REVIEW OF SCIENTIFIC INSTRUMENTS 85, 045104 (2014)
Design of voice coil motor dynamic focusing unit for a laser scanner Moon G. Lee, Gaeun Kim, Chan-Woo Lee, Soo-Hun Lee, and Yongho Jeona) Department of Mechanical Engineering, Ajou University, San 5, Woncheon-dong, Yeongtong-gu, Suwon-si, Gyeonggi-do 443-749, South Korea
(Received 12 February 2014; accepted 11 March 2014; published online 7 April 2014) Laser scanning systems have been used for material processing tasks such as welding, cutting, marking, and drilling. However, applications have been limited by the small range of motion and slow speed of the focusing unit, which carries the focusing optics. To overcome these limitations, a dynamic focusing system with a long travel range and high speed is needed. In this study, a dynamic focusing unit for a laser scanning system with a voice coil motor (VCM) mechanism is proposed to enable fast speed and a wide focusing range. The VCM has finer precision and higher speed than conventional step motors and a longer travel range than earlier lead zirconium titanate actuators. The system has a hollow configuration to provide a laser beam path. This also makes it compact and transmission-free and gives it low inertia. The VCM’s magnetics are modeled using a permeance model. Its design parameters are determined by optimization using the Broyden–Fletcher–Goldfarb– Shanno method and a sequential quadratic programming algorithm. After the VCM is designed, the dynamic focusing unit is fabricated and assembled. The permeance model is verified by a magnetic finite element method simulation tool, Maxwell 2D and 3D, and by measurement data from a gauss meter. The performance is verified experimentally. The results show a resolution of 0.2 μm and travel range of 16 mm. These are better than those of conventional focusing systems; therefore, this focusing unit can be applied to laser scanning systems for good machining capability. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4869339] I. INTRODUCTION
Laser material processing is currently popular in various industries. Laser scanner systems using a galvanometer are widely used because they can control the laser spot more rapidly and accurately than other scanning devices. In material processing with the laser scanner, the laser spot size should be small and uniform in the entire objective flat field for high-quality processing. Defocus errors in the laser scanner cause power attenuation and dimensional distortion. Thus, it is necessary to control the laser spot size using a laser focusing unit.1 For focusing in the objective flat field, a special optical device such as a dynamic focusing unit is necessary. Without this device, a fixed focusing lens has a fixed focal length and therefore forms a curved image field in air. There are two common solutions.2 The first is to use a special fieldflattening optics with an f-theta objective lens, which is based on specially designed optical lenses or a specific optical layout. However, it is only applicable to a narrow flat field. The second is a dynamic focusing unit, which has a moving lens for variable focusing. This is a unique Z-axis scanning device that shifts the moving lens along its optical axis under the precise control of various actuators. The shifted moving lens exhibits a shifted focal length, varies the image range from the scanning mirror, and then produces an exact focus in a broad flat field.3 The dynamic focusing laser scanning system has two important parts. First, two mirrors reflect the laser beam and a) [email protected]
0034-6748/2014/85(4)/045104/8/$30.00
form a two-dimensional image field. Second, the dynamic focusing unit transfers the moving lens and shifts the focal length. Ultimately, it makes three-dimensional material processing possible. However, the speed of the conventional laser dynamic focusing units cannot follow the velocity of the galvanometers. Moreover, the small travel range of the moving lens shifts the limits of the focal length. Therefore, the dynamic focusing unit is used in very limited applications. To overcome the working range limitations, two solutions have been applied. The first is to change the optical design of the moving lens. As shown in Fig. 1, the large value of the ratio f/L makes it easy to shift the focal length with a short moving lens shift. However, this solution requires a more complex lens deign and precise actuator control. The other is to enlarge the range of motion of the dynamic focusing unit so that the shifted focal length is expanded sufficiently by the large travel range of the moving lens. In this paper, the second solution is adopted. A conceptual design is proposed to lengthen the travel range and increase the scanning speed. This is because the newly designed dynamic focusing unit has a hollow configuration. The VCM’s performance is further enhanced by design optimization to achieve a high actuating force, because a large force can generate high-speed motion, good disturbance immunity, and fine precision. This paper also presents a model of the magnetics of the VCM and the design optimization for a large actuating force. The model is validated by a finite element method (FEM) model and experiment. A prototype of the design was fabricated, and a simple control algorithm was applied to verify the performance of the mechanism.
85, 045104-1
© 2014 AIP Publishing LLC
045104-2
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
FIG. 3. Design of hollow VCM for long travel, high precision, and fast speed.
FIG. 1. Laser scanning system with galvanometric scanner and dynamic focusing unit for laser material processing.
II. CONCEPTUAL DESIGN
Most conventional focusing systems have adopted step motors for the focusing actuators.4 However, step motors are too slow for use in laser scanners. For dynamic focusing, Zhiqiang proposed a moving-coil-type permanent magnet (PM) VCM having a ±5 mm displacement range.3 A similar mechanism for camera anti-shaking was designed and controlled by Lin et al.4 The motors moves the lens along an axis parallel to the laser beam path. The motion is guided by a linear motion (LM) guide. Because the lens holder is connected to the motors with an asymmetric mechanical offset, the stiffness is so low that the system is weak against disturbances such as vibration and manufacturing errors. Xie used galvano actuators to move the focusing lens, but because the actuator’s rotational motion is converted to linear motion by a friction drive,1 the motion is not smooth, and the mechanism is large. Xu designed a small rotary positioner mechanism with VCM and multi-stage compound flexure spring for large working range and high precision. It has good stroke but the positioner was for rotary motion.5 In this paper, a new hollow dynamic focusing unit that outperforms conventional units is proposed, as shown in Fig. 2. It also has a hollow VCM, which is guided by four
linear motion (LM) guides placed along the perimeter of the hollow at equal angles of 90◦ . The laser beam is delivered through the hollow path along the optical axis, which connects the center of the VCM, the four guides, and the lens. This type of VCM configuration has effective usage of the coil current without a non-effective coil length, as shown in Fig. 3, so that it generates a higher actuating force than conventional step motors. Compared with other linear actuators, the VCM simultaneously provides a greater range of motion, high resolution, and faster response time.6–8 Because the VCM is connected directly to the lens holder by four short arms placed along the perimeter of the hollow at equal angles of 90◦ , the actuator directly drives the lens along the optical axis, and the centers of force and motion are on the same axis. These features make it possible to have no transmission mechanism and a shorter moment arm between the lens holder and the VCM; therefore, the unit has low inertia, high stiffness, and a compact size. III. DESIGN OPTIMIZATION OF A VCM DYNAMIC FOCUSING UNIT
The size of the proposed dynamic focusing unit is limited because it should be mountable on an operating laser scanner system. Therefore, the design of the lens transfer system has been optimized for a high response and large travel range in limited space. The objective of the optimal design is to maximize the force and obtain a high lens speed. To optimize the VCM design, several researchers have used a permeance model. The magnetic flux flow is considered to be analogous to the current flow in an electric circuit. The permeance indicates how well the magnetic flux can flow through a magnetic circuit consisting of materials such as air, magnets, and yokes.9, 10 In this study, the magnetics of the VCM are modeled numerically using a similar permeance model. The design was optimized using the numerical model. A. Modeling
1. Modeling of electromagnetic circuit FIG. 2. Conceptual design of novel dynamic focusing unit with symmetric hollow configuration and long range of motion.
Magnetic and electric circuits are analogous, as shown in Table I. The permeance, which is the inverse of the reluctance,
045104-3
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
TABLE I. Analogies between magnetic and electric circuits. Magnetic circuit
Electric circuit
Characteristic
Symbol
Characteristic
Symbol
MMF Reluctance Magnetic flux Flux density Magnetic field Permeability
F (A) R (A/Wb) (Wb) B (T) H (A/m) μ (H/m)
EMF Resistance Current Current density Electric field Resistance coef.
V (V) R () I (A) J (A/m2 ) E (V/m) ρ (m)
indicates how well magnetic flux passes through a magnetic circuit. The proposed axisymmetric model of VCM in Fig. 4(a) is converted to that in Fig. 4(b) according to the permeance method. As a result, the magnetic flux density in the air gap is obtained. The magnetic flux density Bg is obtained as follows: (1) Magnetic flux r flowing from the PM can be viewed as the current source in an electric circuit. The flux, NI from the coil current is similar to that from a voltage source. (2) The permeance of the yoke, air gap, and leakage are considered. The leakage flux other than the air gap flux is considered using the leakage permeance. (3) All the elements can be numerically designed using the design parameters. Finally, the magnetic flux g and magnetic flux density Bg are obtained.
FIG. 5. Design parameters of coil and coil winding. (a) Three closely packed coil wires. (b) Cross section of coil winding.
wc hc 2 × √ −1 +1 , (2) dc 3 dc where lc is the length of the coil and [x] is the largest integer not greater than x.
n=
B. Cost function
2. Coil parameters
The diameter of the coil is related to the coil resistance, which also affects heat generation in the system. To determine the coil diameter, the number of coil turns should be selected. Equations (1) and (2) and Fig. 5 present the numerical design for the coil parameters. Here, dc is the bare coil diameter (only the bare copper), and dc ∗ is the total diameter including the enamel coating; n is the total number of coil turns, which affects the coil resistance Rc . nlc Rc = ρ π , d2 4 c
To obtain high acceleration and high stiffness, it is recommended that the VCM provides a large force. The design was optimized to maximize the acceleration (= force/mass) under constraints. The acceleration is expressed in Eq. (3), and the cost function is the inverse function of the acceleration, as shown in Eq. (4). The object of optimization is to minimize the cost function. For rapid convergence to the final value, the cost function takes a quadratic form. The design parameters to be optimized are tm , lg , ty , and dc . The final optimal parameters will minimize the cost function nBg il F = , m m
(1)
J = min
1 F /m
(3) 2 .
(4)
C. Constraints
1. Geometric constraints
The volume of the VCM is limited by the desired cost and size of the system. Therefore, in the optimal design, the total diameter of the VCM, air gap, and external yoke are limited, as shown in Eqs. (5) and (6). g(1) = FIG. 4. Magnetic analysis models of the VCM. (a) Design parameters of VCM. (b) Magnetic circuit of VCM.
tm + lm + ty − 1.0 < 0, 17[mm]
(5)
w c − lg + 1.0 < 0. 2.5[mm]
(6)
g(2) =
045104-4
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
2. Current limit
The current is limited by the power supply system, and the operating current is usually 1 A. Fmax is the force required to actuate the system and fx is the force when 1 A of current is applied. By using Eq. (7), the maximum current and force can be satisfied. g(3) =
Fmax − 1.0[A] < 0, fx
(7)
where fx is the force constant of the VCM and is equal to nBg lc . FIG. 7. Example convergence of the cost function.
3. Heat dissipation
Heat is generated by the current that flows through the coil resistance. To avoid overheating, the heat dissipation should be larger than the heat generation. In this system, heat generation occurs because of the coil resistance, and heat is dissipated by conduction to a bobbin and convection to air. The heat generation and dissipation are calculated using the thermal circuit shown in Fig. 6. g(4) =
Qs − 1.0 < 0, Qout
(8)
where Qs = i2 Rc , and Qout = Q1out + Q2out + Q3out + Q4out .
nate the optimization process if w
1 n−1 − ≤ w. n−w−2 2
(9)
That is, if Eq. (9) is satisfied, the majority with the same cost functions and design parameters among the w minima is selected as the global optimum. In summary, the total optimization design can be written as 2 1 J = min , (10) F /m
D. Results of optimization
To find the optimal VCM parameters, the Broyden– Fletcher–Goldfarb–Shanno (BFGS) method and the sequential quadratic programming (SQP) algorithm in MATLAB Toolbox were used. The BFGS method is known as a general algorithm for obtaining a search direction. The SQP algorithm is also popular for finding the search step size. They have received considerable attention for their superior rate of convergence to the final value.11 However, the result is not the global optimum. To determine whether a local minimum is the global optimum, the Bayesian simple stopping rule is used.12 If w different local minima have been discovered in n local searches, the Bayesian simple stopping rule is to termi-
FIG. 6. Heat dissipation from coil by conduction and convection. (a) Physical heat emission from coil. (b) Thermal circuit model of heat transfer.
subject to g(i) ≤ 0, i = 1...4 and 0.01 < tm ≤ 17 [mm], 0.01 < lg ≤ 17 [mm], 0.01 < ty ≤ 17 [mm], 0.01 < dc ≤ 3 [mm]. Fig. 7 shows an example convergence of the cost function. The cost function started at 14 random initial positions and converged to 3 local minima. Using the Bayesian stopping rule, the global optima were determined. In Fig. 8, the optimal program converges to the same value at every starting point except for only two points. In these optima, the active constraints are the size and current limitations. All the design parameters converged to the same values. The optimal design parameters were modified for fabrication, as shown in Table II.
FIG. 8. Determination of global optimum from random initial points: n = 14, w = 3.
045104-5
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
TABLE II. Results of design optimization, modified for fabrication. Design variables
TABLE III. Magnetic flux density and force from permeance model, FE analysis, and measured data.
System parameters Parameter
Parameter tm lg ty dc
Value
Parameter
Value
8.5 mm 5 mm 3.5 mm 0.55 mm
Force (N/A) n (coil turns) Bg (flux density) Rc (coil resistance)
3. 054 N/A 219 turns 0.1483 T 1.491
FIG. 9. Prototype of proposed dynamic focusing unit with hollow VCM, lens holder, and LM guides.
Bg Force (N/A)
Calculation
FEM
Gauss meter
148.3 mT 3.054 N/A
157.6 mT 2.802 N/A
151.9 mT ...
IV. EXPERIMENT AND RESULTS
A prototype of the VCM dynamic focusing unit was fabricated according to the optimized parameters. The magnet used in the proposed VCM is of the NdFeB family, which is known to have the highest flux density per unit volume. The ring-type magnets and yokes were attached using an adhesive from Devcon, which was designed for cementing metal pieces together and is a non-magnetic substance unaffected by magnetism. An assembly jig was also used for the magnet and yoke assembly. The jig keeps the magnets from adhering to the side yoke. It is mounted between the yokes until the adhesive material hardens and then slides away after adhesion.13 Fig. 9 shows the fabricated VCM dynamic focusing unit. The linear bushings and VCM bobbin are combined with the lens holder that mounts the focusing lens. The holder is actuated by the VCM, and its motion is guided by an LM guide.
FIG. 10. FE analysis of VCM’s magnetostatics. (a) Magnetic lines of force. (b) Magnetic flux density.
FIG. 11. Magnetic flux density by FE analysis and by measurement. (a) B measurement by Gauss meter. (b) Comparison between FEA and measurement.
045104-6
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
FIG. 12. Experimental setup for testing open loop characteristics.
Each LM guide is comprised of linear bushing (LHFS4), shaft (RSFAD4), and rubber washer (WRBNA) from Misumi USA. Friction coefficient is 0.002–0.006 and the clearance between the bushing and shaft is about 0.004 mm. The linear guide has stick-slip effect because of bushing’s ball contact and rubber washer’s sealing. This will be severe for low speed motion when the guides do not have sufficient parallelism by misalignment. In the laser focusing system, the oscillating laser beam passes through the aperture in the base, the VCM, and the lens in sequence along the same axis. After the prototype was fabricated and before the performance test, the permeance model used for optimization was verified. To validate the model, the magnetic flux density from a FEM analysis by Maxwell (Ansys, Inc.) and measurement data from a TM-701 Gauss meter (KANTEC Co., Ltd.) were compared with that from the model. The results of the comparison in the air gap are shown in Figs. 10 and 11 and Table III. The results verified that the model has good agreement with the real device. In addition to the validation, an experiment was conducted as a performance test and to verify the proposed
FIG. 13. Frequency response from open loop test.
FIG. 14. Experimental setup for performance test with closed loop control.
045104-7
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
FIG. 15. Block diagram for control of dynamic focusing unit.
FIG. 16. Resolution of the dynamic focusing unit.
FIG. 17. Travel range of the dynamic focusing unit.
FIG. 18. Positioning speed test by sinusoidal command input. (a) Amplitude: 5 mm and frequency: 30 rad/s. (b) Amplitude: 3 mm and frequency: 40 rad/s.
045104-8
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
design. The position of the moving lens for focusing is calculated by optical theories. A lookup table based on the ZEMAX model is one of the methods because the shift in the focal length is a nonlinear and discrete function. The error motions due to inevitable disturbances are compensated by simple closed-loop control. In order to investigate the performance of dynamic focusing unit, open loop frequency response was obtained to be used in closed loop control. The experimental setup is shown in Fig. 12 and the results are presented in Fig. 13. To measure the motion of the dynamic focusing unit, a Laser Doppler Vibrometer (LDV) was used. The LDV can simultaneously measure a wide displacement range. Using the output data from the LDV, the displacement of the VCM was measured; a 4122Z VCM amplifier (Copley Controls Corp.) generated a pulse-width modulated signal and supplied it to the VCM. In the results, the stick-slip played a role as stiffness in low frequency region, therefore, the flat curve between 10 and 40 Hz appeared in the magnitude graph. The resonant frequency of the device was about 45 Hz. The experimental setup for closed-loop control is shown in Fig. 13. The closed-loop control is illustrated in Fig. 14; the reference input X indicates the desired displacement of the VCM. In addition to the experimental setup in Fig. 15, the actual displacement of the VCM was measured; the error was also calculated by comparing the input and the measured. For real time closed-loop control, a DS2002/DS2003 A/D converter, DS2102 D/A converter, and DS1005 PPC boards (dSPACE) were used. Using MATLAB and dSPACE, a control panel was also built and the VCM was controlled in real time. A range of motion test to verify the proposed design and a resolution test to confirm the precision of the lens position were conducted. Fig. 16 shows the results of the closed-loop resolution test; the resolution is 0.2 μm. The range of motion of the dynamic focusing unit was ±8 mm, as shown in Fig. 17. The results satisfy industry requirements. After the displacement and resolution were tested, other tests were conducted to verify the smooth motion and high speed of the unit. The results are presented in Figs. 18(a) and 18(b). The measured data demonstrate that it has accurate tracking capability according to the input signal, despite a small tracking error. As a result, the proposed dynamic focusing unit has a positioning speed of 40 rad/s, which is higher than the 18 rad/s of conventional systems.14 The comparison between the conventional and the proposed focusing units are listed in Table IV.14 The proposed unit has superior characteristics compared to the conventional devices, therefore, it can be applied to industry. TABLE IV. Performances comparison between conventional and proposed focusing units.
Beam input aperture Maximum lens travel Typical positioning speed Resolution
Conventional
Proposed
8 mm ±4 mm 18 rad/s Not published
8 mm ±8 mm 40 rad/s 0.2 μm
V. CONCLUSIONS
In this paper, a novel dynamic focusing unit exhibiting a long travel range, high speed, and fine precision was proposed. It uses a VCM as an actuator, linear bushings as guides, and a hollow configuration for the laser beam path. The configuration has the advantages of compact size, low inertia, and a large actuating force. The design of the VCM in the dynamic focusing unit was optimized to obtain a high actuating force under the constraints of size, current, and temperature. This force ensures high speed and good tracking capability in the focusing unit. A magnetic circuit model was used in the optimization to predict the magnetic flux of the coil. This model was validated by FEM analysis and experiments after prototyping. After the theoretical design was obtained, a prototype of the dynamic focusing unit was fabricated, and its wide range of motion and fine resolution were confirmed experimentally. Through real-time closed-loop control, the error motion of the VCM was reduced and improved because of its high actuating force. As a result, the resolution of the dynamic focusing unit is 0.2 μm, the moving range is ±8 mm, and the maximum response speed is 40 rad/s along the optical axis, which is also the laser beam path axis. Compared to conventional technology, the unit can make fast and accurate repetitive movements. In conclusion, the proposed dynamic focusing unit with a hollow cylindrical VCM can provide an alternative for wider, faster laser scanning systems. ACKNOWLEDGMENTS
This work was supported by the Industrial Strategic technology development program, 10039982, for the development of next-generation multifunctional machining systems for eco/bio components, funded by the Ministry of Knowledge Economy (MKE, Korea). This paper was also supported by an Ajou University research fellowship. 1 J.
Xie, L. You, S. Huang, Z. Duan, and G. Chen, Opt. Laser Technol. 40, 330 (2008). 2 A. Engelmyer, Proceedings of the 2005 Advanced Laser Applications Conference and Exposition, Ann Arbor, Michigan, 2005. 3 D. Zhiqiang, Z. Zude, A. Wu, and C. Youping, Int. J. Adv. Manuf. Technol. 32, 1211, (2007). 4 S.-K. Lin, C.-M. Wang, and S.-J. Wang, J. Appl. Phys. 103(7), 07F128 (2008). 5 Q. Xu, Rev. Sci. Instrum. 84(5), 055001 (2013). 6 J.-D. Hwang, Y.-K. Kwak, H.-J. Jung, S.-H. Kim and J.-H. Ahn, Int. J. Control Autom. Syst. 6(1), 54 (2008). 7 Y.-T. Liu, R.-F. Fung, and C.-C. Wang, Precis. Eng. 29, 411 (2005). 8 A. M. Madni, J. B. Vuong, M. Lopez, and R. F. Wells, “A smart linear actuator for fuel management system,” Automation Congress, 2002 Proceedings of the 5th Biannual World (IEEE, 2002), Vol. 14, pp. 615–624. 9 S. Q. Lee, Ph.D. thesis, Korea Advanced Institute of Science and Technology, Korea, 2001. 10 J. Jeong, Ph.D. thesis, Korea Advanced Institute of Science and Technology, Korea, 2005. 11 Mathworks Inc., “Matlab Optimization Toolbox,” 2012. 12 C. G. E. Boender and A. H. G. Rinnooy Kan, Math. Program. 37, 59 (1987). 13 D. Hwang, J.-Y. Kim, H.-S. Kim and M. G. Lee, Proceedings of ASPE Spring Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, 2008. 14 Sintec Optronics Homepage, July 22, 2013, see http://www.sintecoptr onics.com/MarkingHeaedDynamic.asp.
Review of Scientific Instruments is copyrighted by the American Institute of Physics (AIP). Redistribution of journal material is subject to the AIP online journal license and/or AIP copyright. For more information, see http://ojps.aip.org/rsio/rsicr.jsp
Design of voice coil motor dynamic focusing unit for a laser scanner Moon G. Lee, Gaeun Kim, Chan-Woo Lee, Soo-Hun Lee, and Yongho Jeona) Department of Mechanical Engineering, Ajou University, San 5, Woncheon-dong, Yeongtong-gu, Suwon-si, Gyeonggi-do 443-749, South Korea
(Received 12 February 2014; accepted 11 March 2014; published online 7 April 2014) Laser scanning systems have been used for material processing tasks such as welding, cutting, marking, and drilling. However, applications have been limited by the small range of motion and slow speed of the focusing unit, which carries the focusing optics. To overcome these limitations, a dynamic focusing system with a long travel range and high speed is needed. In this study, a dynamic focusing unit for a laser scanning system with a voice coil motor (VCM) mechanism is proposed to enable fast speed and a wide focusing range. The VCM has finer precision and higher speed than conventional step motors and a longer travel range than earlier lead zirconium titanate actuators. The system has a hollow configuration to provide a laser beam path. This also makes it compact and transmission-free and gives it low inertia. The VCM’s magnetics are modeled using a permeance model. Its design parameters are determined by optimization using the Broyden–Fletcher–Goldfarb– Shanno method and a sequential quadratic programming algorithm. After the VCM is designed, the dynamic focusing unit is fabricated and assembled. The permeance model is verified by a magnetic finite element method simulation tool, Maxwell 2D and 3D, and by measurement data from a gauss meter. The performance is verified experimentally. The results show a resolution of 0.2 μm and travel range of 16 mm. These are better than those of conventional focusing systems; therefore, this focusing unit can be applied to laser scanning systems for good machining capability. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4869339] I. INTRODUCTION
Laser material processing is currently popular in various industries. Laser scanner systems using a galvanometer are widely used because they can control the laser spot more rapidly and accurately than other scanning devices. In material processing with the laser scanner, the laser spot size should be small and uniform in the entire objective flat field for high-quality processing. Defocus errors in the laser scanner cause power attenuation and dimensional distortion. Thus, it is necessary to control the laser spot size using a laser focusing unit.1 For focusing in the objective flat field, a special optical device such as a dynamic focusing unit is necessary. Without this device, a fixed focusing lens has a fixed focal length and therefore forms a curved image field in air. There are two common solutions.2 The first is to use a special fieldflattening optics with an f-theta objective lens, which is based on specially designed optical lenses or a specific optical layout. However, it is only applicable to a narrow flat field. The second is a dynamic focusing unit, which has a moving lens for variable focusing. This is a unique Z-axis scanning device that shifts the moving lens along its optical axis under the precise control of various actuators. The shifted moving lens exhibits a shifted focal length, varies the image range from the scanning mirror, and then produces an exact focus in a broad flat field.3 The dynamic focusing laser scanning system has two important parts. First, two mirrors reflect the laser beam and a) [email protected]
0034-6748/2014/85(4)/045104/8/$30.00
form a two-dimensional image field. Second, the dynamic focusing unit transfers the moving lens and shifts the focal length. Ultimately, it makes three-dimensional material processing possible. However, the speed of the conventional laser dynamic focusing units cannot follow the velocity of the galvanometers. Moreover, the small travel range of the moving lens shifts the limits of the focal length. Therefore, the dynamic focusing unit is used in very limited applications. To overcome the working range limitations, two solutions have been applied. The first is to change the optical design of the moving lens. As shown in Fig. 1, the large value of the ratio f/L makes it easy to shift the focal length with a short moving lens shift. However, this solution requires a more complex lens deign and precise actuator control. The other is to enlarge the range of motion of the dynamic focusing unit so that the shifted focal length is expanded sufficiently by the large travel range of the moving lens. In this paper, the second solution is adopted. A conceptual design is proposed to lengthen the travel range and increase the scanning speed. This is because the newly designed dynamic focusing unit has a hollow configuration. The VCM’s performance is further enhanced by design optimization to achieve a high actuating force, because a large force can generate high-speed motion, good disturbance immunity, and fine precision. This paper also presents a model of the magnetics of the VCM and the design optimization for a large actuating force. The model is validated by a finite element method (FEM) model and experiment. A prototype of the design was fabricated, and a simple control algorithm was applied to verify the performance of the mechanism.
85, 045104-1
© 2014 AIP Publishing LLC
045104-2
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
FIG. 3. Design of hollow VCM for long travel, high precision, and fast speed.
FIG. 1. Laser scanning system with galvanometric scanner and dynamic focusing unit for laser material processing.
II. CONCEPTUAL DESIGN
Most conventional focusing systems have adopted step motors for the focusing actuators.4 However, step motors are too slow for use in laser scanners. For dynamic focusing, Zhiqiang proposed a moving-coil-type permanent magnet (PM) VCM having a ±5 mm displacement range.3 A similar mechanism for camera anti-shaking was designed and controlled by Lin et al.4 The motors moves the lens along an axis parallel to the laser beam path. The motion is guided by a linear motion (LM) guide. Because the lens holder is connected to the motors with an asymmetric mechanical offset, the stiffness is so low that the system is weak against disturbances such as vibration and manufacturing errors. Xie used galvano actuators to move the focusing lens, but because the actuator’s rotational motion is converted to linear motion by a friction drive,1 the motion is not smooth, and the mechanism is large. Xu designed a small rotary positioner mechanism with VCM and multi-stage compound flexure spring for large working range and high precision. It has good stroke but the positioner was for rotary motion.5 In this paper, a new hollow dynamic focusing unit that outperforms conventional units is proposed, as shown in Fig. 2. It also has a hollow VCM, which is guided by four
linear motion (LM) guides placed along the perimeter of the hollow at equal angles of 90◦ . The laser beam is delivered through the hollow path along the optical axis, which connects the center of the VCM, the four guides, and the lens. This type of VCM configuration has effective usage of the coil current without a non-effective coil length, as shown in Fig. 3, so that it generates a higher actuating force than conventional step motors. Compared with other linear actuators, the VCM simultaneously provides a greater range of motion, high resolution, and faster response time.6–8 Because the VCM is connected directly to the lens holder by four short arms placed along the perimeter of the hollow at equal angles of 90◦ , the actuator directly drives the lens along the optical axis, and the centers of force and motion are on the same axis. These features make it possible to have no transmission mechanism and a shorter moment arm between the lens holder and the VCM; therefore, the unit has low inertia, high stiffness, and a compact size. III. DESIGN OPTIMIZATION OF A VCM DYNAMIC FOCUSING UNIT
The size of the proposed dynamic focusing unit is limited because it should be mountable on an operating laser scanner system. Therefore, the design of the lens transfer system has been optimized for a high response and large travel range in limited space. The objective of the optimal design is to maximize the force and obtain a high lens speed. To optimize the VCM design, several researchers have used a permeance model. The magnetic flux flow is considered to be analogous to the current flow in an electric circuit. The permeance indicates how well the magnetic flux can flow through a magnetic circuit consisting of materials such as air, magnets, and yokes.9, 10 In this study, the magnetics of the VCM are modeled numerically using a similar permeance model. The design was optimized using the numerical model. A. Modeling
1. Modeling of electromagnetic circuit FIG. 2. Conceptual design of novel dynamic focusing unit with symmetric hollow configuration and long range of motion.
Magnetic and electric circuits are analogous, as shown in Table I. The permeance, which is the inverse of the reluctance,
045104-3
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
TABLE I. Analogies between magnetic and electric circuits. Magnetic circuit
Electric circuit
Characteristic
Symbol
Characteristic
Symbol
MMF Reluctance Magnetic flux Flux density Magnetic field Permeability
F (A) R (A/Wb) (Wb) B (T) H (A/m) μ (H/m)
EMF Resistance Current Current density Electric field Resistance coef.
V (V) R () I (A) J (A/m2 ) E (V/m) ρ (m)
indicates how well magnetic flux passes through a magnetic circuit. The proposed axisymmetric model of VCM in Fig. 4(a) is converted to that in Fig. 4(b) according to the permeance method. As a result, the magnetic flux density in the air gap is obtained. The magnetic flux density Bg is obtained as follows: (1) Magnetic flux r flowing from the PM can be viewed as the current source in an electric circuit. The flux, NI from the coil current is similar to that from a voltage source. (2) The permeance of the yoke, air gap, and leakage are considered. The leakage flux other than the air gap flux is considered using the leakage permeance. (3) All the elements can be numerically designed using the design parameters. Finally, the magnetic flux g and magnetic flux density Bg are obtained.
FIG. 5. Design parameters of coil and coil winding. (a) Three closely packed coil wires. (b) Cross section of coil winding.
wc hc 2 × √ −1 +1 , (2) dc 3 dc where lc is the length of the coil and [x] is the largest integer not greater than x.
n=
B. Cost function
2. Coil parameters
The diameter of the coil is related to the coil resistance, which also affects heat generation in the system. To determine the coil diameter, the number of coil turns should be selected. Equations (1) and (2) and Fig. 5 present the numerical design for the coil parameters. Here, dc is the bare coil diameter (only the bare copper), and dc ∗ is the total diameter including the enamel coating; n is the total number of coil turns, which affects the coil resistance Rc . nlc Rc = ρ π , d2 4 c
To obtain high acceleration and high stiffness, it is recommended that the VCM provides a large force. The design was optimized to maximize the acceleration (= force/mass) under constraints. The acceleration is expressed in Eq. (3), and the cost function is the inverse function of the acceleration, as shown in Eq. (4). The object of optimization is to minimize the cost function. For rapid convergence to the final value, the cost function takes a quadratic form. The design parameters to be optimized are tm , lg , ty , and dc . The final optimal parameters will minimize the cost function nBg il F = , m m
(1)
J = min
1 F /m
(3) 2 .
(4)
C. Constraints
1. Geometric constraints
The volume of the VCM is limited by the desired cost and size of the system. Therefore, in the optimal design, the total diameter of the VCM, air gap, and external yoke are limited, as shown in Eqs. (5) and (6). g(1) = FIG. 4. Magnetic analysis models of the VCM. (a) Design parameters of VCM. (b) Magnetic circuit of VCM.
tm + lm + ty − 1.0 < 0, 17[mm]
(5)
w c − lg + 1.0 < 0. 2.5[mm]
(6)
g(2) =
045104-4
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
2. Current limit
The current is limited by the power supply system, and the operating current is usually 1 A. Fmax is the force required to actuate the system and fx is the force when 1 A of current is applied. By using Eq. (7), the maximum current and force can be satisfied. g(3) =
Fmax − 1.0[A] < 0, fx
(7)
where fx is the force constant of the VCM and is equal to nBg lc . FIG. 7. Example convergence of the cost function.
3. Heat dissipation
Heat is generated by the current that flows through the coil resistance. To avoid overheating, the heat dissipation should be larger than the heat generation. In this system, heat generation occurs because of the coil resistance, and heat is dissipated by conduction to a bobbin and convection to air. The heat generation and dissipation are calculated using the thermal circuit shown in Fig. 6. g(4) =
Qs − 1.0 < 0, Qout
(8)
where Qs = i2 Rc , and Qout = Q1out + Q2out + Q3out + Q4out .
nate the optimization process if w
1 n−1 − ≤ w. n−w−2 2
(9)
That is, if Eq. (9) is satisfied, the majority with the same cost functions and design parameters among the w minima is selected as the global optimum. In summary, the total optimization design can be written as 2 1 J = min , (10) F /m
D. Results of optimization
To find the optimal VCM parameters, the Broyden– Fletcher–Goldfarb–Shanno (BFGS) method and the sequential quadratic programming (SQP) algorithm in MATLAB Toolbox were used. The BFGS method is known as a general algorithm for obtaining a search direction. The SQP algorithm is also popular for finding the search step size. They have received considerable attention for their superior rate of convergence to the final value.11 However, the result is not the global optimum. To determine whether a local minimum is the global optimum, the Bayesian simple stopping rule is used.12 If w different local minima have been discovered in n local searches, the Bayesian simple stopping rule is to termi-
FIG. 6. Heat dissipation from coil by conduction and convection. (a) Physical heat emission from coil. (b) Thermal circuit model of heat transfer.
subject to g(i) ≤ 0, i = 1...4 and 0.01 < tm ≤ 17 [mm], 0.01 < lg ≤ 17 [mm], 0.01 < ty ≤ 17 [mm], 0.01 < dc ≤ 3 [mm]. Fig. 7 shows an example convergence of the cost function. The cost function started at 14 random initial positions and converged to 3 local minima. Using the Bayesian stopping rule, the global optima were determined. In Fig. 8, the optimal program converges to the same value at every starting point except for only two points. In these optima, the active constraints are the size and current limitations. All the design parameters converged to the same values. The optimal design parameters were modified for fabrication, as shown in Table II.
FIG. 8. Determination of global optimum from random initial points: n = 14, w = 3.
045104-5
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
TABLE II. Results of design optimization, modified for fabrication. Design variables
TABLE III. Magnetic flux density and force from permeance model, FE analysis, and measured data.
System parameters Parameter
Parameter tm lg ty dc
Value
Parameter
Value
8.5 mm 5 mm 3.5 mm 0.55 mm
Force (N/A) n (coil turns) Bg (flux density) Rc (coil resistance)
3. 054 N/A 219 turns 0.1483 T 1.491
FIG. 9. Prototype of proposed dynamic focusing unit with hollow VCM, lens holder, and LM guides.
Bg Force (N/A)
Calculation
FEM
Gauss meter
148.3 mT 3.054 N/A
157.6 mT 2.802 N/A
151.9 mT ...
IV. EXPERIMENT AND RESULTS
A prototype of the VCM dynamic focusing unit was fabricated according to the optimized parameters. The magnet used in the proposed VCM is of the NdFeB family, which is known to have the highest flux density per unit volume. The ring-type magnets and yokes were attached using an adhesive from Devcon, which was designed for cementing metal pieces together and is a non-magnetic substance unaffected by magnetism. An assembly jig was also used for the magnet and yoke assembly. The jig keeps the magnets from adhering to the side yoke. It is mounted between the yokes until the adhesive material hardens and then slides away after adhesion.13 Fig. 9 shows the fabricated VCM dynamic focusing unit. The linear bushings and VCM bobbin are combined with the lens holder that mounts the focusing lens. The holder is actuated by the VCM, and its motion is guided by an LM guide.
FIG. 10. FE analysis of VCM’s magnetostatics. (a) Magnetic lines of force. (b) Magnetic flux density.
FIG. 11. Magnetic flux density by FE analysis and by measurement. (a) B measurement by Gauss meter. (b) Comparison between FEA and measurement.
045104-6
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
FIG. 12. Experimental setup for testing open loop characteristics.
Each LM guide is comprised of linear bushing (LHFS4), shaft (RSFAD4), and rubber washer (WRBNA) from Misumi USA. Friction coefficient is 0.002–0.006 and the clearance between the bushing and shaft is about 0.004 mm. The linear guide has stick-slip effect because of bushing’s ball contact and rubber washer’s sealing. This will be severe for low speed motion when the guides do not have sufficient parallelism by misalignment. In the laser focusing system, the oscillating laser beam passes through the aperture in the base, the VCM, and the lens in sequence along the same axis. After the prototype was fabricated and before the performance test, the permeance model used for optimization was verified. To validate the model, the magnetic flux density from a FEM analysis by Maxwell (Ansys, Inc.) and measurement data from a TM-701 Gauss meter (KANTEC Co., Ltd.) were compared with that from the model. The results of the comparison in the air gap are shown in Figs. 10 and 11 and Table III. The results verified that the model has good agreement with the real device. In addition to the validation, an experiment was conducted as a performance test and to verify the proposed
FIG. 13. Frequency response from open loop test.
FIG. 14. Experimental setup for performance test with closed loop control.
045104-7
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
FIG. 15. Block diagram for control of dynamic focusing unit.
FIG. 16. Resolution of the dynamic focusing unit.
FIG. 17. Travel range of the dynamic focusing unit.
FIG. 18. Positioning speed test by sinusoidal command input. (a) Amplitude: 5 mm and frequency: 30 rad/s. (b) Amplitude: 3 mm and frequency: 40 rad/s.
045104-8
Lee et al.
Rev. Sci. Instrum. 85, 045104 (2014)
design. The position of the moving lens for focusing is calculated by optical theories. A lookup table based on the ZEMAX model is one of the methods because the shift in the focal length is a nonlinear and discrete function. The error motions due to inevitable disturbances are compensated by simple closed-loop control. In order to investigate the performance of dynamic focusing unit, open loop frequency response was obtained to be used in closed loop control. The experimental setup is shown in Fig. 12 and the results are presented in Fig. 13. To measure the motion of the dynamic focusing unit, a Laser Doppler Vibrometer (LDV) was used. The LDV can simultaneously measure a wide displacement range. Using the output data from the LDV, the displacement of the VCM was measured; a 4122Z VCM amplifier (Copley Controls Corp.) generated a pulse-width modulated signal and supplied it to the VCM. In the results, the stick-slip played a role as stiffness in low frequency region, therefore, the flat curve between 10 and 40 Hz appeared in the magnitude graph. The resonant frequency of the device was about 45 Hz. The experimental setup for closed-loop control is shown in Fig. 13. The closed-loop control is illustrated in Fig. 14; the reference input X indicates the desired displacement of the VCM. In addition to the experimental setup in Fig. 15, the actual displacement of the VCM was measured; the error was also calculated by comparing the input and the measured. For real time closed-loop control, a DS2002/DS2003 A/D converter, DS2102 D/A converter, and DS1005 PPC boards (dSPACE) were used. Using MATLAB and dSPACE, a control panel was also built and the VCM was controlled in real time. A range of motion test to verify the proposed design and a resolution test to confirm the precision of the lens position were conducted. Fig. 16 shows the results of the closed-loop resolution test; the resolution is 0.2 μm. The range of motion of the dynamic focusing unit was ±8 mm, as shown in Fig. 17. The results satisfy industry requirements. After the displacement and resolution were tested, other tests were conducted to verify the smooth motion and high speed of the unit. The results are presented in Figs. 18(a) and 18(b). The measured data demonstrate that it has accurate tracking capability according to the input signal, despite a small tracking error. As a result, the proposed dynamic focusing unit has a positioning speed of 40 rad/s, which is higher than the 18 rad/s of conventional systems.14 The comparison between the conventional and the proposed focusing units are listed in Table IV.14 The proposed unit has superior characteristics compared to the conventional devices, therefore, it can be applied to industry. TABLE IV. Performances comparison between conventional and proposed focusing units.
Beam input aperture Maximum lens travel Typical positioning speed Resolution
Conventional
Proposed
8 mm ±4 mm 18 rad/s Not published
8 mm ±8 mm 40 rad/s 0.2 μm
V. CONCLUSIONS
In this paper, a novel dynamic focusing unit exhibiting a long travel range, high speed, and fine precision was proposed. It uses a VCM as an actuator, linear bushings as guides, and a hollow configuration for the laser beam path. The configuration has the advantages of compact size, low inertia, and a large actuating force. The design of the VCM in the dynamic focusing unit was optimized to obtain a high actuating force under the constraints of size, current, and temperature. This force ensures high speed and good tracking capability in the focusing unit. A magnetic circuit model was used in the optimization to predict the magnetic flux of the coil. This model was validated by FEM analysis and experiments after prototyping. After the theoretical design was obtained, a prototype of the dynamic focusing unit was fabricated, and its wide range of motion and fine resolution were confirmed experimentally. Through real-time closed-loop control, the error motion of the VCM was reduced and improved because of its high actuating force. As a result, the resolution of the dynamic focusing unit is 0.2 μm, the moving range is ±8 mm, and the maximum response speed is 40 rad/s along the optical axis, which is also the laser beam path axis. Compared to conventional technology, the unit can make fast and accurate repetitive movements. In conclusion, the proposed dynamic focusing unit with a hollow cylindrical VCM can provide an alternative for wider, faster laser scanning systems. ACKNOWLEDGMENTS
This work was supported by the Industrial Strategic technology development program, 10039982, for the development of next-generation multifunctional machining systems for eco/bio components, funded by the Ministry of Knowledge Economy (MKE, Korea). This paper was also supported by an Ajou University research fellowship. 1 J.
Xie, L. You, S. Huang, Z. Duan, and G. Chen, Opt. Laser Technol. 40, 330 (2008). 2 A. Engelmyer, Proceedings of the 2005 Advanced Laser Applications Conference and Exposition, Ann Arbor, Michigan, 2005. 3 D. Zhiqiang, Z. Zude, A. Wu, and C. Youping, Int. J. Adv. Manuf. Technol. 32, 1211, (2007). 4 S.-K. Lin, C.-M. Wang, and S.-J. Wang, J. Appl. Phys. 103(7), 07F128 (2008). 5 Q. Xu, Rev. Sci. Instrum. 84(5), 055001 (2013). 6 J.-D. Hwang, Y.-K. Kwak, H.-J. Jung, S.-H. Kim and J.-H. Ahn, Int. J. Control Autom. Syst. 6(1), 54 (2008). 7 Y.-T. Liu, R.-F. Fung, and C.-C. Wang, Precis. Eng. 29, 411 (2005). 8 A. M. Madni, J. B. Vuong, M. Lopez, and R. F. Wells, “A smart linear actuator for fuel management system,” Automation Congress, 2002 Proceedings of the 5th Biannual World (IEEE, 2002), Vol. 14, pp. 615–624. 9 S. Q. Lee, Ph.D. thesis, Korea Advanced Institute of Science and Technology, Korea, 2001. 10 J. Jeong, Ph.D. thesis, Korea Advanced Institute of Science and Technology, Korea, 2005. 11 Mathworks Inc., “Matlab Optimization Toolbox,” 2012. 12 C. G. E. Boender and A. H. G. Rinnooy Kan, Math. Program. 37, 59 (1987). 13 D. Hwang, J.-Y. Kim, H.-S. Kim and M. G. Lee, Proceedings of ASPE Spring Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, 2008. 14 Sintec Optronics Homepage, July 22, 2013, see http://www.sintecoptr onics.com/MarkingHeaedDynamic.asp.
Review of Scientific Instruments is copyrighted by the American Institute of Physics (AIP). Redistribution of journal material is subject to the AIP online journal license and/or AIP copyright. For more information, see http://ojps.aip.org/rsio/rsicr.jsp
