The Dynamics of Lead-Screw Drives: Low-Order Modeling and Experiments

2004 ◽  
Vol 126 (2) ◽  
pp. 388-396 ◽  
Author(s):  
Kripa K. Varanasi ◽  
Samir A. Nayfeh
Keyword(s):  
Transfer Functions ◽  
Ball Screw ◽  
Distributed Parameter ◽  
Viscoelastic Damper ◽  
Thrust Bearings ◽  
Screw Drive ◽  
Lead Screw ◽  
Distributed Parameter Model ◽  
Modeling And Experiments ◽  
Low Order

The closed-loop performance of a lead-screw drive is usually limited by a resonance in which the carriage oscillates in the direction of motion as the screw undergoes longitudinal and torsional deformation. In this paper, we develop a model of lead-screw system dynamics that accounts for the distributed inertia of the screw and the compliance and damping of the thrust bearings, nut, and coupling. The distributed-parameter model of the lead-screw drive system is reduced to a low-order model using a Galerkin procedure and verified by experiments performed on a pair of ball-screw systems. The model is found to accurately predict the presence of a finite right-half plane zero in the transfer function from motor torque to carriage position. A viscoelastic damper incorporated into one of the lead-screw support bearings is shown to give rise to significant, deterministic damping in the system transfer functions.

Finite Element Modeling and Tansfer Function Prediction of Ball-Screw Drive System

2010 ◽  
Vol 431-432 ◽  
pp. 225-228
Author(s):  
Li Hua Lu ◽  
Ying Chun Liang ◽  
Fu Li Yu ◽  
Bao Ku Su
Keyword(s):  
Finite Element ◽  
Closed Loop ◽  
Constraint Equation ◽  
Ball Screw ◽  
The Finite Element Method ◽  
Worst Case ◽  
Thrust Bearings ◽  
Screw Drive ◽  
Ball Screw Drive ◽  
Ball Screw Drives

The closed-loop performance of a ball-screw drive is usually limited by a resonance in which the carriage oscillates in the direction of motion as the screw undergoes longitudinal and torsional deformation. By means of the finite element method (FEM), a model of ball-screw system dynamics is presented by taking into account the distributed inertia of the screw and the compliance and damping of thrust bearings, nut and coupling. Transmission ratio is modeled using DOFs (degree of freedoms) constraint equation. The model is found to accurately predict the transfer function from motor torque to carriage position. Comparing the predicted responses with experiments performed on a pair of ball-screw drives, the resonance frequency is misestimated as much as 5% in the worst case.

Multivariable Transfer Functions for a Slewing Piezoelectric Laminate Beam

1995 ◽  
Vol 117 (3) ◽  
pp. 352-359 ◽  
Author(s):  
H. R. Pota ◽  
T. E. Alberts
Keyword(s):  
Air Force ◽  
Transfer Functions ◽  
Distributed Parameter ◽  
Laplace Domain ◽  
Distributed Parameter Model ◽  
Us Air Force ◽  
Beam Experiment ◽  
Special Cases ◽  
The Us ◽  
Domain Transfer

In this paper a distributed parameter model of a slewing beam system with piezoelectric actuators and sensors is considered. The system has a torque motor at a pinned (proximal) end, an endpoint motion sensor at the distal end, and patches of thin piezoelectric laminates attached to its surface. The partial differential equation of motion for this system is transformed to Laplace domain transfer functions after application of the appropriate boundary conditions. Transfer functions relating the various actuator/sensor pairs are developed. The results are shown to reduce to previously known results which are special cases of the system under consideration. Examples and experimental results are presented using a beam experiment at the US Air Force, Frank J. Seller Research Laboratory.

The influence of ball screw drive positioning errors on the accuracy of part manufacturing

2021 ◽  
pp. 40-52
Author(s):  
L. V. Ibaeva ◽  
Yu. M. Orlov
Keyword(s):  
Total Error ◽  
Roll Angle ◽  
Ball Screw ◽  
Numerical Estimation ◽  
Screw Drive ◽  
Lead Screw ◽  
Machine Drive ◽  
Temperature Deformations ◽  
Ball Screw Drive ◽  
Machine Drives

The article considers the components of the total error of mechanical processing that occur when positioning the working units of the machine: ball screw drive elements. The reasons for the loss of positioning accuracy of the machine drives are described. The accuracy of the positioning of the machine spindle in determining the axes of the holes to be processed is analyzed. The numerical estimation of the values of the errors of the temperature deformations of the lead screw is carried out on the example of drilling holes in the workpiece. The causes of heating of the ball screw drive of the machine are identified. The dependence of the unit heating on the speed of movement of the operating elements of the machine is described. The optimal trajectory of the tool movement when processing holes in the workpiece is presented. The criterion of optimality of this trajectory is described. The values of the deviations of each hole in the workpiece from the specified accuracy of their location are obtained. The scheme of accumulation of errors of linear displacements resulting from the temperature deformation of the lead screw of the CNC machine drive is presented. The value of the accumulated total error of the temperature deformations of the ball screw pair is obtained. The error associated with the movement of the machine drive carriage is considered. The geometric characteristics of the carriage orientation are given. The schemes of occurrence of the error caused by the change of the roll angle and the carriage tilt angle are presented. The maximum axial load of the lead screw at translational acceleration is calculated. The scheme of possible carriage deflection under the action of the maximum translational force of a ball screw pair is presented. The numerical estimation of the maximum possible roll angle of the carriage, as well as the maximum deviation from the specified accuracy of the carriage, at the maximum load on the lead screw, is carried out. As a result, it is concluded that the total error of the machine drives positioning can go beyond the tolerances of the linear dimensions of the processed holes, which significantly affects the accuracy of the part manufacturing.

Dynamic Modeling of a Bi-Driven High Speed Ball Screw System

2010 ◽  
Author(s):  
Jinsong Wang ◽  
Yan Liu ◽  
Tong Zhao ◽  
Peiqing Ye
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Modeling Method ◽  
Ball Screw ◽  
Distributed Parameter ◽  
Test Bed ◽  
Thrust Bearings ◽  
Driven System ◽  
Optimized Model ◽  
Parameter Approach

The traditional lumped modeling method in 2 degree of freedoms of a bi-driven high-speed ball screw system can not accurately characterize the high frequency mechanical resonance, which usually limits the dynamic performance of the system. This paper proposes a hybrid parameter modeling method for the bi-driven system. The workbench is modeled with lumped method in 3 degree of freedoms considering the physical dimension of the workbench and the installation location of the ball-nut and slider. The ball screw is modeled with a novel distributed parameter approach with the boundary conditions of the thrust bearings and coupling to describe its elastic characteristics. The ball screw model is integrated into the workbench one to construct a hybrid one, which is optimized by simulation on a typical test bed. The optimized model ignores unimportant parameters of the workbench one and reduces the order of the ball screw one. Compared with the experiment, the optimized hybrid model accurately characterizes both the workbench and ball screw resonance frequency of the bi-driven ball screw system.

scholarly journals Open-loop temperature control for a distributed parameter model of a pipe

2020 ◽  
Vol 53 (2) ◽  
pp. 7765-7770
Author(s):  
Simon Bachler ◽  
Jens Wurm ◽  
Frank Woittennek
Keyword(s):  
Temperature Control ◽  
Open Loop ◽  
Distributed Parameter ◽  
Distributed Parameter Model
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