laser welding is stabilized. Also in the mode of  FIG. 3 , the conditions of the above formulas (1) to (4) can be satisfied. 
     As described above, in laser welding, the application of the laser beam is performed from around the electrode tip  450  toward the electrode tip  450  and the electrode base material  410  at  10  to  20  locations which are located at substantially equal angular positions with respect to the axis CA. Then, the three-dimensional shape of the formed melt portion  455  is desirably rotationally symmetrical about the axis CA (see  FIG. 3 ). In such a mode, stress is unlikely to be concentrated on a portion of the melt portion  455 . As a result, a crack is unlikely to occur. Thus, the possibility can be further reduced that a crack occurs and grows at the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 . 
     The melting point of the material (e.g., platinum (Pt), iridium (Ir), ruthenium (Ru), rhodium (Rh), etc.) of the electrode tip  450  is higher than the melting point of the nickel alloy which is the material of the electrode base material  410 . Thus, when the temperature of a predetermined range near the interface ISO between the electrode tip  450  and the electrode base material  410  becomes a temperature between the melting point of the electrode tip  450  and the melting point of the electrode base material  410  by the application of the laser beam, the electrode base material  410  at this site melts, but the electrode tip  450  does not melt. As a result, as in the vicinity of the point Pa 1  in  FIG. 2 , the melt portion  455  is in contact with the end surface of the electrode tip  450  that has not been melted. 
       FIG. 4  is a cross-sectional view showing still another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . In the mode of  FIG. 2 , in the cross section RP, the melt portion  455  is not present near the axis CA, but the interface ISO at which the electrode tip  450  and the electrode base material  410  are in contact with each other is present. On the other hand, in the mode shown in  FIG. 4 , the melt portion  455  extends from the outer surface  451  of the electrode tip  450  at the one side with respect to the axis CA through an area around the axis CA to the outer surface  452  of the electrode tip  450  at the other side with respect to the axis CA. The point Pa 2  farthest from the end surface  453 , on the melt portion  455  at the other side with respect to the axis CA, is located on the axis CA. Regarding the other points, the shape of the melt portion  455  in  FIG. 4  is the same as the shape of the melt portion  455  in  FIG. 2 . 
     The melt portion  455  in the mode of  FIG. 4  can be formed by a method in which, for example, as compared to the formation of the melt portion  455  in the mode of  FIG. 2 , the output of the laser beam is increased, or positions to which the laser beam is to be applied are made closer to the end surface  453  of the electrode tip  450 . Also in the mode of  FIG. 4 , the conditions of the above formulas (1) to (4) can be satisfied. 
     The thermal expansion coefficient of the material (e.g., platinum (Pt), iridium (Ir), ruthenium (Ru), rhodium (Rh), etc.) of the electrode tip  450  is lower by 20 to 30% than the thermal expansion coefficient of the nickel alloy which is the material of the electrode base material  410 . Thus, in a mode where the interface ISO between the electrode tip  450  and the electrode base material  410  is present (see  FIGS. 2 and 3 ), due to temperature change in the thermal cycle of the engine, greater strain occurs at the interface ISO as compared to the other interfaces IS 1  to IS 4 . The strain becomes maximum at the end of the interface ISO (see the points Pa 1  and Pa 8  in  FIGS. 2 and 3 ), and there is a possibility that a crack occurs therefrom. In addition, there is a possibility that the crack grows not only at the interface ISO but also to the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 , leading to falling-off of the electrode tip  450  from the electrode base material  410 . 
     On the other hand, in the mode shown in  FIG. 4 , the entirety of the end portion  454  of the electrode tip  450  at the electrode base material  410  side is joined to the electrode base material  410  via the melt portion  455 . The melt portion  455  is present between the electrode tip  450  and the electrode base material  410 , and the interface ISO between the electrode tip  450  and the electrode base material  410  (see  FIGS. 2 and 3 ) is not present. Thus, a possibility can be reduced that a crack grows from inside of the ground electrode  400  (the interface ISO) to the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 . 
       FIG. 5  is a cross-sectional view showing still another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . In the mode of  FIG. 2 , in the cross section RP, the melt portion  455  formed by the laser beam applied to the outer surface  451  of the electrode tip  450  does not reach the axis CA. In addition, the melt portion  455  formed by the laser beam applied to the outer surface  452  of the electrode tip  450  also does not reach the axis CA. On the other hand, in the mode of  FIG. 5 , the melt portion  455  formed by the laser beam applied to the outer surface  451  of the electrode tip  450  reaches the opposite side across the axis CA. The melt portion  455  formed by the laser beam applied to the outer surface  452  of the electrode tip  450  also reaches the opposite side across the axis CA. As a result, the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410  each have a complicated curved surface as compared to the mode of  FIG. 2 . Regarding the other points, the shape of the melt portion  455  in  FIG. 5  is the same as the shape of the melt portion  455  in  FIG. 2 . 
     The melt portion  455  in the mode of  FIG. 5  can be formed by a method in which, for example, as compared to the formation of the melt portion  455  in the mode of  FIG. 2 , the diameter of the laser beam is decreased, or the output of the laser beam is increased. Also in the mode of  FIG. 5 , the conditions of the above formulas (1) to (4) can be satisfied. 
     In the mode of  FIG. 5 , boundaries representing the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410  each draw a complicated curved line which sharply bends. Thus, even when a crack occurs at the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410 , the crack is unlikely to grow along the interfaces IS 3  and IS 4 . 
     In addition, the melt portion  455  and the electrode base material  410  are disposed in a manner where the melt portion  455  and the electrode base material  410  mesh with each other. In other words, the melt portion  455  and the electrode base material  410  are disposed in a manner where a projection of the electrode base material  410  is fitted into a recess of the melt portion  455  and a projection of the melt portion  455  is fitted into a recess of the electrode base material  410 . Thus, even when a crack occurs at the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410 , the melt portion  455  is unlikely to fall off from the electrode base material  410 . 
       FIG. 6  is a cross-sectional view showing still another structure around the electrode tip  450  provided at the ground electrode  400  of the spark plug  10 . In the mode of  FIG. 4 , in the cross section RP, the shape of the melt portion  455  is asymmetrical about the axis CA. On the other hand, in the mode shown in  FIG. 6 , in the cross section RP, the shape of the melt portion  455  is substantially symmetrical about the axis CA. The points Pa 1  and Pa 2  farthest from the end surface  453 , on the melt portion  455 , are the same. In addition, in the mode shown in  FIG. 6 , the point Pa 9  farthest from the end surface  453  of the electrode tip  450 , on the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 , is located at a position closer to the end surface  453  of the electrode tip  450  than in the mode of  FIG. 4  (at a higher position in  FIGS. 4 and 6 ). Regarding the other points, the shape of the melt portion  455  in  FIG. 6  is the same as the shape of the melt portion  455  in  FIG. 4 . 
     The melt portion  455  in the mode of  FIG. 6  can be formed by a method in which, for example, as compared to the formation of the melt portion  455  in the mode of  FIG. 4 , the diameter of the laser beam is increased, or the positions to which the laser beam is to be applied are made closer to the end surface  453  of the electrode tip  450  in the axial direction. Also in the mode of  FIG. 6 , the conditions of the above formulas (1) to (4) can be satisfied. 
     As described above, the three-dimensional shape of the formed melt portion  455  is desirably rotationally symmetrical about the axis CA (see  FIG. 6 ). In such a mode, a portion of the melt portion  455  is unlikely to be provided with a site where a crack is likely to occur. Thus, the possibility can be further reduced that a crack occurs and grows at the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450 . 
     In addition, over the entirety of the end portion  454  of the electrode tip  450 , the melt portion  455  is present between the electrode tip  450  and the electrode base material  410  with a large thickness in the axial direction. Thus, the difference between the thermal expansion coefficient of the electrode tip  450  and the thermal expansion coefficient of the electrode base material  410  is likely to be absorbed by the melt portion  455 . Therefore, the possibility can be further reduced that a crack occurs and grows at the interfaces IS 1  and IS 2  between the melt portion  455  and the electrode tip  450  and at the interfaces IS 3  and IS 4  between the melt portion  455  and the electrode base material  410 . 
     The electrode tip  450  in the present embodiment corresponds to the “tip” in “Means for Solving the Problems”. The axis CA corresponds to the “central axis”. The cross section RP corresponds to the “cross section passing through the central axis”. The points Pa 1  to Pa 6  correspond to the “first point” to “sixth point”, respectively. 
     A 4 . Examples 
     A test for evaluating the peeling resistance of the electrode tip  450  was carried out by using samples formed with the above-described respective dimensions being set at various values. Prior to the test, samples in which the interface ISO between the electrode tip  450  and the electrode base material  410  is present, that is, samples in which an unmelted portion of the bottom of the electrode tip  450  is present (see  FIGS. 2, 3 , and  5 ), and samples in which the interface ISO, that is, an unmelted portion, is not present (see  FIGS. 4 and 6 ) were prepared. The ground electrode of each spark plug used in the test has the following configuration. 
     Material of the electrode base material: INCONEL 601 
     Width of the ground electrode: 2.5 mm 
     Material of the electrode tip: an alloy containing platinum (Pt) as a principal component and 20 mass % of rhodium (Rh). 
     The “width of the ground electrode” is a dimension of a surface to which the electrode tip is attached, in a direction in which the ground electrode extends and in a direction perpendicular to the axial direction (the X axis direction). The portion to which the electrode tip is attached has a sufficient dimension equal to or larger than the width, in the direction in which the ground electrode extends (the Y axis direction). 
     A spark plug which is a test sample was mounted to one cylinder of a four-cylinder engine having a displacement of 1.5 L, plugs which are the same were mounted to the other cylinders for all experiments, and the test was carried out. In the test, a process in which the engine was operated at full throttle (an engine speed: 5000 rpm) for 1 minute and then operation was stopped for 1 minute was repeated for 100 hours. 
     The evaluation was carried out by measuring the size of oxide scale at the interface between the electrode tip and the melt portion in the cross section RP which passes through the axis CA of the spark plug and includes the direction in which the ground electrode  400  extends toward the axis CA (see the lower part of  FIG. 2 ). Specifically, the peeling resistance was evaluated based on a ratio Ra, relative to W, of the total value of the length of oxide scale in the direction perpendicular to the axis CA (in the Y axis direction in  FIG. 2 ) when the oxide scale was projected in the axial direction. In the present embodiment, the cross section RP is a surface which does not include the portion WPL melted last by the applied laser beam in laser welding (see the lower part of  FIG. 2 ). 
       FIG. 7  is a table showing the results of the peeling resistance test carried out under the conditions described above. In the table of  FIG. 7 , the unit of each dimension is “mm”. In the table of  FIG. 7 , a double circle which indicates “excellent” is given to a sample in which the ratio Ra of the total value of the length of the oxide scale relative to W is equal to or lower than 50%. A circle which indicates “good” is given to a sample in which Ra is higher than 50% and equal to or lower than 90%. X which indicates “poor” is given to a sample in which Ra is higher than 90%. Although not shown in the table, the spark plugs of the samples 1 to 15 satisfy the condition of the above formulas (3) and (4). 
     In the table of  FIG. 7 , the samples 3 to 5, the samples 7 to 10, and the samples 12 to 15 have both C 1 /D 1  of 1.0 or higher and C 2 /D 2  of 1.0 or higher, and satisfy both of the above formulas (1) and (2). For these samples, the peeling resistance was “excellent” (double circle) or “good” (circle). Thus, it is recognized that the peeling resistance is favorable in each spark plug that satisfies both of the above formulas (1) and (2). 
     Furthermore, in the table of  FIG. 7 , the samples 3 to 5, the samples 8 to 10, and the samples 13 to 15 satisfy both of the following formulas (5) and (6). For these samples, the peeling resistance was “excellent” (double circle). Thus, it is recognized that the peeling resistance is further favorable in each spark plug that satisfies both of the following formulas (5) and (6).
 
 C 1/ D 1≧1.2  (5)
 
 C 2/ D 2≧1.2  (6)
 
     In the spark plug including the melt portion  455  having a shape that satisfies the formulas (5) and (6), the proportion of the material of the electrode tip  450  in the material of the melt portion  455  can be further increased as compared to a mode where the above formulas (5) and (6) are not satisfied. As a result, the thermal expansion coefficient (linear expansion coefficient) of the melt portion  455  can be close to the thermal expansion coefficient of the electrode tip  450 . Thus, the possibility can be further reduced that when the engine is operated so that a combustion cycle is executed, a crack occurs and grows at the interface between the melt portion  455  and the electrode tip  450 . In addition, as a result, the possibility can be further reduced that oxide scale grows at the crack portion. 
     In addition, in the table of  FIG. 7 , the samples 3 to 5, the samples 9 and 10, and the sample 15 are samples that satisfy both of the above formulas (1) and (2) and further have no unmelted portion of the tip bottom (see  FIGS. 4 and 6 ). For these samples, the peeling resistance was “excellent” (double circle). Thus, it is recognized that the peeling resistance is further favorable in each spark plug that satisfies both of the above formulas (1) and (2) and further has no unmelted portion of the tip bottom (see  FIG. 4 ). 
     B. Modified Embodiments 
     B 1 . Modified Embodiment 1 
     In the embodiments described above, the electrode tip  450  has a cylindrical shape before being joined to the electrode base material  410 , and the end portion  450   p  of the electrode tip  450  has a cylindrical shape after the electrode tip  450  is joined to the electrode base material  410 . However, before being joined to the electrode base material, the electrode tip may have another shape such as a square column and a hexagonal column. After the electrode tip is joined to the electrode base material, the end portion of the electrode tip may have another shape such as a square column and a hexagonal column. However, each of the electrode tip and the end portion of the electrode tip preferably has a columnar shape, and further preferably has a shape having rotational symmetry about the axis. 
     In the present specification, the “columnar shape” means a three-dimensional shape in which a cross-sectional shape in any cross section perpendicular to a predetermined direction is uniform along the direction. In addition, the “central axis of the columnar shape” is an axis which: is parallel to a direction in which the columnar portion extends; and passes through the centroid of a cross section of the columnar portion on a plane perpendicular to the direction in which the columnar portion extends. 
     B 2 . Modified Embodiment 2 
     In the embodiment of  FIG. 2 , the shape of the melt portion  455  satisfies the condition of A 1 +A 2 &gt;B 1 +B 2 . However, the shape of the melt portion  455  may satisfy A 1 +A 2 ≦B 1 +B 2 . 
     B 3 . Modified Embodiment 3 
     In the embodiments shown in  FIGS. 2 to 6 , the points Pa 3  and Pa 4  farthest from the axis CA, on the melt portion  455 , are located on the surface of the electrode base material  410 . Thus, the reference line RL, which is a straight line passing through the point Pa 3  and the point Pa 4 , coincides with a line representing the surface of the electrode base material  410 . However, the point Pa 3  and the point Pa 4  do not necessarily need to be located on the surface of the electrode base material  410 . 
     In addition, in the embodiments described above, the surface of the electrode base material  410  is a flat surface. Thus, in the embodiments described above in which the points Pa 3  and Pa 4  are located on the surface of the electrode base material  410 , the surface of the electrode base material  410  on the cross section RP coincides with the reference line RL. However, the surface of the electrode base material  410  may not be a flat surface. 
     Also in a mode where the points Pa 3  and Pa 4  are not located on the surface of the electrode base material  410  or the surface of the electrode base material to which the electrode tip is joined is not a flat surface, as long as the above formulas (1) and (2) which are defined based on the reference line RL are satisfied, the thermal expansion coefficient (linear expansion coefficient) of the melt portion  455  can be close to the thermal expansion coefficient of the electrode tip  450  as compared to the mode where the above formulas (1) and (2) are not satisfied. Thus, occurrence and growth of a crack and oxide scale at the interface between the electrode tip and the melt portion can be suppressed. 
     B 4 . Modified Embodiment 4 
     In the embodiments shown in  FIGS. 2, 3, and 5 , the interface ISO between the electrode tip  450  and the electrode base material  410  is present. In the embodiments shown in  FIGS. 4 and 6 , there is no interface ISO, and the entirety of the end portion  454  of the electrode tip  450  is joined to the melt portion  455 . However, the mode in which the electrode tip  450  is joined to the melt portion  455  may be another mode. For example, the end portion  454  of the electrode tip  450  may have an interface with a component other than the melt portion  455  and the electrode base material  410 . 
     B 5 . Modified Embodiment 5 
     In the Examples described above, the test was carried out for the samples each having an electrode tip diameter W of 0.8 mm, 1.0 mm, or 1.5 mm. However, even when the electrode tip diameter W is another size, as long as the above formulas (1) and (2) are satisfied, the thermal expansion coefficient of the melt portion can be close to the thermal expansion coefficient of the electrode tip as compared to the mode where the above formulas (1) and (2) are not satisfied. Thus, occurrence and growth of a crack and oxide scale at the interface between the electrode tip and the melt portion can be suppressed. 
     B 6 . Modified Embodiment 6 
     In the embodiments described above, the cross section RP which is used as a reference when the cross-sectional shape of the melt portion is determined is a surface which does not include the portion WPL melted last by the applied laser beam, of the melt portion  455 . However, the cross section which is used as a reference when the cross-sectional shape of the melt portion is determined may include the portion WPL melted last by the applied laser beam, of the melt portion  455 . 
     The present invention is not limited to the embodiments, examples, and modified embodiments described above, and can be embodied in various configurations without departing from the gist of the present invention. For example, the technical features in the embodiments, examples, and modified embodiments corresponding to the technical features in each mode described in the Summary of the Invention section can be appropriately replaced or combined to solve some of or all of the foregoing problems, or to achieve some of or all of the foregoing effects. Further, such technical features may be appropriately deleted if not described as being essential in the present specification. 
     DESCRIPTION OF REFERENCE NUMERALS 
     
         
         
           
               10 : spark plug 
               90 : internal combustion engine 
               100 : center electrode 
               190 : metal terminal 
               200 : insulator 
               290 : axial bore 
               300 : metallic shell 
               310 : end surface 
               400 : ground electrode 
               410 : electrode base material 
               450 : electrode tip 
               450   p : end portion of electrode tip 
               451 ,  452 : outer surface of electrode tip 
               453 : end surface of electrode tip 
               455 : melt portion 
               910 : inner wall 
               920 : combustion chamber 
             CA: axis 
             ISO: interface between electrode tip  450  and electrode base material  410   
             IS 1 , IS 2 : interface between melt portion  455  and electrode tip  450   
             IS 3 , IS 4 : interface between melt portion  455  and electrode base material  410   
             RL: reference line 
             SG: gap (spark gap) 
             Pa 1 : point farthest from end surface  453 , on melt portion  455  at one side with respect to axis CA 
             Pa 2 : point farthest from end surface  453 , on melt portion  455  at other side with respect to axis CA 
             Pa 3 : point farthest from axis CA, on melt portion  455  at one side with respect to axis CA 
             Pa 4 : point farthest from axis CA, on melt portion  455  at other side with respect to axis CA 
             Pa 5 : point closest to end surface  453 , on melt portion  455  at one side with respect to axis CA 
             Pa 6 : point closest to end surface  453 , on melt portion  455  at other side with respect to axis CA 
             Pa 7 : end point of interface ISO at one side with respect to axis CA 
             Pa 8 : end point of interface ISO at other side with respect to axis CA 
             Pa 9 : point farthest from end surface  453  of electrode tip  450 , on interfaces IS 1  and IS 2   
             WPL: portion welded last in welding of electrode tip and electrode base material