Machine having reciprocating slider crank mechanism, and method for designing machine having reciprocating slider crank mechanism

A machine having a reciprocating slider crank mechanism, the machine comprising:

• a cylinder;
• a reciprocal movement portion including
• a piston configured to reciprocate in a cylinder,
• a piston pin, and
• a small end portion of a conrod, the small end portion being connected to the piston by the piston pin;
• a rotary movement portion including
• a rotatable crankshaft having a crank pin portion, and
• a big end portion of the conrod, the big end portion being connected to the crank pin portion of the crankshaft;
• a first balancer shaft configured to rotate, together with the rotation of the crankshaft, in an opposite rotation direction to that of the crankshaft at a same rotation speed as that of the crankshaft;
• and
• a second balancer shaft arranged on an opposite side from the first balancer shaft with respect to a center line of the cylinder as seen from the axial direction of the crankshaft, the second balancer shaft configured to rotate, together with the rotation of the crankshaft, in an opposite rotation direction to that of the crankshaft at the same rotation speed as that of the crankshaft, wherein:
• an axis of the crankshaft, an axis of the first balancer shaft and an axis of the second balancer shaft are not arranged on a same plane;
• as seen from the axial direction of the crankshaft, a center line of the cylinder is offset from the axis of the crankshaft;
• and
• the reciprocating slider crank mechanism is configured so as to satisfy a setting formulae below:
• UCr=UP×0.5×{1+(δ/l)2}1/2,
• αCr=180°−arctan(δ/l),
• UB(Fr)={(U1B(Fr)+U3B(Fr))2+(U2B(Fr)+U4B(Fr))2}1/2,
• U1B(Fr)=−UP×0.5×{Lx′B(Rr)/(Lx′B(Rr)−Lx′B(Fr))}×{1+(δ/l)2}1/2,
• U2B(Fr)=−UP×0.5×{Ly′B/(Lx′B(Rr)−Lx′B(Fr))}×{1+(δ/l)2}1/2,
• U3B(Fr)=−UP×{δ/(Lx′B(Rr)−Lx′B(Fr)}×sin β×{1+(δ/l)2}1/2,
• U3B(Fr)=−UP×{δ/(Lx′B(Rr)−Lx′B(Fr)}×cos β×{1+(δ/l)2}1/2,
• αB(Fr)=180°−arctan {(U2B(Fr)+U4B(Fr)/(U1B(Fr)+U3B(Fr)}+arctan(δ/l),
• UB(Rr)={(U1B(Rr)+U3B(Rr))2+(U2B(Rr)+U4B(Rr))2}1/2,
• U1B(Rr)=UP×0.5×{Lx′B(Fr)/(Lx′B(Fr)−Lx′B(Rr)}×{1+(δ/l)2}1/2,
• U2B(Rr)=−U2B(Fr),
• U3B(Rr)=−U3B(Fr),
• U4B(Rr)=−U4B(Fr), and
• αB(Rr)=180°−arctan {(U2B(Rr)+U4B(Rr)/(U1B(Rr)+U3B(Rr))}+arctan(δ/l),
• where
• as seen from the axial direction of the crankshaft, the axis of the crankshaft is an origin, an axis extending from the origin toward the piston in parallel to the center line of the cylinder is a Y axis and an axis perpendicular to the Y axis is an X axis,
• as seen from the axial direction of the crankshaft, the rotation direction of the crankshaft is a forward rotation direction and an opposite direction to the rotation direction of the crankshaft is a reverse rotation direction,
• LxB(Fr):
• a X coordinate value of the axis of the first balancer shaft as measured on the X axis
• LyB(Fr):
• a Y coordinate value of the axis of the first balancer shaft as measured on the Y axis
• LxB(Rr):
• a X coordinate value of the axis of the second balancer shaft as measured on the X axis,
• LyB(Rr):
• a Y coordinate value of the axis of the second balancer shaft as measured on the Y axis
• l:
• a distance between a center of the piston pin and a center of the crank pin portion,
• δ:
• an amount of offset of the cylinder,
• β:
• as seen from the axial direction of the crankshaft, a first angle, in the forward rotation direction, being measured between a straight line, connecting between the axis of the first balancer shaft and the axis of the second balancer shaft, and the Y axis, the first angle being 90°+arctan {(LyB(Rr)−LyB(Fr))/(LxB(Rr)−LxB(Fr))},
• γB(Fr):
• as seen from the axial direction of the crankshaft, a second angle, in the forward rotation direction, between a straight line, connecting between the axis of the first balancer shaft and the axis of the crankshaft, and the Y axis, the second angle being 90°+arctan(LyB(Fr)/LxB(Fr)),
• γB(Rr):
• as seen from the axial direction of the crankshaft, a third angle, in the forward rotation direction, between a straight line, connecting between the axis of the second balancer shaft and the axis of the crankshaft, and the Y axis, the third angle being 90°+arctan(LyB(Rr)/LxB(Rr)),
• X′ axis:
• an axis inclined from the X axis by β-90° in the forward rotation direction,
• Y′ axis:
• an axis inclined from the Y axis by β-90° in the forward rotation direction,
• Lx′B(Fr):
• a X′ coordinate value of the axis of the first balancer shaft as measured on the X′ axis=(LxB(Fr)−LyB(Fr)/(tan β)×sin β,
• Ly′B:
• a Y′ coordinate value of the axis of the first balancer shaft and the second balancer shaft as measured along the Y′ axis=(LxB(Fr)+LyB(Fr)×tan β)×cos β,
• Lx′B(Rr):
• a X′ coordinate value of the axis of the second balancer shaft as measured on the X′ axis=(LxB(Rr)−LyB(Rr)/tan β)×sin β,
• θCr:
• an angle of rotation of the crankshaft in the forward rotation direction (where θCr is assumed to be 0° when the crank pin portion of the crankshaft is on the Y axis),
• UP:
• an unbalance amount of the reciprocal movement portion=mP×R (where mP is the mass of the reciprocal movement portion, and R is a crank radius),
• UCr:
• an unbalance amount of the rotary movement portion=mCr×rCr (where mCr is the mass of the rotary movement portion, and rCr is a distance between the axis of the crankshaft and the center of gravity of the rotary movement portion),
• αCr:
• an angle in an unbalance direction, which is in the forward rotation direction from the Y axis, of the rotary movement portion when θCr=arctan(δ/1°),
• UB(Fr):
• an unbalance amount of the first balancer shaft=mB(Fr)×rB(Fr) (where MB(Fr) is the mass of the first balancer shaft, and rB(Fr) is a distance between the axis of the first balancer shaft and the center of gravity of the first balancer shaft),
• U1B(Fr):
• a Y-axis direction component 1 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• U2B(Fr):
• a X-axis direction component 1 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• U3B(Fr):
• a Y-axis direction component 2 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• U4B(Fr):
• a X-axis direction component 2 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• αB(Fr):
• an angle in an unbalance direction, which is in the forward rotation direction from the Y axis, of the first balancer shaft when θCr=arctan(δ/l)°,
• UB(Rr) an unbalance amount of the second balancer shaft=mB(Rr)×rB(Rr) (where mB(Rr) is the mass of the second balancer shaft, and rB(Rr) is a distance between the axis of the second balancer shaft and the center of gravity of the second balancer shaft),
• U1B(Rr):
• a Y-axis direction component 1 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°,
• U2B(Rr) a X-axis direction component 1 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°,
• U3B(Rr):
• a Y-axis direction component 2 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°,
• U4B(Rr):
• a X-axis direction component 2 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°, and
• αB(Rr):
• an angle in an unbalance direction, that is in the forward rotation direction from the Y axis, of the second balancer shaft when θCr=arctan(δ/1°).

A method for manufacturing a machine having a reciprocating slider crank mechanism, the method comprising:

• providing a reciprocal movement portion including
• a piston configured to reciprocate in a cylinder,
• a piston pin, and
• a small end portion of a conrod, the small end portion being connected to the piston by the piston pin;
• providing a rotary movement portion including
• a rotatable crankshaft having a crank pin portion, and
• a big end portion of the conrod, the big end portion being connected to the crank pin portion of the crankshaft;
• providing a first balancer shaft configured to rotate, together with the rotation of the crankshaft, in an opposite rotation direction to that of the crankshaft at a same rotation speed as that of the crankshaft;
• and
• providing a second balancer shaft arranged on an opposite side from the first balancer shaft with respect to a center line of the cylinder as seen from the axial direction of the crankshaft, the second balancer shaft configured to rotate, together with the rotation of the crankshaft, in an opposite rotation direction to that of the crankshaft at the same rotation speed as that of the crankshaft, wherein:
• an axis of the crankshaft, an axis of the first balancer shaft and an axis of the second balancer shaft are not arranged on a same plane;
• and
• UCr, αCr, UB(Fr), UB(Rr), αB(Fr) and αB(Rr) are set so as to satisfy a setting formulae below:
• UCr=UP×0.5,
• αCr=180°,
• UB(Fr)={U1B(Fr)2+UB(Fr)2}1/2,
• U1B(Fr)=−UP×0.5×{Lx′B(Rr)/Lx′B(Rr)−Lx′B(Fr))},
• U2B(Fr)=−UP×0.5×{Ly′B/(Lx′B(Rr)−Lx′B(Fr))},
• αB(Fr)=180°−arctan(U2B(Fr)/U1B(Fr)),
• UB(Rr){U1B(Rr)2+UB(Rr)2}1/2,
• U1B(Rr)=−UP×0.5×{Lx′B(Fr)/(Lx′B(Fr)−Lx′B(Rr))},
• U2B(Rr)=−U2B(Fr), and
• αB(Rr)−180°−arctan(U2B(Rr)/U1B(Rr)),
• where
• as seen from the axial direction of the crankshaft, the axis of the crankshaft is an origin, an axis extending from the origin toward the piston along the center line of the cylinder is a Y axis and an axis perpendicular to the Y axis is an X axis,
• as seen from the axial direction of the crankshaft, the rotation direction of the crankshaft is a forward rotation direction and an opposite direction to the rotation direction of the crankshaft is a reverse rotation direction,
• LxB(Fr):
• a X coordinate value of the axis of the first balancer shaft as measured on the X axis
• LyB(Fr):
• a Y coordinate value of the axis of the first balancer shaft as measured on the Y axis
• LxB(Rr):
• a X coordinate value of the axis of the second balancer shaft as measured on the X axis
• LyB(Rr):
• a Y coordinate value of the axis of the second balancer shaft as measured on the Y axis
• β:
• as seen from the axial direction of the crankshaft, a first angle, in the forward rotation direction, being measured between a straight line connecting between the axis of the first balancer shaft and the axis of the second balancer shaft, and the Y axis, the first angle being 90°+arctan {(LyB(Rr)−LyB(Fr))/(LxB(Rr)−LxB(Fr))},
• γB(Fr):
• as seen from the axial direction of the crankshaft, a second angle, in the forward rotation direction, between a straight line connecting between the axis of the first balancer shaft and the axis of the crankshaft, and the Y axis, the second angle being 90°+arctan(LyB(Fr)/LxB(Fr)),
• γB(Rr):
• as seen from the axial direction of the crankshaft, a third angle, in the forward rotation direction, between a straight line connecting between the axis of the second balancer shaft and the axis of the crankshaft, and the Y axis, the third angle being 90°+arctan(LyB(Rr)/LxB(Rr))
• X′ axis:
• an axis inclined from the X axis by β-90° in the forward rotation direction,
• Y′ axis:
• an axis inclined from the Y axis by β-90° in the forward rotation direction,
• Lx′B(Fr) a X′ coordinate value of the axis of the first balancer shaft as measured on the X′ axis=(LxB(Fr)−LyB(Fr)/tan β)×sin β,
• Ly′B:
• a Y′ coordinate value of the axis of the first balancer shaft and the second balancer shaft as measured on the Y′ axis=(LxB(Fr)+LyB(Fr)×tan β)×cos β,
• Lx′B(Rr):
• a X′ coordinate value of the axis of the second balancer shaft as measured on the X′ axis=(LxB(Rr)−LyB(Rr)/tan β)×sin β,
• θCr:
• an angle of rotation of the crankshaft in the forward rotation direction (where θCr is assumed to be 0° when the crank pin portion of the crankshaft is on the Y axis),
• UP:
• an unbalance amount of the reciprocal movement portion=mP×R (where mP is the mass of the reciprocal movement portion, and R is a crank radius),
• UCr:
• an unbalance amount of the rotary movement portion=mCr×rCr (where mCr is the mass of the rotary movement portion, and rCr is a distance between the axis of the crankshaft and the center of gravity of the rotary movement portion),
• αCr:
• an angle in an unbalance direction, which is in the forward rotation direction from the Y axis, of the rotary movement portion when θCr=0°,
• UB(Fr):
• an unbalance amount of the first balancer shaft=mB(Fr)×rB(Fr) (where MB(Fr) is the mass of the first balancer shaft, and rB(Fr) is a distance between the axis of the first balancer shaft and the center of gravity of the first balancer shaft),
• U1B(Fr):
• a Y-axis direction component of the unbalance amount of the first balancer shaft=UB(Fr) when θCr=0°,
• U2B(Fr):
• a X-axis direction component of the unbalance amount of the first balancer shaft=UB(Fr) when θCr=0°,
• αB(Fr):
• an unbalance direction (the angle in the forward rotation direction from the Y axis) of the first balancer shaft when θCr=0°,
• UB(Rr):
• an unbalance amount of the second balancer shaft=mB(Rr)×rB(Rr) (where mB(Rr) is the mass of the second balancer shaft, and rB(Rr) the is a distance between the axis of second balancer shaft and the center of gravity of the second balancer shaft),
• U1B(Rr):
• a Y-axis direction component of the unbalance amount of the second balancer shaft=UB(Rr), when θCr=0°,
• U2B(Rr):
• a X-axis direction component of the unbalance amount of the second balancer shaft=UB(Rr), when θCr=0°, and
• αB(Rr):
• an angle in an unbalance direction, which is in the forward rotation direction from the Y axis, of the second balancer shaft when θCr=0°.

A method for manufacturing a machine having a reciprocating slider crank mechanism, the method comprising:

• providing a reciprocal movement portion including
• a piston configured to reciprocate in a cylinder,
• a piston pin, and
• a small end portion of a conrod, the small end portion being connected to the piston by the piston pin;
• providing a rotary movement portion including
• a rotatable crankshaft having a crank pin portion, and
• a big end portion of the conrod, the big end portion being connected to the crank pin portion of the crankshaft;
• providing a first balancer shaft configured to rotate, together with the rotation of the crankshaft, in an opposite rotation direction to that of the crankshaft at a same rotation speed as that of the crankshaft;
• and
• providing a second balancer shaft arranged on an opposite side from the first balancer shaft with respect to a center line of the cylinder as seen from the axial direction of the crankshaft, and the second balancer shaft configured to rotate, together with the rotation of the crankshaft, in an opposite rotation direction to that of the crankshaft at the same rotation speed as that of the crankshaft, wherein:
• an axis of the crankshaft, an axis of the first balancer shaft and an axis of the second balancer shaft are not arranged on a same plane;
• as seen from the axial direction of the crankshaft, a center line of the cylinder is offset from the axis of the crankshaft;
• and
• UCr, αCr, UB(Fr), UB(Rr), αB(Fr) and αB(Rr) are set so as to satisfy a setting formulae below:
• UCr=UP×0.5×{1+(δ/l)2}1/2,
• αCr=180°−arctan(δ/l),
• UB(Fr)={(U1B(Fr)2+U3B(Fr))2+(U2B(Fr)+U4B(Fr))2}1/2,
• U1B(Fr)=−UP×0.5×{Lx′B(Rr)/(Lx′B(Rr)−Lx′B(Fr))}×{1+(δ/l)2}1/2,
• U2B(Fr)=−UP×0.5×{Ly′B/(Lx′B(Rr)−Lx′B(Fr))}×{1+δ/l)2}1/2,
• U3B(Fr)=−UP×{δ/(Lx′B(Rr)−Lx′B(Fr))}×sin β×{1+(δ/l)2}1/2,
• U4B(Fr)=−UP×{δ/(Lx′B(Rr)−Lx′B(Fr))}×cos β×{1+(δ/l)2}1/2,
• αB(Fr)=180°−arctan {(U2B(Fr)+U4B(Fr)/(U1B(Fr)+U3B(Fr)}+arctan(δ/l),
• UB(Rr)={(U1B(Rr)+U3B(Rr))2+(U2B(Rr)+U4B(Rr))2}1/2,
• U1B(Rr)=−UP×0.5×{Lx′B(Fr)/(Lx′B(Fr)−Lx′B(Rr)}×{1+δ/l)2}1/2,
• U2B(Rr)=−U2B(Fr),
• U3B(Rr)=−U3B(Fr),
• U4B(Rr)=−U4B(Fr), and
• αB(Rr)=180°−arctan {(U2B(Rr)+U4B(Rr)/(U1B(Rr)+U3B(Rr))}+arctan(δ/l),
• where
• as seen from the axial direction of the crankshaft, the axis of the crankshaft is an origin, an axis extending from the origin toward the piston in parallel to the center line of the cylinder is a Y axis and an axis perpendicular to the Y axis is an X axis,
• as seen from the axial direction of the crankshaft, the rotation direction of the crankshaft is a forward rotation direction and an opposite direction to the rotation direction of the crankshaft is a reverse rotation direction,
• LxB(Fr):
• a X coordinate value of the axis of the first balancer shaft as measured on the X axis,
• LyB(Fr):
• a Y coordinate value of the axis of the first balancer shaft as measured on the Y axis,
• LxB(Rr):
• a X coordinate value of the axis of the second balancer shaft as measured on the X axis,
• LyB(Rr):
• a Y coordinate value of the axis of the second balancer shaft as measured on the Y axis,
• l:
• a distance between a center of the piston pin and a center of the crank pin portion,
• δ:
• an amount of offset of the cylinder,
• β:
• as seen from the axial direction of the crankshaft, a first angle, in the forward rotation direction, being measured between a straight line, connecting between the axis of the first balancer shaft and the axis of the second balancer shaft, and the Y axis, the first angle being 90°+arctan {(LyB(Rr)−LyB(Fr))/(LxB(Rr)−LxB(Fr))},
• γB(Fr):
• as seen from the axial direction of the crankshaft, a second angle, in the forward rotation direction, between a straight line, connecting between the axis of the first balancer shaft and the axis of the crankshaft, and the Y axis, the second angle being 90°+arctan(LyB(Fr)/LxB(Fr)),
• γB(Rr):
• as seen from the axial direction of the crankshaft, a third angle, in the forward rotation direction, between a straight line, connecting between the axis of the second balancer shaft and the axis of the crankshaft, and the Y axis, the third angle being 90°+arctan(LyB(Rr)/LxB(Rr))
• X′ axis:
• an axis inclined from the X axis by β-90° in the forward rotation direction,
• Y′ axis:
• an axis inclined from the Y axis by β-90° in the forward rotation direction,
• Lx′B(Fr):
• a X′ coordinate value of the axis of the first balancer shaft as measured on the X′ axis=(LxB(Fr)−LyB(Fr)/tan β)×sin β,
• Ly′B:
• a Y′ coordinate value of the axis of the first balancer shaft and the second balancer shaft as measured on the Y′ axis=(LxB(Fr)+LyB(Fr)×tan β)×cos β
• Lx′B(Rr):
• a X′ coordinate value of the axis of the second balancer shaft as measured on the X′ axis=(LxB(Rr)−LyB(Rr)/tan β)×sin β
• θCr:
• an angle of rotation of the crankshaft in the forward rotation direction (where θCr is assumed to be 0° when the crank pin portion of the crankshaft is on the Y axis),
• UP:
• an unbalance amount of the reciprocal movement portion=mP×R (where mP is the mass of the reciprocal movement portion, and R is a crank radius),
• UCr:
• an unbalance amount of the rotary movement portion=mCr×rCr (where mCr is the mass of the rotary movement portion, and rCr is a distance between the axis of the crankshaft and the center of gravity of the rotary movement portion),
• αCr:
• an angle in an unbalance direction, which is in the forward rotation direction from the Y axis of the rotary movement portion when θCr=arctan(δ/l)°,
• UB(Fr):
• an unbalance amount of the first balancer shaft=mB(Fr)×rB(Fr) (where MB(Fr) is the mass of the first balancer shaft, and rB(Fr) is a distance between the axis of the first balancer shaft and the center of gravity of the first balancer shaft),
• U1B(Fr):
• a Y-axis direction component 1 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• U2B(Fr):
• a X-axis direction component 1 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• U3B(Fr):
• a Y-axis direction component 2 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• U4B(Fr):
• a X-axis direction component 2 of the unbalance amount of the first balancer shaft UB(Fr) when θCr=arctan(δ/l)°,
• αB(Fr):
• an angle in an unbalance direction, which is in the forward rotation direction from the Y axis, of the first balancer shaft when θCr=arctan(δ/l)°,
• UB(Rr):
• an unbalance amount of the second balancer shaft=mB(Rr)×rB(Rr) (where mB(Rr) is the mass of the second balancer shaft, and rB(Rr) is a distance between the axis of the second balancer shaft and the center of gravity of the second balancer shaft),
• U1B(Rr):
• a Y-axis direction component 1 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°,
• U2B(Rr):
• a X-axis direction component 1 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°,
• U3B(Rr):
• a Y-axis direction component 2 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°,
• U4B(Rr):
• a X-axis direction component 2 of the unbalance amount of the second balancer shaft UB(Rr) when θCr=arctan(δ/l)°, and
• αB(Rr):
• an angle in an unbalance direction, that is in the forward rotation direction from the Y axis, of the second balancer shaft when θCr=arctan(δ/l)°.