Patent Publication Number: US-11652335-B2

Title: Spark plug

Description:
FIELD OF THE INVENTION 
     The present disclosure relates to a spark plug. 
     BACKGROUND OF THE INVENTION 
     A spark plug that includes an insulator having a through-hole extending in an axial-line direction and a center electrode disposed inside the through-hole is known as an example of an ignition spark plug employed for a gasoline engine (for example, Japanese Unexamined Patent Application Publication No. 11-67422, hereinafter “PTL 1”). In the spark plug described in PTL 1, a stepped portion formed in the through-hole of the insulator by reducing the diameter of the through-hole toward the front end supports a flange of a center electrode protruding radially outward. In such a spark plug, a sealant is filled in the through-hole around the flange to fix the center electrode to the insulator. 
     Technical Problem 
     The sealant may be filled in the through-hole from the rear end during manufacture of the spark plug, and may intrude into a space between the flange and the stepped portion while being filled. Generally, the coefficient of thermal expansion of the center electrode is larger than the coefficient of thermal expansion of the insulator. Thus, when the spark plug is used under high-temperature environments, the center electrode is more likely to thermally expand more than the insulator. Thus, when a spark plug where the sealant intrudes between the flange and the stepped portion is installed in the internal combustion engine under high-temperature environments, the flange of the center electrode comes into contact with the stepped portion of the insulator via the sealant interposed therebetween attributable to thermal expansion of the center electrode. When the center electrode thermally expands further from this state, a stress may be exerted from the flange to the stepped portion through the sealant, and the insulator may crack. Foreign objects such as soot may intrude between the flange and the stepped portion from a combustion chamber. Also in such a case, a stress may be exerted from the flange of the center electrode to the stepped portion of the insulator through the foreign object, and the insulator may crack. To avoid this, a technology for preventing a sealant from intruding between the flange and the stepped portion during manufacture of a spark plug and preventing the insulator from cracking during use of the spark plug has been desired. 
     SUMMARY OF THE INVENTION 
     The present disclosure can be embodied in the following form. 
     (1) An aspect of the present disclosure provides a spark plug. The spark plug includes a center electrode, an insulator, and a sealant. The center electrode includes a leg extending in an axial-line direction parallel to an axial line, and a flange that is continuous with a rear end side of the leg in the axial-line direction and protrudes radially outward beyond the leg. The insulator has a through-hole extending in the axial-line direction. The insulator holds the center electrode in the through-hole. The sealant is filled in the through-hole to fix the flange and the insulator to each other. The insulator includes a stepped portion in which the through-hole reduces a diameter toward the front end side in the axial-line direction to support the flange, and a small-diameter portion that is continuous with a front end side of the stepped portion and in which the diameter of the through-hole is smaller than in the stepped portion. An angle θ 1  formed by the stepped portion and a plane perpendicular to the axial line and an angle θ 2  formed by the plane and an opposing surface of the flange opposing the stepped portion satisfy θ 1 −θ 2 ≥6°. In a cross section including the axial line, a maximum diameter D 1  of the flange and a diameter D 2  of the through-hole at a rear end of the small-diameter portion in the axial-line direction satisfy 0.15 mm≤(D 1 −D 2 )/2. In the spark plug with this aspect, an angle θ 1  formed by the stepped portion and a plane perpendicular to the axial line and an angle θ 2  formed by the plane perpendicular to the axial line and an opposing surface of the flange opposing the stepped portion satisfy θ 1 −θ 2 ≥6°. Thus, the flange of the center electrode and the stepped portion of the insulator can be brought into point contact with each other. This structure can thus improve adhesion between the flange and the stepped portion. This structure can thus prevent a sealant from intruding between the flange and the stepped portion during manufacture of the spark plug. In addition, in a cross section including the axial line, a maximum diameter D 1  of the flange and a diameter D 2  of the through-hole at a rear end of the small-diameter portion in the axial-line direction satisfy 0.15 mm≤(D 1 −D 2 )/2. This structure can secure a relatively large gap between the stepped portion and the opposing surface of the flange. This structure can thus prevent the gap from being filled up with a foreign object that intrudes from a combustion chamber into the gap. This structure can thus prevent a stress from being applied from the flange of the center electrode to the stepped portion of the insulator via the sealant or the foreign object attributable to thermal expansion of the center electrode during use of the spark plug. The spark plug according to this aspect can thus prevent a sealant from intruding between the flange and the stepped portion during manufacture of the spark plug and prevent the insulator from cracking during use of the spark plug. 
     (2) In the spark plug according to the above aspect, the angle θ 1  may satisfy 25°≤θ 1 ≤35°. In the spark plug according to this aspect, the angle θ 1  satisfies 25°≤θ 1 ≤35°. This structure can thus prevent a sealant from intruding between the flange and the stepped portion during manufacture of the spark plug. 
     (3) In the spark plug according to the above aspect, the angle θ 1  and the angle θ 2  may satisfy θ 1 −θ 2 ≤20°. In the spark plug according to this aspect, the angle θ 1  and the angle θ 2  satisfy θ 1 −θ 2 ≤20°. This structure can thus prevent an excessive increase of the gap between the stepped portion and the opposing surface of the flange, and thus can reduce an amount of a high-temperature gas that intrudes from the combustion chamber into the gap. This structure can thus prevent deformation of the flange attributable to thermal expansion caused by a temperature rise of the center electrode and the insulator with the high-temperature gas, and thus can prevent reduction of adhesion between the flange and the stepped portion. 
     The present invention can be embodied in various forms, for example, can be embodied in the form of a method for manufacturing a spark plug, or an engine head to which a spark plug is attached. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a partial cross-sectional view of a schematic structure of a spark plug. 
         FIG.  2    is an enlarged cross-sectional view of an area around a flange and a stepped portion. 
         FIG.  3    is an enlarged view schematically illustrating an area Ar 1  in  FIG.  2   . 
         FIG.  4    is an enlarged view schematically illustrating an area Ar 2  in  FIG.  3   . 
         FIG.  5    is a diagram illustrating thermal expansion of a center electrode. 
         FIG.  6    is a schematic diagram illustrating part of a spark plug according to Comparative Example 1. 
         FIG.  7    is a schematic diagram illustrating thermal expansion of a center electrode of the spark plug according to Comparative Example 1. 
     
    
    
     DETAILED DESCRIPTION OF INVENTION 
     A. Embodiment 
       FIG.  1    is a partial cross-sectional view of a schematic structure of a spark plug  100  according to an embodiment of the present disclosure.  FIG.  1    illustrates the external appearance of the spark plug  100  on the left side, and a cross section of the spark plug  100  on the right side with respect to an axial line CA serving as an axis of the spark plug  100 . In the following description, the lower side in  FIG.  1    (side on which a ground electrode  40 , described below, is located) in the axial line CA will be referred to as a front end side, the upper side in  FIG.  1    (side on which a metal terminal  50 , described below, is located) is referred to as a rear end side, and the direction parallel to the axial line CA is referred to as an axial-line direction AD. For illustration purposes,  FIG.  1    illustrates, with a broken line, an engine head  90  to which the spark plug  100  is attached. 
     The spark plug  100  includes an insulator  10 , a center electrode  20 , a metal shell  30 , a ground electrode  40 , and a metal terminal  50 . The axial line CA of the spark plug  100  is coaxial with the axial lines CA of the insulator  10 , the center electrode  20 , the metal shell  30 , and the metal terminal  50 . 
     The insulator  10  has a substantially cylindrical profile with a through-hole  11  extending in the axial-line direction AD. The through-hole  11  accommodates part of the center electrode  20  on the front end side, and accommodates part of the metal terminal  50  on the rear end side. The insulator  10  thus holds the center electrode  20  inside the through-hole  11 . Substantially a half of the insulator  10  on the front end side is accommodated in an axial hole  38  in the metal shell  30 , described later, and substantially a half of the insulator  10  on the rear end side is exposed from the axial hole  38 . The insulator  10  is a ceramic insulator formed by sintering a ceramic material such as alumina. 
     The insulator  10  includes a large-diameter portion  14 , a locking portion  15 , a stepped portion  17 , and a small-diameter portion  16 . The large-diameter portion  14  is located on the rear end side in the insulator  10  in the axial-line direction AD. The through-hole  11  in the large-diameter portion  14  has a substantially uniform diameter. A portion of the locking portion  15  located closer to the front end side than the large-diameter portion  14  has an outer diameter reducing toward the front end side in the axial-line direction AD. 
       FIG.  2    is an enlarged and schematic cross-sectional view of an area around a flange  22  and the stepped portion  17 .  FIG.  2    is a cross-sectional view including the axial line CA. The diameter of the through-hole  11  in the stepped portion  17  reduces toward the front end side in the axial-line direction AD. In other words, the stepped portion  17  in the through-hole  11  protrudes radially inward. The stepped portion  17  supports the flange  22  of the center electrode  20 . The small-diameter portion  16  illustrated in  FIGS.  1  and  2    is continuous with a front end side of the stepped portion  17 , and the diameter of the through-hole  11  in the small-diameter portion  16  is smaller than the diameter of the through-hole  11  in the stepped portion  17 . The through-hole  11  in the small-diameter portion  16  accommodates part of a leg  21  of the center electrode  20 , described later. 
     The center electrode  20  is a bar-shaped electrode extending in the axial-line direction AD. The center electrode  20  is held in the through-hole  11  in the insulator  10 . The center electrode  20  includes the leg  21 , the flange  22 , and a head  23 . 
     As illustrated in  FIG.  1   , the leg  21  extends in the axial-line direction AD, and has a portion on the front end side exposed from the through-hole  11 . A noble metal tip formed from, for example, an iridium alloy may be joined to the front end of the leg  21 . 
     As illustrated in  FIG.  2   , the flange  22  is continuous with the rear end side of the leg  21 , and protrudes radially outward beyond the leg  21 . The flange  22  has an opposing surface S that opposes the stepped portion  17 . The opposing surface S is continuous with the leg  21 . The flange  22  comes into contact with the stepped portion  17  of the insulator  10  from the rear end side to fix the position of the center electrode  20  in the through-hole  11  in the insulator  10 . The head  23  is continuous with the rear end side of the flange  22 , and extends in the axial-line direction AD. 
     The center electrode  20  according to the present embodiment is formed by embedding a highly thermal conductive core material  25  in an electrode member  26 . In the present embodiment, the core material  25  is formed from an alloy containing copper as a main component, and the electrode member  26  is formed from a nickel alloy containing nickel as a main component. 
     As illustrated in  FIG.  1   , part of the center electrode  20  is received in the front end side of the through-hole  11  in the insulator  10 , and part of the metal terminal  50  is received in the rear end side of the through-hole  11  in the insulator  10 . Between the center electrode  20  and the metal terminal  50  in the through-hole  11  in the insulator  10 , a far-end sealant  61 , a resistor element  62 , and a rear-end sealant  63  are arranged in order from the front end side toward the rear end side. Thus, the center electrode  20  is electrically connected, on the rear end side, to the metal terminal  50  via the far-end sealant  61 , the resistor element  62 , and the rear-end sealant  63 . 
     The resistor element  62  is made of ceramic powder, an electrical conducting material, glass, and an adhesive. The resistor element  62  functions as electric resistance between the metal terminal  50  and the center electrode  20 , and prevents occurrence of noise when a spark discharge is caused. The far-end sealant  61  and the rear-end sealant  63  are made of electrically conductive glass powder. In the present embodiment, the far-end sealant  61  and the rear-end sealant  63  are made of a powder mixture of copper powder and calcium borosilicate glass powder. The far-end sealant  61  is in contact with the flange  22 , the insulator  10 , and the resistor element  62  to fix these components to each other. The rear-end sealant  63  is in contact with the resistor element  62 , the insulator  10 , and the metal terminal  50  to fix these components to each other. 
     The metal shell  30  has a substantially cylindrical profile having an axial hole  38  extending in the axial-line direction AD, and holds the insulator  10  inside the axial hole  38 . More specifically, the metal shell  30  surrounds and holds a portion of the insulator  10  from part of the large-diameter portion  14  to the small-diameter portion  16 . The metal shell  30  is made of, for example, low-carbon steel, and entirely plated with, for example, nickel or zinc. 
     The metal shell  30  includes a tool engagement portion  31 , an external-thread portion  32 , a seating portion  33 , a protrusion  34 , a crimping portion  35 , and a compressed-deformed portion  36 . 
     To attach the spark plug  100  to the engine head  90 , the tool engagement portion  31  is engaged with a tool, not illustrated. The external-thread portion  32  has a thread ridge on the outer peripheral surface of the metal shell  30  at the front end portion, and is screwed on an internal thread  93  of the engine head  90 . The seating portion  33  is continuous with the rear end side of the external-thread portion  32  to be in a flange form. An annular gasket  65  formed by folding a plate is inserted into a space between the seating portion  33  and the engine head  90 . The protrusion  34  protrudes radially inward from the inner peripheral surface of the external-thread portion  32 . The locking portion  15  of the insulator  10  is in contact with the protrusion  34  on the rear end side. The protrusion  34  supports the insulator  10  inserted into the axial hole  38 . Annular plate packing, not illustrated, is disposed between the protrusion  34  and the locking portion  15 . 
     The crimping portion  35  on the rear end side of the tool engagement portion  31  has a small thickness. The compressed-deformed portion  36  between the tool engagement portion  31  and the seating portion  33  has a small thickness. From the tool engagement portion  31  to the crimping portion  35  in the axial-line direction AD, annular ring members  66  and  67  are interposed between the axial hole  38  in the metal shell  30  and the outer peripheral surface of the large-diameter portion  14  of the insulator  10 . Powder talc  69  is filled between the ring members  66  and  67 . As will be described later, the metal shell  30  is crimped at the crimping portion  35  to be assembled to the insulator  10 . 
     The ground electrode  40  is formed from a bent metal bar. As in the case of the center electrode  20 , the ground electrode  40  is made of a nickel alloy containing nickel as a main component. The ground electrode  40  has a first end fixed to a front end surface  37  of the metal shell  30 , and a second end bent to oppose the front end portion of the center electrode  20 . An electrode tip  42  is disposed at a portion of the ground electrode  40  opposing the front end portion of the center electrode  20 . Between the electrode tip  42  and the front end portion of the center electrode  20 , a gap G 1  for spark discharges is formed. The gap G 1  is also referred to as a discharge gap or a spark gap. 
     The metal terminal  50  is disposed at the rear end of the spark plug  100 . The front end side of the metal terminal  50  is accommodated in the through-hole  11  in the insulator  10 , and the rear end side of the metal terminal  50  is exposed from the through-hole  11 . A high-voltage cable, not illustrated, is connected to the metal terminal  50 , and a high voltage is applied to the metal terminal  50 . This application causes a spark discharge in the gap G 1 . The spark discharge caused in the gap G 1  ignites an air-fuel mixture in a combustion chamber  95 . 
     In the present embodiment, the far-end sealant  61  corresponds to a sealant according to the present disclosure. The front end side corresponds to the front end side in the axial-line direction according to the present disclosure. The rear end side corresponds to the rear end side in the axial-line direction according to the present disclosure. 
     A method for manufacturing the spark plug  100  will be described, below. 
     First, the center electrode  20  is inserted into the through-hole  11  in the insulator  10  from the rear end side. Thereafter, a powder material for the far-end sealant  61  is filled into the through-hole  11  from the rear end side and compressed (hereinafter also referred to as a “sealant filling step”). Thereafter, a material for the resistor element  62  is filled into the through-hole  11  from the rear end side and compressed, and then, a powder material for the rear-end sealant  63  is filled into the through-hole  11  from the rear end side and compressed. Each compression may be performed by inserting, for example, a bar-shaped tool into the through-hole  11  to press the material. Thereafter, the front end of the metal terminal  50  is inserted into the through-hole  11 , to compress the materials with a predetermined pressure exerted from the side closer to the metal terminal  50  while the entirety of the insulator  10  is heated (hereinafter also referred to as a “heat compression step”). In the heat compression step, the materials filled in the through-hole  11  are compressed and sintered. Thus, the far-end sealant  61 , the resistor element  62 , and the rear-end sealant  63  are formed in the through-hole  11 . The center electrode  20  is fixed to the insulator  10  in this manner. 
     Thereafter, the insulator  10  to which the center electrode  20  is fixed is inserted into the axial hole  38  in the metal shell  30  from the rear end side. The crimping portion  35  of the metal shell  30  is then crimped to fix the metal shell  30  and the insulator  10  to each other. Here, the crimping portion  35  of the metal shell  30  has its front end side pressed while being folded radially inward, so that the compressed-deformed portion  36  is compressed and deformed. The compression and deformation of the compressed-deformed portion  36  presses the insulator  10  toward the front end side inside the metal shell  30  via the ring members  66  and  67  and the talc  69 . Thus, the spark plug  100  is complete. 
       FIG.  3    is an enlarged view schematically illustrating an area Ar 1  in  FIG.  2   .  FIG.  4    is an enlarged view schematically illustrating an area Ar 2  in  FIG.  3   . The spark plug  100  according to the present embodiment satisfies Formula (1), where an angle formed by the stepped portion  17  and a plane P perpendicular to the axial line CA is denoted with θ 1 , and an angle formed by the plane P and the opposing surface S of the flange  22  opposing the stepped portion  17  is denoted with θ 2 :
 
θ1−θ2≥6°  Formula (1).
 
     As illustrated in Formula (1) and  FIGS.  3  and  4   , the angle θ 1  is greater than the angle θ 2 , and the angle difference (θ 1 −θ 2 ) between the angles θ 1  and θ 2  corresponds to the angle formed by the opposing surface S and the stepped portion  17  in a cross section taken along the axial line CA. In this structure, the flange  22  of the center electrode  20  and the stepped portion  17  of the insulator  10  are in point contact with each other. Thus, compared to a spark plug where the flange  22  of the center electrode  20  and the stepped portion  17  of the insulator  10  are in surface contact with each other, adhesion between the flange  22  and the stepped portion  17  can be improved. Thus, in the sealant filling step during manufacture of the spark plug  100 , the powder material for the far-end sealant  61  can be prevented from intruding between the flange  22  and the stepped portion  17 . In the heat compression step during manufacture of the spark plug  100 , the far-end sealant  61  is prevented from intruding between the flange  22  and the stepped portion  17 . Thus, the spark plug  100  according to the present embodiment satisfying Formula (1) can prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 . 
     In the present embodiment, the angle θ 1  is not limited to a particular one, but preferably greater than or equal to 25° and smaller than or equal to 35°. The angle θ 1  greater than or equal to 25° and smaller than or equal to 35° can further improve adhesion between the flange  22  and the stepped portion  17 . This structure can thus further prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 . 
     The upper limit of the angle difference (θ 1 −θ 2 ) is not limited to a particular value, but the angle difference (θ 1 −θ 2 ) is preferably smaller than or equal to 20°. The angle difference (θ 1 −θ 2 ) smaller than or equal to 20° can prevent an excessive increase of a gap between the opposing surface S of the flange  22  and the stepped portion  17 , and thus can reduce an amount of the high-temperature gas intruding into the gap from the combustion chamber  95 . This structure can prevent an excessive increase of the quantity of heat provided to the center electrode  20  and the insulator  10 , and thus can prevent an excessive increase of thermal expansion of the center electrode  20  and the insulator  10 . This structure can thus prevent deformation of the flange  22  attributable to thermal expansion caused by a temperature rise of the center electrode  20  and the insulator  10  with a high-temperature gas, and thus can prevent reduction of adhesion between the flange  22  and the stepped portion  17 . 
     The angle difference (θ 1 −θ 2 ) smaller than or equal to 20° can also prevent a portion of the flange  22  of the center electrode  20  that is in point contact with the stepped portion  17  of the insulator  10  from having a shape with a nearly acute angle. This structure can thus further prevent reduction of adhesion between the flange  22  and the stepped portion  17 . This structure can thus further prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 . More specifically, for example, this structure can prevent the powder material of the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  due to vibrations or other causes caused during, for example, a transportation step between the sealant filling step and the heat compression step. 
     As illustrated in  FIG.  3   , the spark plug  100  according to the present embodiment satisfies Formula (2) where, in a cross section including the axial line CA, the maximum diameter of the flange  22  is denoted with D 1 , and the diameter of the through-hole  11  in the small-diameter portion  16  at the rear end is denoted with D 2 :
 
0.15 mm≤( D 1 −D 2)/2  Formula (2).
 
     In Formula (2), when a half of a difference (D 1 −D 2 ) between the maximum diameter D 1  of the flange  22  and the diameter D 2  of the through-hole  11  in the small-diameter portion  16  at the rear end is denoted with a dimension X, as illustrated in  FIG.  3   , the dimension X corresponds to the difference between the radius of the flange  22  at a portion radially protruding to the outermost, and the radius of the through-hole  11  in the small-diameter portion  16  at the rear end. Here, a dimension Y in the axial-line direction AD between the flange  22  and the front end of the stepped portion  17  increases radially inward. Thus, in the spark plug  100  according to the present embodiment, the dimension X greater than or equal to 0.15 mm allows the dimension Y in the axial-line direction AD between the flange  22  and the front end of the stepped portion  17  to be relatively large. To allow the dimension Y to be relatively large, the dimension X is preferably greater than or equal to 0.17 mm, or more preferably, greater than or equal to 0.3 mm. In view of preventing an increase of a radial dimension of the spark plug  100 , the dimension X is preferably smaller than or equal to 0.6 mm, and more preferably smaller than or equal to 0.4 mm. 
       FIG.  5    is a diagram illustrating thermal expansion of the center electrode  20 .  FIG.  5    is a cross-sectional view corresponding to  FIG.  4   . 
     Generally, a coefficient of thermal expansion of the center electrode  20  of the spark plug  100  is greater than the coefficient of thermal expansion of the insulator  10 . Also in the spark plug  100  according to the present embodiment, as described above, the center electrode  20  is made of a copper alloy and a nickel alloy, and the insulator  10  is made of ceramics. The coefficient of thermal expansion of the center electrode  20  is thus greater than the coefficient of thermal expansion of the insulator  10 . Thus, when the spark plug  100  is used under high-temperature environments, the center electrode  20  is more likely to thermally expand further than the insulator  10  toward the front end side in the axial-line direction AD as indicated with a solid-white arrow in  FIG.  5   . 
     The spark plug  100  according to the present embodiment satisfies Formula (1) and Formula (2), and thus forms a relatively large gap G 2  between the stepped portion  17  and the opposing surface S of the flange  22 . This structure can thus prevent an application of stress to the stepped portion  17  of the insulator  10  from the flange  22  of the center electrode  20  attributable to thermal expansion of the center electrode  20  during use of the spark plug  100 . This structure can thus prevent the insulator  10  from cracking during use of the spark plug  100 . 
     As illustrated in  FIG.  1   , the spark plug  100  is generally attached to the engine head  90 , and used while having the front end portion exposed to the inside of the combustion chamber  95 . In the combustion chamber  95 , soot or other matter attributable to carbon in a combustion gas is present. Such soot or other matter may intrude into the through-hole  11  in the insulator  10  from the front end side, arrive at the gap G 2  between the stepped portion  17  and the opposing surface S of the flange  22  through the space between the through-hole  11  and the leg  21  of the center electrode  20 , and accumulate as a foreign object B, as illustrated in  FIG.  5   . 
     Unlike in the spark plug  100  according to the present embodiment, in a structure having a small gap between the stepped portion and the opposing surface of the flange that fails to satisfy at least one of Formula (1) and Formula (2), the gap is filled up with the foreign object B, and a stress is applied from the flange of the center electrode to the stepped portion of the insulator via the foreign object B attributable to thermal expansion of the center electrode during use of the spark plug. Thus, the insulator is cracked during the use of the spark plug. 
     On the other hand, the spark plug  100  according to the present embodiment satisfying Formula (1) and Formula (2) has a relatively large gap G 2  between the stepped portion  17  and the opposing surface S of the flange  22 . Thus, the gap G 2  is prevented from being filled up with the foreign object B regardless of when the foreign object B accumulates in the gap G 2 . This structure can thus prevent a stress from being applied from the flange  22  of the center electrode  20  to the stepped portion  17  of the insulator  10  attributable to thermal expansion of the center electrode  20  during use of the spark plug  100 , and thus can prevent the insulator  10  from cracking during use of the spark plug  100 . 
     The spark plug  100  according to the present embodiment satisfies Formula (1), and thus allows the flange  22  of the center electrode  20  and the stepped portion  17  of the insulator  10  to be in point contact with each other. This structure can thus improve adhesion between the flange  22  and the stepped portion  17 , and can prevent the powder material of the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  in the sealant filling step during manufacture of the spark plug  100 . This structure can also prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  in the heat compression step during manufacture of the spark plug  100 . Thus, the spark plug  100  according to the present embodiment satisfying Formula (1) can prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 . This structure can prevent the flange  22  of the center electrode  20  and the stepped portion  17  of the insulator  10  from coming into contact with each other via the far-end sealant  61  interposed in between attributable to thermal expansion of the center electrode  20  during use of the spark plug  100 . This structure can thus prevent stress from being applied from the flange  22  of the center electrode  20  to the stepped portion  17  of the insulator  10  via the far-end sealant  61  interposed therebetween due to further progress in thermal expansion of the center electrode  20 . Thus, the insulator  10  can be prevented from being cracked during use of the spark plug  100 . 
     The spark plug  100  according to the present embodiment satisfies Formula (1) and Formula (2), and thus has a relatively large gap G 2  between the stepped portion  17  and the opposing surface S of the flange  22 . This structure can thus prevent a stress from being applied from the flange  22  of the center electrode  20  to the stepped portion  17  of the insulator  10  attributable to thermal expansion of the center electrode  20  during use of the spark plug  100 . This structure including the relatively large gap G 2  can prevent the gap G 2  from being filled up with the foreign object B regardless of when the foreign object B intrudes into the gap G 2  from the combustion chamber  95  and accumulates in the gap G 2 . This structure can thus prevent a stress from being applied from the flange  22  of the center electrode  20  to the stepped portion  17  of the insulator  10  via the foreign object B attributable to thermal expansion of the center electrode  20  during use of the spark plug  100 . Thus, the insulator  10  can be prevented from being cracked during use of the spark plug  100 . 
     The spark plug  100  according to the present embodiment satisfies Formula (1) and Formula (2). This structure can prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 , and prevent the insulator  10  from cracking during use of the spark plug  100 . 
     In addition, the angle θ 1  is greater than or equal to 25° and smaller than or equal to 35°. This structure can further improve adhesion between the flange  22  and the stepped portion  17 , and thus can further prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 . 
     The angle difference (θ 1 −θ 2 ) is smaller than or equal to 20°. This structure can prevent an excessive increase of a gap G 2  between the opposing surface S of the flange  22  and the stepped portion  17 , and thus can reduce an amount of the high-temperature gas intruding into the gap G 2  from the combustion chamber  95 . This structure can thus prevent deformation of the flange  22  attributable to thermal expansion caused by a temperature rise of the center electrode  20  and the insulator  10  with the high-temperature gas, and thus can prevent reduction of adhesion between the flange  22  and the stepped portion  17 . 
     The angle difference (θ 1 −θ 2 ) smaller than or equal to 20° can prevent a portion of the flange  22  of the center electrode  20  that is in point contact with the stepped portion  17  of the insulator  10  from having a shape with a nearly acute angle. This structure can thus further prevent reduction of adhesion between the flange  22  and the stepped portion  17 . This structure can thus prevent the powder material of the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  in, for example, a transportation step during manufacture of the spark plug  100 . This structure can thus further prevent the far-end sealant  61  from intruding between the flange  22  and the stepped portion  17  during manufacture of the spark plug  100 . This structure can prevent a portion of the flange  22  of the center electrode  20  that is in point contact with the stepped portion  17  of the insulator  10  from having a shape with a nearly acute angle. This structure can thus prevent abrasion of the stepped portion  17  at a portion where the flange  22  and the stepped portion  17  are in point contact with each other when the center electrode  20  thermally expands. 
     B. Example 
     The present invention will be further specifically described below using examples, but not limited to the following examples. 
     The spark plugs  100  with different angle differences (θ 1 −θ 2 ) between the angles ° 1  and θ 2  were evaluated for the occurrence of intrusion of the far-end sealant  61  and cracking of the insulator  10 . 
     &lt;Samples&gt; 
     The spark plugs  100  satisfying Formula (1) and Formula (2) were fabricated as Examples 1 to 5. Table 1 below shows the angle differences (θ 1 −θ 2 ) in the spark plugs  100  of Examples 1 to 5. Spark plugs that satisfy Formula (2) without satisfying Formula (1) were fabricated as Comparative Examples 1 and 2. Table 1 below shows the angle differences (θ 1 −θ 2 ) in the spark plugs of the Comparative Examples 1 and 2. Throughout the spark plugs of Examples 1 to 5 and the Comparative Examples 1 and 2, a half of the value (D 1 −D 2 ) was 0.17 mm. 
       FIG.  6    is a schematic diagram illustrating part of a spark plug according to Comparative Example 1.  FIG.  6    is a cross-sectional view corresponding to  FIG.  4   . In the spark plug according to Comparative Example 1, an angle θ 1  formed by a stepped portion  117  and the plane P perpendicular to the axial line CA is equal to an angle θ 2  formed by the plane P and the opposing surface S of a flange  122  opposing the stepped portion  117 . Specifically, the spark plug according to Comparative Example 1 with the angle difference (θ 1 −θ 2 ) of 0° fails to satisfy Formula (1). In the spark plug according to Comparative Example 1, the flange  122  of a center electrode  120  and the stepped portion  117  of an insulator  110  are in surface contact with each other. Thus, the spark plug according to Comparative Example 1 has a small gap G 2  between the stepped portion  117  and the opposing surface S of the flange  122 . 
     The spark plugs  100  satisfying Formula (1) and Formula (2) were fabricated as Examples 6 and 7. Table 2 shows halves of the value (D 1 −D 2 ) in the spark plugs  100  of Examples 6 and 7. Spark plugs that satisfy Formula (1) without satisfying Formula (2) were fabricated as Comparative Examples 3 and 4. Table 2 shows halves of the value (D 1 −D 2 ) in the spark plugs of Comparative Examples 3 and 4. Throughout the spark plugs of Examples 6 and 7 and Comparative Examples 1 and 2, the angle difference (θ 1 −θ 2 ) was 6°. 
     &lt;Evaluation of Cracking of Insulator&gt; 
     The samples of Examples 1 to 7 and Comparative Examples 1 and 2 were immersed in exhaust condensate and heated to be exposed to the high-temperature exhaust condensate. The exhaust condensate refers to moisture contained in the exhaust gas cooled at a muffler to condensate and drip. With the above processing, the foreign object B was caused to accumulate in the gap G 2  between the stepped portion  17  or  117  and the opposing surface S of the flange  22  or  122 . Thereafter, each sample was assembled to the metal fitting, and placed in a high-temperature furnace of approximately 400° C. simulating the inside of an engine. Thereafter, occurrence of cracking of the insulator  10  was evaluated using a scanning electron microscope. The evaluation standards are as follows, and the number of pieces for each sample was between 5 to 10: 
     A: Not Cracked 
     C: Cracked. 
     &lt;Evaluation of Intrusion of Sealant&gt; 
     The samples of Examples 1 to 5 and Comparative Examples 1 and 2 were evaluated for occurrence of intrusion of the far-end sealant  61  into the gap G 2  using a scanning electron microscope. The evaluation standards are as follows, and the number of pieces for each sample was between 5 to 10: 
     A: Not Intruded 
     B: Partially Intruded 
     C: Entirely Intruded 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 Intrusion 
                 Cracking of 
               
               
                   
                 θ1-θ2 (°) 
                 of Sealant 
                 Insulator 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Comparative 
                 0 
                 C 
                 C 
               
               
                   
                 Example 1 
               
               
                   
                 Comparative 
                 2 
                 A 
                 C 
               
               
                   
                 Example 2 
               
               
                   
                 Example 1 
                 6 
                 A 
                 A 
               
               
                   
                 Example 2 
                 10 
                 A 
                 A 
               
               
                   
                 Example 3 
                 20 
                 A 
                 A 
               
               
                   
                 Example 4 
                 22 
                 B 
                 A 
               
               
                   
                 Example 5 
                 25 
                 B 
                 A 
               
               
                   
                   
               
            
           
         
       
     
     The results in Table 1 reveal the followings. In Examples 1 to 5, no cracking was observed in the insulator  10 . In Comparative Examples 1 and 2, on the other hand, cracking was observed in the insulator  110 . 
       FIG.  7    is a schematic diagram illustrating thermal expansion of the center electrode  120  of the spark plug according to Comparative Example 1.  FIG.  7    is a cross-sectional view corresponding to  FIG.  6   . 
     In the spark plug according to Comparative Example 1, the foreign object B is filled in the gap G 2 . Thus, it is assumed that, in the spark plug according to Comparative Example 1, under high-temperature environments, the center electrode  120  thermally expands as indicated with a solid-white arrow in  FIG.  7   , and a stress is applied from the flange  122  of the center electrode  120  to the stepped portion  117  of the insulator  110 . As a result, the insulator  110  is assumed to have cracked. 
     The results of Table 1 reveal the followings. Specifically, in Examples 1 to 3 and Comparative Example 2 where the angle difference (θ 1 −θ 2 ) falls within the range of 2° to 20°, no intrusion of the far-end sealant  61  was observed. In Examples 4 and 5 where the angle difference (θ 1 −θ 2 ) falls within the range of 22° to 25°, intrusion of the far-end sealant  61  was observed, but by only a small amount. On the other hand, in Comparative Example 1 where the angle difference (θ 1 −θ 2 ) was 0°, intrusion of the far-end sealant  61  was observed by a large amount. 
     In Comparative Example 1, the flange  122  and the stepped portion  117  were in surface contact with each other. Thus, adhesion between the flange  122  and the stepped portion  117  in Comparative Example 1 is assumed to be smaller than that in Examples 1 to 5. The powder material of the far-end sealant  61  is thus assumed to have intruded between the flange  122  and the stepped portion  117  in the sealant filling step during manufacture of a spark plug. The far-end sealant  61  is also assumed to intrude between the flange  122  and the stepped portion  117  in the heat compression step during manufacture of the spark plug. 
     In Examples 4 and 5, the flange  22  and the stepped portion  17  are in point contact with each other. Thus, it is assumed that the flange  22  and the stepped portion  17  adhere to each other with high adhesion, and the far-end sealant  61  is prevented from intruding in the step of manufacturing the spark plug  100 . On the other hand, Examples 4 and 5 have a relatively high angle difference (θ 1 −θ 2 ), and thus have a portion of the flange  22  that is in point contact with the stepped portion  17  in a shape with a nearly acute angle. Thus, the powder material of the far-end sealant  61  is assumed to have intruded between the flange  22  and the stepped portion  17  attributable to, for example, vibrations caused in a transportation step between the filling step of the far-end sealant  61  to the heat compression step. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 (D1-D2)/2 
                 Cracking of 
               
               
                   
                 (mm) 
                 Insulator 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Comparative 
                 0.11 
                 C 
               
               
                   
                 Example 3 
               
               
                   
                 Comparative 
                 0.13 
                 C 
               
               
                   
                 Example 4 
               
               
                   
                 Example 6 
                 0.15 
                 A 
               
               
                   
                 Example 7 
                 0.17 
                 A 
               
               
                   
                   
               
            
           
         
       
     
     The results in Table 2 reveal the followings. In Examples 6 and 7 where a half of the value (D 1 −D 2 ) is greater than or equal to 0.15 mm, no cracking of the insulator  10  was observed. On the other hand, in Comparative Examples 3 and 4 where a half of the value (D 1 -D 2 ) is smaller than or equal to 0.13 mm, cracking of the insulator  110  was observed. These results are assumed to be caused due to an insufficient size of the gap G 2  between the stepped portion  117  and the opposing surface S of the flange  122  since a half of the value (D 1 −D 2 ) is smaller than or equal to 0.13 mm in Comparative Examples 3 and 4. Thus, it is assumed that, in Comparative Examples 3 and 4, the foreign object B is filled up in the gap G 2 , and the center electrode  120  thermally expands under high-temperature environments, and a stress is applied from the flange  122  of the center electrode  120  to the stepped portion  117  of the insulator  110 . This is assumed to be a cause of cracking of the insulator  110 . 
     C. Other Embodiments 
     The present invention is not limited to the above embodiments, and may be embodied in various forms within the range not departing from the gist thereof. For example, the technical features in the embodiments corresponding to the technical features in each form described in Summary of Invention may be changed or combined as appropriate to solve part or entirety of the above problem or to achieve part or entirety of the above effects. The technical features may be deleted as appropriate unless otherwise described as being essential herein. 
     REFERENCE SIGNS LIST 
     
         
         
           
               10  insulator 
               11  through-hole 
               14  large-diameter portion 
               15  locking portion 
               16  small-diameter portion 
               17  stepped portion 
               20  center electrode 
             leg 
               22  flange 
               23  head 
               25  core material 
               26  electrode member 
               30  metal shell 
               31  tool engagement portion 
               32  external-thread portion 
             seating portion 
               34  protrusion 
               35  crimping portion 
               36  compressed-deformed portion 
               37  front end surface 
               38  axial hole 
               40  ground electrode 
               42  electrode tip 
               50  metal terminal 
               61  far-end sealant (sealant) 
               62  resistor element 
               63  rear-end sealant 
               65  gasket 
               66 ,  67  ring member 
               69  talc 
               90  engine head 
               93  internal thread 
               95  combustion chamber 
               100  spark plug 
               110  insulator 
               117  stepped portion 
               120  center electrode 
               122  flange 
             AD axial-line direction 
             B foreign object 
             CA axial line 
             G 1  gap 
             G 2  gap 
             P plane 
             S opposing surface 
             X dimension 
             Y dimension