Friction. Modeling, Identification, & Analysis

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1 Friction Modeling, Identification, & Analysis Objectives Understand the friction phenomenon as it relates to motion systems. Develop a control-oriented model with appropriate simplifying assumptions for the phenomenon. Determine system identification techniques for the parameters in the model. Analyze the model and run simulations using the model to demonstrate its effectiveness. Friction: Modeling, Identification, & Analysis K. Craig 1

2 Friction: Modeling, Identification, & Analysis K. Craig 2

3 Key Papers on Friction Modeling These four papers, along with the references listed in each paper, represent the state-of-the-art in friction modeling. They were all published in the IEEE Control Systems Magazine, December Characterization of Friction Force Dynamics by F. Al- Bender and J. Swevers. Modeling and Measuring Friction Effects by A. Harnoy, B. Friedland, and S. Cohn. Nanotribilogy and Nanoscale Friction by Y. Guo, Z. Qu, Y. Braiman, and J. Barhen. Revisiting the Lugre Friction Model by K. Astrom and C. Canudas-De-Wit. Friction: Modeling, Identification, & Analysis K. Craig 3

4 Background on Friction Friction, the tangential reaction force between two surfaces in contact, is one of nature s most useful phenomena. Without friction there would be no belt drives, no clutches, no wheels, and no brakes. Walking, and even standing upright on a moderately inclined surface, would be impossible. The cork would not stay in the wine bottle! However, in machinery in which friction is not the driving force, it is an undesirable parasitic phenomenon, generating heat and wasting energy. Conserving energy and sustainability are today the most compelling reasons for a mechatronics approach to design. Friction: Modeling, Identification, & Analysis K. Craig 4

5 The most promising alternative energy source is energy efficiency Machines must do more with less energy and efficiency results from many components working well together. Like any design variable, there is a price associated with efficiency, but the greater costs are incurred when efficiency is overlooked. In industrial equipment, consider the relationship between excess heat and imprecision, vibration and premature wear, thermal cycles and lifetime, energy consumption and profitability. Efficiency matters, and in motion systems, it is a collective property, resulting from many components working together. Friction: Modeling, Identification, & Analysis K. Craig 5

6 What is Ecotribology? Ecotribology: Environmentally-Acceptable Tribological Practices, Wilfried Bartz, Tribology is the study of friction and wear. To reduce friction and wear in machines, main energy culprits, the proper combination of geometry, materials, and lubrication must be employed in a design, i.e., a proper tribological approach. It has been estimated that the correct application of tribology throughout U.S. industry could save the country $500 billion annually. Saving resources and energy and reducing impact on the environment through optimum design and operation practices covering the life of a machine are the two most important aspects. Friction: Modeling, Identification, & Analysis K. Craig 6

7 When friction is the source of traction and braking, it is important to keep friction at a high level. In traction applications, the process starts with the vehicle at rest. In braking applications, the process ends with the vehicle at rest. In both applications, the behavior of friction when the velocity of the vehicle crosses zero is of little interest. In motion-control applications, the velocity of the controlled object typically crosses zero, often several times, during operation. Therefore, it is necessary to understand the behavior of friction in the vicinity of zero velocity. Friction: Modeling, Identification, & Analysis K. Craig 7

8 The challenge to good control posed by friction is often thought of as being stick-slip, which is an alternation between sliding and sticking due to static friction. Stickslip is most common when integral control is used and can prevent a machine from ever reaching its intended goal position. Other forms of frictional disturbance can be of equal or greater importance. The tracking error introduced by friction into multi-axis motion is an example. A two-axis machine will fail to accurately track a desired circular contour because as one axis goes through zero velocity, it is arrested for a moment by static friction while the other axis continues to move. Friction: Modeling, Identification, & Analysis K. Craig 8

9 Physical Model of Friction Friction Model Friction effects can be imagined as resulting from two surfaces with asperities, one inverted above the other. The motion, or tendency of motion, of one surface relative to the other causes the friction force. The height and sharpness of the asperities represent the roughness of the surfaces. Friction: Modeling, Identification, & Analysis K. Craig 9

10 Dry Surfaces Surfaces with Lubrication Lower Friction Force Friction: Modeling, Identification, & Analysis K. Craig 10

1 unit of force 1 unit of force 1 unit of force

Friction is independent of the overall surface

11 1 unit of force 1 unit of force 1 unit of force The same force is needed to move the block shown regardless of its orientation with respect to the ground. Friction is independent of the overall surface area. This is the 1 st Law of Friction. Friction: Modeling, Identification, & Analysis K. Craig 11

1 block Friction varies directly with load.

1 unit of force 3 blocks 2 blocks 3 units of

more deeply the upper surface penetrates into

12 1 block Friction varies directly with load. This is the 2 nd Law of Friction. 1 unit of force 3 blocks 2 blocks 3 units of force 2 units of force The larger the load, the more deeply the upper surface penetrates into the lower, making it more difficult for the surfaces to move apart. Friction force depends on the normal force. Friction: Modeling, Identification, & Analysis K. Craig 12

13 F = F =μ N f stick s impending motion F = F =μ N f slip k motion μ <μ k s μ N< F <μ N s f s static equilibrium Control-Oriented Model Friction: Modeling, Identification, & Analysis K. Craig 13

14 Friction: Modeling, Identification, & Analysis K. Craig 14

15 Linear Damping Effect Stribeck Effect 4 Regimes 1 No sliding elastic deformation 2 boundary lubrication 3 partial fluid lubrication 4 full fluid lubrication Enhanced Model Friction: Modeling, Identification, & Analysis K. Craig 15

16 Friction Model Example Shows effects of Viscous and Coulomb friction. pivot Consider the simple pendulum consisting of a rigid, massless rod of length l and a point mass m attached. 2 m θ + mg (sin θ ) + Bθ + Tf = 0 inertia gravity torque torque Four Cases Case 1: frictionless pivot viscous damping torque B θ Case 2: linear viscous damping torque at pivot Case 3: Coulomb friction torque T f at pivot Case 4: Case 2 & Case 3 combined Coulomb friction torque Friction: Modeling, Identification, & Analysis K. Craig 16

17 l = 1; % meters m = 1; % kg g =9.81; % meters/sec^2 T_stick = 0.2; % 0 or 0.2 N-m Average T_slip = 0.8*T_stick; % N-m B = 0.5; % B = 0 or 0.5 N-m-sec 2 m θ + mg (sin θ ) + Bθ + Tf = 0 Friction: Modeling, Identification, & Analysis K. Craig 17

18 Friction: Modeling, Identification, & Analysis K. Craig 18

19 Coulomb Friction Response Envelope: Linear Decay Viscous Friction Response Envelope: Exponential Decay Friction: Modeling, Identification, & Analysis K. Craig 19

20 Linear Viscous Friction: Exponential Decay Envelope Friction: Modeling, Identification, & Analysis K. Craig 20

21 Nonlinear Coulomb Friction: Linear Decay Envelope Friction: Modeling, Identification, & Analysis K. Craig 21

22 Coulomb + Viscous Friction Response Envelope: Between a Linear Decay and an Exponential Decay Friction: Modeling, Identification, & Analysis K. Craig 22

Stick-slip motion is a common behavior associated with friction. A typical stick-slip experiment is to attach one end of a spring to a block sitting on an unlubricated horizontal surface.

When the spring force exceeds F stick, the mass accelerates, the spring elongates, and the mass comes to rest. The process then repeats, creating the stickslip behavior.

23 Stick-slip motion is a common behavior associated with friction. A typical stick-slip experiment is to attach one end of a spring to a block sitting on an unlubricated horizontal surface. The other end of the spring is moved horizontally with a constant velocity. How will the block move? Of course, it is highly dependent on the physical system parameters (e.g., nature of the surfaces in contact, dynamics of the spring-mass system, driving velocity V 0 ), but one possible outcome is stick-slip motion, as shown in the figure. When the spring force exceeds F stick, the mass accelerates, the spring elongates, and the mass comes to rest. The process then repeats, creating the stickslip behavior. A model used to describe the friction phenomenon must be able to show this behavior. Friction: Modeling, Identification, & Analysis K. Craig 23

24 Friction Model Example: Stick-Slip Behavior mx + kx + Ff = kx0 Friction: Modeling, Identification, & Analysis K. Craig 24

25 mx+ kx+ F = kx f 0 1 x = k(x x) F m [ ] 0 f Friction: Modeling, Identification, & Analysis K. Craig 25

26 Friction: Modeling, Identification, & Analysis K. Craig 26

27 Friction: Modeling, Identification, & Analysis K. Craig 27

28 Parameter Identification Static and Dynamic Coulomb Friction Torque Linear Viscous Friction Torque For a motor + load system, to determine the friction characteristics of the system, follow the following steps: Run the motor + load with a servo-amplifier in the torque mode (1 A/V). Input a trapezoid voltage profile with a period of slow linearly-increasing voltage, a period of constant voltage, and a period of slow linearly-decreasing voltage. Insure that the power supply is not saturated during the test. Record the velocity from a tachometer or encoder as a function of time during the test. See plots on next two slides for procedure. Friction: Modeling, Identification, & Analysis K. Craig 28

29 Jω+ Bω+ T = K i f t rad/s B = Ki t T ω fd t = 35.4 s t = s T fs = K i t T fd = K i t Friction: Modeling, Identification, & Analysis K. Craig 29

30 i = 0.15 A at 50 < t < 80 i = A at t = 35.4 sec i = A at t = sec Friction: Modeling, Identification, & Analysis K. Craig 30

8*Tfs; Kt = 0.0141; Kb = 0.0141; R = 7; L = 0.

31 Simulation to Validate Friction ID Procedure 6-Volt Brushed DC Motor J = 1.06E-6; B = 2.85E-6; Tfs = ; Tfd = 0.8*Tfs; Kt = ; Kb = ; R = 7; L = 0.120; Ka = 1; SI Units Friction: Modeling, Identification, & Analysis K. Craig 31

32 J = 1.06E-6; B = 2.85E-6; Tfs = ; Tfd = 0.8*Tfs; Kt = ; Kb = ; R = 7; L = 0.120; Ka = 1; SI Units Friction: Modeling, Identification, & Analysis K. Craig 32

33 Friction: Modeling, Identification, & Analysis K. Craig 33

Mechatronics. MANE 4490 Fall 2002 Assignment # 1

Mechatronics. MANE 4490 Fall 2002 Assignment # 1 Mechatronics MANE 4490 Fall 2002 Assignment # 1 1. For each of the physical models shown in Figure 1, derive the mathematical model (equation of motion). All displacements are measured from the static