DESIGN AND CALCULATION OF BALL MANDRELS FOR HOLE BURNISHING

V. D. VARLAKOV

(Presented by Prof. A. N. Eremin, Doctor of Technical Sciences)

In this article we present several designs of ball mandrels and the calculations associated with their manufacture.

All the designs of mandrels for burnishing holes proposed by us—or, as we shall call them hereafter, burnishing tools—can be divided into three main groups:

1. Rigid nonadjustable burnishing tools.
2. Rigid adjustable burnishing tools.
3. Elastic adjustable burnishing tools.

The design features of the indicated types of mandrels are as follows:

Fig. 1. Designs of ball burnishing tools

First type—rigid nonadjustable burnishing tools

This type of burnishing tool is the simplest in design (Fig. 1—1). Here the main element of the burnishing tool is a hardened ring with a V-shaped groove. The angle between the side faces of the ring may be taken from 60 to 90°. These surfaces of the ring must be ground to roughness class 9–10 according to GOST 2789-51. To reduce wear of the grinding-wheel angle, it is desirable to provide, at the bottom of the V-shaped groove, wheel relief in the form of a rectangular groove 1–2 mm wide. With such a support design, it is difficult to check the setting diameter of the balls during manufacture of the ring. To check this dimension, one has to use a micrometer; between its tips, balls of a diameter corresponding to the diameter of the mandrel balls are placed at the bottom of the groove. To keep the balls in a strictly diametral position, it may be recommended that special small tips in the form of tubes be fitted onto the micrometer jaws.

This type of burnishing tool is applicable for machining holes with tight tolerances on the order of accuracy classes 2 and 3. This type of mandrel requires no special calculation. The entire calculation reduces to determining the setting diameter of the burnishing balls. The dimensions of the individual elements may be taken on the basis of design considerations. The balls are retained in the V-shaped groove by means of two shaped washers fastened together with a ring at the end of the rod, which serves for mounting the mandrel in the machine spindle, in the tool-holder of the carriage, or in the socket of a turret head.

Depending on the method used to fasten the mandrel (the type of machine), the reverse end of the rod must be made in the form of a cylinder, a cone, or a square. The number of balls is chosen on the basis of the most complete filling of the entire V-shaped groove.

The disadvantages of this design are the necessity of maintaining the precise position of the sides of the V-shaped groove.

Second type—a rigid adjustable burnishing tool (Figs. 1–2)

In this design of burnishing tool, as in the preceding one, the setting diameter during operation remains constant. Its difference consists in the fact that here, instead of one solid ring, the supporting surface of the balls is made in the form of two cones. This simplifies the manufacturing technology of the burnishing tool. When grinding the cones, instead of a specially dressed grinding wheel, an ordinary cylindrical or cup wheel may be used. Inspection during grinding of the cones and lathe machining are simplified.

Fig. 2. Reamer tolerance diagram

The required size of the burnishing tool \((d_y)\) is set by changing the distance between the cones. The balls are retained either by a separator of the ordinary type, or by one of the type described in the preceding burnishing-tool design.

The advantage of the second type of burnishing tool is the possibility of adjusting the size over fairly wide limits, which is especially important under the conditions of small-lot production and repair shops, where holes of various diameters can be machined with a single mandrel.

Third type—elastic adjustable mandrel (Figs. 1–3, 4)

Burnishing does not change the accuracy of the preceding operation [2]. In practice, however, it may be necessary to obtain a high surface finish of holes in parts when considerable permissible deviations are allowed. This occurs when machining large-diameter holes in the 2nd and 3rd classes and small diameters in the lower accuracy classes. In these cases, machining with a rigid mandrel will prove impossible without the risk of leaving traces of the preceding operation or overstressing the material. The thickness of the work-hardened layer is then quite indeterminate.

In such cases an elastic adjustable mandrel is indispensable. Its size is always set so that the elastic member works under a certain stress. The presence of an elastic member makes it possible to compensate for considerable fluctuations in the limiting dimensions of the holes being machined, to ensure constancy of the pressure of the mandrel balls on the surface being machined and constancy of its deformation, surface finish—which is especially important—and changes in dimensions.

The elastic member compensating for fluctuations in the dimensions of the hole in the part may be a spring (Figs. 1–3) or an elastic rod (Fig. 1–4). The first design differs in no way, except for the spring, from the rigid mandrel of the second type. The spring is calculated for the total radial pressure.

The length of the elastic rod (Fig. 1–4) is determined from the equation:

\[ l=\frac{\Delta l F E}{P}, \]

where
\(\Delta l\)—magnitude of the hole tolerance,
\(P\)—force of radial pressure,
\(E\)—modulus of elasticity for steel,
\(F\)—cross section of the rod elastically absorbing the pressure,
\(l\)—length of the rod.

Calculation of the mandrel size or, as we have called it, of the setting diameter \((d_y)\), consists in adding to the nominal diameter of the hole to be burnished the difference between the diameters of the mandrel and the hole. On the basis of our investigations, this difference may be taken as equal to 0.15–0.20 mm for holes up to 100 mm in diameter.

The matter is considerably more complicated in calculating reamers for burnishing. When calculating the reamer size, it is necessary to take into account the enlargement of the hole during reaming [1] and the possible increase in the hole diameter during burnishing [2].

Schematically, the mutual arrangement of the tolerance fields is shown in Fig. 2a, where \(P\) is the amount by which the hole is enlarged by the reamer. In our case, to this enlargement value there must also be added the increase in the hole diameter \(\Delta d\). The upper and lower limiting deviations of the reamer are shifted by the amount \(\Delta d\). The scheme of the tolerance for a reamer for burnishing, depending on the tolerance for the hole, is presented in Fig. 2b. Values of \(\Delta d\) may be taken from the author’s work [2].

REFERENCES

1. Semenchenko I. I. Cutting Tool, Vol. 1, ONTI, 1936.
2. Varlakov V. D. Burnishing of holes as a finishing method. Izvestiya TPI, Vol. 75, 1954.