Electromagnetism-like algorithms for optimized tool path planning in 5-axis flank machining

https://doi.org/10.1016/j.cie.2014.11.023Get rights and content

Highlights

  • Enhances the practical values of tool path planning in 5-axis flank milling.

  • New algorithms derived from the electromagnetism-like (EM) mechanism.

  • Those EM-based algorithms yield more effective optimal solutions than does PSO.

  • Incorporate an SPSA technique to improve the search results.

Abstract

Optimization of tool path planning using metaheuristic algorithms such as ant colony systems (ACS) and particle swarm optimization (PSO) provides a feasible approach to reduce geometrical machining errors in 5-axis flank machining of ruled surfaces. The optimal solutions of these algorithms exhibit an unsatisfactory quality in a high-dimensional search space. In this study, various algorithms derived from the electromagnetism-like mechanism (EM) were applied. The test results of representative surfaces showed that all EM-based methods yield more effective optimal solutions than does PSO, despite a longer search time. A new EM-MSS (electromagnetism-like mechanism with move solution screening) algorithm produces the most favorable results by ensuring the continuous improvement of new searches. Incorporating an SPSA (simultaneous perturbation stochastic approximation) technique further improves the search results with effective initial solutions. This work enhances the practical values of tool path planning by providing a satisfactory machining quality.

Introduction

5-axis CNC machining has been commonly used in manufacturing of complex geometries in automobile, aerospace, energy, and mold industries. This advanced machining operation provides better shaping capability and higher productivity compared to traditional 3-axis machining. Tool path planning becomes a challenging task in most 5-axis machining operations due to additional degrees of freedom in the tool motion. A primary goal in planning the tool path is to avoid tool collision. In 5-axis flank machining, the flank part of a cutter is used to remove stock materials and finish the design surface. To completely eliminate geometrical deviations when creating complex shapes with a cylindrical cutter is highly difficult, if not impossible. The cutter will induce substantial deviations near twisted surface regions, or in a mathematical term, not locally developable (Chu & Chen, 2006). Precise control of the machining deviations is lack of solutions.

The geometrical deviations in 5-axis flank finishing of ruled surfaces can be reduced by adjusting all cutter locations of a tool path simultaneously. Previous studies (Chu et al., 2011, Hsieh and Chu, 2010, Hsieh and Chu, 2012) have proposed various optimization schemes based on meta-heuristic algorithms to conduct the adjustment. Chu et al. (2011) transformed the tool path planning of a ruled surface into a 2D curve matching problem. An Ant Colony Systems (ACS) algorithm was applied to calculate an optimal matching with the accumulated geometrical deviations on the machined surface as the objective function. Their method restricted that the cutter contacts the surface at pre-defined discrete points on its boundary curves. Hsieh & Chu (2010) relaxed this constraint by allowing the cutter freely contact the surface and applied the particle swarm optimization (PSO) algorithm to search for optimal solutions. They adopted GPU computing techniques to accelerate the search process. This approach still suffered from unsatisfactory quality of the search results, as the cutter had to make contact with the boundary curves of the surface to be machined.

To overcome this problem, their later study (Hsieh & Chu, 2012) proposed a new encoding scheme of cutter locations in the tool path planning driven by PSO. The cutter could deviate from the surface along the normal, tangent, and bi-normal directions at the end points of the surface rulings. Such additional freedoms in the tool motion enlarge the solution space in the optimization, thus yielding better search results than those of previous studies. Hsieh and Chu (2013) compared the performance of various particle swarm algorithms such PSO, Advanced Particle Swarm Optimization (APSO), and Fully Informed Particle Swarm Optimization (FIPS) algorithms on the tool path planning problem. They constructed a set of representative test surfaces by systematic variations of three surface properties. The test results showed that FIPS perform best in all trials with a large number of cutter locations, but the improvement was not significant when the number is small. Besides, the search process easily converged to local optima and results in poor solutions.

The above reviews have shown that meta-heuristic algorithms provide a systematic approach to controlling and reducing the geometrical deviations in 5-axis flank finishing cut of ruled surfaces through optimization of tool path planning. However, the optimization schemes employed by previous studies including ACS and various PSO algorithms failed to produce good search results due to high dimensionality of the solution space. This study applied optimization methods based on the electromagnetism-like mechanism (EM) to further enhance the solution quality. Two new algorithms were developed from the original EM: a Simplified Electromagnetism-like Mechanism (SEM) algorithm and an electromagnetism-like mechanism with move solution screening (EM-MSS) algorithm. The SEM algorithm simplifies calculation of the interaction forces between particles. The EM-MSS algorithm guarantees continuous improvement of search results by adding a solution screening step. These algorithms were used to optimize the tool path planning with a set of representative test surfaces. The test results were compared with those produced by PSO on computational time and solution quality. In addition, the EM-MSS algorithm incorporates a simultaneous perturbation stochastic approximation (SPSA) procedure to start search with good initial solutions. Conclusion remarks were given to summarize the effectiveness of the EM-based methods on reducing the geometrical deviations in 5-axis flank finishing cut of ruled surfaces.

Section snippets

Tool path encoding

A CNC tool path is defined by a set of cutter locations (CL). The cutter normally follows a linearly interpolated tool motion between consecutive cutter locations. In 5-axis flank finishing cut of a ruled surface, the simplest method for tool path planning is to allow the cutter to move along the surface rulings. The resultant path produces excessive machining deviations in twisted surface regions, though.

A cutter location is specified with respect to a ruled surface as shown in Fig. 1. The

Electromagnetism-like mechanism (EM)

Electromagnetism-like mechanism (EM) is a stochastic optimization method based on electromagnetism (Birbil & Fang, 2003). It is a population-based random search algorithm similar to GA. The original EM algorithm imitates the attraction–repulsion mechanism of the electromagnetism theory. In the algorithm, a solution is a charged particle in search space and its charge relates to the objective function value. Due to the electromagnetic force between two particles, a particle with more charge

Test results

The algorithms described above have been applied to generate optimized tool paths with various test surfaces. The previous study (Hsieh & Chu, 2013) proposed a set of representative ruled surfaces for comparing the effectiveness of different tool path planning methods. These surfaces were constructed by varying three intrinsic properties: curvature (C), twist (T), and the length difference (L) between two boundary curves defining a ruled surface. The surface curvature refers to the maximum

Conclusion

Previous studies have shown that optimized tool path planning driven by meta-heuristic algorithms provides a systematic approach to reducing the geometrical deviations in 5-axis flank finishing cut of ruled surfaces. For example, PSO was applied to simultaneously adjust cutter locations comprising of a tool path so as to minimize the accumulated deviations on the finished surface. The search results thus generated seem to quickly converge to local optima and are difficult to be further

References (12)

There are more references available in the full text version of this article.

Cited by (24)

  • Path optimization for multi-axis EDM drilling of combustor liner cooling holes using SCGA algorithm

    2021, Computers and Industrial Engineering
    Citation Excerpt :

    Finally, conclusions are drawn in Section 7. For decades, to improve machining accuracy and efficiency of part manufacturing, tool path optimization or process planning has drawn intensive attention in different production scenarios such as milling (Chu, Chen, & Chang, 2020; Kuo, Chu, Li, Li, & Gao, 2015), drilling (Ghaiebi & Solimanpur, 2007; Wang et al., 2020), laser cutting (Castelino, D’Souza, & Wright, 2003; Sherif, Jawahar, & Balamurali, 2014), etc. As one of the major basic operations, cost optimization for drilling processes remains one of the major issues (Dewil et al., 2019).

  • Continuity-preserving tool path generation for minimizing machining errors in five-axis CNC flank milling of ruled surfaces

    2020, Journal of Manufacturing Systems
    Citation Excerpt :

    Our previous work [26] has shown that the EM algorithms have a satisfactory performance under such a parameter setting in the similar tool path planning problem. In the previous work [23], the cutter center and axis were changed for all CLs of a tool path using the similar EM and SPSA algorithms. Fig. 8 compares the results obtained by this approach and the optimization scheme proposed in this work.

  • Physics based meta heuristics in manufacturing

    2020, Materials Today: Proceedings
    Citation Excerpt :

    The charge of each point was compared to the objective solution of the problem. If the particle has higher charge then it was found to have better objective solution [45]. The basic steps of EM algorithm are initialization of the value, selection of optimal value in the local region, evaluation of total forces exerted on a charged particle from different fields, assessment of movement of charged particle towards higher interactive fields.

  • Optimized tool path planning for five-axis flank milling of ruled surfaces using geometric decomposition strategy and multi-population harmony search algorithm

    2018, Applied Soft Computing Journal
    Citation Excerpt :

    It can be seen that the minimum speed up is 5x, and maximum speed up reaches 70x. In the above experiments and previous literatures [11,12], the number of CLs is considered as a fixed value (40). Since the tool motion trajectory is consists of a set of CLs and the intermediate CLs of linear interpolation between them, it is a natural idea to set as many CLs as possible to attain a smooth tool motion trajectory and therefore it may bring higher machining quality.

  • A multi-granularity NC program optimization approach for energy efficient machining

    2018, Advances in Engineering Software
    Citation Excerpt :

    Li et al. [9] developed a multi-objective optimization model for scheduling to improve material removal rate (i.e. MRR) and energy efficiency. Different from the research on the manufacturing system level, the research on the machining process level focuses on modeling for decision making [15,16] and the optimization of the aspects involved in the NC machining processes, which mainly include the optimization of NC machining parameters [17–27] and the optimization of tool path [28–38]. In order to support decision making for energy efficient machining, some research work focuses on developing specific models of unit process energy consumption.

View all citing articles on Scopus
View full text