42 CHAPTER 3 PROBLEM DEFINITION 3.1 INTRODUCTION Assemblers are often left with many components that have been inspected and found to have different quality characteristic values. If done at all, matching (mating) components together to result in the best final assemblies may be both awkward and hectic. Mathematical models are proposed in this chapter to evolve newer approaches that can match mating parts together in order to get the minimum possible variation of producing assemblies. The rest of this chapter is organized as follows: In section In section 3.2, piston, piston ring and cylinder assembly is defined. Section 3.3 describes the background of the problem. Section 3.4 explains number of assumptions to outline the problem focused. Section 3.5 details the quality characteristics of the mating parts. Clearances of the assembly are defined in section 3.6. Section 3.7 concludes this chapter. 3.2 PISTON, PISTON RING AND CYLINDER ASSEMBLY PROBLEM A complex assembly, consisting of three components namely, piston, piston ring and cylinder assembly of an automobile head is considered in this work. Selective assembly approach is extensively used in automobile industries and the traditional application in the assembly of piston and cylinder is studied by many researchers. Shun Matsuura & Nobuo Shinozaki
43 (2011) analysed a piston and cylinder assembly. The authors derived an optimal manufacturing mean design that minimises the number of surplus components. David Mease et al. (2012) described about the piston and cylinder assembly and developed optimum binning strategies with different loss functions. In the piston, piston ring and cylinder assembly, there is a target value for clearance and also a tolerance constraint on the clearance. The clearance must be neither too small nor too large, so that the piston scuffing may not occur and also piston must not vibrate. Random assembling of piston, piston ring and cylinder leads to large clearance variations and many products will not satisfy tolerance constraint and so selective assembly is followed in the automobile industry. The piston, piston ring and cylinder are sorted into different subgroups according to their dimensions and the mating parts from subgroups are assembled so that the clearance variation of the assembly is minimized. Furthermore, there are more than one quality characteristics available in the mating parts, which lead to more clearances resulting in change in clearance variations. The schematic representation of the piston, piston ring and cylinder assembly with the different dimensional tolerances is given in Figure 3.1. Figure 3.1 Piston, Piston ring and Cylinder assembly
44 3.3 BACKGROUND OF THE PROBLEM In a complex assembly, there are three or more mating components are assembled together to perform the intended function. The quality of the complex assembly relies on the quality of its mating parts. Each mating parts are produced by various types of manufacturing processes in more numbers, using different types of machineries. The dimensional distribution of a particular mating part is not uniform and is depending upon the process capability of manufacturing process and the operating condition of the machine. Further, the dimensional distribution of the mating parts will be equivalent to manufacturing tolerance or process capability (±3σ) which leads to the quality characteristics of the mating part. In the complex assembly, the dimensional tolerancing specifies the acceptable size of the mating part feature which is typically limited to linear dimensions. In an interchangeable assembly system, the mating parts are manufactured and assembled at random. So, the maximum and the minimum tolerance limits of the assembly will be the sum of the maximum and minimum tolerances of the mating parts respectively. But, to minimize the clearance variations of the assembly, it is strictly required to reduce the individual mating part tolerance through better manufacturing process or by better machines. This is not advisable in economic point of view and furthermore, it may not possible to achieve a closer tolerance in interchangeable assembly. In complex assembly, it is possible to achieve closer tolerance from relatively low precision mating parts by selective assembly. 3.4 ASSUMPTIONS The assumptions made in both the proposed model include i. All the component measurements are taken for the whole batch.
45 ii. iii. iv. There is no mean shift from the nominal dimensions of components. The assembly functions are linear. There is no error in measured dimension values. v. No dimension value is dispersed beyond 3σ level. vi. vii. Normal dimensional distribution is considered. There is no constraint on the availability of mating parts. 3.5 QUALITY CHARACTERISTICS OF THE MATING PARTS In the assembly, there are seven key characteristics in which the piston and piston ring contribute three key dimensions each and the cylinder has one. The quality characteristics of the piston, piston ring and cylinder considered in this work are given in Table 3.1. Table 3.1 Quality characteristics of the piston and cylinder assembly Sl. No. Component Characteristic Representation Tolerance 1 Piston Piston groove diameter A 18 µm 2 Piston Piston diameter B 12 µm 3 Piston Piston groove thickness C 12 µm 4 Piston ring Piston ring width D 18 µm 5 Piston ring Piston ring thickness E 6 µm 6 Piston ring Piston ring outer diameter F 24 µm 7 Cylinder Cylinder inner diameter G 24 µm
46 Figure 3.2 Dimensional distributions of quality characteristics with six sub groups 3.6 CLEARANCES OF THE ASSEMBLY From the quality characteristics given in table 3.1, the following four possible combinations of clearance may contribute to the clearance variations of the assembly, i) Clearance 1 (C1): Piston groove diameter (A) Piston ring width (D) Cylinder inner diameter (G) ii) Clearance 2 (C2): Piston groove thickness (C) Piston ring thickness (E) iii) Clearance 3 (C3): Piston diameter (B) Cylinder inner diameter (G) iv) Clearance 4 (C4): Piston ring outer diameter (F) Cylinder inner diameter (G)
47 If the mating parts are interchangeably assembled, the assembly clearance will be calculated as the sum to the maximum tolerances of the characteristics of the parts minus sum of the minimum tolerances of the characteristics of the parts. But, in selective assembly the parts are sorted according to the ascending order of the dimensional values within the tolerance limits of the quality characteristics. Rubenchik et al. (1979) focused on attaining the required assembly precision by employing equal width partitioning where every class has an equal width. Accordingly, the parts are portioned into sub groups by equal width scheme in which the tolerance of the quality characteristics is divided by number of sub groups. In this work, the seven characteristic are grouped into six groups, so that the sub group tolerance for characteristic A is 3 µm, B is 2 µm, C is 2 µm, D is 3 µm, E is 1 µm, F is 4 µm and G is 4 µm. The dimensional distribution of the quality characteristics with six sub groups are shown in Figure 3.2. For an assembly set, the selection of the combinations of sub groups from different characteristics will lead to numerous different solutions and there is a challenge to find out the better combination of sub groups with minimal clearance variations. Further, in the piston, piston ring and cylinder assembly, four different clearances (C1,C2, C3 and C4) contributes to the quality of the assembly, it is needed to go for multi characteristics optimization. 3.7 CONCLUSION As product assembly comprises of many components with multiple characteristics, optimization of assembly tolerance variation is becoming tougher and tougher. Also, only by the efficient search mechanism, the desired performance measures of the assembly can be improved.hence, the objective of this research work is to evolve intelligent search heuristic
48 procedures to generate satisfactory, nearer-to-optimal selective group combinations. In this chapter, the background of the problem has been defined. Piston, piston ring and cylinder assembly has been described. Required assumptions were outlined for the problem focused. With the details the quality characteristics of the mating parts, Clearances of the assembly have been defined. The search heuristics developed in this work such as modified particle swarm algorithm and ant colony algorithm are evaluated by conducting experiments through simulation.