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Modelling, analysis and control of linear feed axes in precision machine tools
Abstract
The precision control of linear feed axes in machine tools is examined in this thesis. Al¬though high precision in machining has been a focal point for engineers for over 200 years, the traditional solutions have often been based on complex mechanical designs. In this thesis, two aspects of feed axis controller design are examined: i) the use of appropriate mathematical models and ii) the significance of three of the most common performance limiting factors that have traditionally affected precision in linear feed axes. The three particular performance limiting factors considered are: i) dynamic stiffness, ii) torsional vibrations and iii) backlash. The most effective way of obtaining knowledge about a control system is through appro¬priate mathematical modelling. A new two-body model for a simple motor-transmission¬load system is presented in this thesis. This new model is shown to provide a more accurate representation of both the total inertia and lowest natural frequency of a system, when compared with the two-body model that is traditionally used by researchers and system designers. A new model to represent backlash in a two-body system is also pre¬sented. These new models are then extended to provide accurate mathematical models of four common linear feed axis drive configurations: i) a rotary motor driving a rack and pinion transmission, ii) a rotary motor directly driving a ballscrew transmission, iii) a rotary motor driving a ballscrew transmission via a synchronous belt, and iv) a linear motor directly driving the axis. Different control solutions to the problems of dynamic stiffness, torsional vibrations and backlash are examined in this thesis, with each controller implemented on specially con¬structed test-beds. An approach using Quantitative Feedback Theory (QFT) is presented xxi for systems with inherently low dynamic stiffness. This QFT approach is shown to pro¬vide a transparent design process, which results in high dynamic stiffness. Different controllers for torsional vibrations are compared both theoretically and experimentally, with many previously published solutions shown to be theoretically equivalent. A new backlash controller is also presented, which is shown experimentally to provide dynamic stability and good tracking performance at both high and low velocities. The importance of treating these performance limiting factors simultaneously is also ad¬dressed in this thesis, with the control solutions developed to address some factors shown to also affect the other factors. The QFT approach is shown to provide a suitable inte¬grated design process, where the implications of any compromises, on the control of each factor, are clearly visible.
... Torsional vibration can occur in every drive because of the flexibility of mechanical coupling between the motor and load [12,13] The torque applied by the motor will give an acceleration and the system increases in speed, the system has to pass through its critical speed leading to some deformation like shaft twist. ...
... The rotating system may suffer stability problems due to inertia mismatch. In reality, all coupling devices have finite stiffness and the load respond is not identical to that of the motor [13]. From this standpoint, this work addresses certain case study that has inertia mismatch between motor and load that can result torsional vibrations. ...
Unstable torque produced by electrical motors and external disturbances from
load side cause torsional vibration to the entire rotating system due to low
inherent damping with inertia forces of the main system shaft sides. As a result
the response of the system exhibits poorly damped oscillations. Control of
system shaft torsional vibration by application two types of dual loop controllers
work as low pass filter to enhance the performance using Matlab/Simulink
software. Some other controllers like proportional-integral-derivative (PID),
Fuzzy Logic, Fuzzy – PID and PID - Fuzzy are applied and did not give desired
stability. The preferable performance was achieved by replacing the
conventional single loop circuits by two types of dual loop controllers, the first
type constructed by moving the proportional and derivative parameters to the
feedback loop while remaining the integrated parameter in the forward path
(I-PD). The second type (PID-D) formed by adding derivative gain to the
feedback loop with the aid of forward conventional (PID) controller. Placing
dual loop feedback sensors on both motor and load sides took the flexibility of
shaft into account. Such controllers gave minimum oscillations, overshot has
been decreased, smoother steady state and good transient responses with high
accuracy. It was observed that using (PID-D) controller had decreased settling
time from (1.5 seconds) with uncontrolled system to (0.2 second) and the
torsional displacement amplitude had reduced from (7*10-3 rad) to (2.12*10-3
rad), while using I-PD controller had the advantage to decrease settling time to
about (0.13 second) and the torsional displacement amplitude had reduced more
to about (1.05*10-3 rad). A comparison with other study proved that the
proposed (I-PD) controller in this study gave better performance.
... In number of papers [22][23][24][25] it was shown that the use of feedforward control taking into account the motion differential characteristics significantly increase the accuracy of movement along the tool path. Fig. 1 Generalized structure of CNC system [14] In papers [26][27][28][29], various schemes of the CNC controllers are considered, in which feedforward control is used according to the differential characteristics of motion. The flow of position and speed commands is shown, but the requirements for these commands and the accuracy of setting the data that determine the position and speed of the controlled axis in the CNC are not specified. ...
Improving the accuracy, reliability, and performance of cyber-physical systems such as high-speed machining, laser cutting, welding and cladding etc. is one of the most pressing challenges in modern industry. CNC system carries out data processing and significantly affect on accuracy of operation such equipment. The paper considers the problem of controlled axes motion differential characteristics data processing in the internal representation of the discrete space of the CNC system. Equations for determining the required discreteness of the differential characteristics position and resolution, such as the speed, acceleration, and jerk are proposed. For the most widely used CNC equipment specific discreteness and resolution values have been determined.
This chapter introduces the design of linear feed drive systems used in machine tools. The key factors to improve the precision of linear motion are summarized, and the design principle of the precision linear drives is given. The types of the linear motion guides and the drive systems commonly used in machine tools are described. Finally, a typical case on the design of hydrostatic slide is presented.
Control of mechanical system with backlash is a topic well studied by many control practitioners. This interest has been motivated by the fact that backlash is one of the most important nonlinearities, that primary limit the performance of speed and position loop in industrial motion system, such as robotics, automation and many other motion systems. This research deals with backlash in two-mass system, which well represents the majority of such systems. In this research backlash is treated as torque disturbance, which enter the system at the location of the backlash. Then a disturbance observer (DOB) is constructed in order to estimate and compensate the disturbance in an inner feedback loop fusion, such that the outer controller will used to control “backlash-free” system. Also the issue of torsional vibrations is investigated. Such vibrations are often generated because of the elastic shaft connected between the two masses (usually motor and load inertias). The torsional torque disturbance is estimated and compensated by using the disturbance observer in the same manner as the backlash.
This paper presents a model of a target tracking system assembled in a moving body. The system is modeled in time domain as a nonlinear system, which includes dry friction, backlash in gear transmission, control input tensions saturation, and armature current saturation. Time delays usually present in digital controllers are also included, and independent control channels are used for each motor. Their inputs are the targets angular errors with respect to the system axial axis and the outputs are control tensions for the motors. Since backlash in gear transmission may reduce the systems accuracy, its effects should be compensated. For that, backlash compensation blocks are added in the controllers. Each section of this paper contains a literature survey of recent works dealing with the issues discussed in this article.
In a two-inertia motor system with flexible shaft, a torsional
vibration is often generated, as a quick speed response close to the
primary resonant frequency is required. This vibration makes it
difficult to achieve a quick response of speed and disturbance
rejection. The objective of this paper is to provide a systematic
analysis and a design of a pole placement controller by using the
weighted ITAE performance index for a two-inertia motor system. Three
kinds of speed controllers (I-P, I-PD, and state feedback) are used. The
simulation results show that the full state feedback controller has the
best performance compared to other controllers in terms of oscillation
and settling time. The proposed controller is expected to be the
standard for controlling a two-inertia motor system with flexible shaft
This paper deals with adaptive control of nonlinear dynamic systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is described by a dynamic equation. By utilizing this dynamic model and by combining a fuzzy universal function approximator with adaptive control techniques, a stable adaptive fuzzy control algorithm is developed without constructing a hysteresis inverse. The stability of the closed-loop system is shown using Lyapunov arguments. The effectiveness of the proposed method is demonstrated through simulations.
The ever-increasing demands placed on industrial machine tool manufacturers, for greater speeds and accuracies, are beginning to exceed the capabilities of current machine tool technologies. How- ever, the ongoing revolution in computer, sensor and actuator technologies has introduced the poten- tial of economically meeting these higher demands through new approaches in machine tool design. One actuator technology currently influencing high precision industrial automation is the linear mo- tor. This paper details the development of a single axis linear motor test-bed, replicating one axis of a laser cutting machine tool. Through analysis of system stiffness and torque disturbances, the performance of the linear motor driven axis is compared to that of a more common ball screw driven axis.
There are a number of performance limiting factors that concern
the designers of machine tool servo systems. One such factor is the
mismatch that often exists between motor and load inertias. This paper
briefly discusses the results of a previous study on the factors that
interact to introduce stability problems in the presence of a high
motor-load inertia mismatch. The effects of such an inertia mismatch, on
servo system performance, are then discussed and analysed using closed
loop frequency responses. Various methods of improving the system
response using fast feedback control are presented, including
traditional PI control and modern methods incorporating full order state
observation. The effectiveness of these control methods are then
compared after comprehensive testing on a specially constructed
experimental rig
Torque Perturbations and Dynamic Stiffness of Linear Motors for Grinding Machines
- Jeff Moscrop
- Phil Commins
- Chris Cook
Jeff Moscrop, Phil Commins and Chris Cook, " Torque Perturbations and Dynamic
Stiffness of Linear Motors for Grinding Machines, " in Proceedings of the 6th International Symposium on Linear Drives for Industrial Applications, Lille France,
2007
xxiv
Industrial Automation Research at the University of Wollongong
- Chris Cook
- Fazel Naghdy
- Zheng Li
- Jeff Moscrop
- John Simpson
Chris Cook, Fazel Naghdy, Zheng Li, Jeff Moscrop and John Simpson, " Industrial Automation Research at the University of Wollongong, " in Proceedings of the
International Manufacturing Leaders Forum, Adelaide, 2002, pp. 113-118.
An Analysis of Motor/Load Inertia Mismatch in Machine Tool Servo Systems
- Jeff Moscrop
- Chris Cook
- Fazel Naghdy
Jeff Moscrop, Chris Cook and Fazel Naghdy, " An Analysis of Motor/Load Inertia
Mismatch in Machine Tool Servo Systems, " in Proceedings of the 1st IFAC Conference on Mechatronic Systems, Darmstadt -Germany, 2000, pp. 235-240.
Comparative Study of Feedback Sensor Locations for Servo Systems with Motor/Load Inertia Mismatch
- Jeffrey Moscrop
- Chris Cook
- Fazel Naghdy
Jeffrey Moscrop, Chris Cook and Fazel Naghdy, "Comparative Study of Feedback Sensor Locations for Servo Systems with Motor/Load Inertia Mismatch," in
Proceedings of the Australian Conference on Robotics and Automation, Brisbane,
1999, pp. 202-207.