US 5,643,051 AGranted

Centerless grinding process and apparatus therefor

AssigneeUniversity of Connecticut

InventorsShiping Steven Zhou, Joseph R. Gartner, Trevor D. Howes

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Abstract

In a method for minimizing the roundness error in an workpiece having a generally circular periphery during centerless grinding of the workpiece, the workpiece is rotatably supported on the upper surface of a first workpiece support between the grinding wheel and the second workpiece support, with the first support rotatably supporting the workpiece in contact with said grinding wheel and said second support. The .alpha.-setup angle and .beta.-setup angle cooperate with a cutting ratio to define the transfer function of a lobing loop system in the complex u-plane, and the lobing stability of the lobing loop system is thereby determined. The workpiece is rotated against the rotating grinding surface of the grinding wheel, and the magnitude and frequency of grinding disturbances causing the roundness error in the workpiece are detected. The .beta.-setup angle is modified to minimize the workpiece roundness error by minimizing the response of the lobing loop system corresponding to the detected grinding disturbances, and the ratio of the rotational speed of the grinding wheel to the rotational speed of the workpiece is adjusted to further minimize the workpiece roundness error by generating only precessing waves of minimum magnitude in the workpiece.

Claims17

Dependent claims

In a method for minimizing the roundness error in a workpiece having a generally circular periphery during centerless grinding of the workpiece in a grinding machine having a bed mounting a grinding wheel and two spaced workpiece supports, the steps comprising:

(i) rotatably supporting a workpiece on the upper surface of a first workpiece support, between a grinding wheel and a second workpiece support, said first support rotatably supporting the workpiece in contact with said grinding wheel and said second support, with an d-setup angle being defined by a first imaginary line extending through the axis of said grinding wheel and the workpiece and a second imaginary line extending through the axis of the workpiece and the point of contact with said first support, and a .beta.-setup angle being defined by said first line and a third imaginary line extending across the axis of the workpiece and the point of contact with said second support, and .alpha.-setup angle and .beta.-setup angle cooperating with a cutting ratio to define the transfer function of a lobing loop system in a complex s-plane;
(ii) determining the characteristic equation of said transfer function of said lobing loop system;
(iii) transforming said characteristic equation from said complex s-plane to the complex u-plane so that the frequency and the growth rate of the surface waves of said lobing loop system are independent of the workpiece rotational speed;
(iv) determining the distribution of the characteristic roots of said characteristic equation representing said lobing loop system in terms of the frequency and the growth rate of said surface waves of said lobing loop system;
(v) rotating said grinding wheel and rotating said workpiece against the grinding surface of said grinding wheel;
(vi) detecting and determining the magnitude and frequency of grinding disturbances causing surface waves in said workpiece;
(vii) combining said distribution of said characteristic roots and said grinding disturbances to determine the response of said lobing loop system;
(viii) determining the preferable wave frequencies of said distribution of said characteristic roots having relative low growth rates based upon said .beta.-setup angle;
and
(ix) adjusting said .beta.-setup angle so that said preferable wave frequencies are at or near the frequencies of said grinding disturbances to minimize the workpiece roundness error by minimizing the response of said lobing loop system under said grinding disturbances.

7 more elements

Apparatus for centerless grinding an associated workpiece having a generally circular periphery, comprising:

(a) a generally planar bed tiltable from a level position;
(b) a grinding wheel rotatably mounted on said bed;
(c) a regulating wheel rotatably mounted on said bed spaced from the periphery of said grinding wheel to permit an associated workpiece to be disposed therebetween;
(d) a support blade mounted on said bed intermediate said grinding wheel and said regulating wheel, said blade rotatably supporting the workpiece on its upper surface in contact with said grinding wheel and said regulating wheel whereby, when a workpiece is supported thereon, a workpiece center height is defined by the distance of the axis of the workpiece from a first imaginary line extending between the axis of said grinding wheel and the axis of said regulating wheel, and a blade top angle is defined by a second imaginary line parallel to said first imaginary line and passing through the point of contact between the workpiece and said support blade and a third imaginary line tangent to the upper surface of said blade, said blade top angle being approximately 0.degree.;
(e) means for determining the characteristic equation of a transfer function of a lobing loop system in the complex s-plane, said transfer function of said lobing loop system being defined by said blade top angle, said workpiece center height, and a cutting ratio;
(f) means for transforming said characteristic equation from said complex s-plane to the complex u-plane so that the frequency and the growth rate of the surface waves of said lobing loop system are independent of the workpiece rotational speed;
(g) means for determining the distribution of the characteristic roots of said characteristic equation representing said lobing loop system in terms of the frequency and the growth rate of said surface waves of said lobing loop system;
(h) means for rotating the workpiece against the grinding surface of said grinding wheel as it rotates;
(i) means for detecting and determining the magnitude and frequency of grinding disturbances causing surface waves in the workpiece;
(j) means for combining said distribution of said characteristic roots and said grinding disturbances to determine the response of said lobing loop system;
(k) means for determining the preferable wave frequencies of said distribution of said characteristic roots having relative low growth rates based upon said workpiece center height;
and
(l) means for adjusting said workpiece center height so that said preferable wave frequencies are at or near the frequencies of said grinding disturbances to minimize the workpiece roundness error.

10 more elements

Dependencies are inferred from the claim text.