Cylindrical member, elastic roller for electrophotography, process cartridge, and electrophotographic apparatus

An elastic roller for electrophotography comprising:

• a core metal;
• and
• an elastic layer configured to cover a peripheral surface of the core metal,
• wherein the core metal is a cylindrical member made of metal,
• wherein let A denote a centroid of area of one end surface of the cylindrical member,
• let B denote a centroid of area of another end surface,
• let Z-axis denote a line passing through the centroid A of area and the centroid B of area,
• let Y-axis denote a line perpendicular to the Z-axis,
• let X-axis denote a line perpendicular to the Z-axis and the Y-axis,
• let AB denote a line segment connecting the centroid A of area to the centroid B of area,
• let E1 to E9 denote nine points that divide the line segment AB into 10 equal parts from a side adjacent to the centroid A of area,
• let Q1 to Q9 denote nine planes each including any one of the points E1 to E9 and parallel to the Y-axis,
• let S1 to S9 denote nine virtual cross sections obtained by virtually cutting the cylindrical member by the planes Q1 to Q9, respectively, and
• let C1 to C9 denote centroids of areas of the virtual cross sections S1 to S9, respectively,
• then when positions of the centroids C1 to C9 of areas relative to the centroid A of area are plotted on an XY coordinate plane having an origin at the centroid A of area,
• all of the centroids C1 to C9 of areas lie on or within a circle centered at the centroid A of area with a radius of 10 μm in the XY coordinate plane having an origin at the centroid A of area,
• wherein after the cylindrical member is heated until a temperature of the entire cylindrical member reaches a recrystallization temperature of the metal to obtain the heated cylindrical member,
• let K denote a centroid of area of one end surface of the heated cylindrical member on the same side as the centroid A of area,
• let L denote a centroid of area of the other end surface on the same side as the centroid B of area,
• let Z-axis denote a line passing through the centroid K of area and the centroid L of area, let Y-axis denote a line perpendicular to the Z-axis,
• let X-axis denote a line perpendicular to the Z-axis and the Y-axis,
• let KL denote a line segment connecting the centroid K of area to the centroid L of area,
• let F1 to F9 denote nine points that divide the line segment KL into 10 equal parts from a side adjacent to the centroid K of area,
• let R1 to R9 denote nine planes each including any one of the points F1 to F9 and parallel to the Y-axis,
• let T1 to T9 denote nine virtual cross sections obtained by virtually cutting the heated cylindrical member by the planes R1 to R9, respectively, and
• let D1 to D9 denote centroids of areas of the virtual cross sections T1 to T9, respectively,
• then when positions of the centroids D1 to D9 of areas relative to the centroid K of area are plotted on the XY coordinate plane having the origin at the centroid K of area,
• at least one of the centroids D1 to D9 of areas lies outside of a circle centered at the centroid K of area with a radius of 10 μm in the XY coordinate plane having an origin at the centroid K of area, and
• wherein let Dmax denote the farthest one out of the centroids D1 to D9 of areas from the centroid K of area,
• let KDmax denote a half line passing through the centroid K of area and the centroid Dmax of area and having an end point at the centroid K of area, and
• let a reference half line be a half line that lies in a first quadrant of the XY coordinate plane having the origin at the centroid K of area and passes through the centroid K of area and that has an end point at the centroid K of area and has a slope of 1,
• then when the half line KDmax is made to coincide with the reference half line, all of the centroids D1 to D9 of areas in the XY coordinate plane having an origin at the centroid K of area lie in the first quadrant of the XY coordinate plane having an origin at the centroid K of area.

A process cartridge comprising:

• a photosensitive drum;
• and
• a charge roller disposed in contact with the photosensitive drum,
• wherein the charge roller is an elastic roller including a core metal and an elastic layer covering a peripheral surface of the core metal,
• wherein the core metal is a cylindrical member made of metal,
• wherein let A denote a centroid of area of one end surface of the cylindrical member,
• let B denote a centroid of area of another end surface,
• let Z-axis denote a line passing through the centroid A of area and the centroid B of area,
• let Y-axis denote a line perpendicular to the Z-axis,
• let X-axis denote a line perpendicular to the Z-axis and the Y-axis,
• let AB denote a line segment connecting the centroid A of area to the centroid B of area,
• let E1 to E9 denote nine points that divide the line segment AB into 10 equal parts from a side adjacent to the centroid A of area,
• let Q1 to Q9 denote nine planes each including any one of the points E1 to E9 and parallel to the Y-axis,
• let S1 to S9 denote nine virtual cross sections obtained by virtually cutting the cylindrical member by the planes Q1 to Q9, respectively, and
• let C1 to C9 denote centroids of areas of the virtual cross sections S1 to S9, respectively,
• then when positions of the centroids C1 to C9 of areas relative to the centroid A of area are plotted on an XY coordinate plane having an origin at the centroid A of area,
• all of the centroids C to C9 of areas lie on or within a circle centered at the centroid A of area with a radius of 10 μm in the XY coordinate plane having an origin at the centroid A of area,
• wherein after the cylindrical member is heated until a temperature of the entire cylindrical member reaches a recrystallization temperature of the metal to obtain the heated cylindrical member,
• let K denote a centroid of area of one end surface of the heated cylindrical member on the same side as the centroid A of area,
• let L denote a centroid of area of the other end surface on the same side as the centroid B of area,
• let Z-axis denote a line passing through the centroid K of area and the centroid L of area,
• let Y-axis denote a line perpendicular to the Z-axis,
• let X-axis denote a line perpendicular to the Z-axis and the Y-axis,
• let KL denote a line segment connecting the centroid K of area to the centroid L of area,
• let F1 to F9 denote nine points that divide the line segment KL into 10 equal parts from a side adjacent to the centroid K of area,
• let R1 to R9 denote nine planes each including any one of the points F1 to F9 and parallel to the Y-axis,
• let T1 to T9 denote nine virtual cross sections obtained by virtually cutting the heated cylindrical member by the planes R1 to R9, respectively, and
• let D1 to D9 denote centroids of areas of the virtual cross sections T1 to T9, respectively, then when positions of the centroids D1 to D9 of areas relative to the centroid K of area are plotted on the XY coordinate plane having the origin at the centroid K of area, at least one of the centroids D1 to D9 of areas lies outside of a circle centered at the centroid K of area with a radius of 10 μm in the XY coordinate plane having an origin at the centroid K of area, and
• wherein let Dmax denote the farthest one out of the centroids D1 to D9 of areas from the centroid K of area,
• let KDmax denote a half line passing through the centroid K of area and the centroid Dmax of area and having an end point at the centroid K of area, and
• let a reference half line be a half line that lies in a first quadrant of the XY coordinate plane having the origin at the centroid K of area and passes through the centroid K of area and that has an end point at the centroid K of area and has a slope of 1,
• then when the half line KDmax is made to coincide with the reference half line, all of the centroids D1 to D9 of areas in the XY coordinate plane having an origin at the centroid K of area lie in the first quadrant of the XY coordinate plane having an origin at the centroid K of area.

An electrophotographic apparatus comprising:

• a photosensitive drum;
• and
• a charge roller disposed in contact with the photosensitive drum,
• wherein the charge roller is an elastic roller including a core metal and an elastic layer covering a peripheral surface of the core metal,
• wherein the core metal is a cylindrical member made of metal,
• wherein let A denote a centroid of area of one end surface of the cylindrical member,
• let B denote a centroid of area of another end surface,
• let Z-axis denote a line passing through the centroid A of area and the centroid B of area,
• let Y-axis denote a line perpendicular to the Z-axis,
• let X-axis denote a line perpendicular to the Z-axis and the Y-axis,
• let AB denote a line segment connecting the centroid A of area to the centroid B of area,
• let E1 to E9 denote nine points that divide the line segment AB into 10 equal parts from a side adjacent to the centroid A of area,
• let Q1 to Q9 denote nine planes each including any one of the points E1 to E9 and parallel to the Y-axis,
• let S1 to S9 denote nine virtual cross sections obtained by virtually cutting the cylindrical member by the planes Q1 to Q9, respectively, and
• let C1 to C9 denote centroids of areas of the virtual cross sections S1 to S9, respectively,
• then when positions of the centroids C1 to C9 of areas relative to the centroid A of area are plotted on an XY coordinate plane having an origin at the centroid A of area,
• all of the centroids C1 to C9 of areas lie on or within a circle centered at the centroid A of area with a radius of 10 μm in the XY coordinate plane having an origin at the centroid A of area,
• wherein after the cylindrical member is heated until a temperature of the entire cylindrical member reaches a recrystallization temperature of the metal to obtain the heated cylindrical member,
• let K denote a centroid of area of one end surface of the heated cylindrical member on the same side as the centroid A of area,
• let L denote a centroid of area of the other end surface on the same side as the centroid B of area,
• let Z-axis denote a line passing through the centroid K of area and the centroid L of area,
• let Y-axis denote a line perpendicular to the Z-axis,
• let X-axis denote a line perpendicular to the Z-axis and the Y-axis,
• let KL denote a line segment connecting the centroid K of area to the centroid L of area,
• let F1 to F9 denote nine points that divide the line segment KL into 10 equal parts from a side adjacent to the centroid K of area,
• let R1 to R9 denote nine planes each including any one of the points F1 to F9 and parallel to the Y-axis,
• let T1 to T9 denote nine virtual cross sections obtained by virtually cutting the heated cylindrical member by the planes R1 to R9, respectively, and
• let D1 to D9 denote centroids of areas of the virtual cross sections T1 to T9, respectively,
• then when positions of the centroids D1 to D9 of areas relative to the centroid K of area are plotted on the XY coordinate plane having the origin at the centroid K of area,
• at least one of the centroids D1 to D9 of areas lies outside of a circle centered at the centroid K of area with a radius of 10 μm in the XY coordinate plane having an origin at the centroid K of area, and
• wherein let Dmax denote the farthest one out of the centroids D1 to D9 of areas from the centroid K of area,
• let KDmax denote a half line passing through the centroid K of area and the centroid Dmax of area and having an end point at the centroid K of area, and
• let a reference half line be a half line that lies in a first quadrant of the XY coordinate plane having the origin at the centroid K of area and passes through the centroid K of area and that has an end point at the centroid K of area and has a slope of 1,
• then when the half line KDmax is made to coincide with the reference half line,
• all of the centroids D1 to D9 of areas in the XY coordinate plane having an origin at the centroid K of area lie in the first quadrant of the XY coordinate plane having an origin at the centroid K of area.