Yuqiao Zheng， Honghong Jin and Chengcheng Zhang

（School of Mechanical and Electronical Engineering, Lanzhou University of Technology,Lanzhou 730050, China）

Abstract: A method for hub assembly sequence planning oriented to the fixed position layout is proposed. An assembly relationship model was constructed to describe the relationship between hub assembly components and workstations, considering the layout of the hub assembly line and process constraints, including the assembly precedence matrix, workstation assembly capability table and criticality table of components. The evaluation mechanism for the assembly sequence was established. Values from the evaluation functions with engineering significance were used to select the optimal assembly sequence from the perspective of assembly time, assembly index and assembly path distance. In function, the criticality of components was introduced into the traditional assemblability index, comparing the multi-objective dragonfly algorithm (MODA) with non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ) to complete the assembly sequence planning and assignment for workstations. The optimized results show that the presented method is feasible and efficient for solving the hub assembly sequence planning problem.

Key words: wind turbine hub；fixed-position layout；assembly sequence planning

The hub is one of the most complex stresses and highly reliable components in wind turbines.Its assembly consists of multiple processes, with a considerable number of components and a complex structure[1-3]. The riveting assembly process is a very effective method for assembling lightweight, integrated and highly reliable automobile hub bearings[4]. Assembly production is the final production link before the hub is put into use, and it has a pivotal role in determining the performance of the hub. In the modern wind turbine industry, one of the core processes is the hub assembly of bolt and nut connections to obtain a well-distributed clamping force throughout the hub[5]. In the assembly of the wind turbine hub, assembly sequence planning (ASP) is a combinatorial optimization problem under typical constraints and aims to generate an optimal assembly sequence to assemble the different components into the hub. There is evidence that ASP plays a crucial role in regulating the assembly quality, production efficiency and other aspects,thus directly affecting the assembly cost[6].

The past thirty years have seen the rapid development of intelligent optimization algorithms in solving ASP, but few studies have investigated the optimization of hub assembly sequences in any systematic way. Therefore, this paper discusses ASP for the wind turbine hub to acquire a better assembly sequence, to ensure the hub assembly quality, and to increase production efficiency. ASP has long been a question of great interest in a wide range of fields. One of the most important innovations of the 1980s was that several approaches were researched to generate assembly sequences, such as the SAAT system of Stanford University and the GAPP system of the flexible manufacturing center of Mc-Master University in Canada[7]. The first serious discussions and analyses of applying computers to solve the assembly process planning problems emerged from this era, which was an essential milestone for ASP issues[8]. Subsequently, there has been an increasing interest in the assembly sequence planning problem[9-10]. Laperriere et al.published a paper in which they described a generative assembly process planner (GAPP) to generate and evaluate assembly sequence alternatives.

Previous ASP research has not dealt with the key process, and most studies in the field of ASP have only focused on the ordinary assembly line, ignoring the fixed position layout of the assembly line. The traditional assembly sequence of the hub is mainly completed by technicians towards the end of the product design phase based on design drawings, technical documents and related experience etc. It’s almost impossible to achieve the best effect in different assembly environments, and the method has a large and inefficient workload.

The overall objective of this paper is to propose a novel solution to address the assembly sequence planning model for the hub of a fixed-position layout, while the components are distributed and assembled at different workstations[11-12].This is the first study on the optimization of the hub assembly, and the present research explores,for the first time, the effects of key processes on ASP in order to remedy the shortcomings of traditional assembly sequence planning for the wind turbine hub, combined with the characteristics of fixed production object and team operation of the fixed position layout production model. We took the assembly of a wind turbine hub as the research object to begin this process, then introduced the hub assembly process and the characteristics of the hub assembly production line in detail, identified the crucial process by the improved Taguchi quality loss function, and then constructed an assembly relationship model of the hub that provides a variety of assembly information[13]. The second question was designed to establish the evaluation mechanism for the assembly sequence by minimizing assembly time,assembly index, and assembly path distance.Then a multi-objective assembly sequence planning model was presented. Finally, a method using the NSGA-Ⅱ and MODA was developed for completing the component assembly sequence and workstation assembly task planning. A new encoding scheme was developed, which is suitable for simultaneously performing assembly sequence generation and workstation assignment[14-15]. The term total assemblyability index will be used to refer to the traditional assemblability index and the criticality of the components.

1 Assembly Relationship Model of the Wind Turbine Hub

The assembly relationship model not only satisfies the information requirements in the assembly sequence planning of hub, but it’s the primary task for assembly sequence planning.

1.1 Introduction to an assembly production line

The hub serves as the connection between the wind turbine blade and the spindle, and its importance becomes more apparent as the capacity of the wind turbine increases. The material of the hub is QT400, the weight is up to 14.65 T,and the hub weight after finally assembly is 21.8 T.

The assembly production line adopts the fixed position principle layout, because the hub is extremely bulky and heavy. In this layout, the components and equipment are around the main hub body according to the order of use. During the assembly process, 15 types of components such as a pitch reducer and pitch bearing are installed and commissioned on the hub body.Therefore, the position where the hub body and components are placed can be regarded as the workstation for the layout analysis of the hub assembly. Fig.1 presents an overview of the hub assembly workstations layout.

Fig.1 Hub assembly workstations layout

1.2 Workstation assembly capacity

The workstation assembly tasks are determined by workstation assembly capability, and the components need to be assigned to the workstation that meets the assembly requirements. The available workstation assembly capability needs to be formulated for the modeling requirements,the workstation assembly capacity table of the hub was developed to signify the workstation assembly capacity, according to the actual production process of the 2.5 MW wind turbine hub assembly in China, as shown in Tab.1.

Where, if the value is 1 in Tab.1, it indicates that component j can be assembled in workstation i; otherwise, component j cannot be assembled in workstation i.

1.3 Assembly priority relationship

In the hub components, the limit switch bracket and the limit switch must be assembled in order at one time, and this is regarded as a component consideration when building the model. In the same way, the mounting of encoder brackets and encoders, the installation of lubricated gear brackets and the lubrication gears are regarded as a single component consideration, so the 16 types of components can be simplified to 13 types. (1. Hub body, 2. Pitch reducer, 3.Pitch bearing, 4. Control cabinet, 5. Pitch motor,6. Limit switch bracket and limit switch, 7. Encoder bracket and encoder, 8. Impact bar, 9.Trunking, 10. Pitch lubricated gear bracket and pitch lubrication gear, 11. Lubrication system,12. Shroud bracket, 13. Shroud).

During the assembly process of the hub, the connection between one component and another component is described by the assembly connection matrix A={amn}:

Tab. 1 Hub workstation assembly capacity

From the matrix below, the hub assembly connections are expressed as

The assembly precedence graph (APG) is developed to represent the components and the assembly operations. Therefore, it can be viewed as a directed graph showing the precedence of the components and the assembly operations. The APG of the hub components is shown in Fig.2. It is apparent from Fig.2 that components are divided into 3 levels, component 1 is the first level,components 2, 3, 4, 9, 10, 12 are the second level,and the third level includes components 5, 6, 7,8, 11, 13.

Fig.2 Assembly precedence graph (APG) of hub components

The assembly precedence graph needs to be converted into a digital matrix when analyzing and evaluating assembly sequences. The assembly precedence matrix (APM) for the components of the hub is shown in Fig.2.

jmand jnare hub components, and m and n are the number of components. The value bmn=0 signifies that there is no precedence between two the components jmand jn, otherwise component jmmust be assembled before component jn.

1.4 Criticality of the components

The key processes directly affect product quality, reliability and cost[13]. They focuse on how to identify critical processes. This problem was solved by electing 12 quantitative quality characteristics of the hub assembly, using key characteristics as a link, and adopting the improved Taguchi quality loss function to identify the key processes for hub assembly. Then, we use key processes to determine the criticality of the hub components.

For an assembly production system consisting of n processes, the improved Taguchi quality loss function is represented as

where the production cost of the ith process is Ai,the raw material cost is A0, the quality loss coefficient is ki, the quality characteristic detection value is Yi, the target value is Ti, the tolerance is Δi.

The total quality loss and degree of quality loss were introduced to study the relative quality loss, shown as

The calculation and comparison of the loss of the quality characteristics of the hub assembly yields:

It can be determined from Eq.(5) that the installation of the pitch bearing and the adjustment of the eccentricity of the pitch reducer are key processes. These key processes result in the assembly process of the hub component 3. Tab.2 illustrates the criticality of hub components.

Tab. 2 Criticality of hub components

2 Assembly Sequence Planning Model of Hub

Proper assembly sequence can be advantageous in terms of time and capital, and also increase the market competitiveness of different enterprises[16-17]. The evaluation mechanism for an assembly sequence to achieve the optimum is established by the value determined by the evaluation function with engineering significance. The assembly sequence planning model, which included the generation and evaluation of assembly sequences according to the state of the hub assembly, was built.

2.1 Total assemblability index and membership

The total assemblability index decides which of the new sequences should be used. Moreover,it is a relative conceptual indicator that is affected by various factors such as component structure and assembly resources. There were six indicators to consider when developing a total assemblability index solution to this problem. This included the number of assembly relationships,weight and volume, geometric relationship constraints, assembly symmetry, and components criticality, and were converted into dimensionless data with fuzzy sets.

2.1.1 Number of assembly relationships

To a certain extent, the difficulty degree of assembly is determined by the connection relationships between components. The components with many connection relationships should be assembled first. For the hub assembly process, the assembly relationship number weight function is defined as

where L is the number of connections of the hub components; ajis the weight of the assembly relationship number.

We divided the assembly relationship of the components into four levels: {1, 4}, {3}, {2, 7,11}, {5, 6, 8, 9, 10, 12, 13}, according to the assembly relationship number weighting function,which endowed a relationship weight of 1.0, 0.7,0.3, and 0.1, respectively.

2.1.2 Weight and volume

During the assembly process of the wind turbine hub, large and heavy components should be assembled first. Components of medium weight and volume should be assembled second, and the light-weight components should be assembled last.

where G is the weight of the hub assembly components and gjis the weight of the component.

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The membership of each hub component’s weight was determined, according to Eq.(7), and the components were divided into five-levels: {1},{3}, {0}, {2, 4, 5, 12}, {6, 7, 8, 9, 10, 11, 13}, endowed a weight of 1.0, 0.8, 0.6, 0.4, 0.2, respectively. In the same way, the components were arranged in descending order into five degrees: {1,13}, {2, 3, 4}, {5, 12}, {11}, {6, 7, 8, 9, 10} according to the volume relationship of each hub component, respectively endowed the volume weights of 1.0, 0.8, 0.6, 0.4, 0.2.

2.1.3 Geometric relationship constraints

Geometric relationship constraint, which is the ability to meet the space requirements of component assembly, is critical for the hub assembly. During the assembly process, the internal components are assembled first, followed by the external components, which are mainly completed manually. We divided the components into the following four levels according to the inner-outer relationship of the hub components:{1}, {2, 4, 5, 11}, {3, 6, 7, 9, 10, 12}, {8,13}, respectively assigned geometric constraint weights of 1.0, 0.7, 0.3, and 0.1.

2.1.4 Assembly symmetry

This index is not fully applicable to hub assembly and we have changed it to geometric regularity since the rotor proportion in the hub assembly components is deficient. The geometric regularity of the hub components was arranged in descending order of three levels: {1, 2, 3, 4, 12,13}, {5}, {6, 7, 8, 9, 10, 11}. The weight of this index is small due to its minor influence on assembly sequence, so the geometric regular weights of 0.1, 0.2, and 0.3 were assigned respectively.

2.1.5 Criticality of components

It is obvious that when the hub is assembled, components of great criticality should be assembled with priority. According to the criticality of the hub components table, component 3 was given a critical weight of 1.

Tab. 3 illustrates the comprehensive weight calculation results of the total assemblyability index of the hub components, which includes a variety of assembly information. What stands out in Tab. 3 is that components 1-5 have a more comprehensive weight and should be assembled first as much as possible, components 6-13 have a smaller overall weight, and the assembly sequence can be postponed.

2.2 Mathematical description of the hub assembly process

2.2.1 Limitation of the hub assembly process

The debugging and inspection processes arenot considered when the hub assembly sequence is optimized, because these do not include the assembly of the component. Instead, they are added according to the logical relationship after optimization. In order to build the assembly sequence planning model, we first outline the hub assembly process:

Tab. 3 Comprehensive weight of the total assemblability index

① The assembly process of the hub is closed,and the assembly of other components can only start after the assembly of one component is completed;

② Each type of component only has one operational requirement, and the same type of components are in the order of assembly;

③ Each workstation can be equipped with up to 2 types of components, bur workstation 1 can only assemble component 1;

④ Information on the hub assembly model is given as a known condition.

2.2.2 Mathematical description of the assembly

sequence optimization process

The hub assembly process arranges 13 types of components to 7 workstations for assembly.For example, the jth (j=1, 2, ···,13) components assigned to the ith (i=1, 2, ···,7) workstations achieve assembly.

Here, a Boolean variable xijis used to indicate interactions between the components and the workstations is defined with

The assembly state of the components is represented by a Boolean vector P = {pj1, pj2, ···,pjn}, where j1, j2, ···, jn are a given assembly sequence.

The constraints of the hub assembly process include component constraints and workstation constraints, which can be expressed as

① Components constraints

xmj≤xnk,?(j,k)∈APM, m, n=1,2,··· ,7(component assembly must meet the priority relationship)

②Workstations constraints

If xij=1, then prj?wri(the assembly capability of the workstation i meets the tooling requirements of the hub assembly components j )

Where xij, xwj, xnkdenote the relationship between the components and the workstations;prjdenotes the tooling requirements of the component j; wridenotes the assembly ability of the workstation i; pjndenotes the assembly status of component j.

2.3 Evaluation function of hub assembly sequence planning

This unit decides which newly generated assembly sequence should be used based on the evaluation function. If the evaluation function value is superior, then the assembly sequence may be used.

2.3.1 Evaluation function of assembly time

When the evaluation index is the assembly time, the calculation of assembly time does not simply add up the assembly time of all the components. It is necessary to distinguish whether the components are assembled in parallel. For serial components, the time is directly added.But for parallel components, the assembly time of two parallel components should be compared,and the longer assembly time of the two components is counted in the total assembly time. The hub assembly process includes parallel components (the assembly between components 6, 7, 8,and 9 can be treated as a parallel process).Therefore, the evaluation function is

where tjis the assembly time of parallel components j1, j2, and tj= {tj1, tj2}; tj＇is the assembly time of serial components j; J is a set of hub assembly components, J={6, 7, 8, 9}, J ={1, 2, 3,4, 5, 10, 11, 12, 13}; aj1j2is a Boolean vector that identifies parallel components, and

2.3.2 Evaluation function of the total assemblability index

The assembly sequence of the hub components is closely related to the comprehensive weight of the total assemblability index. The evaluation function of the total assemblability index can be cumulatively represented by the product of the position of the component assembly sequence and the full weight of the assemblability total index:

where Wsy(j) is the comprehensive weight of the total assemblability index of component j; sjis the assembly order of component j.

2.3.3 Evaluation function of assembly path distance

Because the layout of the hub assembly line adopts the positioning principle, the heavier components should be as close as possible to the body of the hub. Taking the shortest assembly path as the evaluation index and considering the fuction weight, the evaluation function is

where d1iis the distance from the workstation i to the hub body; njis the number of component j; gjis the weight of component weight; xijis the relationship between the component j and the workstation i.

3 Solving and Analyzing the Hub Assembly Sequence Planning Model

3.1 Solution using an NSGA-Ⅱ method

NSGA-Ⅱ was selected to settle the hub assembly sequence planning model because of its reliability and validity. The hub assembly sequence and workstation allocation can be optimized under the effective constraint of the workstations and the components after performing a series of genetic operations and satisfying the terminal conditions. According to the purpose of the hub assembly sequence planning, in this work, a new encoding scheme was used to represent the integrated assembly sequences. The chromosome adopts a two-layer coding method, and the first and second layers of codes respectively determine the assembly order and the assembly workstation of the components. The hub assembly sequence currently used is represented by chromosome coding as Tab.4 and is assessed under the evaluation function: f1=27.7, f2=138.3, f3=35.6.

Tab. 4 Current hub assembly sequence

At the initial stage of optimization, a stochastic initialization assembly sequence is selected. Although some invalid solutions may be generated, the diversity of the population is guaranteed and premature algorithms can be avoided.

The genetic operation of NSGA-Ⅱ involves the selection, crossover, and mutation of populations. The tournament method is selected such that parents are chosen based on their hierarchical value and the crowding distance, that is, after non-dominated sorting of the population. For the two-layer coding method of the hub assembly,the crossover probability is set to Pc, and the mutation probability is Pm. When the random number generated by the chromosome is smaller than Pcor Pm, cross operation or mutation operation is performed, and the random number is again generated and compared with 0.5. Therefore, the two layers of coding each have a 50%probability of crossing and mutating. At the same time, in order to ensure the correctness and validity of the obtained hub assembly sequence,it is necessary to perform the workstation constraint test and the component constraint test on the chromosome, then use the penalty function to eliminate the chromosomes that do not meet the constraint. The specific application of NSGA-Ⅱin assembly sequence planning is as shown in Fig.3.

The detailed NSGA-Ⅱ algorithm is introduced as follows.

Step 1 Set up parameters.

Set iteration t=0. T Number: the iteration(generation) number defining the condition that the algorithm stops. P Size: the population size defining the number of chromosomes. Probability Pcand probability Pmare the probabilities defining the crossover and mutation, respectively.

Step 2 Initialize a population of chromosomes and Non-dominated sorting of population.

Step 3 Check feasibility of the solution. Perform the workstation constraint test and the component constraint test on the chromosome.Use the penalty function to eliminate unfit chromosomes.

Step 4 Non-dominated sorting and selection.Non-dominated sorting of Rtand selection of N individuals through pushing out and elite strategy to frame a new generation population Pt+1.

Step 5 Check and go. Check end conditions.If the stopping criterion is not reached, then go to Step 4, otherwise, return to Step 1.

Step 6 Interpret the best solution.

3.2 Solution using a MODA method

Fig.3 Flowchart of the NSGA-II method

The advantage of using MODA is that it is simple to deliver. The single-layer and doublelength coding method is adopted when solving the hub assembly sequence planning model. Each dragonfly position represents an assembly sequence of the hub, the first half of the coding determines the assembly order of the hub components, and the latter half of the coding determines the assembly workstation of the components.Through the five behaviors of separation, alignment, cohesion, food attraction, and natural enemy rejection, the dragonfly position is continuously updated. The Pareto solution set is dilivered when the termination condition is satisfied.

3.3 Implementation and comparison results

In this section, the optimization results demonstrate that the proposed method is feasible and efficient. The NSGA-Ⅱ method is selected to solve the hub assembly sequence planning model in MATLAB. The configurations of the optimization environment are as follows: the initial population size is set to 200, the iteration number is 100, the crossover probability Pc=0.8,and the mutation probability Pm=0.1; The MODA parameters in the MATLAB environment are set as follows: the population size is 300 and the iteration number is 100. The results of the comparison iteration curves of f1-f3analysis are shown in Fig.4.

As observed from the optimization results,the developed models present a feasible and efficient solution methodology with a near optimal result. From the comparison results of the optimal solution, we can find that the convergence accuracy and optimization ability of NSGA-Ⅱ are better than that of MODA. What stands out is the evaluation function f2. The optimal solution of NSGA-Ⅱ is obviously better than that of MODA. At the same time, MODA takes significantly longer than NSGA-Ⅱ. Therefore, we can conclude that NSGA-Ⅱ’s overall performance is excellent. The target solution accuracy is extremely high, while MODA has premature convergence and local optimality. According to the curve comparison between MODA and NSGA-Ⅱ,it can be found that the blue line converges faster than the red line. Fig.4 shows that the convergence rate of MODA is faster than that of NSGA-Ⅱ, and the ability of the algorithm to avoid local extrems is better than that of NSGA-Ⅱ. It is obvious that MODA has enough information exchange when searching for excellence.

Fig.4 Comparison of the results of the NSGA-II method and the MODA method

Further analysis showed that NSGA-Ⅱ is more suitable for the optimization of the hub assembly sequence, as the NSGA-Ⅱ algorithm produced six Pareto solutions. Since the importance relationship of f1-f3is: f1＞f2＞f3, the function value of the selected pareto solution is f1=27.7,f2=135.1, f3=34.4, and the chromosome decoding information shows that the components assembly sequence is 1-2-3-4-5-10-11-9-7-6-8-12-13,and the corresponding workstations are 1-2-2-3-3-4-4-5-5-6-6-7-7. Overall, these results indicate that the total assembly ability index of the selected Pareto solution is reduced by 3.2, the assembly path distance based on the weight of components’ weight is reduced by 0.6, and the two components of the adjacent processing sequence are in the same workstation. This optimization solution has a better optimization than the previous solution.

The equilibrium diagram of the pareto solution is shown in Fig.5, showing the correspondence between the hub components and the workstations. Component 6 and the component 8 are assembled in parallel.

Fig.5 Production line balance chart of Pareto solution

4 Conclusion

The hub assembly process is complex and the assembly quality requirements are high. In this investigation, the aim was to present a new approach for hub assembly sequence planning to perform two tasks: assembly sequence planning and workstation assignment, taking the characteristics of fixed position layout assembly line into consideration. This study has shown that the assembly relationship model, assembly sequence planning model and the evaluation mechanism are all effective. The NSGA-Ⅱ method and MODA method were presented to search for better solutions of multi-workstation assembly sequences. Both solution accuracy and convergence rate were analyzed and compared between the NSGA-Ⅱ and MODA method. Preliminary results show that in comparing the optimal solution with the current solution, the total assembly index is reduced by 3.2, the assembly path distance based on part weight is reduced by 0.6. Moreover, two subsequent parts in the processing sequence were at the same station. This thesis has provided a more in-depth insight into assembly sequence planning of a wind turbine hub.