Dynamic Response and Nonlinear Characteristic Analysis of Rigid–Flexible Coupling Mechanism with Lubricated Revolute Clearance and Prismatic Clearance
Abstract
1. Introduction
2. Dynamics Model of RFC-MLM with Revolute Lubrication Clearance and Prismatic Clearance
2.1. Prismatic Pair Clearance Model
- As shown in Figure 2a, the slider is in a free state without any collision phenomenon;
- As shown in Figure 2b, a corner of the slider collides with the guide rail surface;
- As shown in Figure 2c, the diagonal of the slider collides with the guide rail surface;
- As shown in Figure 2d, the same side of the slider collides with the guide rail surface.
2.2. Revolute Lubrication Clearance Model
2.3. Flexible Beam Element Model
2.4. Dynamic Model of RFC-MLM with Revolute Lubrication Clearance and Prismatic Clearance
3. Nonlinear Dynamics Behaviour Analysis of RFC-MLM with Clearance
3.1. Comparative Analysis of Lubrication and Dry Friction Revolute Clearance on Nonlinear Dynamics Behaviour of RFC-MLM
3.1.1. Comparative Analysis of Dynamic Response
3.1.2. Chaos Identification
- (1)
- Phase diagrams visually display the dynamic behaviour of a system by plotting the trajectories of system state variables in phase space;
- (2)
- Poincaré maps transform a continuous system into a discrete map by selecting a section in phase space and recording the state of the system trajectory each time it passes through that section. If the system is chaotic, the Poincaré map will display a complex distribution of points, which will not converge to a finite number but form a seemingly random distribution;
- (3)
- The maximum Lyapunov exponent quantifies the average exponential rate at which adjacent trajectories diverge or converge in phase space, and is a key indicator for determining chaotic behaviour. If the maximum Lyapunov exponent of a system is positive, it indicates that the adjacent trajectories will diverge exponentially, which is a sign of chaotic behaviour. If the maximum Lyapunov exponent is zero, the system may be periodic or quasi periodic. If it is negative, the system tends to be stable and there is no chaotic behavior.
3.2. Influence of Different Driving Velocity on Dynamic Behaviour
3.2.1. Analysis of Dynamics Response
3.2.2. Analysis of Nonlinear Characteristics
3.3. Influence of Various Dynamics Viscosity on Dynamic Behaviour
3.3.1. Analysis of Dynamics Response
3.3.2. Analysis of Nonlinear Characteristics
3.4. Influence of Various Clearance Value on Dynamic Behaviour
3.4.1. Analysis of Dynamics Response
3.4.2. Analysis of Nonlinear Characteristics
3.5. Virtual Prototype Simulation Verification
4. Conclusions
- (1)
- A dynamics model of a planar multi-link mechanism, considering the coupling effects of revolute lubrication clearance, the prismatic clearance pair, and the flexibility of the component, is built;
- (2)
- A comparative analysis is conducted on the effects of lubrication clearance and dry friction clearance on the dynamic response and nonlinear characteristics of a rigid–flexible coupled multi-link mechanism. Our research found that lubrication can reduce the peak dynamic response, improve the stability, and reduce the chaotic characteristics of the mechanism. Under the research parameters of this paper, after lubrication of the motion pair, the peak value of acceleration of the slider and the driving torque of the crank decreased by 35.93% and 73.10%, respectively;
- (3)
- The influences of different driving speeds, dynamic viscosities, and clearance sizes on the dynamic response and nonlinear characteristics of rigid–flexible coupling multi-link mechanisms with rotational lubrication clearance and prismatic clearance are discussed. When the driving speed increases from 30 rpm to 75 rpm, the peak value of acceleration of the slider and the driving torque of the crank increase by 84.18% and 64.62%, respectively. When the dynamic viscosity increases from 100 Cp to 500 Cp, the peak value of acceleration of the slider and the driving torque of the crank decrease by 23.68% and 65.65%, respectively. When the clearance value increases from 0.1 mm to 0.5 mm, the peak value of acceleration of the slider and the driving torque of the crank increase by 69.66% and 81.72%, respectively. Our research has found that, the higher the driving speed, the smaller the dynamic viscosity, the larger the clearance value, the greater the peak response of the mechanism, and the more obvious the chaos phenomenon;
- (4)
- The correctness of the theoretical model is verified through ADAMS virtual prototype simulation.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Component | Length (m) | Centroid Position Length (m) | Mass (kg) | Moment of Inertia (10−3 kg·m2) |
---|---|---|---|---|
Crank 1 | 0.075 (L1) | 0.0375 (Ls1) | 0.751 (m1) | 1.408 (J1) |
Rod 2 | 0.700 (L2) | 0.350 (Ls2) | 6.601 (m2) | 269.541 (J2) |
Rod 3 | 0.584 (L3) | 0.292 (Ls3) | 5.515 (m3) | 156.744 (J3) |
Rod 4 | 0.450 (L4) | 0.225 (Ls4) | 4.261 (m4) | 71.904 (J4) |
Slider 5 | — | — | 5.776 (m5) | 4.813 (J5) |
Parameter | Parameter Values |
---|---|
Length of slider (LT) | 150 mm |
Width of slide (WT) | 100 mm |
Thickness of slide (TT) | 50 mm |
Bearing radius (R1) | 15 mm |
Restitution coefficient (ce) | 0.9 |
Poisson ratio (νm, νn) | 0.3 |
Elastic modulus (Em, En) | 207 GPa |
Friction coefficient (cf) | 0.15 |
Young modulus (Ef) | 207 GPa |
Cross section area (Af) | 0.06 × 0.02 m2 |
Second moment of area (I) | 4 × 10−8 m4 |
Density (ρ) | 7801 kg/m3 |
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MLE | Clearance A in X Direction | Clearance A in Y Direction | Clearance B in X Direction | Clearance B in Y Direction |
---|---|---|---|---|
Dry friction clearance | 0.0127 | 0.01542 | −0.051 | 0.0726 |
Lubrication clearance | −0.0168 | −0.0143 | −0.052 | 0.0416 |
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Niu, J.; Meng, K.; An, M.; Jiang, S. Dynamic Response and Nonlinear Characteristic Analysis of Rigid–Flexible Coupling Mechanism with Lubricated Revolute Clearance and Prismatic Clearance. Lubricants 2025, 13, 142. https://doi.org/10.3390/lubricants13040142
Niu J, Meng K, An M, Jiang S. Dynamic Response and Nonlinear Characteristic Analysis of Rigid–Flexible Coupling Mechanism with Lubricated Revolute Clearance and Prismatic Clearance. Lubricants. 2025; 13(4):142. https://doi.org/10.3390/lubricants13040142
Chicago/Turabian StyleNiu, Jun, Kai Meng, Mingxuan An, and Shuai Jiang. 2025. "Dynamic Response and Nonlinear Characteristic Analysis of Rigid–Flexible Coupling Mechanism with Lubricated Revolute Clearance and Prismatic Clearance" Lubricants 13, no. 4: 142. https://doi.org/10.3390/lubricants13040142
APA StyleNiu, J., Meng, K., An, M., & Jiang, S. (2025). Dynamic Response and Nonlinear Characteristic Analysis of Rigid–Flexible Coupling Mechanism with Lubricated Revolute Clearance and Prismatic Clearance. Lubricants, 13(4), 142. https://doi.org/10.3390/lubricants13040142