When sliding bearings are used, the main factors causing the pure radial runout of the machine tool spindle are the roundness error of the journal surface and the bearing bore (see 1). When turning the outer circle on a lathe, the direction of action of the cutting force can be considered to be basically unchanged. As shown by -a, under the action of the cutting force, the main journal is in contact with a fixed part of the inner diameter of the bearing at different positions. The roundness error of the spindle journal has a great influence on the pure radial runout error of the main shaft, while the roundness error of the inner diameter of the bearing has little effect on the pure radial runout error of the main shaft; when the bore is made on the trampoline, due to the cutting force The direction rotates with the rotation of the main shaft. As shown by -b, under the action of the cutting force, the main journal is in contact with a different fixed part and the inner diameter of the bearing. At this time, the roundness error of the inner diameter of the bearing is on the pure diameter of the main shaft. The influence on the runout error is large, and the roundness error of the spindle journal has less influence on the pure radial runout error of the main shaft.
When the machine tool adopts rolling bearing, the main factors causing the pure radial runout of the machine tool spindle are the cylindricity error of the inner and outer ring raceways of the rolling bearing, the wall thickness difference of the inner ring, the waviness of the inner ring and the roundness error and dimensional error of the rolling element. Etc. As shown. In addition, assembly errors, etc. will also cause pure radial runout of the machine tool spindle.
a) Geometric error of the inner and outer ring raceways of the bearing b) Roundness error and dimensional error of the rolling element 2 Factors causing the pure radial runout of the main shaft when using the rolling bearing 2 The pure radial runout axis trajectory equation of the main shaft is a lathe with the sliding bearing structure as the main axis When turning the outer circle, in order to analyze the expression of the pure radial runout error of the main shaft, the radial section of the main shaft is simplified into an elliptical shape. Since a fixed part of the inner diameter of the bearing is in contact with a different part of the main shaft diameter (-a), the fixed part (point) of the inner diameter of the bearing is set as the coordinate origin, and the horizontal diameter of the inner diameter of the bearing is used as the axis to pass the contact point. And a straight line perpendicular to the horizontal diameter is used as the axis to establish a coordinate system as shown. This problem can be described as a rotating ellipse that contacts the point at different points in time, and the tangent is always the axis. As long as the rotation trajectory of the ellipse center is obtained (the trajectory of the spindle with pure radial runout), the expression of the pure radial runout error of the spindle can be further analyzed.
Establish a coordinate system as shown, and take a point P in the second quadrant (x<0, y>0, 0≤α≤π2, π2≤θ≤π), so that the tangent to the P point and the negative Y-axis The angle formed is α, and the angle between the OP and the positive X-axis is θ. When the angle α is rotated counterclockwise around the P point, the tangent PQ is exactly perpendicular to the x-axis, and then the coordinate origin is translated to the P point to obtain a coordinate of the ellipse center O at this time; this is counterclockwise rotated around the O point. The angle α, and then the translation of the coordinate origin to the P point can get the same result, in order to facilitate the calculation of the latter approach. When the coordinate system established by the simplified angle α3 is arbitrarily selected within 0 ≤ α ≤ π2, the elliptical center rotation trajectory of 14 rotation periods is obtained, and when this method is extended to the entire coordinate plane, a complete ellipse is obtained. (Set a>b) Center rotation track.
When the tangent PQ and the negative direction of the Y-axis form an angle α=0, PQ is perpendicular to the X-axis, and the ellipse is e-point at the center of the initial position E; when the ellipse starts to rotate counterclockwise from the horizontal position, α is gradually increased. When α=arctana-bab, the ellipse rotates to F, and the center f point ordinate y0 takes the maximum value ab; continues to rotate. When α increases to π2, y0 gradually decreases to 0, and the ellipse rotates to the G center at g point. The short axis of the ellipse coincides with the X axis; while continuing to rotate, α continues to increase by π2 and continues to decrease. When α=arctanb-aab=π2+arctana-bab, the ellipse is rotated to H, and the center h point y0 is minimized. Value ba; continue to rotate, then y0 gradually increases to 0, the ellipse returns to the initial position E, the ellipse center trajectory forms a complete closed shape, at this time the ellipse just rotates π, the long axis of the ellipse coincides with the axis.
It can be seen that the axis of the spindle rotates along the trajectory for two weeks per revolution, and the axis of rotation of the spindle oscillates twice in a radial direction, that is, the formation of the trajectory of the pure radial runoff axis of the spindle 7 is trajectory. The trajectory rotation frequency is the spindle rotation frequency. Twice, the axis of the spindle rotates four times per revolution of the axis. Therefore, when the surface of the main shaft has a waviness, a high-frequency radial circular runout will occur when the main shaft rotates. The axial trajectory amplifies the influence of the pure radial runout error of the main shaft on the shape error of the workpiece to be machined.
When turning on a lathe, since the workpiece being machined rotates with the spindle, the cross-sectional geometry of the workpiece is determined by the relative trajectory of the tool in the moving coordinate system. When boring is performed on a trampoline, since the tool rotates with the spindle, the shape of the hole in which the workpiece is machined is determined by the relative trajectory of the tool in the absolute coordinate system. When the roundness error (a/b) of the spindle journal is gradually increased, the pure radial runout error of the spindle increases correspondingly, and the influence on the shape of the workpiece to be processed is more and more.
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