vertical dynamics - ## 전산설계자동화 실험실 ## 방문해 주셔서...
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김성수
Vertical Dynamics
Vehicle Dynamics (Lecture 5)
2
Vertical Vehicle Performance
Vertical Dynamics and its applications
3
Vehicle Ride Performance Model
Vertical Dynamics and ride evaluation
승차감을 객관적 지수로 평가할 수 있는 방법 활용을 위한 수직 동역학 모델
4
Vertical Vehicle Dynamics
Ride evaluation• ISO 2631 (인체 진동 노출 평가 기준, 1974년 제정)• 노출한계 범위: 안전이나 건강에 치명적인 영향을 줄 수 있는 범위• 피로 및 작업능률 저하 범위: 운전 등과 같은 작업능률 저하 범위• 안락감 감소 범위: 차안에서의 독서 식사 등의 행동에서 안락감이 감소되는
범위
• 앉은자세, 선 자세 4-8Hz z방향 가속도에 민감• 누운자세 1-2 Hz에서 민감
5
Road roughness
Vertical Vehicle Dynamics
G: 거칠기 계수-거칠기 정도를 나타내는 거칠기 진폭W: 파동정도를 나타내는 파동계수 - 스펙트럼 밀도함수의 기울기
스펙트럼 밀도 함수
6
Road roughness
Vertical Vehicle Dynamics
스펙트럼 밀도 함수는 일정속도 v 로 차량이주행할 때 주파수 f 의 식으로 표시 가능
동일한 도로면을 달릴때도 속도에 따라서 가진입력이 달라지는 것을 알수 있음.
7
Road roughness
Vertical Vehicle Dynamics
8
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model Assumptions
- Single car body
- No wheel mass
- Tire stiffness is relatively small
compared with suspension stiffness
- Voigt-Kelvin model is used for
suspension spring and damper
9
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model
10
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model
Quarter Car Model
Vertical Vehicle Dynamics
• Single DOF model 현가 설계시 스프링 K 조건
• 구동력이 바퀴에 전달될 수 있도록 접지력 확보• 인체의 걷는 주파수 1-1.3 Hz 로 조정 (motion
sickness), 4-8Hz (유해한 주파수 (0.1-0.5Hz human fatigue)) 회피 설계
••
고려한 설계
Vertical Vehicle Dynamics
• Single DOF model
Quarter Car Model
Vertical Vehicle Dynamics
Quarter Car Model (1 DOF)
Vertical Vehicle Dynamics
• Single DOF model
Quarter Car Model (1 DOF)
Vertical Vehicle Dynamics
Quarter Car Model (1 DOF)
Quarter Car Model (1 DOF)
Vertical Vehicle Dynamics
• Forced vibration – sinusoidal road input
assume
Vertical Vehicle Dynamics
Quarter Car Model (1 DOF)• Forced vibration – sinusoidal road input
Vertical Vehicle Dynamics
• 차체진동이 도로가진 보다 낮게 되기위해서는
고유진동수를 아래의 P점 이상 되는 방진구역에 위치
D 의 크기도 작게 (보통 D= 0.25-0.5)
•
을 높이기 위해서는 주어진 w 에 대해서 고유진동수 wo 값이
작을 수록, 일정 질량의 차량에 대해서는k 값이 작을 수록 유리 ( 3-5)
Quarter Car Model (1 DOF)• Forced vibration – sinusoidal road input
Vertical Vehicle Dynamics
Car body acceleration vs road vibration도로 부가력
Quarter Car Model (1 DOF)• Forced vibration – sinusoidal road input
Vertical Vehicle Dynamics
Quarter Car Model (1 DOF)
Vertical Vehicle Dynamics
Quarter Car Model (1 DOF)
Quarter Car Model (2 DOF model)
Vertical Vehicle Dynamics
Sprung mass
Un-sprung mass
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
Free vibration
assume
Characteristic equation
No damping case:
Undamped frequency vs. damped frequency = 5% difference
Un-sprung mass vs. sprung mass = 10% neglect un-sprung mass
Vertical Vehicle Dynamics
No damping case:
Undamped frequency vs. dampled frequency = 5% difference
Un-sprung mass vs. sprung mass = 10% neglect un-sprung mass
Primary ride frequency for the sprung mass Damping ratio for the sprung mass
Quarter Car Model (2 DOF model)
Secondary ride frequency for the un-sprung mass Damping ratio for the un-sprung mass
Vertical Vehicle Dynamics
Primary ride frequency for the sprung mass Damping ratio for the sprung mass
Quarter Car Model (2 DOF model)
Secondary ride frequency for the un-sprung mass Damping ratio for the un-sprung mass
Dynamic wheel force
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
Forced vibration - Sinusoidal road profile input
assume and
Frequency response function for the sprung mass
Frequency response function for the un-sprung mass
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
Vertical Vehicle Dynamics
Frequency response function for the sprung mass Frequency response function for the un-sprung mass
Kb soft, ride comfort increase
Vertical Vehicle Dynamics
Sprung mass FRF Un-sprung mass FRF
Cb hard, ride comfort increase
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
Forced vibration - Ramdom road profile input
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
Mb increase, ride comfort increase
Mb does not affect to dynamic axle force much
• Sprung mass variation simulation
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
• Mt does not affect to ride comfort and dynamic axle force in near the natural
frequency of the sprung mass
• Mt does affect to ride comfort and dynamic axle force in near the natural
frequency of the un-sprung mass
• Mt decrease, Ride comfort increase, dynamic force decrease
• Un-sprung mass variation simulation
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
• Suspension stiffness variation simulation
• Kb decrease, Ride comfort increase, But handling (Roll, pitch) problem
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
• Suspension damper variation simulation
• Cb hard, Accel decrease in near 1.25 Hz
• Cb soft, Accel decrease in near 1- 10 Hz
Need variable damper control according to frequency
• Cb hard, dynamic force decrease in near 10 Hz (natural
frequency of un-sprung mass) Wheel hop motion decrease
Vertical Vehicle Dynamics
Quarter Car Model (2 DOF model)
• Tire stiffness variation simulation
• Softer tire Natural frequency of unsprung mass decrease,
• Softer tire amp. of unsprung mass decrease
Thus, Softer tire increase ride comfort and handling. However, softer tire increase
rolling resistance and tire deformation in high speed.
Vertical Vehicle Dynamics
One track Half-Car Model (4 DOF model)
Vertical Vehicle Dynamics
One track Half-Car Model (4 DOF model)• EQM for sprung mass for vertical motion
• EQM for sprung mass for pitch motion
• EQM for front un-sprung mass for vertical motion
• EQM for rear un-sprung mass for vertical motion