Study on Heating Mechanism in Ultrasonic Welding of Thermoplastics X. Li, S. F. Ling and Z. Sun Abstract - Heating of workpieces plays an influential role in ultrasonic welding. In the present paper, an attempt was made to further understand the heating mechanism during ultrasonic welding. Three equations in this regard were derived. Firstly, based on the viscoelastic properties of the workpieces, the equation governing heat generation was derived. Secondly, a thermal equivalent circuit model was developed in order to describe the heat transfer process from the joint interface into the surrounding air. Lastly, based on the first law of thermodynamics, the governing equation of temperature distribution in a weld sample was deduced. Finite element method was also engaged to solve these equations to reveal the transient behaviour of the heat transfer during a welding process. The observations and numerical results match well with the measured temperature distribution. It is concluded that the temperature of the joint interface is the most characteristic variable of a welding process.

heat generated in ultrasonic welding process. He found that the highest temperature rise rates were produced at displacement nodes. This was confirmed by Ng [5] in studying the vibration and heating mechanism during welding with finite element method. Tolunay et al. [6] found that increasing the static pressure resulted in higher power levels, although bond strengths did not differ substantially and the bonding strength increases with time at the elevated temperature as diffusion interlinks polymer chains from opposing sides of the interface. Tateishi, et al. [7] studied ultrasonic welding of oriented polypropylene (OPP) using tie-layer material whose function is like energy directors. They found that the total time required for completion of the welding operation decreases with increase in vibration amplitude and in applied pressure. Benatar [8] analysed heat transfer and flow during ultrasonic welding process. From his work, heat conduction is much greater than the convective heat loss to the air, and the flow in the weld zone and the local dissipation in the weld zone depend on the temperature distribution.

Keywords: Ultrasonic welding, Heating mechanism, Finite element

2 1

OBJECTIVE

BACKGROUND According to the literature survey, these research works mainly focused on the heating behaviours from their experimental results. In the present study, heat generation and heat transfer will be studied numerically to further understand heating mechanism, and Finite Element Method is used to simulate the heating process to get the temperature distribution during welding process based on the temperatures of the joint interface and the near joint interface.

Ultrasonic welding is one of the most widely used methods for joining thermoplastics because it is fast, economical, easily automated and repeated high quality joints. During ultrasonic welding process, high frequency (20-40 kHz) and low amplitude (0.001-0.025 mm) mechanical vibrations are applied to the parts being welded. The vibrations generate heat at the joint interface of the parts, resulting in melting of the thermoplastic materials and weld formation after cooling [1]. In ultrasonic welding process, heating process directly affects the melting behaviour of the joint, and consequently affects the weld strength, so it is very important to study heating process during ultrasonic welding process. Menges and Potente [2] found that heat was produced mainly by internal friction instead of interface friction. Then, Aloisio, et al. [3] found that the temperature increase sharply and reached polymer’s transition or melting temperature in a very short time. Mori [4] investigated the effects of vibration strain distribution in long plastic rods on the amount of

3

METHODOLOGY

3.1

Heat generation

Since ultrasonic welding system only works at one single frequency, the sample is subjected to a sinusoidal stress

σ * = σ 0 sin ωt

(1)

The complex compliance J * is defined as

J* =

1

ε* = J '−iJ ' ' σ*

(2)

Study on Heating Mechanism in Ultrasonic Welding of Thermoplastics

equivalent thermal circuit model for heat transfer during welding process. In this equivalent thermal circuit model, TJI (t ) , TS (t ) and T∞ are the

According to the complex compliance, the strain can also be expressed as:

ε * = J 'σ 0 sin ωt − J ' 'σ 0 cos ωt

(3)

temperatures of the joint interface, the surface, the infinite respectively. RS is used to describe

Therefore, the total work done in one cycle W can be calculated based on the definition of the dynamic compliance as follows [9]:

W = ∫ σ * (t )dε * (t )

the heat conduction from the joint interface to the surface, R A is used to describe the heat convection from the surface to the air, and R H , R F are used to describe the heat conduction from the surface to the horn and to the fixture respectively. C S is used to describe the thermody-

(4)

Substitute Eq. (1) and Eq. (3) into Eq. (4), we can get

W = πJ ' 'σ 0

2

namic energy of the welding sample.

(5)

TJI (t )

RS

This formula shows that the dissipated energy depends on the loss compliance. For the cross sectional area A and height L specimen, the average energy dissipated rate can be expressed as

TS (t )

RA

T∞

RH CS

RF

Fig. 1. Equivalent thermal circuit for AWS sample. 2

ωσ 0 J ' ' AL ωF J ' ' L = Q& = 2 2A 2

(6)

The heat transfer of the cross sectional area along the energy director direction should be same for AWS sample because of its symmetric structure. In order to get the governing equation of the heat transfer, a two-dimensional model is considered (Fig. 2). In this figure, the tip of the energy director is the origin of the coordinate.

where F is the applied force to the parts. According to the four-pole model of the actuating mechanism [10], F can be derived from the input voltage and current through the transduction matrix of the actuating mechanism. Therefore, Equation 6 can also be expressed as

ωJ ' ' | T11 E + T12 I | 2 L & Q= 2A

(7)

From this equation, we can see that the difference of the heat generation inside the welding samples is mainly determined by the cross sectional area, and the dissipated energy is inversely proportional to the local cross sectional area. Therefore, heating and plasticizing will be concentrated in the joint interface. The energy director is the major heat generator, while the heat generation of other parts is much less than that of the energy director. 3.2

Fig. 2. Two-dimensional model for heat transfer of AWS sample.

Heat transfer during welding process According to the first law of thermodynamics, there will be the following relationship [11]:

Since the heat generation mainly occurs at the joint interface, the heat of the joint interface will be transferred to other parts by heat conduction, and then dissipated to the surrounding. When the heat is transferred to other parts, some energy of the heat also increases the thermodynamic energy of the parts. Fig. 1 shows the

Q x + Q y + Q& ldxdy = Q x + dx + Q y + dy + ρc

2

∂T ldxdy ∂t

(8)

Study on Heating Mechanism in Ultrasonic Welding of Thermoplastics

From Fourier’s Law for conduction, we can get

∂ 2T ∂T ρc ldxdy = k 2 ldxdy ∂t ∂x 2 ωF 2 J ' ' L ∂ T ldxdy + k 2 ldxdy + 2A ∂y

(13)

dS is the differential length along the boundary curve, and n x , n y are defined as the components of the n vector along the x and y

T = T ( x, y, t ) , l is the length of sample,

axes respectively. Based on the contour integral over the flux boundary, S , the first item in Eq. (13) can also be rewritten as

∂T

∫ (kv ∂x )n

Finite element simulation

x

+ (kv

S

The governing equation of heat transfer (Eq. (10)) is very difficult to be solved. Finite element method can be used to solve this equation. By applying Galerkin weighted residual method, the governing equation is first expressed in the weighted residual form as follows [12]:

∫ [− vq n x

x

S

∂T )n y dS = ∂y

]

− vq y n y dS = − ∫ vq n dS

(14)

S

Then, Eq. (14) can be rewritten in the following:

∂T 0 k ∂x ∂v ∂v ∫∫A ∂x ∂y 0 k ∂T dxdy = ∂y ∂T ωF 2 J ' ' Lv ∫∫A 2 A dxdy − ∫∫A ρcv ∂t dxdy

∂ 2T ∂ 2T ωF 2 J '' L ∂T + v k k ∫∫A ∂x 2 ∂y 2 + 2 A − ρc ∂t dxdy =0 (11)

v ≡ v( x, y ) is a weight function.

(15)

− ∫ vq n dS

Using the integration by parts for the first and second items in Eq. (11), we can get

S

For the boundary condition, from the equivalent thermal circuit, the heat mainly loses to the air by heat convection, and by heat conduction of the horn and the fixture. The governing equation of the heat convection for the two dimensional model is

∂ ∂T ∂ ∂T ∫∫A ∂x (kv ∂x ) + ∂y (kv ∂y )dxdy ∂T ∂v ∂T ∂v dxdy − ∫∫ k ⋅ +k ⋅ ∂x ∂x ∂y ∂y A ωF 2 J ' ' Lv + ∫∫ dxdy 2 A A ∂T − ∫∫ ρcv dxdy = 0 ∂t A

∂T )n y dS ∂y

where

and k is the thermal conductivity. This equation is the governing equation for two dimensional transient heat conduction of AWS sample. In order to obtain a more exact solution, here, we consider the volumetric heating inside the parts.

where

+ (kv

∂T ∂v ∂T ∂v ⋅ dxdy − ∫∫ k ⋅ +k ∂ x ∂ x ∂ y ∂y A ωF 2 J ' ' Lv + ∫∫ dxdy 2A A ∂T − ∫∫ ρcv dxdy = 0 ∂ t A

(9)

∂ 2T ∂ 2T ωF 2 J ' ' L ∂T k 2 +k 2 + − ρc = 0 (10) 2A ∂t ∂x ∂y

3.3

x

S

It will reduces to

where

∂T

∫ (kv ∂x )n

q n1 = h(TS − T∞ )

(16)

where h is the thermal convection coefficient of the material. The governing equations of heat conduction are

(12)

q n 2 = k h (TS − T∞ ) / l h

The Green’s theorem can be used to rewrite the terms in the first integral of Eq. (12), then Eq. (12) becomes

3

(17)

Study on Heating Mechanism in Ultrasonic Welding of Thermoplastics

q n3 = k f (TS − T∞ ) / l f

coefficients of the horn and the fixture respectively, and l h and l f are the equivalent lengths

{c}T ∫∫ k[ B]T [ B]{T (t )}dxdy A 2 ωF J ' ' L − ∫∫ [ N ]T dxdy 2A A

for heat conduction of the horn and the fixture respectively. It is easy to see that

+ ∫∫ [ N ]T ρc

where

(18)

k h and k f are the thermal conduction

A

q n = q n1 + q n 2 + q n 3

∂T dxdy + ∫ [ N ]T q n dS = 0 ∂t S (25)

(19) Since

Another boundary condition is the temperature of the joint interface.

{c}T in Eq. (25) is arbitrary, we can get

∫∫ k[ B]

T

TJI (t ) = T (0,0, t )

(20)

[ B]{T (t )}dxdy =

A

T ∫∫[ N ]

ωF 2 J ' ' L

The solution in the domain of the two dimensional model is divided into m elements of n nodes each. Consider the trial solution for T ≡ T ( x, y, t ) in terms of the shape functions and nodal temperatures in the form

dxdy 2 A A ∂T − ∫∫ [ N ]T ρc dxdy − ∫ [ N ]T q n dS ∂t A S

T = [ N ]{T (t )}

This equation is the element matrix function for finite element simulation.

where

(21)

(26)

[ N ] is the shape function matrix. 4

{T (t )} is nodal temperature vector defined as {T (t )} = [T1 (t ) T2 (t )

T

... Tn (t )]

The experimental setup for measuring temperatures is shown in Fig. 3. In this experiment, one thermocouple (Type K, 36 AWG PFA) was put at the joint interface of the welding sample, where Omegabond 100 (fast setting room temperature epoxy adhesive) was used to fix the thermocouple at the joint interface, and the other thermocouple (Type K, 36 AWG PFA) was put near to the joint interface, where a 0.5 mm hole is drilled, and Omegatherm 201 (high thermal conductivity paste) was used to fill with the hole. The two thermocouples were connected with an electric reference junction temperature compensator (Chino Model TO-K), whose function was as the reference point. Then, an analog filter (KrohnHite Model 3944) was used to cut down the noise and avoid aliasing before sampling, and a digital oscilloscope (Nicolet Integra 40) was used to collect the data.

(22)

N i is the shape function of the element and Ti (t ) is the nodal temperature corresponding to a typical node i . where

In the Galerkin weighted residual method, the test function, v ≡ v ( x, y ) , uses the same shape functions as the trial function. Therefore it can be written in the form

v = [ N ]{c}

(23)

Since the test function can be chosen arbitrarily, the vector {c} is arbitrary, i.e., its elements can take any arbitrary numerical values. Moreover, as v is one number and as the transpose of a number is equal to the number itself, i.e. Equation 23 can also be written as

v = {c}T [ N ]T

RESULTS

Firstly, the temperature changes of the joint interface and the inner point of the welding sample was investigated. For the PP materials, the typical measured result with welding time 700 ms is plotted in Fig. 4. For the PC materials, the typical measured result with welding time 500 ms is plotted in Fig. 5. As shown in the two figures, at the beginning of the welding process, the heat generation rates at the joint interface are very high, so the temperatures of the joint interface

v = vT , (24)

Using Eq. (21) and Eq. (24) in Eq. (15), we get

4

Study on Heating Mechanism in Ultrasonic Welding of Thermoplastics

change rapidly, while the temperatures of the inner point change slowly. For PP material, when the temperature of the joint interface reaches the melting temperature of PP material, the temperature of the joint interface keeps the melting temperature, while the temperature of the inner point continues to go up because of the localized heating and heat conduction from the joint interface. For PC material, when the temperature of the joint interface reaches the glass transition temperature of PC material, the change rate of the temperature becomes a little lower and lower because the dynamic loss compliance decreases with temperature, and the same change is also applied to the temperature of the inner point because of the localized heating and heat conduction from the joint interface. Finally, when the welding time ends, all the temperatures begin to go down because of the cooling, and the difference between the temperature of the joint interface and the temperature of the inner point becomes less and less because of the heat transfer. All the temperature changes of the joint interface and the inner point during the welding process show the performance of the heat generation and heat transfer theory.

Fig. 5. Temperatures for PC.

5

CONCLUDING REMARKS

The present study analysed the heat generation, heat transfer numerically during ultrasonic welding process, and finite element method is also proposed to reveal the transient behaviour of the welding process. The experimental results are well matched qualitatively with the observations from heat generation and heat transfer theory. It is concluded that the heating mostly occurs at the joint interface, and the total heating during ultrasonic welding is a combination of volumetric heating and localized heating at the interface, so the heating of the other parts is the combination of heat conduction from the joint interface and volumetric heating. Using the finite element method, the temperatures of other parts can be derived from the temperature of the joint interface. Therefore, the temperature of the joint interface is the most characteristic variable of a welding process because its variations reflect the welding process and should be taken into consideration into detailed investigation of ultrasonic welding of thermoplastics.

Fig. 3. Experimental setup.

6

INDUSTRIAL SIGNIFICANCE

Ultrasonic welding is widely used for various component assembly applications in the biomedical, chemical, electrical industries and automotive as well as others. These include liquid bearing vessels, hearing aids, cardiometry reservoirs, electronic assemblies, monitors and diagnostic components. During ultrasonic welding process, the temperature of the joint interface is the most characteristic variable, and its variations reflect the welding process. The temperature of the joint interface can be used to monitor ultrasonic welding process. The results obtained from this investigation have great potential to provide industry with good tools for

Fig. 4. Temperatures for PP.

5

Study on Heating Mechanism in Ultrasonic Welding of Thermoplastics

sonic Welding of Thermoplastics”, Polymer Engineering and Science, Vol. 23(13), pp. 726-733, (1983). [7] N. Tateishi, T.H. North and R.T. Woodhams, “Ultrasonic Welding Using Tie-Layer Materials. Part 1: Analysis of Process Operation”, Polymer Engineering and Science, Vol. 32(9), pp. 600-611, (1992). [8] A. Benatar, “Ultrasonic Welding - Theory”, in Ultrasonic Welding of Advanced Thermoplastic Composites, Ph.D Thesis, UMI, pp. 216-328, (1987). [9] J.D. Ferry, “Viscoelastic Heating”, in Viscoelastic Properties of Polymers, Wiley, New York, pp. 537-582, (1980). [10] J. Luan, “SCA Technology and Its Application in Ultrasonic Welding”, in Modeling and Monitoring of Ultrasonic Welding of Thermoplastics, Ph.D Thesis, Nanyang Technological University, pp. 32-79, (2001). [11] F.P. Incropera and D.P. Dewitt, “Thermodynamics”, in Fundamentals of Heat and Mass Transfer, Third Edition, John Wiley & Sons, New York, pp. 156-189, (1990). [12] N.S. Ottosen and H. Petersson, “Galerkin Weighted Residual Method”, in Introduction to the Finite Element Method, Prentice Hall, pp. 78-93, (1992).

monitoring of the ultrasonic welding process for various applications. REFERENCES [1] Plastics Design Library, “Ultrasonic Welding”, in Handbook of Plastics Joining, The Library, Norwich, New York, pp. 37-66, (1997). [2] G. Menges and H. Potente, “Study on the Weldability of Thermoplastic Materials by Ultrasound”, Welding in the World, Vol. 9(1/2), pp. 46-59, (1971). [3] C.J. Aliosio, D.G. Wahl and E.E. Whetsel, “A Simplified Thermoviscoelastic Analysis of Ultrasonic Bonding”, SPE Technical Papers, Brookfield, CT, pp. 26-32, (1972). [4] E. Mori, S. Kaneko, M. Gakumazawa and Y. Okawa, “Ultrasonic Welding of Plastics”, Proceedings of Ultrasonics International, London, UK, pp. 16-19, (1973). [5] W.C. Ng, “Theory”, in Study of Vibration and Viscoelastic Heating of Thermoplastic Parts Subjected to Ultrasonic Excitation, Ph.D Thesis, UMI, pp. 126-187, (1996). [6] M.N. Tolunay, P.R. Dawson and K.K. Wang, “Heating and Bonding Mechanisms in Ultra-

6