It is proposed to cut a plain milling cutter having 10 flutes. The end view of the cutter is shown in Fig. 16.45. The flute is to have a right hand cut and a right- hand helix with a 25 degree helix angle.
The cutter blank is made from high speed steel that has been carefully annealed to a hardness of 240 BHN. The blank has been turned and bored with some stock left on each surface for finish grinding after it has been hardened. Assume that the lead of the milling machine is 250 mm.
Make all the necessary calculations and show how you will proceed to fabricate this job, drawing the complete set up.
Step I:
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Make all the necessary calculations:
(i) Calculate the Change Gears Required to Cut Helix Angle:
Lead corresponding to helix angle of 25° = πD cot 25° = π x 100 x 2.1445 = 673.725 mm.
In such a situation where this ratio is a complicated number, use of slide rule may be made. Set index of C scale on the slide rule opposite 2.6949, and slide runner along C scale until hairline reaches the nearest matching whole numbers on the D and C scales.
In this case it will be found that hairline is over 35 on D scale and 13 on C scale. (Although there may be other numbers also, e.g., 5.4 and 2, i.e., 54 and 20 in this case; but it is always better to use the lowest number on the C scale and its matching number on the D scale).
Thus the ratio becomes:
i.e., there will be an error of 673.725 – 673.075 = 0.650 mm.
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(ii) Calculate the Required Movement of the Dividing Head:
Since there are 10 teeth on the cutter, the indexing movement will consist of making four complete turns of the Index crank which can be done by using any index plate.
(iii) Calculate the Corrected Angle of Table Swivel:
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The table must be swivelled in order to cut the helix. Generally, when cutting the helix, the fluting cutter is offset or set over. This offset will cause an error in the helix angle cut on the cutter blank if the table is swivelled to the designated helix, i.e., 25 degrees in this case.
The corrected angle of swivel is given by the formula:
tan Sc = tan h cos (r + ac)
where Sc = corrected angle of swivel of the milling machine table
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h = helix angle to be cut on cutter blank
r = radial rake angle to be cut on the cutter blank
ac = the angle of the fluting cutter (angle a projected to the axis of the cutter blank)
and angle a is the side angle on that side of the fluting cutter which will cut the face of the cutting edge on the cutter blank.
In the case of a single-angle fluting cutter, angle a is zero [Fig. 16.66 (a)]. In cutting flute as in this case, a double- angle fluting cutter is recommended over a single angle fluting cutter because the latter will tend to back cut, leaving the face of the flute marred with cutter marks. When double- angle fluting cutters are used to mill flutes with a large helix angle, some back cutting may occur unless a special fluting cutter is used.
As the difference between angle ac and a is usually small, ac can be assumed to be equal to angle a.
In this case, radial rake angle to be produced is r = 10° and side angle of the fluting cutter is ac = 15°
... tan Sc = tan h cos (r + ac) tan 25° cos (10° + 15°)
= 0.4663 x 0.9063 = 0.4226
and Sc = 22° 55′.
(iv) Calculate the Included Angle of the Fluting Cutter:
The 55 degree included angle in the base of the flute is measured on the end face, which is a plane perpendicular to the axis of the cutter blank. The angle is represented by angle fc in Fig. 16.67. The cutter blank will be swivelled at the angle Sc when the flutes are being cut.
Thus, the included angle of the fluting cutter must be angle f (which is called the normal flute angle) in order to produce the required angle, fc, in the plane on the end face of the cutter blank.
The formula for determining the included angle of cutter is:
tan f = tan fc cos Sc.
Although angle of swivel of the milling machine table has been calculated at 22° 55′, the calculations may be made by taking it as 25°.
tan f = tan fc cos Sc = tan 55° cos 25°
= 1.4281 x 0.9063 = 1.2943
... f = 52° 20′
Thus a fluting which is ground to this included angle will cut an angle of 55° on the end face of the cutter blank. On the other hand, if a fluting cutter with a 55° included angle is available it would cut the following included angle at the end face of the cutter blank;
In case the small error of 2° 35′ is acceptable in the included angle of the cutter blank, standard 55° fluting cutter may be used, otherwise the fluting cutter must be ground to have an included angle of 52° 20′.
(v) Calculate the Transverse and Vertical Cutter Offsets:
The values of transverse offset n and vertical offset m are given by the formulae:
The value of ac can be calculated by the formula:
The value of ac can be determined only by hit and trail method from this formula. Here a = 15°, h = 25°, r = 10°.
As the value of ac is quite close to a, assuming it to be 16°, we have:
Since the two sides do not balance, the assumed value of ac is incorrect.
On a second trial, it will be found that a = 16° 10′.
Substituting the value in n and m, we have:
n = (D/2) sin (ac + r) – d sin ac – R (cos ac – sin ac)
(vi) Calculate the Cutting Speed and Feed Rate:
From manufacturer recommendations, it will be found that for high speed steel form-relieved type milling cutter and job of high speed steel (tool steel) annealed to hardness of 220 BHN
Cutter speed = V = 20 m per min,
and feed rate = 0.075 mm per thread
Step II:
Set up the cutter blank on the universal milling machine and mount the fluting cutter on the arbor. The cutter blank is mounted on mandrel and held in place by a nut. The mandrel is then mounted between the centre of the dividing head.
A form relieved shaped profile fluting cutter (right-hand) is mounted on the arbor with its largest diameter opposite the spindle (Fig. 16.69). In this way the profile cutter will mill the flute by the conventional or up milling method.
A double-angle milling cutter with the desired radius on the end of the teeth and with a 55 degree included angle could also be used. This type of cutter will require taking two separate cuts through each flute, the first one of the 55° profile in the base of the flute and second one to form the 30° profile located behind the cutting edge.
Step III:
Position the blank with respect to the fluting cutter: Before swiveling the table, the work-piece and the milling cutter should be aligned with respect to each other. For this, first align the centre of the cutter blank with the largest diameter of the fluting cutter. Touch up the cutter blank against the rotating fluting cutter using a paper feeler.
Then adjust the table to compensate for the thickness of the paper feeler as well as for the difference in diameter of the cutter blank and its diameter when it has become a completely finished plain milling cutter. Finally offset the table by 16.52 mm and 16.41 mm in the transverse and vertical directions.
Step IV:
Swivel the table to the required swivel angle in the right hand direction. After that the change gear should be installed. Whenever possible the direction of the table feed should be such that the load caused by the cutting action is directed against the dividing headstock, because the headstock centre rotates with the workpiece. The tailstock centre, on the other hand is a dead centre and the cutting load can impose a heavy load on it which can result in excessive wear.
Step V:
Cut the flutes. Usually two cuts, a roughening and a finishing cut, are taken through each flute.