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서보 모터를 이용한 전자 가변 밸브 시스템의 제어 성능 시험

조충일1, 안형준2,#

Control Performance Test of an Electrically-Controlled Variable Valve Timing System Using Servo Motors

Chung-Il Cho1, Hyeong-Joon Ahn2,#
Journal of the Korean Society for Precision Engineering 2017;34(6):397-403.
Published online: June 1, 2017

1 숭실대학교 일반대학원 융합소프트웨어학과

2 숭실대학교 기계공학과

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#E-mail: ahj123@ssu.ac.kr, TEL: +82-2-820-0654, FAX: +82-2-820-0668
• Received: February 22, 2017   • Revised: March 8, 2017   • Accepted: April 12, 2017

Copyright © The Korean Society for Precision Engineering

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  • Recently, technologies related to green cars are gaining attention. A variable valve-timing system (VVT) is widely used in internal-combustion engines to improve fuel efficiency and engine performance by controlling the valve open-close timing. Since conventional hydraulically controlled VVT has problems, such as slow response and low efficiency, an electrically controlled variable valve timing (ECVVT) system was developed as an alternative the conventional VVT. This paper presents a performance test rig for an ECVVT system using servo motors. The performance test rig consists of an ECVVT module with a cycloid reducer, an engine cylinder block, a driving part, and a motion controller. A small servo motor drives the ECVVT module through the cycloid gear, while a large servo motor drives the camshafts by means of a timing belt. We carried out simulations using a mathematical model of the ECVVT module, cam shaft, valve, and motion control. We then built a performance test rig for the ECVVT system, and did experiment of cam phase variations of the ECVVT system to confirm its performance.
  • KEYWORDS: Electrically-controlled variable valve timing system, Camshafts phase, Control performance test
  • KEYWORDS: 전자 가변 밸브 시스템, 캠축 위상, 제어 성능 시험

bm

Viscous friction coefficient

c 1

Damping coefficient of 1st mass

c2

Damping coefficient of 2nd mass

D 1

Derivative gain of position control

D 2

Derivative gain of speed contro

I

Current of armature circuit

Jc

Cam moment of inertia

Jeq

Equilibrium moment of inertia

Jm

Engine moment of inertia

k 1

Spring coefficient of 1st mass

k 2

Spring coefficient of 2nd mass

kt

Torque constant of motor

kv

Voltage constant

L

Inductance of armature circuit

M 1

1st mass of valve system

M 2

2nd mass of valve system

n 1

Angular speed of eccentric input shaft

n 2

Angular speed of output shaft

n 3

Angular speed of outer gear (Housing)

P 1

Proportional gain of position control

P 2

Proportional gain of speed control

R

Resistance of armature circuit

Tm

Torque of the motor

Tr

Resistant torque

Va

Voltage of armature circuit

W

Total work generated by servo motor

x

Displacement of 1st mass in the valve system

y

Displacement of 2nd mass in the valve system

z

Gear ratio of cycloid reducer

z g1

Number of tooth of 1st stage cycloid gear

z g2

Number of tooth of 2nd stage cycloid gear

α

Rotation angle of camshaft

λ

Numerical coefficient

η

Deflections of the springs

ϕ

Rotation angle of servo motor
차량의 환경 문제에 대한 규제가 날이 갈수록 엄격해짐에 따라 이와 관련한 다양한 기술이 개발되고 있다. 이 중에서도 연속가변 밸브(Continuous Variable Valve Timing, CVVT) 시스템은 밸브의 개폐 시기를 조절하여 엔진의 성능 및 효율을 향상시키는 기술로, 내연기관에 널리 사용되고 있다.1
가변 밸브 제어 시스템에 대한 연구는 캠축의 회전을 제어하는 기초적인 방식부터 최근의 캠축이 없는 제어까지 다양한 영역으로 확대되고 있다. Wislati2은 캠축을 대신하는 전자석을 이용한 액추에이터 방식을 연구하였고, Wong3와 Liu4, Turner5은 순유압 방식으로 밸브의 개폐 시기 및 기간, 양정까지 제어가 가능한 완전 가변 밸브 기구(Fully Variable Valve Timing, FVVT)을 연구하여 현재는 차세대 소자인 압전 액추에이터 방식까지 연구가 진행되고 있다.6 국내의 경우, 전자기 밸브(Electro-Mechanical Valve, EMV)를 가변 밸브 시스템에 장착하여 제어하는 기술에 관한 연구가 현대자동차를 중심으로 2000년대 초기에 시작되었으며, 최근에는 캠-기계식 밸브 변위 가변 기술을 상용화하는 연구가 진행되고 있다.6
기존 캠-기계식에 널리 사용되던 유압식 제어 방식은 응답 속도가 느리고 효율이 좋지 않은 단점이 있다. 이를 개선하기 위하여 모터를 이용한 전자 가변 밸브 시스템(Electrically Controlled Variable Valve Timing System, ECVVT)이 개발되었지만 제어 성능 검증 연구는 미흡한 편이다.7
이 논문은 서보 모터를 이용한 전자 가변 밸브 시스템의 제어 성능 시험에 관한 것이다. 가변 밸브 시스템의 제어 성능 시험 장치는 두 개의 크기가 다른 서보 모터를 이용하여 캠 축과 위상 가변부를 구동하고, 각 서보 모터의 토크와 회전 속도를 측정하여 제어 성능 파악이 용이하도록 구성한다. 위상 가변부의 감속 장치로 이단 사이클로이드 감속기를 사용하고, 캠축 구동을 위해서는 타이밍 벨트를 사용한다. 서보 모터, 위상 가변부, 캠축, 밸브 그리고 제어기의 수학적 모델을 바탕으로 ECVVT 시스템의 모의 시험을 수행한다. 마지막으로 ECVVT 제어 성능 시험 장치를 구성하고 서보 모터 구동을 통해 캠축의 상대적인 위상 변화를 실험적으로 확인한다.
전자 가변 밸브 시스템은 Fig. 1과 같이 크게 위상 가변부(ECVVT Module), 실린더 헤드 블록(Cylinder Head Block), 구동부(Driving Part), 그리고 모션 제어기(Motion Controller)로 구성된다.
Fig. 1

Schematic diagram of the ECVVT system

KSPE_2017_v34n6_397_f001.jpg
위상 가변부는 소형 서보 모터와 이단 사이클로이드 감속기로 구성되며, 서보 모터가 회전함으로써 감속기를 통해 캠 축의 위상을 조절한다. 실린더 헤드 블록은 캠축과 캠 포지션 센서를 포함하며, 모터의 속도 제어에 의한 캠 축 사이의 위상 변화를 측정할 수 있다. 캠 축은 구동부의 중형 서보 모터와 타이밍 벨트로 연결되어 일정한 속도로 회전한다. 모션 제어기는 각 서보 모터의 속도를 제어하며 캠 위상을 측정하여 궤환제어함으로써 밸브 시스템의 개폐 시간을 조절한다.
이 논문의ECVVT 시스템은 Fig. 2와 같은 이단사이클로이드 감속기를 적용한다. 사이클로이드 감속기는 일반 평치차 감속기에 비해 작은 크기로 큰 감속비를 얻을 수 있는 장점을 가지고 있다.8 ECVVT에 적용되는 사이클로이드 감속기는 크랭크축과 체인으로 연결되어 캠 축을 구동하기 위한 스프라켓과 2단 사이클로이드 디스크, 그리고 외측기어 하우징과 입력 편심축 및 출력 축으로 구성된다. 사이클로이드 디스크와 핀-롤러는 여러 점에서 접촉하여 하중이 분산되기 때문에 강성이 높고 내충격성이 좋아 수명이 길고 효율이 좋다.7,8
Fig. 2

Structure of the cycloid reducer for the ECVVT

KSPE_2017_v34n6_397_f002.jpg
1단과 2단 감속기가 하나의 입력 편심축을 공유하며 고정된 외측기어 하우징과 출력 축의 사이클로이드 치형과 접촉함으로써 감속이 이루어진다. ECVVT에 사용된 사이클로이드 감속기의 원리를 개략적으로 표현하면 Fig. 3과 같으며 1단 사이클로이드 감속비는 식(1)과 같으며, 2단 사이클로이드 감속비는 식(2)로 표현된다.
(1)
n2=-n1/zg1
(2)
zg2=-n3-n1/n3-n2
Fig. 3

Operation principle of the cycloid reducer

KSPE_2017_v34n6_397_f003.jpg
식(1)과 식(2)를 이용하여 최종 감속비를 구하면 다음의 식(3)과 같이 정리되며, 각 감속기의 잇수 곱으로 큰 감속비를 얻을 수 있으며, 1단과 2단의 잇수 차이를 줄일수록 더 큰 감속비를 얻을 수 있다.
(3)
z=-zg1zg2+1zg1-zg2
4.1 밸브의 움직임을 고려한 동적 모델링
밸브의 움직임은 라그랑지(Lagrange) 방정식에 의해 운동에너지와 위치 에너지, 그리고 레일리(Rayleigh) 함수와 전체 일을 고려하여 유도한다.9
캠 축을 따라 움직이는 밸브의 질량을 M1, M2로 가정하고 캠축의 회전 각도 α가 식(4)와 같이 회전 각도에 대한 함수로 정의될 때, 질량 M1의 이동거리 y에 관한 식(5)를 얻을 수 있다.
(4)
y=y(α)
(5)
y˙=y'αα˙
캠 축과 결합하여 회전하는 감속기의 감속비가 z=α˙/φ˙일 때, 서보 모터에 의하여 발생한 전체 일 W는 식(6)과 같다.
(6)
δW=Tmδφ-Trδα=Tm/z-Trδα
모터의 토크 Tm는 전류 I에 비례하며 식(7)로 정의할 수 있다.
(7)
Tm=ktI
저항 토크 Tr은 캠 축의 각속도 α에 비례하므로 다음의 식(8)과 같이 쓸 수 있다.
(8)
Tr=λα˙
위의 식(4)부터 식(8)을 정리하면 전체 토크와 캠 축의 가속도에 관한 두개의 미분 방정식인 식(9)를 얻을 수 있다. 여기서, Jeq ≡ Jc + Jm이다.
(9)
Ttotal=Tm-Tr=Jeq+M1y'2α¨+M1y'y''α˙2  +k1y''y-x+η+c1y'(y'α˙-x˙)]x¨=1M2[-k1+k2x+k1y-c1+c2x˙+c1y'α˙]
4.2 캠 형상을 고려한 밸브 모델링
밸브는 굴곡 형상을 가진 캠의 회전에 의하여 개폐를 반복한다. 캠의 형상은 사용 목적에 따라 다양하며, 이 형상에 따라 밸브의 개폐 속도 차이가 있다. 캠축이 회전하는 동안 캠 표면의 기준점에 대한 밸브의 상하운동을 곡선으로 표현한 것을 캠 곡선(Cam Profile)이라 하며, 일반적으로 단순한 운동 표현을 위한 캠 곡선으로 주로 사다리꼴, 사이클로이드, 단일 조화 함수, 다항식 곡선 등의 수학적 모델로 표현되나 자동차 엔진의 고속회전을 위한 캠곡선은 고차 다항식, 고차 조화 성분 등이 사용되고 있다.10 이 논문에서는 Fig. 4의 다항식 형상 곡선을 이용하여 캠 축의 회전에 따른 밸브의 속도 변화를 표현한다.
Fig. 4

Cam profile

KSPE_2017_v34n6_397_f004.jpg
4.3 모터의 간략 모델
서보 모터는 이상적인 동작을 한다고 가정하여 DC 모터로 근사하여 모델링하였다. 모터의 아마추어 회로 전압 Va를 식(10)으로 정의하며, 모터의 회전 토크 Tm는 식(11)로 표현할 수 있다.
(10)
Va=RI+LdIdt+kvφ˙
(11)
Tm=Jmθ¨t+bmθ˙t=ktI
5.1 제어 블럭선도
ECVVT시스템은 Fig. 5와 같은 블럭선도에 따라 캠축의 위상을 제어한다.11,12 엔진이 일정한 속도로 회전함에 따라 두 개의 캠축이 함께 회전하고, 두 캠 축은 동일한 위상을 가진다. 이 때, 사용자가 목표 위상 각도를 입력하면 위상 제어기가 적절한 모터 속도 명령을 생성하고 모터 속도 제어기가 모터의 아마추어 전압을 계산한다. 응답 속도는 각 PD 제어이득의 설정에 따라 달라지며, 최종적으로 캠 축의 위상이 변화한다.
Fig. 5

Block diagram of the ECVVT system

KSPE_2017_v34n6_397_f005.jpg
5.2 모의 시험의 결과
수학 모델을 바탕으로 모의 시험을 진행하여 Fig. 6과 같이 제어 이득 변화에 따른 제어 응답의 변화를 확인하였다. 캠 축이 1,000 RPM으로 일정하게 회전하도록 설정하고, 10도의 목표 위상을 입력한 후, 위상 제어기와 모터 속도 제어기의 제어 이득을 각각 변화시켜 모의 시험을 수행하였다.
Fig. 6

Responses of ECVVT system according to control gain variations

KSPE_2017_v34n6_397_f006.jpg
Fig. 6(a)는 위상 제어기의 제어 이득을 고정하고, 속도 제어기의 제어 이득을 변화시킨 결과로 응답 속도 변화가 미미하였다. Fig. 6(b)는 속도 제어기의 제어 이득을 고정하고, 위상 제어기의 제어 이득을 변화시킨 결과로서 응답 속도의 차이가 현저하게 나타났다.
6.1 구성
Table 1의 사양의 부품들을 이용하여 Fig. 7과 같이 전자 가변 밸브 시스템의 제어 성능 시험 장치를 구성하였다. 제어 성능 시험 장치는 소형 서보 모터와 감속기로 이루어진 위상 가변부(ECVVT Module), 캠축을 포함하는 실린더 헤드 블록(Cylinder Head Block), 제어부 (Motion Controller), 그리고 중형 서보 모터와 구동축, 타이밍 벨트로 이루어진 구동부(Driving Part)로 구성된다.13
Table 1

Part specification of the ECVVT system

Table 1
Part name Specification Value
Cylinder head block
(θ−1.8 2.0/2.4)		 Torque
(at 4600 RPM)		 198 Nm
Servomotor
(Driving part)		 Rated output 1500 W
Rated torque 7.15 Nm
Max. torque 21.5 Nm
Servomotor
(ECVVT module)		 Rated output 200 W
Rated torque 0.64 Nm
Max. torque 1.91 Nm
Cycloid reducer Gear ratio 1:100
IR position sensor Measurable range 20 - 45 mm
Sampling period 0.33 ms
Cam position sensor Measurable range 0 - 5 mm
Controller 80/240 Mhz Turbo PMAC2
Fig. 7

Performance test rig of the ECVVT system

KSPE_2017_v34n6_397_f007.jpg
중형 서보 모터는 실제 엔진의 크랭크축과 같은 역할을 하며 그 구동력을 Fig. 8의 구동축(Driving Shaft)과 타이밍 벨트(Timing Belt)를 통해 Fig. 9의 사이클로이드 감속기로 전달한다.
Fig. 8

Timing belt for power transfer

KSPE_2017_v34n6_397_f008.jpg
Fig. 9

Camshafts connected with timing belt

KSPE_2017_v34n6_397_f009.jpg
소형 서보 모터는 Fig. 9와 같이 사이클로이드 감속기의 입력축(Input Shaft)에 결합되며, 사이클로이드 감속기의 감속비에 따라 출력 축(Output Shaft)의 속도를 변화시켜 캠축의 회전 각도(위상)를 변화시킨다.
6.2 개루프 ECVVT 구동
캠 축 위상 변화 특성을 파악하기 위해 캠 축 위상의 궤환 제어없이 서보 모터의 속도 조절을 이용한 개루프 위상 제어를 수행하였다. 중형 서보 모터를 통해 캠 축을 일정한 속도로 회전시키고, 위상 가변부의 소형 서보 모터의 상대 속도를 변화시켜 캠 축의 위상 변화를 확인하였다.
750 RPM의 캠축 회전 속도와 30도의 목표 위상을 입력할 때 각 서보 모터의 구동에 따른 응답 특성을 Figs. 10부터 12에 나타냈다.
Fig. 10

Variation of motor rotations during control

KSPE_2017_v34n6_397_f010.jpg
Fig. 11

Variation of motor torques during control

KSPE_2017_v34n6_397_f011.jpg
Fig. 12

Valve displacement variation during control

KSPE_2017_v34n6_397_f012.jpg
제어 입력에 따른 서보 모터의 각도 즉 위상 변화를 Fig. 10에나타냈고, 소요되는 서보 모터의 토크를 Fig. 11에 나타냈다. 구동부의 중형 서보 모터의 토크는 0.8 Nm로 거의 일정하게 유지되나 위상 가변부의 소형 서보 모터의 토크는 캠 축의 형상과 밸브의 움직임으로 인하여 상대적으로 크게 변동한다. Fig. 12에 밸브의 개폐 상태를 나타내었다. Fig. 12(a)는 모터가 동작하는 전체 시간 동안 밸브의 개폐 상태를 나타낸 것이며, Fig. 12(b)는 위상 변화가 일어나는 시점을 확대한 그래프이다. 0.5초에서 1초 사이에 위상 가변부의 서보 모터 회전 속도가 증가함으로써 밸브가 기준 축에 비해 빠른 시기에 개폐한다. 또한 3초에서 3.5초 사이에는 위상 가변부의 서보 모터 회전 속도가 감소함에 따라 밸브의 개폐 시기가 기준 축과 동일한 상태로 복귀한다.
사이클로이드 감속기가 적용된 전자 가변 밸브 제어 시스템에 대하여 수학적 모델링을 수행하고 제어 모의 시험을 진행하여 시스템의 제어 특성을 파악하였다. 또한 전자 가변 밸브 시스템의 제어 성능 시험 장치를 구성하고, ECVVT 모듈의 모터 회전 속도 변경에 따른 캠 축의 위상 제어 특성을 확인하였다. 이후로 센서를 이용한 캠축들의 위상을 측정하고 궤환 제어를 적용하여 전자 가변 밸브 시스템의 동적 성능을 시험한다. 또한, 지속적인 연구 진행을 위해 동적 성능을 실시간으로 분석할 수 있는 모니터링 시스템을 구현할 것이다.
본 논문은 중소기업청의 2013년도 산학연협력 기술개발사업(No. C0119673) 의 지원으로 수행되었습니다.
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Control Performance Test of an Electrically-Controlled Variable Valve Timing System Using Servo Motors
J. Korean Soc. Precis. Eng.. 2017;34(6):397-403.   Published online June 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.6.397
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Control Performance Test of an Electrically-Controlled Variable Valve Timing System Using Servo Motors
J. Korean Soc. Precis. Eng.. 2017;34(6):397-403.   Published online June 1, 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.6.397
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Control Performance Test of an Electrically-Controlled Variable Valve Timing System Using Servo Motors
Image Image Image Image Image Image Image Image Image Image Image Image
Fig. 1 Schematic diagram of the ECVVT system
Fig. 2 Structure of the cycloid reducer for the ECVVT
Fig. 3 Operation principle of the cycloid reducer
Fig. 4 Cam profile
Fig. 5 Block diagram of the ECVVT system
Fig. 6 Responses of ECVVT system according to control gain variations
Fig. 7 Performance test rig of the ECVVT system
Fig. 8 Timing belt for power transfer
Fig. 9 Camshafts connected with timing belt
Fig. 10 Variation of motor rotations during control
Fig. 11 Variation of motor torques during control
Fig. 12 Valve displacement variation during control

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Control Performance Test of an Electrically-Controlled Variable Valve Timing System Using Servo Motors
Part name Specification Value
Cylinder head block
(θ−1.8 2.0/2.4)		 Torque
(at 4600 RPM)		 198 Nm
Servomotor
(Driving part)		 Rated output 1500 W
Rated torque 7.15 Nm
Max. torque 21.5 Nm
Servomotor
(ECVVT module)		 Rated output 200 W
Rated torque 0.64 Nm
Max. torque 1.91 Nm
Cycloid reducer Gear ratio 1:100
IR position sensor Measurable range 20 - 45 mm
Sampling period 0.33 ms
Cam position sensor Measurable range 0 - 5 mm
Controller 80/240 Mhz Turbo PMAC2
Table 1 Part specification of the ECVVT system

Table 1

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