Development of experimental Vibro-acoustic transfer function for a system with impact

Shripad Kumar Milind Rewanand 1

Indian Institution of Technology Yerpedu – Venkatagiri Road, Yerpedu Post, Tirupati District, Andhra Pradesh – 517619, India

Saurabh Sanjayrao Suryawanshi 2

Indian Institution of Technology Yerpedu – Venkatagiri Road, Yerpedu Post, Tirupati District, Andhra Pradesh – 517619, India

Sriram Sundar 3

Indian Institution of Technology Yerpedu – Venkatagiri Road, Yerpedu Post, Tirupati District, Andhra Pradesh – 517619, India

ABSTRACT Systems with combined sliding-rolling contacts such as cam-follower, clutches, and gearbox are prone to have clearance(s) as per the design and due to manufacturing imperfections or wearing as a result of sliding between components. This clearance non-linearity results in an impact between components, which in turn generates a significant rattle during operation. The noise generation mechanism in rattle is a strong function of impact-velocity and contact forces. The objective of this study is to develop an experimental transfer function to quantify the Vibro-acoustics of a cam-follower system with clearance non-linearity. Contact between the cam and the follower is lubricated to minimize the sound generated due to friction. Follower acceleration, reaction forces, and acoustic pressure are measured on a cam-follower setup with combined rolling-sliding contact during impacts under various conditions. Impact velocity is back-calculated using the measured signal. Transfer functions relating the acoustic pressure to reaction forces and velocity are estimated in the frequency domain. These transfer functions provide insights into the Vibro-acoustic system and can be directly used in conjunction with dynamics models. The output of the study can be used in designing quieter systems with impact.

1 me19s503@iittp.ac.in

2 me18b029@iittp.ac.in

3 sriram@iittp.ac.in

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

1. INTRODUCTION

The acoustics of a system with combined rolling-sliding motion without impact was studied by Shripad et al. [1], and Ramesh et al. [2] where, the vibro-acoustic system was assumed to be linear. Whereas, the system impacts, the behavior of the vibration system changes due to the contact non- linearity caused by the clearance between components [3,4]. The contact parameters can be estimated using theory and signal processing techniques. This work aims to study the acoustic behavior and develop an experimental transfer function that quantifies vibro-acoustics of a cam-follower system with clearance non-linearity, under steady impact conditions. Transfer functions were calculated as a ratio of acoustic signal and reaction force.

2. EXPERIMENT SETUP

The experimental setup is similar to the one used by Shripad et al. [1] as shown in Figure 1, which was used for analyzing vibro-acoustics of the vibration system in contact conditions. In addition to the microphone in the transverse direction of the follower, a microphone was also added to the setup in the longitudinal direction. Angular acceleration (¨ α ) of the follower was obtained from tangential acceleration that was measured at the contact point on the follower using an accelerometer. Reaction forces ( R y , R z ) were measured using force sensors. R y is the reaction force along the vertical axis, and R z is along the horizontal axis in the plane of R y and follower. Microphones were used to record acoustic signals at two di ff erent locations; tangential direction ( P t ) and longitudinal direction ( P l ) to the follower.

Figure 1: Experiment setup

3. VIBRO-ACOUSTIC TRANSFER FUNCTION

Experiments were conducted for di ff erent cam speeds ( ω ), with Coconut oil (specific gravity = 0 . 95, kinematic viscosity = 0 . 0033 Ns / m 2 ) as a lubricant at the contact point. The cam speed was kept constant (harmonic excitation) such that there was a single impact per cam rotation. The cam speed and the impact velocity ( v ) were calculated from the acceleration data. And, impact velocity was calculated from the relative velocities of the cam and the follower at the contact point during impact. Cycles of the reaction forces and acoustic signals were analyzed in the frequency domain, and the proposed transfer functions are given as follows:

T l y ( f ) = P l ( f )

R y ( f ) (1a)

T l z ( f ) = P l ( f )

R z ( f ) (1b)

T t y ( f ) = P t ( f )

R y ( f ) (1c)

T t z ( f ) = P t ( f )

R z ( f ) (1d)

f is the frequency in Hz .

P l rms P 0

! (2a)

S PL l = 20 log 10

P t rms P 0

! (2b)

S PL t = 20 log 10

S PL ( dB ) is the sound pressure level of a cycle and P 0 (20 µ Pa ) is the reference pressure. Subscript rms represents the root mean square value of the signal.

4. RESULTS AND DISCUSSION

Figure 2 shows one steady-state period of measured signals in the time domain for ω = 93 rad / s . The time history of ¨ α shows the presence of impact and subsequent oscillations. The magnitude of R z is more than double the R y ; however, the amplitude of P l is 10 − 100 times greater (100 times, in reference to Figures 2e and 2d) than P t . For certain ω , due to the flexural vibrations of the follower, R y , R z and P t have few high-frequency oscillations which are obvious from the multiple oscillations seen within one period. It was observed during signals analysis that depending on v and ω , the periodicity of R y , R z , and P t might be equal to or more than that of ¨ α (or ω ). Flexural rigidity of the follower might be a prominent reason for the period multiplicity. On the other hand, the trend in the response of P l was the same as ¨ α . Figure 3 shows the reaction forces and the sound pressure spectra till 1000 Hz . Except for the magnitude, R y and R z look very similar. However, R y is smoother than R z . Similarly, P t is smoother (lesser irregular) than P l , which is due to the flexibility of the follower as the sound generated in longitudinal is more susceptible to flexural vibration than in transverse direction.

& [rad/s?] x10" 2.5 So a ae -1.5 14.44 14.45 14.46 14.47 t [s] 14.48 14.49 14.5 14.51

(b) Reaction force: R y

(a) Angular acceleration of the follower

INAS 1.5 "44.44 14.45 1446 «1447148144018, 18.54 t [s]

14.45 14.46 14.47 t [s] 14.48 14.49 14.5 14.51

(c) Reaction force: R z

(d) Sound pressure: P t

P' [Pa| 0.1 -0.1> -0.15 : : ; 1444 1445 1446 14.47 t [s] 14.48 14.49 14.5 14.51

(e) Sound pressure: P l

Figure 2: Time-history of one steady-state cycle of measured signals at ω = 93 rad / s , and v = 0 . 43 m / s

; Wan anrelarrnnnMenannnn amen vnnnnnnnnnnneninnrns of 6 14.44 14.45 14.46 1447 14481449 14.50 14.51 t [s]

0 100 200 300 400 500 600 700 800 900 1000 f (Hz

(b) Sound pressures; - , P t ; - , P l

(a) Reaction forces; Key: - , R y ; - , R z

Figure 3: Spectra of measured signals at ω = 93 rad / s , and v = 0 . 43 m / s

P [Pa} 10? 10° 0 100 200 300 400 500 f (Hz 600 700 800 900 1000

All the four transfer functions are shown in Figure 4. The di ff erence is in the magnitudes of alike transfer function curves. The transfer function with a higher magnitude at a particular frequency shows its dominance in the relationship between the corresponding reaction force and the sound pressure. At lower frequencies, both P t and P l are strongly related to R y . The domination of R y started decreasing with an increase in f . For a few smaller frequency bands, T l z and T t z are higher than T l y and T t y , which signifies domination of R z in the particular frequency bands.

Figure 4: Transfer functions; Key: - , T t z ; - , T l z ; - , T t y ; - , T l y

Furthermore, S PL l and S PL t were calculated using Equation 2 for di ff erent impact and ω cycles, to analyze the dependence of S PL on v . There are two branches of S PL t were observed in Figure 5. These correspond to the multiple steady-states of this system with for a given ω clearance non- linearity as demonstrated by Kahraman et al. [5].

0 100 200 300 400 500 600 700 800 900 1000 f (Hz

Figure 5: S PL vs v ; Key: · , S PL t ; · , S PL l

5. CONCLUSION

In this article, the vibro-acoustic behavior of a system with impact was studied. A single DoF vibration experiments were conducted at di ff erent excitation velocities under lubricated contact

SPL [dB] 100 95 90 85 80 75 70 65 0. on Lit 38 0.4 0.42 0.44 0.46 048 05 052 0.54 0.56 0.58 v [m/s]

condition. Steady-state reaction forces and generated sound pressure were measured, and various vibro-acoustic transfer functions were obtained. The presence of sub-harmonics in reaction forces of and sound pressure in the transverse direction, are caused due to the flexibility of the follower. The dissimilar behavior of sound pressures measured at two di ff erent (transverse and longitudinal) was also observed. Based on the discussion, to analyze vibro-acoustics of the systems similar to the experimental system (Figure 1), the microphone should be placed in the transverse direction of the motion of the components. The presence of multiple levels of acoustic response for the system with impact was observed. Transfer functions relating sound pressure to reaction force were analyzed, revealing the domination of a reaction force in controlling the noise generation in longitudinal and transverse directions. Thus, the transfer functions can be used to control the noise generation by controlling the reaction forces. The work can be extended to study the e ff ect of the flexibility of the component on vibro-acoustics.

REFERENCES

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