ISSN 1068�798X, Russian Engineering Research, 2014, Vol. 34, No. 6, pp. 393–395. © Allerton Press, Inc., 2014.Original Russian Text © Yu.V. Kirilin, E.A. Spiridonov, 2013, published in STIN, 2013, No. 11, pp. 6–8.

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It is a challenge to calculate the static and dynamiccharacteristics of the supporting systems in metal�cut�ting machines. Complete solution of this problem byanalytical means, with satisfactory agreement of thecalculation results and experimental data, is practi�cally impossible. Therefore, simplified models andnumerical methods are generally employed. Softwarebased on the finite�element method offers greatpotential here. By that means, the structure of sup�porting systems may be represented, without excessivesimplification, in a form reflecting the actual geometryand properties of the material. That permits more pre�cise calculations.

The finite�element method is used for analysis ofthe dynamic system of metal�cutting machines andspecifically for the simulation and calculation of thestatic and dynamic characteristics of their elastic sys�tems. By theoretical calculation of the machine tool’sdynamic characteristic and calculation of its vibra�tional stability, the productivity and precision of themetal�cutting machine may be calculated at the designstage, before any prototype even exists.

Many software programs are based on the finite�element method. One that permits the solution ofproblems in structural mechanics is ANSYS software.

In simulating the supporting systems of metal�cut�ting machines, the most important step is to develop amodel and to divide it into a grid of finite elements. Toreduce the number of finite elements, a regular gridmust be employed. The size of the finite elements is ofgreat importance.

Note that, after establishing the finite�elementgrid, the model is still not suitable for calculations.The parameters of the materials in the basic compo�nents and the model and the parameters of themachine tool’s supporting systems must be specified[1]. The parameters of the materials will be knownwith some accuracy, since steel or iron with familiarmechanical properties is generally employed. Thegreatest difficulty arises in correct specification of theparameters of the model.

Tables 1 and 2 present the rigidity c, internal�fric�tion coefficient γ, and energy�scattering coefficient λ

of models of moving joints and supports in all relevantcoordinate directions of the 2A622F4 metal�cuttingmachine. In Fig. 1, we show the model of the support�ing system in the metal�cutting machine and thedirections of the coordinate axes.

In Fig. 2, we show the model for the junctions ofthe basic components of the 2A622F4 metal�cuttingmachine with an iron column. Note that the heightand thickness of the housing walls in the model are1 mm and 2 × 10–2 mm, respectively [2]. These param�eters are the same for all the junctions of the model.

The rigidity parameters of the model of the sup�ports are specified directly as the corresponding valuesfor the actual supports (Table 2).

The unknown energy�scattering coefficient λ ofthe components in the supporting system may befound on the basis of the internal�friction coefficient γ.

Dynamic Characteristics of the Supporting System in a Horizontal�Drilling Machine

Yu. V. Kirilin and E. A. SpiridonovUlyanovsk State Technical University, Ulyanovsk

e�mail: stinedit@yandex.ru

DOI: 10.3103/S1068798X14060100

Table 1

Model of jointc × 1011, N/m, in the direction

γOX OY OZ

Chuck–column 0.048 0.082 0.316 0.12

Column–mount 0.621 0.621 0.4913 0.3

Mount–transverse slide 0.16 0.26 2.7 0.3

Transverse slide–top slide

0.13 0.21 2.3 0.3

Top slide–table 0.218 0.2 0.75 0.3

Table 2

Type of support Direction c × 106, N/m λ × 103

Basic supports OX 8.05 11.2

OY 8.05 11.2

OZ 90 125.2

Supports under column

OX 16.1 2.6

OY 24.15 33.6

OZ 300 417.3

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RUSSIAN ENGINEERING RESEARCH Vol. 34 No. 6 2014

KIRILIN, SPIRIDONOV

In accordance with the proposed method, by modalanalysis, we may determine the eigenfrequencies f ofthe system due to the corresponding part of the sup�porting system (basic component, joint, or support).For each part, the energy�scattering coefficient λ isdetermined (Table 2), For the models of the supports,γ = 0.1 and the frequency f = 14 Hz.

Table 2 presents the calculated damping parameters.

The dynamic characteristics of the supporting sys�tem are calculated when a single force is applied to themodel in the direction of the OZ axis (Fig. 1). ForceFx = –1 N is applied to the chuck at the spindle. ForceFx = 1 N is applied to the table. The point of the tableto which the force is applied is directly above the pointon the chuck to which force is applied. This corre�sponds to the experimental conditions.

In Fig. 3, we show the results of the dynamic calcu�lation in the form of amplitude–frequency character�istics.

It is evident from Fig. 3a that the resonant frequen�cies for the 2A622F4 metal�cutting machine are 14,55, 84, 137, and 181 Hz. The maximum amplitude ofthe supporting system’s vibrations corresponds to aresonant frequency of 84 Hz and is determined by thechuck–column joint.

Experimental analysis is necessary in order to con�firm the precision of the dynamic results (obtained bymeans of ANSYS software).

To that end, we select a ZET 017�U8 multifunc�tional low�frequency analyzer. Its basic functions aremeasurement of the signal levels in uniform spectralbands; calculation of the interspectral functions; anal�ysis of the nonlinear distortion; signal filtration; modalanalysis; measurement of the amplitude–frequencyand phase–frequency characteristics; long�termrecording of the signal parameters (automatic multi�channel recording); generation of signals of differentform, amplitude, and frequency; vibrational measure�ment; sequence analysis; and inspection and analysisof the results.

The vibrations of the spindle chuck, column, andtable of the metal�cutting machine are recorded bymeans of the ZET 017�U8 analyzer. Sensors areattached magnetically first to the spindle chuck andtable and then to the upper part of the column. Thevibrations are recorded in the machining of AMg5�16

YX

ZO

Y

X

ZO

Z

Y XO

ZYX

O

Z

OYX Z

OY X

5

6

3

4

2

1

7

8 9

10

490

100

1000

100

800

100695

200

650

5

(a) (b) (c)

(d) (e)

Fig. 2. Model of the mount–transverse slide (a), top slide–table (b), chuck–column (c), column–mount (d), andtransverse slide–top slide (e) joints: (1–10) numbers of thematerials.

Fig. 1. Model of the supporting system for a 2A622F4metal�cutting machine.

2.50

50 100 150 200

123456

A × 10–8, m/N

Im × 10–8, m/NRe × 10–8, m/N

–50

–18

–5 –0.5 0.5 5 50

84 Hz

f, Hz

–0.5181 Hz

–4

–1.6

14 Hz

55 Hz

137 Hz–8

Fig. 3. Calculated amplitude–frequency characteristic ofthe spindle chuck (a) and amplitude–phase–frequencycharacteristic of the model of the machine tool’s support�ing system for the specific finite�element grid adopted (b).

RUSSIAN ENGINEERING RESEARCH Vol. 34 No. 6 2014

DYNAMIC CHARACTERISTICS OF THE SUPPORTING SYSTEM 395

aluminum�alloy plates by means of an end mill (diam�eter 20 mm).

The cutting conditions are as follows: supply s =600 mm/turn; cutting depth t = 10 mm; spindle speedn = 1000 rpm.

Recording the vibration yields a table of amplitudeand frequency values for the spindle chuck, table, andcolumn. In Fig. 4, we show the resulting amplitude–frequency characteristic of the spindle chuck. We seethat the maximum resonant frequency for the spindlechuck is 75 Hz.

CONCLUSIONS

(1) Comparison of the results given by the model forthe vibration of the spindle chuck and the experimentaldata show that the agreement for the first resonant fre�quency is good. The error for the resonant frequency is12%; the error for the dynamic pliability is 5%.

(2) The model developed for the supporting systemof the 2A622F4 metal�cutting machine may be used tocalculate its dynamic characteristics with satisfactoryaccuracy.

REFERENCES

1. Kirilin, Yu.V. and Eremin, N.V., Finite�element calcu�lation of the supporting system of a machine tool,Stanki Instrum., 2002, no. 8, pp. 19–21.

2. Kirilin, Yu.V., Tabakov, V.P., and Eremin, N.V., Analyt�ical simulation of the supporting system of a noncanti�lever milling machine, Vestn. UlGTU, Mashinostr.,2002, no. 1, pp. 4–8.

Translated by Bernard Gilbert

551

90 125 160

3

5

7

f, Hz

A × 10–8, m/N

Fig. 4. Experimental amplitude–frequency characteristicof the spindle chuck.