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Applied Thermal Engineering 31 (2011) 1447e1456

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Numerical and experimental investigation of cooling time in lasermicro-adjustment of two-bridge actuators

Hong Shen a,b,*, Zhenqiang Yao a,b

a School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, Chinab State Key Laboratory of Mechanical System and Vibration, Shanghai 200240, China

a r t i c l e i n f o

Article history:Received 1 November 2010Accepted 7 January 2011Available online 15 January 2011

Keywords:Cooling timeCooling criterionLaser micro-adjustmentLaser forming

* Corresponding author. School of Mechanical EngUniversity, Shanghai 200240, China. Tel.: þ86 21 3420

E-mail address: sh_0320@sjtu.edu.cn (H. Shen).

1359-4311/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.applthermaleng.2011.01.013

a b s t r a c t

Multiple thermal cycles are necessary in laser micro-adjustment to achieve required deformations.Between two consecutive thermal cycles, a cooling time is necessary for the workpiece to cool down. Thispaper presents two cooling criteria including the same temperature (ST) and the room temperature (RT)for laser micro-adjustment of two-bridge actuators. The effects of the scaled geometry of actuators oncooling time are investigated numerically and experimentally for different processing parameters underthe present cooling criteria. Considering the influence of material properties on cooling time, numericalanalysis is conducted for stainless steel and aluminum alloy materials. The effects of the cut-out shapesof actuators are studied using experimental methods. The numerical and experimental results show thatthe cooling time can be saved significantly when using ST cooling criterion, especially for the materialwith high thermal conductivity and large heat capacity. Moreover, it was found that the square cut-outactuator be the best choice for different scales if RT is applied. However, for large scales the circle cut-outactuator was found better if ST is used.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The functionality of many micro-system devices such as DVDdrives, hard drives or micro-optical systems crucially depends onthe accurate geometrical adjustment of specific lenses, sensors orother functional devices. Instead of high precisionmanufacturing ofeach individual component and high accuracy assembly, it hasturned out much cheaper and easier to micro adjust the speciallydesigned actuators which connect the functional devices. Mean-while, as mounted micro components are typically difficult toaccess and highly sensitive to mechanical forces and impacts,contact-free laser adjustment of actuators offers a great potentialfor accurate manipulation of micro devices [1].

Laser micro-adjustment derives from laser forming by trans-ferring this technology to the domain of micro-systems. Thisprocess is typically based on temperature gradient mechanism(TGM) and upsetting mechanism (UM). Recently, laser micro-adjustment of actuators has attracted considerable attentions[2e10]. For example, Hagenah and Wurm [4] presented a conceptand methodology to assist engineers in defining actuator

ineering, Shanghai Jiao Tong6660; fax: þ86 21 34206583.

All rights reserved.

geometries for laser adjustment in micro-technology in order torealize different movements of the actuator. Otto developed ananalyticalenumerical model to describe the thermo-elastoplasticdeformation of two-bridge actuators [5]. Numerical and experi-mental attempts were also made to study the effects of varyingheating duration on thermal upsetting of two-bridge actuators [7].Shen explained the mechanism of deformations [8] and consideredthe size effects in simulation [10] during laser micro-adjustment oftwo-bridge actuators. However, due to the tiny deformationgenerated in a single thermal cycle, several iterations are requireduntil the desired position of the functional component is finallyreached within the given tolerances in laser micro-adjustment.Hence, the process steps of laser adjustment can become quite timeconsuming.

Cooling time in multi-scan laser forming has been investigatedby some researchers. Hennige and Geiger [11] have experimentallyinvestigated cooling effects in multi-scan laser forming ofaluminum sheets using high pressure air cooling and water cooling.The effects of the forced cooling on laser forming process have beenexamined using both numerical and experimental methods [12].Although these results showed that the forced cooling could bequite efficient, it is difficult to use these cooling methods in micro-systems because of the high sensitivity of the systems. Shen et al.[13] numerically studied the interval time between two sequentscans in laser forming under nature cooling condition, but the work

Fig. 1. The sketch of a two-bridge actuator.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e14561448

was only for the laser forming of traditional sheets/plates, whichcannot be applied for the laser micro-adjustment of actuators.

In this paper, we present two cooling criteria for laser micro-adjustment of two-bridge actuators. The cooling time of differentgeometrically scaled actuators of stainless steel and aluminumalloy materials is investigated using finite element methods.Experimental analysis is carried out to examine the numericalresults for the actuators of stainless steel material. Using the pre-sented two cooling criteria, the effects of the cut-out shape ofactuators on cooling time are also examined experimentally.Finally, the influence of cooling criteria on the deformations ofactuators is numerically investigated.

Table 1Dimensions of actuators for different scales (mm).

Scale l b t a ¼ d s r0

4 60 12 0.2 6 20 1.56 90 18 0.3 9 30 2.258 120 24 0.4 12 40 310 150 30 0.5 15 50 3.7516 240 48 0.8 24 80 632 480 96 1.6 48 160 12

2. Cooling criteria

The two-bridge actuator is a metal sheet with a cut-out, asshown in Fig. 1. When one bridge of the actuator is heated bya pulsed laser, the temperature at the heated bridge increasesgreatly until the pulse ends. Then, the heated bridge cools downdue to the heat conduction and heat loss (convection and radia-tion), while the temperature in the rest part of the actuator mayincrease continuously to some extent. During the cooling process,two situations are listed as follows,

(1) the actuator is not cooled sufficiently, but the heated and un-heated bridges have the same temperature, i.e. T1 ¼ T2; and

(2) the actuator is cooled sufficiently to room temperature, i.e.T1 ¼ T2 ¼ T0,

where T1 and T2 are the temperatures at the middle of the heatedand un-heated bridges, respectively, and T0 is the room tempera-ture, as shown in Fig. 1. Therefore, two simple cooling criteria areconsidered as the same temperature cooling criterion (ST) and theroom temperature cooling criterion (RT). Both for numericalsimulation and experimental analysis, the temperatures areconsidered identical if the difference between two temperaturevalues is less than 1 �C.

3. Numerical simulation

The general governing equation of heat conduction for thethree-dimensional transient problem can be expressed as follows,

rcvTvt

¼ v

vx

�kvTvx

�þ v

vy

�kvTvy

�þ v

vz

�kvTvz

�(1)

where r is the material density, c is the specific heat, T is thetemperature, t is the time, k is the thermal conductivity, x, y and zare the coordinates in the rectangular coordinate system (Fig. 1).The boundary conditions of the governing Equation (1) can beexpressed as follows:

T ¼ T (2)

kvTvn

¼ hðTa � TÞ þ eshðTa þ 273Þ4�ðT þ 273Þ4

i¼ ðTa � TÞhðTÞ

(3)

hðTÞ ¼ hþ esðTa þ T þ 2� 273ÞhðTa þ 273Þ2þðT þ 273Þ2

i

kvTvn

¼ q ð4Þ

where T is the temperature on the boundary, n is the normalcoordinate of the boundary, Ta is the environment temperaturesurrounding the boundary, h is the convection coefficient(W/m2 �C), e is the surface radiation factor, s ¼ 5:67�10�8 W/m2K4

0 500 1000 1500 2000 2500

0

50

100

150

200

250

Temperature(°C)

Therm

al conductivity(W

/m

°C

)

Stainless steel

Aluminum alloy

0 500 1000 1500 2000 2500

500

600

700

800

900

1000

1100

1200

Temperature(°C)

Temperature(°C) Temperature(°C)

Temperature(°C) Temperature(°C)

Specific

heat(J/k

goC

)

Stainless steel

Aluminum alloy

0 200 400 600 800 1000 1200 1400

0

50

100

150

200

Youngs M

odulu

s(G

Pa)

Stainless steel

Aluminum alloy

0 200 400 600 800 1000 1200 1400

0

50

100

150

200

250

Yie

ld str

ength

(M

Pa)

Stainless steel

Aluminum alloy

0 500 1000 1500

2000

3000

4000

5000

6000

7000

8000

Density(kg/m

3)

Stainless steel

Aluminum alloy

0 500 1000 1500

0

5

10

15

20

25

Therm

al expansio

n coeffic

ient (10 -6/oC

)

Stainless steel

Aluminum alloy

Fig. 2. Thermal and mechanical properties of the materials used in simulation.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e1456 1449

is Stephan Boltzmann constant, hðTÞ is the mixing coefficient ofconvection and radiation, q is the inward heat flux on the boundary.The research results of temperature histories in laser forming showthat there is almost no difference between the convective boundaryand combined convective and radiation boundary. This implies thatheat exchange through the radiation can be ignored [14].

During the simulation, the thermal load is given in the form ofthe thermal flux density which obeys a normal distribution asfollows:

q ¼ Ie�2r2

r2o (5a)

I ¼ 2PApr2o

(5b)

where I is the heat flux at the center of laser beam, r is the distancefrom the center of the laser beam, r0 is the laser beam radius, P is

the laser power, and A is the absorptivity of the metal surface. Notethat both governing Equation (1) and boundary conditions (3) arenonlinear because the specific heat and conductivity of thematerialare dependent on temperature and the boundary conditioninvolves the heat exchange between the actuator surface andsurrounding environment.

4. Numerical analysis

In order to investigate the effects of the geometrical size ofactuators on the cooling time, the geometrically scaled actuatorsare utilized for scale 4, 8, 16 and 32, as shown in Fig. 1. Table 1 liststhe dimensions of different scales of actuators as well as the cor-responding scaled laser beam radius r0 used in the simulations. Thematerial used for the simulations is the stainless steel. Because hightemperatures are generated during laser heating, the specific heatand thermal conductivity are assumed to be the functions of

Fig. 4. The effects of heat convection coefficient on temperature history.

04 08 16 32

0

100

200

300

400

a

Scales

Cooling T

ime (

s)

Room Temperature

Same Temperature

I = 5 W/mm2

Fig. 5. Cooling time for different scales of st

Fig. 3. A typical mesh model of the two-bridge actuator.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e14561450

temperature, and the density also considered as temperaturedependent, as shown in Fig. 2. The room temperature Ta is set as20 �C and absorption coefficient A is taken as 0.5. The numericalsimulations were performed using commercial software SYSWELD2007.

Due to high peak temperatures, large spatial temperaturegradients, and rapid temporal temperature fluctuations imposed bylaser source, it is necessary to have very small element sizes in theheated area and consistent time steps. 8-node three dimensionalelement was used for both thermal and mechanical analyses. A finemesh to capture the spatial gradients implies a small time step, asshown in Fig. 3. It is necessary to choose a time step which is smallenough to resolve these large temperature variations for a givenmesh. An approximation to the relationship of mesh density to thetime step is developed from the heat conduction equation [15].A characteristic mesh size in heating area is 0.1 mm, and the timestep is 0.01 s for scale 04 actuators.

Fig. 4 shows the effects of heat convection coefficient on peaktemperature and cooling time. For the nature cooling, the heatconvection coefficients 10e40 W/m2 �C are investigated. Fromthe figure, it can be seen that there is no difference for the peaktemperature between different heat convection coefficients.During the cooling period, as expected, the temperature decreasemore quickly when larger heat convection coefficient isemployed and the largest temperature difference is less than 8 �Cbetween h ¼ 10 W/m2 �C and h ¼ 40 W/m2 �C. Thus, the heatconvection coefficient has a slight influence on the temperaturehistory for the nature cooling condition. In this study, the heatconvection coefficient h in numerical simulation is chosen as20 W/m2 �C [16].

The numerical results are shown in Fig. 5 using laser fluxI ¼ 5 W/mm2 and I ¼ 10 W/mm2 respectively, and correspondingheating durations are chosen to keep the peak temperatures at thesame level (1260 �C-1270 �C) for different scales of actuators. It canbe seen that the cooling time for RT is about double of that for ST forscale 04. When the scale increases, the geometry of actuatorsincreases and the time difference between the two cooling criteriabecomes smaller. For scale 32, the cooling time is almost the samefor the two cooling criteria.

In general, the cooling time in laser heating is related to thethermal material property including the thermal conductivity, heatcapacity, heat convection, room temperature, and peak tempera-ture. In order to investigate the effects of the thermal materialproperties on the cooling time, the material of aluminum alloy isused, which has different thermal properties from the stainless

b

04 08 16 32

0

100

200

300

400

Scales

Cooling T

ime (

s)

Room Temperature

Same Temperature

I = 10 W/mm2

ainless steel using two cooling criteria.

04 08 16 32

0

20

40

60

80

100

120

140

Scales

Cooling T

ime (

s)

Room Temperature

Same Temperature

04 08 16 32

0

20

40

60

80

100

120ba

Scales

Cooling T

ime (

s)

Room Temperature

Same Temperature

2I = 10 W/mm I = 20 W/mm2

Fig. 6. Cooling time for different scales of aluminum alloy using two cooling criteria.

04 08 16 32

0

50

100

150

200

250

300

Scales

Cooling T

ime (s)

Aluminum RT

Aluminum ST

Steel RT

Steel ST

Fig. 7. Cooling time under the same peak temperature level for two materials.

04 08 16 32

0

10

20

30

40

50

60

Scales

Difference T

ime (s)

Aluminum

Steel

Fig. 8. Time difference in cooling times between two cooling criteria for two materials.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e1456 1451

steel (Fig. 2). Laser flux I ¼ 10 W/mm2 and I ¼ 20 W/mm2 areapplied respectively and the peak temperatures are maintained560e570 �C for different scales of actuators. Fig. 6 shows thenumerical results of cooling time for the material of aluminumalloy. It can be observed from the figure that the time differencebetween the two cooling criteria is much larger than that obtainedfrom the stainless steel in Fig. 5. For scale 4, the cooling time of RT isabout 8 times of ST. As the increase of the scale, the time differencebetween the two cooling criteria is still remarkable and the coolingtime of RT is still about double of ST for scale 32. The reason that thetime difference is so great for the two criteria is because the highthermal conductivity and large heat capacity of the aluminum alloymaterial.

Note that the peak temperatures achieved in the above cases forthe twomaterials are different (about 700 �C difference), whichwillinfluence the cooling time. Fig. 7 shows the numerical results of thecooling time for different scales of actuators for stainless steel andaluminum alloy under the same level peak temperature(560e570 �C) using laser flux I ¼ 10W/mm2. It can be seen that thetime difference between the two cooling criteria for stainless steelis much smaller. In contrast, for aluminum alloy, the effect of thecooling criteria on cooling time is significant, which implies thatthe cooling time can be saved a lot if STcooling criterion is used. Thetime difference in cooling times between using ST and RT is shown

Fig. 9. Experimental set-up for laser pulsed heating of two-bridge actuators.

0 20 40 60 80 100

200

400

600

800

1000a

b

c

Time (s)

Tem

perature (

oC

)

Experimental data

Numerical results

Scale 04: P=50 W, heating duration=1.5 s

0 20 40 60 80 100

200

400

600

800

1000

Time (s)

Tem

perature (

oC

)

Experimental data

Numerical results

Scale 06: P=100 W, heating duration=1 s

0 20 40 60 80 100

200

400

600

800

1000

Time (s)

Tem

perature (

oC

)

Experimental data

Numerical results

Scale 10: P=200 W, heating duration=1.2 s

Fig. 10. Comparison of temperature histories between numerical simulation andexperiment at the heat area center.

0.5 0.8 1.2

0

10

20

30

40

50

60

70

80

Heating duration (s)

Scale04 Laser Power 40 W

Tim

e (s)

0.5 1

0

20

40

60

80

100

120

140

160

Heating d

Scale06 Las

RT

ST

Fig. 11. Experimental results of co

Laser Power

Energy

1261

1262

1263

1264

1265

1266

1267

1268

1269

1270

Fig. 12. The relation between laser power and energy.

in Fig. 8 for the two materials. As seen from the figure, the trend ofcooling time difference is different for different materials when thescale increases. The time difference increases with the increase ofthe scale for aluminum alloy, but for the stainless steel it is oppo-site. This means that when using a large scale actuator, the timedifference becomes very small for stainless steel between these twocooling criteria, whereas for aluminum alloy, the time difference ismore remarkable for large scale.

From the above numerical analysis, it can be concluded that thecooling time for the laser heating of two-bridge actuators can bereduced if ST cooling criterion is used especially for the small scaleactuators. When the forming material has high thermal conduc-tivity and large heat capacity, the cooling time will be greatly savedeven for the large scale actuators when using ST cooling criterion.

5. Experimental analysis

The experimental set-up for pulsed laser heating of two-bridgeactuators and the temperature measurement is shown in Fig. 9. Thelaser used in this work is a pulsed fiber laser with a wavelength at1085 � 5 nm. The maximum laser power is 300 W and themaximummodulation frequency is 5 kHz. One end of the specimenis clamped by the fixture which is mounted together ona computer-controlled motion stage. To measure the temperatureduring the process, a thermal camera is used to record the

.0 1.2

uration (s)

er Power 80 W

0.5 0.8 1.0 1.5

0

50

100

150

200

250

Scale10 Laser Power 150 W

Heating duration (s)

oling time for different scales.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e1456 1453

temperature history in the process. For experimental analysis,stainless steel material was employed. The geometrical scale 4, 6and 10, and corresponding laser beam radius 1.5 mm, 2.25 mm and3.75 mm were used. In order to improve the absorption, thegraphite is sprayed on the surface of actuators before they areformed.

Fig. 10 shows the comparison of temperature histories betweennumerical simulation and experiment at the center of the heatingbridge for scale 04, 06 and 10. The processing parameters includinglaser power and heating duration are chosen to achieve the peaktemperature about 1000 �C for different scales. It can be seen that

20 40 100

0

10

20

30

40

50

60

70a

b

c

E=20 J

Laser Pow er (W)

Tim

e (

s)

ST

RT

20 30

0

10

20

30

40

50

60

70

80

E=

Laser P

Tim

e (

s)

sca

50 100

0

20

40

60

80

100

E=50 J

Laser Pow er (W)

Tim

e (s)

ST

RT

50

0

50

100

150

E

Laser P

Tim

e (s)

sca

80 150

0

20

40

60

80

100

120

140

160

180

E=120 J

Laser Pow er (W)

Tim

e (s)

ST

RT

100

0

50

100

150

200

250

E=

Laser P

Tim

e (s)

sca

Fig. 13. Experimental results of cooling time unde

the temperature increases quickly due to the laser heating, anddecreases after laser pulse ends due to the heat conduction andheat convection. The peak temperatures simulation and experi-ment agree well, meanwhile the trends of temperature increase inheating period and temperature decrease in cooling period arealmost same, which implies that the thermal material data and heatconvection coefficient used in simulation are quite reliable.

Fig. 11 shows the experimental results of cooling time fordifferent scaled actuators of stainless steel material. For scale 4, theprocessing parameters of laser power 40 W, and heating durationwith 0.5 s, 0.8 s and 1.2 s were applied. The cooling time are found

100 120 150

30 J

ow er (W)

20 50 80 100

0

10

20

30

40

50

60

70

80

E=40 J

Laser Pow er (W)

Tim

e (

s)

le04

150

=75 J

ow er (W)

80 100

0

50

100

150

E=80 J

Laser Pow er (W)

Tim

e (s)

le06

150

150 J

ow er (W)

80 200

0

50

100

150

200

250

E=160 J

Laser Pow er (W)

Tim

e (s)

le10

r the same energy input for different scales.

Square

Circle

Diamond

a b

Fig. 14. (a) The shapes of the cut-out of actuators and (b) geometrical relation fordifferent cut-outs.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e14561454

to be 24.7 s, 37.8 s and 41.8 s when using ST cooling criterion and57.4 s, 65.1 s and 73.2 s when using RT cooling criterion, respec-tively. As the heating duration increases, the peak temperatureincreases too, which causes the cooling time increases no matterwhich cooling criterion is used. The cooling time using ST is nearlyhalf of that of RT. For scale 6, the cooling time using ST is larger thanhalf of that using RT. For scale 10, the cooling time for ST are 99.2 s,120.5 s, 135.2 s and 147.7 s with processing parameters of laserpower of 150 W and heating duration of 0.5 s, 0.8 s, 1.0 s and 1.2 s.The corresponding cooling time for RT are 143.6 s, 162.4 s, 187.1 s,and 216.8 s. The ratio of cooling times for ST to RT is found to beabout 0.7. As it is expected, when geometrical scale increases, thetime difference between these two cooling criteria becomessmaller, which is consistent with what was found in the numericalsimulations.

According to the simulation results, the input energy decreasesdramatically with the increase of laser power for reaching the samelevel peak temperature, as shown in Fig. 12. Therefore, higherpower will produce higher peak temperature if the same inputenergy is used, and therefore a longer cooling time would beexpected. However, as shown in Fig. 13, the experimental results donot behavior like what is expected and the trend of cooling time forthe same input energy is not stable for different scales of actuators.

a b

Fig. 15. The comparison of cooling time fo

The possible reason for this is probably due to the thickness of thecoatings on the actuator, which varies among different samples andcould affect the absorption of the laser energy. Also, the higherpower may destroy the coating more seriously, which could causeless energy absorbed by the actuator. Therefore, for some cases ofthe same energy input with higher power, the cooling time is notlonger than that of lower power.

The shape of the cut-out of actuators may affect the temperaturedistribution, which may have effects on cooling time. Threedifferent cut-outs including square, circle and diamond, as well asthe relation of the geometrical size of these cut-outs are shown inFig. 14.

Due to the influence of the coatings, positioning and environ-ment temperature, experiments may provide varying results.Therefore, a statistical analysis on the obtained experimental datais carried out. In order to analyze the effects of cut-out shapes ofactuators on the cooling time, the time difference of cooling timebetween different cut-outs under the same cooling criteria is used.For example, Cir.-Dia. > 0 using ST means that the cooling time forcircle cut-out is longer than diamond cut-out under the ST coolingcriterion. Fig. 15 shows the comparisons of cooling time fordifferent cut-outs for different scales of actuators. The same pro-cessing parameters are used for different cut-outs. The positive “þ”

means longer cooling time and the negative “�” stands for shortercooling time. For scale 04, it can be clearly seen that the coolingtime for the actuators with the square cut-out is the shortest whenusing RT criterion, while the cooling times for the actuators withthe circle and diamond cut-outs are somewhat equivalent. For theST cooling criterion, compared to the square cut-out, more cases forthe circle cut-out are negative. Meanwhile, there are more positivecases for the diamond cut-out compared with the circle cut-out.This implies that the square cut-out for RT cooling criterion andcircle cut-out for ST cooling criterion need least cooling time forscale 04. In contrast, it is obvious for scale 06 that the actuatorswiththe square cut-out cool down most quickly when using RT.However, when using ST, it is difficult to distinguish which cut-outis the best. For scale 10, the best cut-out shape was found to be thesquare cut-out nomatter which cooling criterion is used. Therefore,for RT, actuators with the square cut-out are the best choice for

c

r different cut-outs in different scales.

a

b

Fig. 16. Numerical results of deformation of actuators.

Fig. 17. Explanation of in-plane deformation of the two-bridge actuator.

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e1456 1455

different scales; and for ST, it is better to use the circle cut-out forsmall scale and the square cut-out for large scale actuators.

6. Mechanical behavior

In order to demonstrate that there is no difference in thedeformation behavior when using the two cooling criteria,numerical analyses are conducted, which are decoupled intothermal analysis and mechanical analysis. It is assumed that bothstainless steel and aluminum alloy have a thermoelastoplasticbehavior with isotropic work hardening. Phase transformation isnot considered in the present simulations. Except for that one endof the two-bridge actuator is assumed to be fully constrained, allother boundaries are assumed to be stress-free surfaces. Themechanical properties of stainless steel and aluminum alloyincluding Young’s modulus, yield strength and thermal expansioncoefficient are considered to be temperature dependent as shownin Fig. 2. The room temperature value of Poisson’s ratio of 0.33 forboth materials is used throughout the calculations. The processingparameters and the time for the start of the second thermal cyclefor different cooling criteria are based on the results shown in Fig. 5(b) and Fig. 6(a). Fig. 16 shows the numerical results of deformation

of actuators with twomaterials for different scales. The actuator hasnot only the in-plane deformation but also the out-of-planebending deformation during the laser heating process [8,10]. Thepositive value stands for the in-plane deformation and the negativevalue is for the out-of-plane bending deformation. Although thereis a slight difference for the out-of-plane deformation in the case ofscale 32 for aluminum alloy, there is almost no difference indeformations between two cooling criteria for other cases for bothmaterials. This can be explained by the TGM in laser forming. TheTGM can be described by the following steps [17]. The local heatingof the surface and thermal expansion of the surface layer againstthe cold bulk material lead to purely elastic strains and the devel-opment of a small counter bend, while further heating reduces theflow stress in the locally heated area and increases expansion. If thethermal strains exceed the elastic strains that can be carried ata temperature (material and geometry specific), then the thermalexpansion converts to plastic compressive strains. As the beammoves on, the surface cools by self-quenching and contracts.Finally, with the upper surface becoming shorter than the lowersurface, a bend angle develops toward the laser beam.

The in-plane deformation of the two-bridge actuator is causedby the upsetting mechanism. However, this deformation behaviorcan also be considered by the temperature gradient in the plane [8].When a laser scans on the top surface of the plate, there will bea strong temperature gradient between the top and bottomsurfaces, which will cause the out-of-plane bending. Similarly, inthe case of laser pulsed heating of the two-bridge actuator, thereexist a strong temperature gradient between the heated and un-heated bridges, which causes the in-plane deformation. If theactuator is taken as a slice of the cross section of a plate, this in-plane deformation can be considered as the out-of-plane bending,as shown Fig. 17. Therefore, for both the RT and ST cooling criteria,there is no temperature gradient between two bridges.

7. Conclusions

Two cooling criteria, namely ST and RT cooling criteria havebeen presented for pulsed laser heating of two-bridge actuators.Numerical and experimental analyses have been conducted toinvestigate the effects of the scaled geometry, material, the cut-out

H. Shen, Z. Yao / Applied Thermal Engineering 31 (2011) 1447e14561456

shape of actuators and processing parameters such as laser powerand heating duration on the cooling time using these two coolingcriteria. The results have showed that the cooling time can be saveda lot when using the ST cooling criterion, especially for the materialwith high thermal conductivity and large heat capacity. Moreover,the square cut-out actuator has been found to be the best choice fordifferent scales if RT is applied. However, it is better to use the circlecut-out actuator for small scale and the square cut-out actuator forlarge scale if the ST is used. Finally, no difference is found in themechanical behavior between these two criteria for the reheatingprocess due to no temperature gradient between heated and un-heated bridges for both cooling criteria.

Acknowledgements

This work was supported by the Specialized Research Fund forthe Doctoral Program of Higher Education of China (20100073120044) and the Research Fund of State Key Lab of MSV, China(Grant No.MSV-MS-2010-12). The authors also would like to thankProf. Vollertsen and Mr. Sakkiettibutra in BIAS, Germany for theirhelpful discussion.

References

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