A second order mechanical model of muscle spindle primary endings

1970 ◽  
Vol 6 (6) ◽  
pp. 205-213 ◽  
Author(s):  
Torstein Rudjord
Keyword(s):  
Muscle Spindle ◽  
Mechanical Model ◽  
Second Order

scholarly journals The method of multiscale virtual power for the derivation of a second order mechanical model

2016 ◽  
Vol 99 ◽  
pp. 53-67 ◽  
Author(s):  
P.J. Blanco ◽  
P.J. Sánchez ◽  
E.A. de Souza Neto ◽  
R.A. Feijóo
Keyword(s):  
Mechanical Model ◽  
Second Order ◽  
Virtual Power

Influence of Blade Flexibility on the Dynamic Response Simulation of a Turbomolecular Pump on Magnetic Bearings

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Alysson Bruno Barbosa Moreira ◽  
Fabrice Thouverez
Keyword(s):  
Mechanical Model ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Coupled System ◽  
Forced Response ◽  
Second Order ◽  
Magnetic Bearings ◽  
Flexible System ◽  
Turbomolecular Pump ◽  
Rigid Body Modes

Abstract This paper proposes the simulation of a complete mechanical model of a turbomolecular pump rotor, including rotor and blades flexibility, suspended by controlled active magnetic bearings. The mechanical model is composed of an eight stage blisk, attached to a shaft. Magnetic forces are linearized by the first-order Taylor expansion around a given point. Including blades and rotor flexibility makes the mechanical system asymmetric, so the equations of motion for the coupled system have periodic terms. A modal controller was designed to control rigid body modes, since the number of sensors is limited and no state observer is implemented. PID controllers are used for low frequency modes combined with the second order filters to damp high frequency modes. First of all, stability analysis was carried out for the axisymmetric case. Second, blades flexibility was included. Forced response of the whole system to an impulsive force was studied. Divergent responses for the system in rotation were obtained as a second order filter pole possibly interacting with blades modes. Taking the second order filters off the control loop allowed the system to be stable. These results show that the analysis method developed here is efficient to evaluate the performance of a controller in closed loop with the complete flexible system. This method may be used in industrial design processes as computation times for the complete system are very short.

Influence of Blade Flexibility on the Dynamic Response Simulation of a Turbomolecular Pump on Magnetic Bearings

2019 ◽  
Author(s):  
Alysson Bruno Barbosa Moreira ◽  
Fabrice Thouverez
Keyword(s):  
Mechanical Model ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Coupled System ◽  
Forced Response ◽  
Second Order ◽  
Magnetic Bearings ◽  
Flexible System ◽  
Turbomolecular Pump ◽  
Rigid Body Modes

Abstract This paper proposes the simulation of a complete mechanical model of a turbomolecular pump rotor, including rotor and blades flexibility, suspended by controlled active magnetic bearings. The mechanical model is composed of an eight stage blisk, attached to a shaft. Magnetic forces are linearized by first order Taylor expansion around a given point. Including blades and rotor flexibility makes the mechanical system asymmetric, so the equations of motion for the coupled system have periodic terms. A modal controller was designed to control rigid body modes, since the number of sensors is limited and no state observer is implemented. PID controllers are used for low frequency modes combined with second order filters to damp high frequency modes. First of all, stability analysis was carried out for the axisymmetric case. Secondly, blades flexibility was included. Forced response of the whole system to an impulsive force was studied. Divergent responses for the system in rotation were obtained as a second order filter pole possibly interacts with blades modes. Taking second order filters off the control loop allowed the system to be stable. These results show that the analysis method developed here is efficient to evaluate the performance of a controller in closed loop with the complete flexible system. This method may be used in industrial design processes as computation times for the complete system are very short.

Sign in / Sign up

Export Citation Format

Share Document