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