1
Force Estimation MethodFor a Magnetic Lead-Screw-Driven Linear Actuator
BG-05
Akira Heya* Yoshihiro Nakata Masahiko Sakai
Hiroshi Ishiguro Katsuhiro Hirata
Osaka University, Japan
2
Introduction
Magnetic lead-screw-driven linear actuator
Force estimation from magnetic phase difference
Experimental results
Conclusion
Contents
3
Introduction
Magnetic lead-screw-driven linear actuator
Force estimation from magnetic phase difference
Experimental results
Conclusion
Contents
4Introduction
Nextage(Kawata Robots)
HAL(CYBERDYNE)
ASIMO(HONDA)
Collaborative robots and exoskeleton robots
• Safety for human-robot interaction
• Need force-controllable actuators
Lightweight, compact, and backdrivable
5Force-controllable actuator
AdvantageNon-contact force transformation• High-efficiency for driving, low noise and vibration• Backdrivability based on magnetic spring• Force limiter function when overloaded • Maintenance-free• Generation of the particle is suppred• Usable under several environment
Transport device for manufacture of medicine,cosmetic, and food
Magnetic lead-screw-driven linear actuator (MLSDLA)• Consists of a magnetic lead screw (MLS) and rotary motor
Slide screw
NS
NS
MLS
6Comparison of conventional MLS
Conventional MLS• Helical permanent magnets radially• Too many permanent magnet pieces magnetized axially
Productivity is low / Downsizing is difficult
[1] J. Wang et al., “Analysis of a Magnetic Screw for High Force Density Linear Electromagnetic Actuators”, 2011[2] T. Shinshi et al., “A New Magnetic Lead Screw and Its Basic Characteristics”, 1998[3] Y. Fujimoto et al., “Direct-drive characteristics of radial-gap helical motors”, 2014[4] Z. Ling et al., “Design of a New Magnetic Screw With Discretized PMs”, 2016
(a) [1] (b) [2] (c) [3] (d) [4]
NutHelical PM
magnetized radially
Helical PM
magnetized radially
Helical PM pieces
magnetized radially
PM pieces
magnetized axially
ScrewHelical PM
magnetized radiallySUY
Helical PM
magnetized radially
PM pieces
magnetized axially
7Proposed MLS■ Conventional structure
Nut
Screw
Backyoke
Air gap
Non-magnetic core
Thread B
Thread A
PM
Nut
Screw
PM
Screw
Nut
Spiral-shaped PM
Arc-shaped PM
■ Proposed structure• Consists of arc-shaped permanent magnets and magnetic poleSimple structure and easy assembly
Magnetic poleBackyoke
8
Linear
actuator
Force
sensor
Magnetic
spring
Research purpose
Force control using force sensor
• Increase system size and weight
Static force of the MLS can be estimated bymeasurement of translational and rotational displacementwithout a force sensor
Propose a force estimation method for MLSDLA
p, θf (p,θ)
Linear
actuator
9
Introduction
Magnetic lead-screw-driven linear actuator
Force estimation from magnetic phase difference
Experimental results
Conclusion
Contents
10
Rotary encoder
Rotary motor
Screw
NutLinear encoder
Linear rail
Base plate
MLSDLA
Basic structure
• Magnetic lead screw (MLS)
• DC geared motor
• Rotary encoder
• Linear encoder
*Matsuoka et al., “Proposal of a Magnetic Lead Screw Actuator without Helical Permanent Magnets”, Journal of the Japan Society of Applied Electromagnetics and Mechanics, 2017 (in Japanese)
Magnetic Lead-Screw-DrivenLinear Actuator
Linear guide
11MLS without spiral-shaped PM
Nut
Screw
(Double thread)
Thread B
(for outward magnetic flux)
Backyoke
Magnetic pole
x
y
z
Thread A
(for inward magnetic flux)
PM magnetized radially inward
x
y
PM magnetized radially outward
Basic structure
• Nut part
Magnetic pole, PM, and backyoke
• Screw part
Double-threaded screw
12
Air gap
Magnetization direction
1. Relative displacement by rotation of the screw part
2. Restoring force caused by relative displacement
3. Linear motion caused by restoring force
Operating principle
Back yoke
PM
Magnetic pole
Nut
Screw
Thread B
Thread A
F = F(p)
MLS without spiral-shaped PM
Rotationalmotion
13Prototype
MLS
MLSDLA
NutScrewRotary motor Linear rail
Rotary encoder Linear encoder
Specification
Design based on magnetic field analysis using 3D-FEM
• Maximum force : 66.1 N
• Entire length : 250 mm
• Stroke : 55 mm
• Mass of the mover : 287 g3-D mesh model
(except the air region)NutScrew
14
Driving motion
• Screw part : Rotational motion by rotary motor
• Nut part : Linear motion by magnetic force
Operation of the MLSDLA
Prototype
15
Introduction
Magnetic lead-screw-driven linear actuator
Force estimation from magnetic phase difference
Experimental results and discussion
Conclusion
Contents
16Force estimation method
Overview
1. Static force characteristics of the MLS are defined based on rotational and translational magnetic phase difference
2. Magnetic phase difference are calculated by the position of the nut and the angle of the screw
3. Relationship of the static force and magnetic phase difference is expressed by polynomial approximation using measured data
4. Output force considered the dynamics of the MLS is estimated by the expressed static force and the friction force
17Force estimation method
Static force based on magnetic phase difference
Magnetic phase differenceRelative displacement between the nut and the screw
• Rotational direction 𝜑𝜃• Translational direction 𝜑𝑝
Back yoke
Magnetic pole
Nut
𝜑𝑝
x
y
𝜑𝜃
z
y
NutScrew
Screw
18
pL
p
2
pgg p ),(
𝐹𝑠:Estimated static force𝐿 :Lead of the screw
:Rotational angle of the screw𝑝 :Position of the nut
x
y
𝜑𝜃
z
y
NutScrew
Rotational magnetic phase difference
No relative displacement
Force estimation method
Dynamics of the MLS
Static force of the MLS
ˆ ( ( , ))s s gF F p
ms ms s fM p C p F F
Estimated output forceconsidered the dynamics of the MLS
ˆ ˆ ( ( , ))ms s g fF F p F
19
Introduction
Magnetic lead-screw-driven linear actuator
Force estimation from magnetic phase difference
Experimental results and discussion
Conclusion
Contents
20
Load cell
Linear stage
Nut Rotary motorScrew
Linear encoder Rotary encoder
Micro computer for calculation of estimated force PC
Measured position
Measuredrotation angleMeasured force
Estimatedforce
Amplifier
Experimental setup
Experimental environmentOutput forceMeasured by load cell (LCM201-100N, Omega engineering)Estimated forceCalculated by the micro computer using proposed method
21Parameter identification
Estimated force expressed as a polynomial approximationusing the least-squares method
Difference between the analysis and the measured values
• Manufacturing tolerances of the prototype• Layer of binding material used for fixing the permanent magnets
Measured and analytical static force
5 4 3 2ˆ 0.378 0.209 8.51 2.59 47.6 4.28sF
-80
-40
0
40
80
-270 -180 -90 0 90 180 270
Fo
rce
[N]
Angle [deg.]
Analytical Measured Fitting curve
22Results and discussion
Comparison
Measured and estimated forceare in good agreement
Mean absolute error
2.3 N-80
-40
0
40
80
0 3 6 9 12 15
Fo
rce [
N]
Time [s]
Measured Estimated
23Results and discussion
Comparison
Measured and estimated forceare in good agreement
Mean absolute error
2.3 N
Limitation
Fitting error
Caused by least-squares approximation
Delay at start and peaks
Cannot estimate forces that exceed the static frictional force
Future work
Reducing of the static frictionExperimental results
-80
-40
0
40
80
0 3 6 9 12 15
Forc
e [
N]
Measured Estimated
0
10
20
30
0 3 6 9 12 15E
rro
r [N
]
-200
0
200
400
600
-4
0
4
8
12
0 3 6 9 12 15
Angle
[deg
.]
Po
siti
on
[m
m]
Time [s]
Position Angle
24Conclusion
Proposal of a force estimation method using the magnetic phase difference in the MLSDLA
• Fabricated the prototype of the MLSDLA
• Derived the force estimation equation considering dynamics
• Parameter identification of the static force characteristics
Experimental results
Measured and estimated force are in good agreement
Future work
Reducing of the static friction in the prototype for improving
the estimation accuracy
25
Thank you for your attention!
26Feed screw mechanism
*1 *2 *3
Slide screw Ball screw SPP screw MLS
Surface contact Point contact Mediate a fluid Non-contact
Noise/Friction
Efficiency
Big Small
HighLow
Transmission
Advantage of magnetic lead screw (MLS)• High-efficiency for driving• Backdrivability based on magnetic spring• Maintenance-free• Usable under several environment
*1: http://www.japanmetal.com/seihin/seihin3.php?id=307 *2: http://www.touhoku.co.jp/original41.html *3: Static Pressure Pneumatic (SPP) screw http://www.toshiba-machine.co.jp/jp/technology/tech_catalog/f3.html
27
Advantage of magnetic lead-screw-driven linear actuator (MLSDLA)
• Force limiter function when overloaded
• Integrated a linear driving mechanism and elastic component
Feed screw mechanism
*1 *2 *3
Slide screw Ball screw SPP screw MLS
Surface contact Point contact Mediate a fluid Non-contact
Noise/Friction
Efficiency
Transmission
*1: http://www.japanmetal.com/seihin/seihin3.php?id=307 *2: http://www.touhoku.co.jp/original41.html *3: Static Pressure Pneumatic (SPP) screw http://www.toshiba-machine.co.jp/jp/technology/tech_catalog/f3.html
Big Small
HighLow
28Actuator with flexible motion
・Backdrivable・Controllability
・Low power
・Backdrivable・High power
・Increase system size
・Backdrivable・High power・Compact
・Friction・Noise
Improve a feed screw mechanism
Linear vernier motor (Nakata, 2012)Airic’s Arm(FESTO) THOR Linear SEA
(Victor L. Orekhov, 2015)
Advantage
Disadvantage
Feed screw
Mechanicalspring
Stator
Mover
Linear electromagneticactuator
Pneumatic actuatorLinear series elastic actuator
29試作機の製作誤差
1.6
1.5
tw
1.6
0.3
6
1.5
3
6
Screw
1.50.91.5
10
Back yoke
Permanent magnet
Magnetic pole
1.5 (-0.1)
1.5
tw1.75 (+0.15)
6
1.5
3
6
Screw
1.50.91.5
10
P
0.2(-0.1)
実機寸法に基づき再度モデル化(試作モデル)
■試作機断面図 Back yoke
PM
Magnetic pole
P
30従来の磁気ねじの比較
Nut partRadial magnetized
Helical PM
Radial magnetized
Helical PM
Radial magnetized
Helical PM pieces
Radial magnetized
PM pieces
Screw partRadial magnetized
Helical PMSUY
Radial magnetized
Helical PM
Parallel magnetized
PM pieces
(a) [1] (b) [2] (c) [3] (d) [4]
[1] Wang et. al., ”Analusis of a Magnetic Screw for High Force Density Linear Electromagnetic Actuators”,IEEE, Vol.47, No.10, 2011
[2] 進士ら:「磁気ねじをもちいた機構の起動時の特性と位置決め精度」,日本機械学会論文集64巻625号,1999
[3] 藤本ら:「ラジアルギャップ型ヘリカルモータのダイレクトドライブ特性について」,IEEJ, MEC-14-136, 2014
[4] Ling et. al., “Design of a New Magnetic Screw With Discretized PMs ”, IEEE, Vol.26, No.4, 2016
Radial magnetized PM Parallel magnetized PM
31従来の磁気ねじの比較
・ 螺旋型磁石が使われている・ 磁石小片を多数用いている
生産性が低く,小型化が困難
Nut partRadial magnetized
Helical PM
Radial magnetized
Helical PM
Radial magnetized
Helical PM pieces
Radial magnetized
PM pieces
Screw partRadial magnetized
Helical PMSUY
Radial magnetized
Helical PM
Parallel magnetized
PM pieces
(a) [1] (b) [2] (c) [3] (d) [4]
[1] Wang et. al., ”Analusis of a Magnetic Screw for High Force Density Linear Electromagnetic Actuators”,IEEE, Vol.47, No.10, 2011
[2] 進士ら:「磁気ねじをもちいた機構の起動時の特性と位置決め精度」,日本機械学会論文集64巻625号,1999
[3] 藤本ら:「ラジアルギャップ型ヘリカルモータのダイレクトドライブ特性について」,IEEJ, MEC-14-136, 2014
[4] Ling et. al., “Design of a New Magnetic Screw With Discretized PMs ”, IEEE, Vol.26, No.4, 2016
32磁気ねじの構造
磁極部材を一体成型できるため,ピッチの精度管理が容易
33発生推力の簡易算出
多項式近似を用いた推力算出
角度もしくは位置により定まる多項式より算出
• 5次成分までの考慮が必要
Thrust expressed by Polynomial approximation
𝐹 = 𝑎5 5 + 𝑎4
4 + 𝑎3 3 + 𝑎2
2 + 𝑎1 𝑔+ 𝑎0
Order Correlation
3 0.983
5 0.999
7 0.999
9 0.999
34螺旋型永久磁石を用いない磁気ねじ