PSO assisted adaptive force control in milling.

Cus, F. ; Zuperl, U.

1. Introduction

The goal of this research is to develop peak force regulation in 3-axis CNC machining through the use of PSO optimized feedrates and adaptive force control. Cutting force is found to be one of the most important process parameters used as a constraint in the cutting operation, as it relates to a large number of abnormal occurrences such as tool breakage and excess tool wear as well as basic data for estimation of chatter vibration and machining error.

Our developed feedrate optimization algorithm is effective in force control but it is subject to inaccuracies caused by errors in the neural network force prediction model. These inaccuracies can result in high peak forces during machining, leading to unacceptable dimensional errors or surface finish. On the other hand, if the peak forces are too low, the machining efficiency is reduced. An on-line adaptive controller is proposed to compensate for these inaccuracies, providing accurate regulation of the reference peak force (Cus et al., 2006).

NC programs generated today, experience a large variation in cutting forces due to non-uniformity in metal removal along the cutter path. This may be due to a variety of factors, surface nature (curvature), tool inclination, cornering etc. In order to increase productivity, process parameters should be assigned according to the NC tool path in addition to the conditions of the part, tools, setup, and the machine. The idea is to change these variables according to the current in-process part geometry and tool path so that the cutting force is in control.

Most optimization studies state one of two objectives: Minimum manufacturing cost (Cus & Balic, 2000), maximum production rate (Milfelner et al., 2004).

It has also been realized that a combination of the minimum production cost and minimum production time (Cus & Balic, 2000), is the most effective objective since neglecting either requirement alone does not do justice to the problem at hand. There are a variety of constraints that have been considered applicable by many researchers for different machining situations: 1. available feed and speeds (machine tool related), power, arbor rigidity, and arbor deflection. 2. Maximum available machine power and maximum permitted cutting edge load for roughing, and allowed maximum tool deflection for finishing (Liu & Wang, 1999).

Adaptive control alone cannot effectively control cutting forces. No controller can respond quickly enough to sudden changes in the cut geometry to eliminate large spikes in cutting forces.

This paper describes the implementation of on-line adaptive force control for machining using off-line optimized feedrates. The optimization is performed with PSO algorithm.

2. Structure of the combined system

The basic idea of this system is to merge the off-line PSO algorithm and adaptive force control (Figure 1). Based on this new combined control system, very complicated processes can be controlled more easily and accurately compared to standard approaches. The objective of the developed combined control system is keeping the metal removal rate (MRR) as high as possible and maintaining cutting force as close as possible to a given reference value.

[FIGURE 1 OMITTED]

Combined control system is automatically adjusted to instant cutting conditions by adaptation of feedrate. When spindle loads are low, the system increases feeds above and beyond pre-programmed values, resulting in considerable reductions in machining time and production costs. When spindle loads are high the feed rates are lowered, safeguarding cutting tool from damage and breakage. When system detects extreme forces, it automatically stops the machine to protect the cutting tool.

Combined control system consists of closed loop control system and PSO optimizer (Zuperl et al., 2007). Closed loop control system consists of reference module, adaptive fuzzy controller, CNC controller Fagor 8040-M, controlled object (milling process), dynamometer Kistler 9255 and algorithm for processing cutting forces.

Step by step description of functioning of the combined system.

1. The recommended cutting conditions are determined by the software for selecting the cutting conditions.

2. The feedrates determined by PSO optimization algorithm are sent to CNC controller of the milling machine. Optimization algorithm works on the basis swarm intelligence algorithm.

3. The measured cutting forces are sent to the adaptive controller.

4. Adaptive controller adjusts the optimal feedrates and sends it back to the machine.

5. Steps 3 to 5 are repeated until termination of machining.

The adaptive controller adjusts the feedrate by assigning a feedrate override percentage to the CNC controller on a Heller, based on a measured peak force (see Figure 1). The actual feedrate is the product of the feedrate override percentage (DNCFRO) and the programmed feedrate. If the PSO optimizer is perfect, the optimized feedrate would always be equal to the reference peak force. In this case the correct override percentage would be 100%. In order for the controller to regulate peak force, force information must be available to the control algorithm at every 20ms. Data acquisition software (LabVIEW) and the algorithm for processing the cutting forces are used to provide this information. The combined control system returns the cutting force value to the desired value level within four or less iteration at the latest.

3. Particle swarm optimization

Particle Swarm Optimization (PSO) is a relatively new technique, for optimization of continuous non-linear functions. It was first presented by (Shi & Eberhart, 1998). PSO is a very simple concept, and paradigms are implemented in a few lines of computer code. It requires only primitive mathematical operators, so is computationally inexpensive in terms of both memory requirements and speed. PSO has been recognized as an evolutionary computation technique and has features of both genetic algorithms (GA) and evolution strategies (ES). Other evolutionary computation (EC) techniques such as genetic algorithm also utilize some searching points in the solution space. It is similar to a GA in that the system is initialized with a population of random solutions (Balic, 2003).

While GA can handle combinatorial optimization problems, PSO can handle continuous optimization problems. However, unlike a GA each population individual is also assigned a randomized velocity, in effect, flying them through the solution hyperspace. PSO has been expanded to handle also the combinatorial optimization problems. As is obvious, it is possible to simultaneously search for an optimum solution in multiple dimensions. Unlike other EC techniques, PSO can be realized with only small program. Natural creatures sometimes behave as a swarm. One of the main goals of artificial life researches is to examine how natural creatures behave as a swarm and reconfigure the swarm models inside a computer.

PSO has two simple concepts. Swarm behaviour can be modelled with a few simple rules. Even if the behaviour rules of each individual (particle) are simple, the behaviour of the swarm can be very complex. The behaviour of each agent inside the swarm can be modelled with simple vectors. This characteristic is the basic concept of PSO. The applications of PSO are: Neural network learning algorithms (Boyd, 2003), Rule extraction in fuzzy neural networks (He et al., 1998), computer controlled milling optimization, power and voltage control. Application of PSO to other fields is at the early stage. More applications can be expected. Most of papers are related to the method itself, and its modification and comparison with other EC methods (Eberhart & Shi, 2003).

4. PSO algorithm

PSO algorithm is developed through simulation of bird flocking in two-dimension space. The position of each agent is represented by XY axis position and also the velocity is expressed by vx (the velocity of X axis) and vy (the velocity of Y axis). Modification of the agent position is realized by the position and velocity information.

Bird flocking optimizes a certain objective function. Each agent knows its best value so far (pbest) and its XY position. this information is analogy of personal experiences of each agent. further, each agent knows the best value so far in the group (gbest) among (pbests).

This information is analogy of knowledge of how the other agents around them have performed. Each agent tries to modify its position using the following information:--the current positions (x, y),--the current velocities (vx, vy),--the distance between the current position and (pbest)--the distance between the current position and (gbest).

this modification can be represented by the concept of velocity. figure 2 shows the general flow chart of PSO strategy.

[FIGURE 2 OMITTED]

5. Machining optimization problem

In order to search for optimal process parameters, neural network model of cutting force was integrated with particle swarm optimizer. the architecture of system is shown in Figure 1.

Multiple neural network models are grouped together under the general neural network model, and its output is fed into the multi-objective particle swarm optimizer where the objective functions and constraints are defined. PSO algorithm is initiated with randomly generated particles that are optimum solution candidates. Neural network model predicts cutting forces for each of the particles. Predicted forces are used in calculation of objective function in which PSO tries to maximize (Zuperl & Cus, 2003).

The optimization process executes in two phases. In first phase, the neural prediction model on the basis of recommended cutting conditions generates 3D surface of cutting forces, which represent the feasible solution space for the PSO algorithm. The cutting force surface is limited with planes which represent the constraints of cutting process.

Seven constraints, which arise from technological specifications, are considered during the optimization process. Those constraints are listed in Table 1. Here we are faced with a non-linear objective function along with a set of inequality constraints that may also be highly non-linear. The presence of non-linearities creates additional problems for finding the minimum. The biggest problem in the implementation of PSO technique is the construction of a fitness (objective) function which adequately optimizing the nature of the problem. The objective function serves as the only link between the optimization problem and the PSO-algorithm. For the objective function a surface of max. cutting forces is selected, generated by ANN. PSO algorithm generates a swarm of particles on the cutting force surface during the second phase. Swarm of particles flys over the cutting force surface and search for maximal cutting force. The coordinates of a particle which has found the maximal (but still allowable) cutting force represent the optimal cutting conditions. Figure 3 shows the PSO flowchart of optimization of milling process.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The optimization process is depicted by the following steps:

1. Generation and initialization of an array of 50 particles with random positions and velocities. Velocity vector has 2 dimensions, feed rate and spindle speed. This constitutes Generation 0.

2. Evaluation of objective (cutting force surface) function for each particle.

3. The cutting force values are calculated for new positions of each particle. If a better position is achieved by particle, the pbest value is replaced by the current value.

4. Determination if the particle has found the maximal force in the population. If the new gbest value is better than previous gbest value, the gbest value is replaced by the current gbest value and stored. The result of optimization is vector gbest (feedrate, spindle speed).

5. Computation of particles' new velocity

6. Update particle's position by moving towards maximal cutting force.

7. Steps 1 and 2 are repeated until the iteration number reaches a predetermined iteration

Figure 4 shows simplificated principle of optimization of cutting conditions by the use of PSO. In this case the swarm flays over the force surface and searches for optimal feeding at constant cheap cross-section A. Optimal feed rate is located at the cross-section of the following three planes: cutting force surface, plane with the constant cheap cross-section (vertical plane) and the desired cutting force plane. The coordinate of the particle which is the nearest to mentioned cross-section represent the optimal feed rate.

6. Conclusion

This work has presented a new approach to optimizing the cutting conditions in end milling subject to a near to comprehensive set of constraints. Next, a production cost objective function was used to define the parameter to optimize.

An algorithm for PSO was then developed and used to robustly and efficiently find the optimum cutting conditions. Both feed and speed were considered during optimization. The new technique has several advantages and benefits and is suitable for use with ANN based models where no explicit relation between inputs and outputs is available. The research described in this paper will lead to the development of new intelligent optimization software. Next step will be implementation of on-line optimization of cutting parameters during machining.

DOI: 10.2507/daaam.scibook.2009.03

7. References

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Zuperl, U. & Cus, F. (2003). Optimization of cutting conditions during cutting by using neural networks. Robot. comput.-integr. manuf., Vol. 19, 189-199, ISSN 0736-5845

Zuperl, U.; Cus, F. & Gecevska, V. (2007). Optimization of the characteristic parameters in milling using the PSO evolution technique, Stroj. vestn., Vol. 53, 354-368, ISSN 0039-2480

This Publication has to be referred as: Cus, F[ranc] & Zuperl, U[ros] (2009). PSO Assisted Adaptive Force Control in Milling, Chapter 03 in DAAAM International Scientific Book 2009, pp. 017-024, B. Katalinic (Ed.), Published by DAAAM International, ISBN 978-3-901509-69-8, ISSN 1726-9687, Vienna, Austria

Authors' data Univ.Prof. Cus, F[ranc]; Dr. Sc. Zuperl, U[ros], University of Maribor, Faculty of mechanical engineering, Smetanova 17, 2000 Maribor, Slovenia, uros zuperl@uni-mb.si, franc.cus@uni-mb.si.