Design of Spindle

       Design of machine tool elements is critical in tool engineering. They must withstand against applied external load. The machine tool elements such as guideways, slideways and spindle unit are discussed in detail in the next section. Additionally, requirements, functions and types of guideways and spindle are also explained.

                                     Figure 13.6 shows schematic diagram of spindle. A spindle represents a shaft with

(a) length ‘a’ which is acted upon by driving force F2, and

(b) cantilever of length ‘m’ acted upon by external force F1.

The spindle is basically designed for bending stiffness which requires that maximum deflection of spindle nose should not exceed a prespecified value, i.e.

                                 

Figure 13.6 : Principle of Working of Spindle

The total deflection of spindle nose consists of deflection d1 of the spindle axis due to bending forces F1 and F2 and deflection d2 of the spindle axis due to compliance of the spindle supports. When the spindle has tapered hole in which a center or cutting tool is mounted, the total deflection of the center or cutting tool consists of deflections d1, d2 and d3 of the center or cutting tool due to compliance of the tapered joint.

Deflection of Spindle Axis due to Bending

To calculate the deflection of the spindle nose due to bending, one must establish a proper design diagram. The following guidelines may be used in this regard.

(a) If the spindle is supported on a single anti-friction bearing at each end, it may be represented as a simply supported beam, and

(b) If the spindle is supported in a sleeve bearing, the supported journal is analyzed as a beam on an elastic foundation; for the purpose of the design diagram the sleeve bearing is replaced by a simple hinged support and a reactive moment M r acting at the middle of the sleeve bearing.

The reactive moment is given as :

                                                                   M r = C . M

where M = bending moment at the support, and

C = constant = 0 for small loads and 0.3 to 0.35 for heavy load.

Figure 13.7(a) shows schematic diagram of spindle. Figure 13.7(b) depicts the design diagram of the spindle and figure 13.7(c) illustrates deflected axis of the spindle.

Consider the spindle shown in Figure 13.7(a). By replacing the rear ball bearing by a hinge and the front sleeve bearing by a hinge and reactive moment M r, the spindle can be reduced to the design diagram as shown in Figure 13.7(b). The deflection at the free end of the beam (spindle nose) can be determined by Macaulay’s method and is found out to be

where,   E is Young’s modulus of the spindle material.

I a is average moment of inertia of the spindle section.

The deflection of the beam is shown in Figure 13.7(c).

Deflection of Spindle Axis due to Compliance of Spindle Supports

Let δE and δG represent the displacement of the rear and front support respectively. Owing to compliance support, the spindle deflects are shown in Figure 13.8. From similarity of triangles OHH’ and OGG’

From similarity of triangles OEE’ and OGG’, we get

l

On substituting these values of x in Eq. (13.30), d2 changes to,

Hence it is clear from above equation that displacement Gδ of the front bearing has greater influence upon deflection d2 of spindle nose than displacement δE of the rear bearing.

Where RE and RG are the support reactions at E and G respectively.

SE and SG are stiffness at E and G respectively.

At equilibrium,

Hence total deflection d (shown in Figure 13.9) is obtained as

   

FUNCTIONS OF SPINDLE

              The spindle is one of the most important elements of the machine tool.

   The functions of the spindle of machine tool are as follows :

(a) It clamps the workpiece or cutting tool in such a way that the workpiece or cutting tool is reliably held in position during the machining operation.

(b) It imparts rotary motion or rotary cum translatory motion to the cutting tool or workpiece.

(c) It is used for centering the cutting tool in drilling machine, milling machine, etc. while it centers the workpiece in lathes, turrets, boring machine, etc.

Requirements of spindle are :

(a) The spindle should rotate with high degree of accuracy. The accuracy of rotation is calculated by the axial and radial run out of the spindle nose. The radial and axial run out of the spindle nose should not exceed certain permissible values. These values depend upon the required machining accuracy. The rotational accuracy is influenced mainly by the stiffness and accuracy of the spindle bearings especially by the bearing which is located at the front end.

(b) The spindle unit must have high dynamic stiffness and damping.

(c) The spindle bearing should be selected in such a way that the initial accuracy of the unit should be maintained during the service life of the machine tool.

(d) Spindle unit should have fixture which provides quick and reliable centering and clamping of the cutting tool or workpiece.

(e) The spindle unit must have high static stiffness. Maximum accuracy is influenced by the bending, axial as well as torsional stiffness.

(f) The wear resistance of mating surface should be as high as possible.

(g) Deformation of the spindle due to heat transmitted to it by workpiece, cutting tool, bearings etc. should be as low as possible. Otherwise it will affect the accuracy of the machining accuracy.

                                         Presented by:

                                                   Aniket Dhede

                                                      Priyanka Jadhav

                                                Gaurav Shah