ANALYSIS OF LATHE VIBRATION ANALYSIS OF LATHE VIBRATION INFLUENCE ON BLANK INFLUENCE ON BLANK

ROUGHNESSROUGHNESS

TALLINN UNIVERSITY OF TECHNOLOGYTALLINN UNIVERSITY OF TECHNOLOGY

Ph.D Gennady Aryassov, M. Sc. Tauno Otto, M. Sc. Svetlana Gromova

AIM OF THE WORKAIM OF THE WORK

The effect of lathe vibrations to the roughness of The effect of lathe vibrations to the roughness of machined surface was investigated on the base of machined surface was investigated on the base of the theoretical and experimental investigations. It the theoretical and experimental investigations. It gives the possibility to control and adjust the gives the possibility to control and adjust the surface roughness of processing details. This surface roughness of processing details. This knowledge gives the possibility to increase the knowledge gives the possibility to increase the accuracy of processing on different conditions of accuracy of processing on different conditions of cutting.cutting.

THEORETICAL THEORETICAL INVESTIGATIONINVESTIGATION

In the work the dynamic models with one and two degrees of freedom are accepted (Fig.1).

Fig.1. Calculation dynamical models.

y

y

x

a) with one degree of freedom

y=y 0s

inpt

l

b) with two degress of freedom

y

x

z

l

y

z

Calculation scheme with one degree of Calculation scheme with one degree of freedom (Fig.1a)freedom (Fig.1a)

tpMlkJ yo sin02

.. (1)

у0 is an amplitude of the foundation vibrations;

JO is a moment of inertia of the blank;

p=2f, f is the frequency of the foundation vibrations in Hz; ky is the spring constant of elastic support of the blank .

tppJ

Mplyv cos

)( 220

0

(2)

The differential equation of forced vibrations induced by the foundation vibrations

From which a velocity of the forced vibrations induced by the foundation vibrations

The differential equations of forced vibrations in The differential equations of forced vibrations in action of the cutting force action of the cutting force FF (Fig.2)(Fig.2)

102

..

0 cossin ltFFtpMlkJ ary

Fig. 2. Calculation scheme in cutting.

(3)

where the cutting force F is reproduced as a sum of two items: the constant component Fr

determined in practice by the simplified empirical formula and the variable component . The amplitude value of the variable component of the cutting force Fa is connected with the

roughness value and changed in a rather wide range.

whence the motion velocity with regard to initial conditions y0 and v0

F

y

y

xl1

F

l

(4) tllEptplDtplDvtllElFyv sincoscossin 101100

)( 220

0

pJ

MD

lk

FF r0

)(22

0

J

FE a

(5)

Calculation scheme with two degrees of Calculation scheme with two degrees of freedom (Fig.1b and Fig.3)freedom (Fig.1b and Fig.3)

Fig.3. Gyroscope system with two degrees of freedom in cutting.  

ptMzlkyAzJ zzb sin20

tlFlFptMylkzAyJ aryyb*

110 coscos (6)

where is angular velocity of rotation of the blank, and are spring constants, A is moment of inertia of the blank with respect to axes of rotation.

)sin()sin(

,)sin()sin(

222211111

2221111

tpatpaz

tpatpay(7)

where and are constants of integrations which are to be determined from the initial conditions; and are rations of the amplitudes for corresponding two principal modes of vibrations; p1 and p2 are

natural frequencies of vibrations with gyroscopic forces

(8)0

420

222,1 5.04 JkklJbbp zy

2220 bzy AkklJb where

x

N

A

z

y

C

z c

yc

yb

z

a

0

c

The The natural frequencies and natural frequencies and principal modes of principal modes of vibrations are given in the (Fig.4).vibrations are given in the (Fig.4).

Fig. 4. Principal modes of vibration corresponding to two different natural frequencies with gyroscope forces.

The analysis shows when value of the is increased then difference between the lower frequency p1 and higher frequency p2 is increased as well (Fig.4).

Usually in studying of steady-state vibration drop the components determining free damping vibrations. However it is impossible to make in this instance, because operating conditions in the cutting due to roughness surface are changed.

PRINCIPAL MODE OF VIBRATION

second mode– reverse precision

first mode – direct precision

NATURAL FREQUENCIES FROM FREQUENCY ROTATION

Frequency rotation of the blank (rpm)

P1 – for direct precision

P2 – for reverse precision

EXPERIMENTAL ANALYSISEXPERIMENTAL ANALYSIS

Fig. 5. Scheme for measuring of the vertical and horizontal rigidity of the lathe.

One of characteristics is the spring constant of the lathe. The test was carried out in the case of two position of the load (Fig.5).

indicators

position I

320

630

N1N3

N2

F

630

position II

N1

indicatorsN2

N3

320

F

In the Fig.6 are given the results of mathematical statistical analysis the experiment data in the form of correlative straight lines, where coefficient of direct regression is the unknown rigidity.

-400

-200

0

200

400

600

800

1000

0 0,2 0,4 0,6 0,8

Displacement, mm

Lo

ad, N

Fig. 6. Correlative function between the load and static displacement.

Experimental analysis of vibration on idling of the latheExperimental analysis of vibration on idling of the lathe

As the basic measurement equipment was used vibration analyzer SigLab 20.22A with programming supply in MATLAB, designed for multi-channel investigations of vibroacoustic signals in frequency band from 2 Hz to 50 kHz.

As transducers piezoelectric accelerometers KISTLER 870B10 and KISTLER 8702B50 were used with sensitivity to 50 v/g. In additions the pocket sized vibrometer was used – collector data PICOLOG CMVL 10 of firm SKF for measuring in frequency band from 30 Hz to 10 kHz.

0

0,05

0,1

0,15

0,2

0,25

0,3

0 100 200 300 400 500Frequency, Hz

Vel

oci

ty, m

m/s

theoretical

exsperiment

The results of measuring of the vibration in horizontal plane are given in Fig.7, where reference theoretical results of vibration velocity according to Eq. (2) are given too.

Fig.7. Experimental and theoretical results of the vibration in horizontal plane.

Measuring of vibration in case of rotation of Measuring of vibration in case of rotation of the blankthe blank

Similar experiment was conducted in case of the rotating blank also.

Frequency, Hz

0

0,1

0,2

0,3

0,4

0,5

0 100 200 300 400 500

Velocity, mm/s

exsperiment

with giroscopic forces forces

theoretical

The test results in horizontal plane and corresponding theoretical results of vibration velocity are given in Fig.8.

Fig.8. Experimental and theoretical results of vibration with gyroscopic forces.

Measuring of vibration in cuttingMeasuring of vibration in cutting

Experimental measuring was performed with different cutting speeds, feeds and depths of cut. Test results and results of the calculation are given in Fig.9.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0test 1 test 2 test 3 test 4 test 5 test 6

Velocity, mm/s

experiment theoretical with giroskopic forces

Fig.9 Comparative analysis of experimental and theoretical results.

After every cutting the surface roughness was measured by profilograph ‘Surftronic 3+’. The amplitude value of the variable component of the cutting force in Eq. (4) was taken according to the experimental value of the roughness.

CONCLUSIONCONCLUSION The processing of the roughness measurements data confirmed

precision of the calculation model. Surface roughness parameters of the blank quite satisfactory agreed

with the corresponding data of the theoretical investigation. The results of experimental and theoretical investigations confirmed

the theoretical hypothesis especially when calculation model with two degrees of freedom was used.

This knowledge gives the possibility to increase the accuracy of processing on different conditions of cutting.

•It was remained without investigation an important question of stability of the blank in the action of the moving cutting force.

•In future calculation models with four degrees of freedom are supposed to use. And finally it is necessary to derivative theoretical expressions with help of which we can exactly determine the roughness.

•The last gives the possibility to control and adjust the surface roughness of processing details. But for it is demanded to conduct the large number of experiments with good equipment.