Forced vibrations in feeding kinematic chain and roughness of surfaces manufactured by milling.

Minciu, Constantin ; Croitoru, Sorin Mihai ; Constantin, George 等

1. INRODUCTION

In the technical literature, there are few researches of studying the technological kinematic chains (main and feed kinematic chains) from the dynamic point of view considering a unitary theory. The feed kinematic chain was treated unilaterally regarding only the self vibrations due to friction or the vibrations induced by gears, neglecting other causes that determine the inconstancy of the feed motion (Minciu et al., 2000).

This paper proposes methodologies for experimental research (Minciu et al., 1995) related to the measurement of vibrations maintained by the variable cutting forces, and also the connection between the vibrations maintained by the variable cutting forces along longitudinal feed direction and roughness of the surfaces machined by milling (Stanescu, 2000).

2. RESEARCH ON FORCED VIBRATIONS

Experimental research was done on a stand consisting of a milling machine with vertical spindle FV-1, a table with stress gauges for cutting forces measurement and a seismic captor for measuring the forced vibrations in case of milling with longitudinal feed, using face milling cutters. The experiments were done using two face milling cutters with the diameters and number of teeth [d.sub.1] = 80 mm, [d.sub.2] = 40 mm, [z.sub.1] = 12, [z.sub.2] = 3. Workpieces were made of OLC 45 (Romanian steel).

During the experiments, the parameters of cutting regime (cutting speed, feed and cutting depth), milling cutter diameter and number of teeth varied (Minciu, 1971).

The milling cutters were ROMASCON type (Romanian patent) having teeth enforced with metal carbide K20 sort plates brazed on the conical body of the tooth-cutter.

For the milling cutter having [z.sub.1] = 12 teeth and [d.sub.1] = 80 mm the experimental conditions are presented in tests 1.1a to 1.9b and for the milling cutter having [z.sub.2] = 3 teeth and [d.sub.2] = 40 mm the experimental conditions are presented in tests 3.1a to 3.9b from Table 1. The following notations were considered: w--feed speed, rpm--spindle number of revolutions per minute, t--cutting depth. Consequently, in order to describe the longitudinal vibrations when milling with these two face milling cutters, 36 tests were done. There are some observations:

--all diagrams correspond to maintained periodical oscillatory movements (forced vibrations);

--the diagrams are repeated by the frequencies corresponding to the spindle rpm, [v.sub.as], and milling cutter's tooth action, [v.sub.z];

--in order to underline the periodical character of the studied dynamic phenomenon the periods corresponding to one rotation of the milling cutter were evidentiated and also the teeth of the milling cutter were numbered;

--amplitude of the forced vibration due to one tooth is much smaller than the amplitude due to one revolution of the tool.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Figure 1 (all figures in this paper are just samples) presents the influence of feed upon the amplitude of the forced vibrations due to the cutting forces, case of face milling cutter in longitudinal milling. Similar graphics showing the influence of cutting speed are presented in Fig. 2.

2.1 Conclusions

Some conclusions result from this research:

--amplitude of the longitudinal forced vibrations increase with feed per tooth, no matter the cutting speed, from 1.5 to 3 times for an increase of the feed per tooth of 4 times; increase of transversal forced vibrations amplitude is approx. 1.2 times;

--increase of cutting depth has a great influence upon the amplitude of longitudinal forced vibrations: 2-3 times for cutting depth increase of 2 times;

--influence of the cutting speed upon the vibrations amplitude is very interesting: decrease of the vibrations amplitude with the increase of the cutting speed; this can be explained by increase of the cutting temperature, which leads to the decrease of the cutting forces, which are the excitation of the elastic system;

--amplitude of transversal forced vibrations is less than the longitudinal ones because of the smaller cutting forces and higher rigidity along this direction.

3. FORCED VIBRATIONS VS. SURFACE ROUGHNESS

Experimental research was done in the same conditions and using the same stand as presented before. For roughness measurement was used a Romanian electronic roughness meter.

Using the results concerning the amplitude of forced vibrations, their influence upon the roughness of the surfaces obtained by milling is determined. The experimental research considered the following variables: cutting speed, feed and cutting depth, milling cutter diameter and number of teeth (Minciu et al., 2002).

Measurement of the roughness was made by means of an inductive transducer, by direct palpation of an instrument having a diamond point. The transducer is in contact with the work surface. During the measurements, the diamond point moves automatically along the reference direction, explores the roughness and the electronic device determines the arithmetical average [R.sub.a]. The diamond point is surrounded and protected by a metallic sheet being also the reference surface.

In case of the end milling cutter with the number of teeth [z.sub.1] = 12 some of the diagrams are shown in Fig. 3.

In case of the end milling cutter having [z.sub.1] = 12 teeth the following conclusions can be underlined:

--no matter the cutting speed, the roughness [R.sub.a] rises together with the growth of the feed per tooth fz from 1.5 to 3 times for a growth of the feed of 4 times;

--the same variation of the roughness [R.sub.a] and the amplitude of induced longitudinal vibrations [A.sub.long] is observed, the percentage of the growths of the two variables are slightly the same.

For the end milling cutter [z.sub.2] = 3 teeth, some of the obtained diagrams are shown in Fig. 4.

In this case the conclusions are almost the same as previous: roughness [R.sub.a] increases with the growth of the feed per tooth fz from 2.5 to 4 times. These values are substantially greater than in the case of the end milling cutter having [z.sub.1] = 12 teeth. This means that the decrease of the tooth number is an inconvenient factor for the workpiece roughness. The same influence was observed for the amplitude of the induced vibrations;

--again is observed the same variation with percentage growth slightly the same of the roughness [R.sub.a] and the amplitude of the induced longitudinal vibrations [A.sub.long];

--in case [v.sub.c] = 79.2 mm/min (v= 10.36 Hz) it was observed a great growth of the roughness, due to the dynamic instability (resonance) of the dynamic system for this frequency, compared to the other two cutting speeds. For the same feed, the roughness is 2 times greater.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

The influence of the cutting speed is presented in Fig. 5.

3.1 Conclusions

Concerning the analysis of the results of the experimental research the following conclusions and observations must be underlined:

--the same growth of the roughness [R.sub.a] and the amplitude of the induced longitudinal vibrations, [A.sub.long], was observed;

--roughness [R.sub.a] is deeply influenced by the feed per tooth fz: for a rise of the feed of 4 times, the roughness growth was of 1.5 to 4 times for both the end milling cutters;

--the cutting speed, [v.sub.c], has a minor but convenient influence upon the roughness: the rise of the cutting speed leads to a diminish of the roughness, even if this diminish is not very important;

--as expected, the number of teeth of the end milling cutter (determining the teeth cutting simultaneously, [z.sub.sim]) influences the variation range of the roughness [R.sub.a] (see Figs. 4 and 5);

--having the same causes, it was expected and it was proved experimentally the "jump" of the roughness of about 2 times, the same as amplitude, in case of resonance (milling with the tool [z.sub.2] = 3 teeth at [n.sub.c] = 622 rev/min).

5. REFERENCES

Minciu, C. (1971). Masurarea preciziei dinamice a lanhilui cinematic de rulare cu ajutorul captorilor seismici pentru vibratii torsionale (Measurement of dynamic precision of the rolling kinematic chain by means of seismic captors for torsional vibrations), Constructia de Masini, No. 2/1971, Bucharest, Romania.

Minciu C.; Velicu St. & Croitoru S. (1995). Bazele aschierii si generarii suprafetelor (Fundamentals of cutting and surface generation), University "Politehnica" of Bucharest.

Minciu, C.; Dumitrescu, E. & Stanescu, I.I. (2000). Vibrations in the feeding kynematic chain, TCMM, No. 41, ISBN 973-31-1492-8, 973-31-1494-4, Edit. Tehnica, Bucharest, Romania.

Minciu, C.; Croitoru, S.M. & Balan, E. (2002). Aspecte privind influenta vibratiilor formate asupra rugozitatii suprafetelor prelucrate prin frezare (Aspects regarding the influence of forced vibrations upon roughness of surfaces processed by milling), Constructia de Masini, No. 6, Bucharest.

Stanescu, I. I. (2000). Cercetari teoretice si experimentale privind precizia si dinamica ianfuiui cinematic de avans (Theoreticai and experimentai researces regarding the precision and dynamics of the feed kinematic chain), PhD Thesis, University "Politehnica" of Bucharest.

Tab. 1. Cutting regime parameters.

 w
Test No. mm/min rpm

1.1a/b * 23.5 154
1.2a/b * 315
1.3a/b * 622
1.4a/b * 47.5 154
1.5a/b * 315
1.6a/b * 622
1.7a/b * 95 154
1.8a/b * 315
1.9a/b * 622

 w
Test no. mm/min rpm

3.1a/b * 23.5 315
3.2a/b * 622
3.3a/b * 1230
3.4a/b * 47.5 315
3.5a/b * 622
3.6a/b * 1230
3.7a/b * 95 315
3.8a/b * 622
3.9a/b * 1230

* a: t = 0.5 mm; b: t = 1 mm