Experiments on Workpiece Supported on a Rubber Pad

5.5 Experimental Verification of the Proposed Theoretical Model

5.5.2 Experiments on Workpiece Supported on a Rubber Pad

To understand further the developed hypothesis for rough datum, two more sets of experiments were done by inserting a 3 mm thickness rubber pad between the cast iron workpiece and machine bed. The top face was machined once by keeping the workpiece on a 3 mm thickness rubber pad and then by keeping it directly on the machine bed. The experimental procedure described in Section 5.2 is repeated in the vertical milling machine both for parallelism and perpendicularity.

Figure 5.10 shows the differences in the Z coordinate values of the top face along diagonals D₁ and D₂ for datum roughness of 3.38 µm for two cases: workpiece placed directly on the machine bed and workpiece resting on the rubber pad. Figure 5.11 shows the results of a similar set of experiment with datum roughness of 2.27 µm. It is observed from Figures 5.10 and 5.11 that at same datum roughness, differences in the Z coordinate values of the points along diagonals D₁ and D₂ are less when the workpiece rests on the rubber pad. The rubber pad allows the workpiece to deflect elastically. Rough datum and rubber pad datum shows similar type of behaviour and the differences in the Z coordinate values are less compared to smooth datum which behaves as a rigid body. Perpendicularity tolerance is 0.0483 mm with the rubber pad at datum roughness of 3.38 µm, which is lower than the perpendicularity tolerance of 0.0984 mm with the smooth datum (1.74 µm).

It is to be noted that owing to the elastic deformation of the rubber pad, the effective depth of cut gets reduced, as evident from equation (5.18). Therefore, in order to maintain proper dimensional tolerance, this effect has to be compensated by providing more depth of cut. Appropriate amount of compensation can be determined experimentally.

Tolerances

(a)

(b)

Figure 5.10. Variation of Z coordinate differences with sample points for cast iron workpiece with rubber pad on vertical milling machine (a) along D1 (b) along D2 for

Experiment 1

(a)

(b)

Figure 5.11. Variation of Z coordinate differences with sample points for cast iron workpiece with rubber pad on vertical milling machine (a) along D₁ (b) along D₂ for

Experiment 2

Tolerances

5.6 Incorporation of the Knowledge Gathered from the Experimental Study into the Setup Planning Expert System

Although it is believed that a smooth datum should be used when geometric tolerance requirements are tight, the present experimental study reveals that it may not be always true. Sometimes, a rough datum may provide better geometric tolerances. Moreover, machining a surface to a smooth finish requires extra cost.

Therefore, the knowledge gathered from the experimental study is incorporated into the knowledge-base of the setup planning expert system in the form of IF–THEN rules. This knowledge is used to decide the required roughness of a datum face for achieving a particular tolerance level. The pseudo code for an IF–THEN rule is given below. Here p is the desired parallelism tolerance, p* and p** are the limits of the range in which p lies, R_a is the datum roughness, and R_a* is the minimum required value of datum roughness for achieving the desired parallelism tolerance p.

IF (desired parallelism tolerance p lies between p* and p**) THEN (datum roughness R_a should be between R_a* and 6 µm)

If Ra value goes below Ra*, i.e. Ra< Ra*, the obtained parallelism tolerance may become more than the desired value. Based on the desired value of parallelism tolerance, Ra* can be obtained from Table 5.1. Although the maximum datum roughness value is 6.35 µm in Table 5.1, it is considered a bit high roughness value for datum surface based on aesthetic consideration, etc. So, the upper limit of datum roughness R_a is kept as 6 µm. The following rules are formed based on the data provided in Table 5.1:

(Defrule::selecting- datum-roughness-rule1 (bind ?Ra* 5.43)

(bind ?p* 0.02) (bind ?p** 0.04)

(test (and(>= ?p ?p*)( <= ?p ?p** )))

=> (assert (and (>= ?R_a ?R_a*) (<= ?R_a 6 ))))

It states that if the desired parallelism tolerance (?p) is within 0.02–0.04 mm, then the datum surface roughness (?R_a) should lie in the range 5.43–6 µm. Here 5.43 µm is the minimum value of R_a, i.e.R_a*.

(Defrule::selecting- datum-roughness-rule2 (bind ?R_a* 4.86)

(bind ?p* 0.04) (bind ?p** 0.09)