CNC end milling optimization using evolutionary computation.

Cus, Franc ; Zuperl, Uros ; Gecevska, Valentina 等

1. INTRODUCTION

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).

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. In this paper, a PSO optimization method is proposed to obtain the optimal parameters in milling processes (Figure 1).

2. 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.

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).

3. 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 1 OMITTED]

4. MACHINING OPTIMIZATION PROBLEM

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. 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 2 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

5. 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 online optimization of cutting parameters during machining.

6. REFERENCES

Cus, F. & Balic, J. (2000). Selection of cutting conditions and tool flow in flexible manufacturing system. The international journal for manufacturing science & technology, Vol. 2, pp. 101-106

Boyd, J. (2003). Thinking is Social: Experiments with the Adaptive Culture Model. Journal of Conflict Resolution, Vol. 42, pp. 56-76

Eberhart, R.C. & Shi Y. (2003). Comparison Between Genetic Algorithm and Particle Swarm Optimization, Proceedings of the 7th ICEC, pp. 611-616

He, Z.C.; Wei, L.; Yang, X.; Gao, S; Yao, R & Eberhart, (1998). Extracting Rules from Fuzzy Neural Network by Particle Swarm Optimization, Proc. of IEEE International Conference on Evolutionary Computation (ICEC'98), pp. 66-71

Liu, Y. & Wang, C. (1999). Neural Network based Adaptive Control and Optimisation in the Milling Process. International Journal of Advanced Manufacturing Technology, Vol. 15, pp. 791-795

Milfelner, M.; Zuperl, U. & Cus, F. (2004). Optimisation of cutting parameters in high speed milling process by GA. Int. j. simul. model., Vol. 3, pp. 121-131

Shi Y., & R. Eberhart (1998). Parameter selection in particle swarm optimization. In Evolutionary Programming VII: Proc. EP98, New York: Springer-Verlag, pp. 591-600.