Parameter Identification Step 1 Friction and Damping

For the lead screw and nut, the equation of motion is given by (5.18) which is repeated here for ease of reference. 

N is the normal contact force between lead screw and nut threads and is given by (5.19). Also, the coefficient of friction is considered here to be a function of the relative sliding velocity (which is expressed more conveniently as a function lead screw angular velocity) and is given by (5.3) and is repeated here  

Remark 9.1. In the actual lead screw system, lubrication, surface conditions, and load distribution on the lead screw and nut threads change as the nut translates along the lead screw. However, in the mafiiematical modeling and the subsequent identification approach, all parameters are taken as their averaged values over a small travel distance of the nut along the lead screw.  

In the first step of the parameter identification approach, the steady-state pure-slip conditions are considered (i.e., no rotational vibrations and constant lead screw angular velocity). The vibration-free operation of the system may be achieved through feedback control. Based on the mathematical model of the system developed in the preceding section, steady-state relationships are derived and by relating the measurable system inputs and states to the internal friction and damping parameters, these parameters are estimated. Table 9.1 lists the measured (or calculated) quantities and the main parameters to be identified in this step. 

COM Motor angular Parameter related to Stribeck Motion 

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