Sheng Yang
email: sheng.yang@mail.mcgill.ca

Florian Santoro
email: florian.santoro@mail.mcgill.ca

Yaoyao Fiona Zhao
email: yaoyao.zhao@mcgill.ca

Towards a numerical approach of finding candidates for additive manufacturing-enabled part consolidation

Keywords: part consolidation, part selection, design for additive manufacturing, product design

Part consolidation (PC) is one of the typical design freedoms enabled by AM processes. However, how to select potential candidates for PC is rarely discussed. This deficiency has hindered AM from wider applications in industry. Currently available design guidelines are based on obsolete heuristic rules provided for conventional manufacturing processes. This paper firstly revises these rules to take account of AM constraints and lifecycle factors so that efforts can be saved and used at the downstream detailed design stage. To automate the implementation of these revised rules, a numerical approach named part consolidation candidate detection (PCCD) framework is proposed. This framework is comprised of two steps: construct functional and physical interaction (FPI) network and PCCD algorithm. FPI network is to abstractly represent the interaction relations between components as a graph whose nodes and edges have defined physical attributes. These attributes are taken as inputs for the PCCD algorithm to verify conformance to the revised rules. In this PCCD algorithm, verification sequence of rules, conflict handling, and the optimum grouping approach with the minimum part count are studied. Compared to manual ad-hoc design practices, the proposed PCCD method shows promise in repeatability,

Introduction

Part consolidation (PC) is an effective design technique to reduce part count and simplify product architecture [START_REF] Boothroyd | Product design for manufacture and assembly[END_REF]. Through PC, it is expected to cut cost, reduce weight, and enhance performance (e.g. avoid leakage). Additive Manufacturing (AM)-enabled PC, because of its freedom of material distribution and composition, has further released the potential of minimizing part count [START_REF] Yang | Assembly-level design for additive manufacturing: issues and benchmark[END_REF][START_REF] Yang | Additive manufacturing-enabled design theory and methodology: a critical review[END_REF][START_REF] Schmelzle | Re) Designing for Part Consolidation: Understanding the Challenges of Metal Additive Manufacturing[END_REF]. Both industries [START_REF]Additive Manufacturing Redefining What's Possible[END_REF][START_REF] Dietrich | Impact of integrative design on additive manufacturing quality[END_REF][START_REF]An Epiphany Of Disruption: GE Additive Chief Explains How 3D Printing Will Upend Manufacturing[END_REF] and academics [START_REF] Schmelzle | Re) Designing for Part Consolidation: Understanding the Challenges of Metal Additive Manufacturing[END_REF][START_REF] Kumke | A new methodological framework for design for additive manufacturing[END_REF][START_REF] Yang | A Generic Sustainability Assessment Model towards Consolidated Parts Fabricated by Additive Manufacturing Process[END_REF] have shown passion to apply the emerging new capabilities into product innovation. In particular, GE reports consolidation of 900 components (including fasteners) of a helicopter engine into 14 parts within which one specific part is derived from an assembly of 300 parts.

The consolidated design is 40 percent lighter and 60 percent cheaper [START_REF]An Epiphany Of Disruption: GE Additive Chief Explains How 3D Printing Will Upend Manufacturing[END_REF]. However, most ad-hoc design practices start directly with carefully selected (sub)assemblies without mentioning the selection criteria.

The knowledge gap of PC feasibility criteria and lack of a systematic decision-support tool hinders PC from much wider applications.

Motivation

Through interview with designers in industry with limited AM expertise, we know that one of their main concerns about PC is how to find potential candidates for AM-enabled PC. We define this problem as part consolidation candidate detection (PCCD) problem. With the input of a given product/assembly, the main task is to cluster all its components into feasible groups where all members can be consolidated and fabricated as one part. Available design guidelines are the three heuristic questions proposed by Boothroyd et al. [START_REF] Boothroyd | Product design for manufacture and assembly[END_REF] as "no relative motion", "no material variance", and "no blockage of assembly access of other components". However, these three heuristic rules do not hold in AM context [START_REF] Yang | Assembly-level design for additive manufacturing: issues and benchmark[END_REF][START_REF] Schmelzle | Re) Designing for Part Consolidation: Understanding the Challenges of Metal Additive Manufacturing[END_REF]. Counter examples can be a 3D printed chainmail [START_REF] Gibson | Additive Manufacturing Technologies:Rapid Prototyping to Direct Digital Manufacturing[END_REF] and a dental implant achieved by functionally graded material [START_REF] Mehrali | Dental implants from functionally graded materials[END_REF]. Sticking to the conventional three heuristic rules will result in ignorance of potential candidates for design innovation. Then, it comes to the first question (Q1) as: what rules should designers follow to check whether two components are feasible to be consolidated or not? Another issue related to the conventional heuristic rules is its localized view of component-pair relation. All the three rules are focused on checking the feasibility of component-pair link relation. If all three rules are satisfied, then the link reserves. However, this approach fails to provide any guidance in such a situation when feasible links are chained into a bigger component group and the size exceeds the limit of 3D printers. Then, the second question (Q2) arises as how to dissect a product into feasible groups with minimum part count in AM context? An example is shown in Figure 1. Each node represents one component and each link represents that there is no relative motion, no material variance, and no assembly access issues between its connected nodes. However, printing all these components as one part is impossible because of size limitation. Manual enumeration of all feasible solutions can be time-consuming ( ) since each combinatory solution has to be checked for its stack up size. Therefore, a more feasible and efficient approach has to be developed. In this paper, both Q1 and Q2 are investigated. In the first place, feasibility rules for AM-enabled PC are proposed on the basis of AM characteristics in Section 3. Secondly, to support informed decision making of product dissection, a numerical approach named PCCD is presented with the core idea of building adjacent graph through which all feasibility rules can be validated semi-automatically. How to construct such an adjacent graph and how to verify feasibility rules on this graph are clearly presented in Section 5 and 6 respectively. Two case studies with different focuses are investigated to demonstrate the 4 effectiveness of the proposed PCCD algorithm. In the end, time expense for heuristics and PCCD is compared and future research is discussed in Section 8.

Concept definition

To clear confusion, some important concepts are defined here.

 Component/part: one inseparable physical entity with no joining process involved in the manufacturing process.

 Assembly: a physical entity joined by multiple components and/or sub-assemblies.

 Node: normally it refers to one component or part; exception is made if users define an assembly as one single unit (e.g. motor).

 Group: a group of nodes.

 Pair-wise link: a link between a pair of nodes.

 Link/edge: connection between two nodes.

Literature review

The previous study related to this paper is distributed into three main streams: conventional heuristic rules, assembly-level DFAM, and PCCD strategies. Each one is briefly summarized as follows.

Conventional heuristic rules

PC is originally studied as one sub-topic of design for manufacture (DFM) and design for assembly (DFA). The number of parts is determined by the balance of ease of manufacture and ease of assembly operation. The most well-known heuristic rules deployed to find potential candidates for PC are proposed by Boothroyd et al. [START_REF] Boothroyd | Product design for manufacture and assembly[END_REF]. These rules are comprised of three questions:

(1) Does the part move with respect to all the parts already assembled? (relative motion rule)

(2) Must the part be made of a different material or be isolated from all other parts already assembled? (material variance rule)

(3) Must the part be separate from all other parts already assembled because necessary assembly or disassembly would otherwise be impossible? (assembly access rule) If these three rules are satisfied, these two parts are suitable for consolidation. As Frey et al. [START_REF] Frey | Part count and design of robust systems[END_REF] pointed out, these rules are helpful to provide guidance for novice designers to avoid mistakes, but it is insufficient to make the final decision for PC because other constraints such as cost, quality, and lifecycle constraints (e.g. manufacturing and maintenance needs) also matter. Fagade and Kazmer [START_REF] Fagade | Optimal component consolidation in molded product design[END_REF] drew five more rules with a focus on economic and ecology factors. These rules are: In total, these eight rules cover the whole spectrum of design stages, but taking the full package into early design stage can be challenging because it requires very high-level knowledge integration. One feasible solution is to selectively deploy these rules at different design stages. Second, these rules fail to synchronize with the advance of manufacturing process, such as AM. For example, rule (4) is unnecessary for AM because it does not require any tooling at all for printing process. Third, heuristic rules need manual interpretation and the result may vary for different designers. It is difficult to document the logic in the decision-making process; therefore, when new technologies emerge, the whole process has to start over again. Lastly, these rules only focus on local information (i.e. a component pair) rather than a group of components. This may work for small-scale product design (part count <10), but when it comes to larger-scale ones especially those with numerical constraints (e.g. building volume size limitation), a manual check for each combination of components can be disastrous. 6

Assembly-level DfAM

In DfAM research, the main tasks are to investigate both the opportunistic and restrictive sides of AM [START_REF] Yang | Additive manufacturing-enabled design theory and methodology: a critical review[END_REF][START_REF] Thompson | Design for Additive Manufacturing: Trends, opportunities, considerations, and constraints[END_REF]. PC belongs to the scope of assembly-level DfAM [START_REF] Yang | Assembly-level design for additive manufacturing: issues and benchmark[END_REF] which maximizes the usage of AM-enabled design freedoms (e.g. multi-material design) with respect to general constraints of an AM process to achieve better performance and more compact design. Comparatively, part-level DfAM is more centralized on developing shape synthesis techniques and understanding the specific manufacturing rules of AM processes [START_REF] Rosen | A review of synthesis methods for additive manufacturing[END_REF]. In this paper, AM manufacturing constraints are classified as two types: general constraints and specific constraints. General constraints are those that determine the manufacturing feasibility of adapting AM processes. Typical constraints are building volume and available materials. In contrast, specific constraints are highly related to geometry or printing parameters, such as wall thickness, anisotropic material properties, and overhang area. Therefore, assembly-level DfAM only needs to account for general constraints while specific constraints are postponed to the detailed design stage (e.g.

part-level DfAM).

Assembly-level design freedom is mainly comprised of articulated mechanisms [START_REF] Calì | 3Dprinting of non-assembly, articulated models[END_REF], functionally graded material (FGM) [START_REF] Hedia | A new design of cemented stem using functionally graded materials (FGM)[END_REF], embedded components [START_REF] Kataria | Building around inserts: Methods for fabricating complex devices in stereolithography[END_REF], multifunctional design [START_REF] Panesar | Design Framework for Multifunctional Additive Manufacturing: Placement and Routing of Three-Dimensional Printed Circuit Volumes[END_REF], and compliant mechanisms [START_REF] Gaynor | Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing[END_REF]. Although all these design freedoms have the potential to reduce part count, most of them are still in the concept development stage.

PCCD strategies

This section summarizes reported PC practices in the AM field and evaluates the reported case studies in terms of PCCD strategies, selected product/assembly, degree of modularization, problem scale, and final part count. Reported literatures [4-6, 8, 21, 22] are case-specific and mostly concentrated on presenting the advantages of consolidated design without specifying any methodological design framework. Detailed review is presented by Yang et al. [START_REF] Yang | Assembly-level design for additive manufacturing: issues and benchmark[END_REF]. For PCCD strategies, most case studies either did not mention how to find the candidates [START_REF]Additive Manufacturing Redefining What's Possible[END_REF][START_REF] Dietrich | Impact of integrative design on additive manufacturing quality[END_REF][START_REF]An Epiphany Of Disruption: GE Additive Chief Explains How 3D Printing Will Upend Manufacturing[END_REF][START_REF] Gibson | Additive Manufacturing Technologies:Rapid Prototyping to Direct Digital Manufacturing[END_REF] or simply use conventional heuristic rules to narrow down the scope [START_REF] Schmelzle | Re) Designing for Part Consolidation: Understanding the Challenges of Metal Additive Manufacturing[END_REF][START_REF] Yang | A new part consolidation method to embrace the design freedom of additive manufacturing[END_REF]. One new approach is to find a potential candidate for part-level DfAM applications first and then search its neighbourhood to see whether adjacent components can be consolidated [START_REF] Kumke | A new methodological framework for design for additive manufacturing[END_REF][START_REF] Reiher | Holistic approach for industrializing AM technology: from part selection to test and verification[END_REF]. This approach is named as "point-to-face" strategy because it starts with one initial potential part/point. This "point-toface" strategy has two typical deficits: 1) if no feasible "point" exists, no candidate for PC is found; 2) it uses heuristic rules to check feasibility of consolidation, which means that it inherits the deficits of heuristic rules as well.

From these reported case studies (Table 1), most of them (6/10) are associated with pipes/manifolds with high degrees of modularization which makes them relatively independent from their external environments (e.g. other sub-systems). The modular degree is determined by its repeatability and dependency on the external environment. In this paper, it is to measure the whole assembly instead of a component. For example, the GE nozzle is regarded as one product, and it is highly modularized inside the engine. Within these well selected systems, material composition is simple, and relative motion is rare; therefore, the decision to consolidate all components into one can be quickly drawn by simply using the rule "relative motion" and rule "material variance". Besides, manufacturing constraints and design iterations are not detailed in these papers. Therefore, these case studies are not general enough to reflect the complexity of the PCCD problem.

To provide a general approach for PCCD, certain screening methods should be taken to search for suitable candidates by clustering components of a given product (assembly) into discrete feasible groups.

Due to its feature of "face-to-point", we define it as "face-to-point" strategy in comparison to the "pointto-face" one. To validate the effectiveness of such a PCCD approach, the selected case study should be a product as general as possible with reasonably high complexity.

Feasibility rules for AM-enabled PC

To compensate for the deficits of conventional heuristic rules, quality, cost, and other lifecycle constraints (e.g. manufacturing and maintenance) are included in the new feasibility ruleset. For those component pairs with relative motion or different materials, although proven to be feasible by using AM processes, the resulted printing quality is low; therefore, rules corresponding to "no relative motion" and "no material variance" stay effective. As for cost, massively-produced standardized components such as regular pipes, are still cost-competitive so that these "cheap components" should be singled out from feasible candidates. Although AM has shown impressive capabilities, its own manufacturing constraints should also be considered in PC design. As discussed in Section 2.2, specific constraints are meant to constrain the architecture design of a part rather than assembly relations. Therefore, specific constraints are ineffective until the detailed architecture of the consolidated design is explicit. In the PCCD stage, only general constraints are considered while postponing specific constraints to later phases (e.g. topology optimization). Manufacturing constraints sequencing brings two benefits: 1) avoid taking all constraints in one shot and quicken the searching process of potential candidates; and 2) stimulate design innovation via conflict solving mechanism as proposed by TRIZ method [START_REF] Savransky | Engineering of creativity: Introduction to TRIZ methodology of inventive problem solving[END_REF]. For example, consolidation leads to internal overhanging structures, which can be avoided by creating self-support structures [START_REF] Rosen | A review of synthesis methods for additive manufacturing[END_REF].

The new ruleset is presented as follows. component pair , if and only if the following rules are all met, ; otherwise, .

(1) Relative motion (R1): there exists no relative motion within ( ? ). If false, return a conflict code "CF_RelativeM";

(2) Material variance (R2): there is no material difference within . If false, return a conflict code "CF_MaterialV";

(3) Assembly access (R3): part consolidation of should not block the assembly access of any other node groups . If it is blocked, return corresponding conflict code "CF_AssemblyX" and ( ; ) & ;

(4) High-quality electronic/standard device (R4): neither nor is a standard or electronic device.

If false, return a conflict code "CF_StandardD" and ( ; ) & ( ; );

(5) Size limitation (R5): size limitation is define by a triplet (Length, Width, Height). If any of this meta element is not met, return a conflict code "CF_SizeLimit" and corresponding node groups;

(6) Material availability (R6): Currently, not all the engineering materials are available for AM processes. If not satisfied, return a conflict code "CF_Material0" and corresponding node ;

(7) Maintenance frequency difference (R7): there should be no significant maintenance frequency difference within . If false, return a conflict code "CF_MaintenanceDiff" and .

The new ruleset integrates the considerations of quality, cost, and main lifecycle constraints of PC design.

Meanwhile, AM design freedoms are also captured via the proposed conflict codes. For example, if relative motion is detected between a component pair , it returns code "CF_RelativeM" that can be retrieved to check whether a specific AM-enabled design solution fulfilling functional requirements can be found by experts. If true, again. All the conflict type codes are summarized in Table 2. It should be advised that these rules can be manually implemented or automated. The applicable sequence of rules are based on time cost of manual implementation (MI) and constraining strength and it varies for these two implementation approaches. Time cost of MI is assessed on the basis of unit time expense of material information acquisition. Assembly access evaluation (AAE) is the most timeconsuming one and it is a function of the number of node groups. For R5, volumetric measurement (X, Y, Z) and validation account for a total of 4 units. In general, constraining strength of rules decreases in the sequence of (R4, R1, R2, R3, R6, R5, R7) considering the current capabilities of AM processes. Thus, the applying sequence of MI is (R4, R1, R2, R7, R6, R5, R3) while automated approach takes an order of (R4, R1, R2, R7, R6, R5, R3) because retrieving information of size and material is much easier for a computer program. The reason why R3 is checked in the very end is to minimize the group count thereby reducing the overall cost. As the scale of product increases, MI becomes highly time-costly because of the dramatic expansion of solution space. For R5 alone, the combinational space could be as large as with m interconnected component pairs. In brief, a numerically-assisted method is highly demanded to prioritize consolidation sequence and automate the process of PCCD.

Overall framework of PC candidate detection

As discussed in Section 3, although manually applying the new set of heuristic rules for small-scale systems is efficient because R1, R4, and R7 may help to enormously eliminate possible combinations, checking R2, R3, R5, and R6 still can be time-consuming. When the complexity scale of a system increases, the usability of deploying heuristic rules can be challenging. Another issue of using heuristic rules is that it highly depends on users' understanding of these rules and it is difficult to document and retrieve considerations taken by other users. To avoid this repeated work, save time for rule verification, and support systematic decision making of PC, a numerically-assisted PCCD framework is proposed in Figure 2.

The framework is mainly comprised of two modules: construct FPI network and PC candidate detection (PCCD). The FPI network is an abstract representation of a given product where components and connections are modeled as nodes and edges respectively. In general, a FPI network can be modeled as follow:

(1)

Where is node, is edge, and is weight. For a FPI network, the specialty lies in the physical attributes of nodes and edges in comparison with a general undirected weighted graph. The attributes are shown in Equations ( 2) and (3).

(

) 2
(

Where is component and is component . , , , and are material, bounding box size, maintenance frequency, and indication of whether it is a high-quality standard electronic device of , respectively. and are to check the similarity of material and maintenance frequency between and . is the stack up size of bounding box of and in assembly state and is to check whether there is relative motion between each other.

The built FPI network is marked as and it serves as the initial input for the PCCD module together with general constraints of the AM processes. In the PCCD module, the main tasks are to verify 12 R1 -R7 and search for the optimal grouping solution with the minimum number of groups. These groups form the final solution which specifies which ones can be consolidated without violating all of these heuristic rules. Steps 1 to 7 follow such a lead: selectively verify rules for node, edge, and node groups. In

Step

Pre-processing kernel

Post-processing

Construct FPI network

Network, graph, or matrix methods have been widely used in the product design field recently. One of the typical applications is to do product modularization (Gu and Sosale [START_REF] Gu | Product modularization for life cycle engineering[END_REF] and Li et al. [START_REF] Li | Function Module Partition for Complex Products and Systems Based on Weighted and Directed Complex Networks[END_REF]) and evaluate the degree of modularity (Sosa et al. [START_REF] Sosa | Identifying modular and integrative systems and their impact on design team interactions[END_REF]). Network based methods not only make it easier to visualize the interaction between components, but also make it possible to apply graph theory to automatically extract certain properties from the graph, e.g. modularity. Likewise, graph-based methods can also be applied for PCCD. In this section, how to construct such an FPI network is discussed.

Formalize initial connectivity

A general weighted undirected graph is comprised of nodes, edges, and weights. This section mainly covers the following questions. 1) How to get the node list directly from the CAD model? 2) How to specify the weight for each link?

To solve the first problem, a special program is needed to traverse all the components in the assembly model and users are required to interactively deselect fasteners and washers. Once the list of components are ready, users are required to analyze the interaction type between components and specify the interaction strength individually because all links are unique. Interaction comes from two different types of needs: functional interaction and physical interaction. As proposed by Gu and Sosale [START_REF] Gu | Product modularization for life cycle engineering[END_REF], different types of interaction scenarios are summarized as follows:

(1) Functional interaction  Exchange of energy (force), material, and/or signal;

(2) Physical interaction  Attachment: physical contacts, fixations and stops, joints, fasteners, couplings, welds and the like;

 Positioning: Components are supposed to have certain alignment requirements (e.g. ease of assembly). For example, relative distance or angle between components, alignment including coaxial, collinear, parallel, perpendicular and flush alignments;

 Motion: components serve as one unit to achieve certain motion. For example, cam controlled objects, trajectory of joints and end-effectors, etc.;

 Containment: components contained within the same housing.

According to these two types of interaction, interaction strength can be divided into 7 levels as shown in Table 3. Four basic rules should be followed:

(1) If there is direct physical contact between ( ), ;

(2) If one function is achieved by multiple components, interaction strength is assigned as "Strong";

(3) Functional interaction has priority over physical interaction if some scenarios are not matched in the table.

(4) Only adjacent components need to be analyzed.

Enrich node and edge properties

Verification of the new ruleset depends on the specific attributes of nodes and links. As defined in Equations ( 2) and (3), the attributes are summarized in Table 4. Data sources for these physical attributes are summarized as a CAD model, manual input, and calculated values. Among all these attributes, MaintFreq and IsStandard attributes need manual identification for such components that need frequent maintenance and have high-quality requirements respectively. For relative motion attribute, users only need to identify those components which have links whose . Normally, FPI matrix is a sparse upper matrix; therefore, time expense at this step is low as well. The mapping relation between these physical attributes and the new rules are summarized in the last column.

PCCD algorithm

The main task of the PCCD algorithm is to find the minimum grouping solution with respect to general AM constraints. The inputs and outputs of PCCD are shown in Figure 3. The initial inputs include FPI matrix, node attributes, and edge attributes, among which all manual inputs are marked in green. In the implementation process, the algorithm needs to retrieve the stack size of each group from geometric models and user needs to manually check assembly access issues in the end and mark the links that obstruct assembly access. The reason why AAE is manually done at this stage is that it needs sophisticated information on the assembly sequence, direction, method, and collision checks, which can be a standalone research topic [START_REF] De Mello | Computer-aided mechanical assembly planning[END_REF]. Both initial inputs and in-process inputs are case-specific while the AM general constraints database is case-neutral. In the end, one single feasible solution with minimum part count is obtained, and all conflicts encountered in the process are summarized for reference. Detailed algorithms corresponding to the three phases of PCCD are presented in Sections 6.1, 6.2, and 6.3. In these algorithms, three basic principles are followed.

Principle of priority: larger link weight indicates higher consolidation priority. Higher interaction strength between components means that the physical bond should be maintained.

Corollary 1:

Weak links between components should be deactivated before strong links when certain rules (e.g. R5) are not met. For example in Step 5, there exist a group of linked nodes while R5 is not met.

Then, deactivation of links should start with the weak ones.

Principle of cost: R3 should be evaluated only after all the other rules are met. Time cost for R3 is a function of the number of node groups. When all the other rules are satisfied, the total number of node groups can be reduced. So the time cost for verifying R3 is also reduced.

Principle of flexibility:

If there are multiple ways to guarantee fulfillment of R3, users have the freedom to take other AM-specific constraints into consideration. These constraints can be overhang area, surface quality, and so on. The main task of pre-processing is to find the pair-wise links that are feasible with respect to R1 throughout R7 with exception of R3. This module serves as a preparatory step for obtaining feasible node groups. The algorithm is detailed in Figure 4. The most important function in this section is the function

PCCD

FPI matrix

Size limit

Available materials

Stack size

Node attributes

Edge attributes

Material MaintFreq IsStandard

ACX node pairs

Case study

In this section, two case studies are presented to demonstrate the basic flow of the PCCD framework as well as the effectiveness of the proposed PCCD algorithm (Throttle pedal). With special attention to validating the efficacy of PCCD kernel function that subdivides the FPI network into feasible groups while ensuring minimum part count, a case study of a tripod that satisfies all other rules except R5 is also tested.

Throttle pedal

A throttle pedal design is exemplified to demonstrate how the proposed PCCD framework works and to validate effectiveness of the PCCD algorithm. The original design is retrieved from an open source CAD database [START_REF] Miessner | Throttle Pedal Design Challenge[END_REF]. As shown in Figure 8, the throttle pedal is comprised of 13 components without counting washers and fasteners. The device functions to transfer human energy to digital signals so that drivers can control the gas emission. To restrict the range of rotation, the notch on the hollow shaft and the block on the rotation limit allow a rotation angle of 40 degrees. The maximum load applied is 250lbs. The complexity of this case study is medium, but it includes all kinds of conflicts discussed in this paper. The current program is implemented in Matlab R2017 in a desktop (Win10, 8G RAM, 3.7GHZ) for validation purpose; therefore, some physical attributes of the CAD models are manually prepared beforehand. These attributes include material and stacksize (L*W*H). However, this information can be automatically retrieved from a commercial CAD software with future developed add-ons. Required physical attributes of each component are shown in Table 5 in which MainFreq and IsStandard are input by the user. In practice, users only need to identify the one with "H" for MainFreq and "1" for IsStandard; therefore, manual interference is very low. To validate the effectiveness of R5 (size limitation), we create an imaginary size limit (L250, W170, H200) at which and must be separated. Similarly, available materials for AM are limited to steel and plastic only for test purposes.

L L L L L L L L L L L L IsStandard 0 0 0 0 0 0 0 0 1 0 0 0 0
First, a FPI network is constructed to visualize the functional and physical interaction between components. This step requires the users to have a good understanding of the working principle of the throttle pedal. In reference to Table 3, each edge is graded with a weight from 0.2 to 1. The constructed FPI network is shown in Figure 9. In reality, and are not physically connected, but they are designed to achieve the function of "constrain rotation angle of 40 degrees", which may easily be ignored without a good understanding of the working principle. Secondly, users are asked to identify whether there is relative motion within if . Since the FPI matrix is an upper matrix, necessary inputs of "1"s are only a few as shown in Table 6. According to Eq. (3) in Section 4, link attributes can be easily calculated except the Stacksize which needs instant communication with CAD software. Currently, the Stacksize is replaced by add-up size that does not account for the overlaps of bounding boxes of components. However, this can be modified in the planned implementation in CAD software.

Figure 9 FPI matrix Table 6 Relative motion matrix

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C1 C2 C3 C4 1 C5 1 1 1 C6 1 1 C7 C8 C9 C10 1 C11 C12 1 C13
With all of these inputs, the program is ready to find feasible node groups which are consistent with R1-R7 except R3. The total computing time is 1.36 seconds. Screenshots for important steps of the PCCD algorithm are shown in Figure 10. In Figure 10 (a), the original Matrix is broken down to by applying R4, R6, and R5 in sequence, and Node 9 and 13 are singled out with corresponding conflict type codes as shown in Figure 11 (a). Then, is further broken down by deploying R1, 2, 7, and 5 to check the feasibility of consolidation in pair-wise sense. The next step is to chain these feasible pairs into a solution by aggregating the remaining links into bigger node groups automatically. For example, between Figure 10 (b) and (c), Nodes , , and are gathered into a node group and R5 (size limitation) is applied to check the feasibility of printing as a whole. However, it is impossible to print these four components in one shot, so the algorithm finds the weakest link among the selected group and breaks the links until all new sub-groups (( ) and ) are printable. Occasionally, the algorithm only needs to break one link to get the feasible sub-groups, but this may not be the case for highly inter-connected large node groups, which will be discussed in the second example. Up to now, all node groups satisfy R1 to R7 except R3. Users are asked to specify the links to be deactivated to guarantee assembly access for each node group. In this case study, consolidation of obstructs assembly operation of so that a possible solution is to break either link or . The latter solution returns one possible final solution as shown in Figure 10 (d).

Comparing solution with solution , we can see that is not synthesized by simply breaking the link . Instead, it loops back to Matrix and redo the step of R5 verification. This iteration helps to find the optimal node groups to satisfy all rules as shown in Figure 10 (d).

All conflict codes encountered in the process are shown in Figure 11 (a). For example, returns a conflict code of "CF_SizeLimit" and throws back a conflict code of "CF_AssemblyX".

The final solution is shown in Figure 11 (c) with 9 parts instead of 13. The result is buildable considering the current capabilities of AM processes. For future work, the selected candidates can be separately optimized for lightweight using topology optimization methods, which is beyond the scope of this paper. Since the capability of finding the minimal grouping solution by calling the PCCD kernel function with respect to R5 is not demonstrated in the throttle pedal case, a more complex graph/product is needed. As shown in Figure 12, a tripod is a structural module in a train to serve as a handle for passengers. The tripod is made of 24 components and all of them are made of stainless steel with no difference in maintenance frequency. Therefore, the only limitation for PC is the available building volume of AM printers. As discussed in Section 6.2, this kernel function is supposed to find the solution with the The graphical representation of the tripod structure is shown in Figure 13 (a) with 24 nodes and 32 edges.

The PCCD kernel function takes around 1.5 seconds to find the grouping solution with minimum part count. Assuming a Renishaw Ren 500M machine (i.e. volume [350, 250, 250]) for example, the grouping result is shown in Figure 13 (b). There are a total of 11 groups out of which 5 groups have more than one component. By checking the stack size of each group in Table 7, we can see that any further combination of node groups will violate R5. Figure 14 depicts the dynamics of grouping in the searching process. One peak represents one global iteration including continuous climbing and a sudden drop in the number of groups. The program undergoes 17 global iterations and a total of 227 iterations (see Figure 14). The distance between each peak represents the time cost for finding one feasible solution and the horizontal line segments mean that breaking some edges does not contribute to the increase of group count because these nodes are still connected with the rest of the nodes. Effective cuts (the very last cut in each global iteration which results in feasible groupings) are summarized in Table 8. For example, to get the first feasible grouping solution, all links with weight coefficients lower than that of link (

), should all be broken but restored later when the effective cut of link is found. The same process repeats until the very solution with minimum group count is found. in Figure 13 (c) instead of ( in Figure 13 (d) because the latter one leads to one more separate group . Therefore, the PCCD kernel function is effective in finding the minimum group solution . However, the derived solution may not always be desired if other constraints are involved such as R3 (assembly access) and ease of post-processing machining (e.g. grooving of ). For example, a feasible solution can be drawn for the graph of feasible, the latter one is more favored if building volume permits because the mutual dependency within is higher than ( ). This phenomenon is called "community [START_REF] Newman | Finding and evaluating community structure in networks[END_REF]" which is planned in our next-step research. For a general network without community characteristics, the PCCD algorithm is fast and effective to find the minimum grouping solution. 5) are and respectively where n is the number of nodes. Cost saving comes from automatic retrieval of material and size information. In the rule verification section, the time cost of MI increases dramatically due to the explosion of combinatory space. Ignoring effort in validating rules R1, 2, and 7, the worst case for verification of R5 for MI and PCCD is and because MI needs to exhaust all combinations while PCCD can break links accordingly (due to weight of edges). Since verification of R3 is manually done, time cost will be the same. Therefore, the total time difference will be:

In total, the time cost difference can be as large as and it is always positive. This gap may vary depending on the specific design. It should be advised that MI may have competitive advantages in terms of efficiency in two situations: 1) size limitation is of no concern; 2) R1 and R2 can efficiently break a large-scale product into small groups.

Conclusions and future research

In this paper, we revise the conventional design rules of candidate selection for PC for DFAM purpose, and propose a numerically assisted approach named PCCD to automate the implementation of some of these new design rules. Although extra effort may be needed for assigning functional and physical interaction strength to component pairs, the weighted graph helps to automate the process of finding the optimum solution of minimum part count. Apart from this, the proposed PCCD approach enables repetitive reuse and shareable documentation between different designers. This repeatability and retrievability avoids unnecessary repetitive work when new techniques are matured. For example, if highquality electronic devices can be printed, deactivated links should be restored and PCCD runs again, so it can return a new solution without repeating the trivial procedure. In this paper, the PCCD algorithm also returns conflict type codes which are very helpful to guide designers to find possible solutions to realize design innovation. For example, conflict type code "CF_RelativeM" can be solved by an embedded component or a compliant mechanism which are typical AM applications.

For future research, there are a few points to be investigated:

(1) Integrate the PCCD algorithm into a CAD environment to retrieve material and stack size instantly;

(2) Get relative motion information directly from CAD models via well-established physical constraints between components;

(3) Integrate existing assembly operation planning approaches into assembly access validation to automate the whole process;

(4) For node groups with conflict type codes, possible solutions derived from AM capabilities should be investigated.

(5) A sensitivity analysis of the grouping results towards strength scoring and size limitation should be conducted to check the robustness of the proposed PCCD algorithm. (c) imaginary building volume

Figure caption list

Table caption list

Figure 1

 1 Figure 1 an illustrative example of assigning components into feasible groups

( 4 )

 4 Consolidated part does not need extra tooling; (5) Components should not have vastly different quality requirements; (6) Consolidation should not significantly increase manufacturing difficulty and cost; (7) Trade-off should be made between part consolidation and standardization & modular design; (8) Increase the possibility of part to be reused and the probability of material recyclability.

Figure 2

 2 Figure 2 PC candidate detection framework

  Figure 3 inputs and outputs of PCCD algorithm

Figure 8

 8 Figure 8 Exploded view of a throttle pedal

Figure 10

 10 Figure 10 Graphic view of PCCD matrix transition

  minimum groups while subject to R5. During the search process, the program is expected to depict a phenomenon of continuous increase and abrupt decrease of group numbers due to the proposed weightbased break and restore mechanism. The dimension of the bounding box of each component is summarized in Appendix I. Same as Case Study 1, the bounding box of a group of components (part count greater than 2) is calculated by directly adding up the dimensions of members in the group instead of the real stack up size. However, an add-on can be developed to instantly communicate with a CAD software to obtain such information in the follow-up research.

Figure 12

 12 Figure 12 physical view of a tripod

Figure 14

 14 Figure 14 dynamics of searching the minimum grouping solution

Figure 13 (

 13 b) when the link is cut and the PCCD kernel function is rerun as requested by the PCCD post-processing function. A similar procedure is conducted for the other two machine sizes, and the final solution is presented in Figure 15 (a)-(c) respectively. One interesting phenomenon is observed when comparing the grouping of component as and in Figure 15 (a) and (b) respectively. Although both groupings are

Figure 15

 15 Figure 15 final grouping solution with R3 in consideration; (a) Renishaw Ren 500M; (b) SLM500; (c) imaginary building volume

  Fig.1 an illustrative example of assigning components into feasible groups Fig.2 PC candidate detection framework Fig.3 inputs and outputs of PCCD algorithm Fig.4 Pseudo code for Steps 1-2 Fig.5 kernel function of finding minimum number of node groups Fig.6 a simple example of the break sequence and the restore sequence Fig.7 pseudo code for steps 6-7 Fig.8 Exploded view of a throttle pedal Fig.9 FPI matrix Fig.10 Graphic view of PCCD matrix transition Fig.11 final outputs of PCCD algorithm Fig.12 physical view of a tripod Fig.13 group division result using PCCD kernel function: (a) original network; (b) Renishaw RenAM 500M; (c) SLM500; (d)imaginary size Fig.14 dynamics of searching the minimum grouping solution Fig.15 final grouping solution with R3 in consideration; (a) Renishaw Ren 500M; (b) SLM500;

Table 1

 1 Comparison of existing PCCD strategies in DFAM

	Literature	Not discussed	strategy Heuristic rules	Point-to-face	Selected object	Modular degree	Scale*	Final #
	GE [5]				fuel nozzle	high	20	1
	Schmelzle et al. [4]				Hydraulic manifold	high	<17	1
	Gibson et al. [10]				air duct	high	16	1
	Dietrich and Cudney [6]				manifold duct	high	>9	1
	Klahn et al. [22]				sawdust blower	high	>4	1
	Lindemann et al. [24]				RW-bracket	low	4	2
	Kumke et al. [8]				housing cover assembly	high	2	1
	Yang et al. [23]				triple clamp	medium	6	3
	Prakash et al. [25]				flow control valve	medium	18	8
	GE aviation [7]				Helicopter Engine	high	<900	14
	* Without counting fasteners, washers

Table 2

 2 Conflict type code table Object refers to the rule to be applied on;& n is the total number of nodes or node groups and time cost varies from n-1 to 1 which depends on sequence of verification.

	Rule #	Rule name	Conflict code	#	Object* Time cost of MI	Apply sequence Manual Auto
	R1	Relative motion	CF_RelativeM	1			2	2	4
	R2	Material variance	CF_MaterialVar	2			2	3	5
	R3	Assembly access	CF_AssemblyX	3			< (n & -1)	7	7
	R4	High-quality electronic/standard device	CF_StandardDev	4 		1	1	1
	R5	Size limitation	CF_SizeLimit	5 		~4	6	2
	R6	Material availability	CF_Material0	6 		1	5	3
	R7	Maintenance frequency difference	CF_MaintenanceDiff 7			2	4	6
	*

  It should be advised that the final solution with the minimum part count may not be the optimal solution if other constraints (e.g. overhanging problem) are applied. Alternative solutions can be either to integrate these more detailed constraints into R3 and recall the PCCD algorithm iteratively or simply dissect the problematical node group into smaller groups without affecting other node groups.

	CAD model
	1-2, the original matrix Functional and physical interaction relation matrix G0 is modified according to whether node 's attributes satisfy rule R5-6 component pair constraints each component and general Physical attributes of AM process Construct FPI network
	and whether edge	's attributes meet rule R1, R2, R7, and R5. If not, corresponding edges are Apply validation rules
	deactivated and conflict type codes are archived in conflict info hub. These two steps are defined as pre-PC candidate detection PC R4, R5, and R6
	process which secures the feasibility of node and edge. In Steps 3-5 (kernel of PCCD algorithm), it aims at chaining feasible node pairs into feasible node groups by iteratively breaking and restoring edges of according to the weight S2 Conflict info hub Satisfied? N Optimal solution Apply validation rules R1,R2,R5,and R7 Matrix G1 candidate Matrix G2 Chain node pairs into node groups detection Apply validation rule links R5 Deactivate links in sequence and restore module Initial optimal solution S0 Matrix G3
			Initial optimal Y		Matrix G4
			solution S1
			Apply validation rule		Specify the links to be
			R3		deactivated in G2
	detection End of PC candidate	Optimal solution S2 Y Satisfied?	N	code Conflict type pair Trouble node Conflict info hub
			13

. Through these steps, feasible node groups are found, and it awaits for a final evaluation of R3 which is defined as post-processing. This step is manually done. If R3 is not met, users have to specify links to be deactivated to guarantee assembly access for each node group. The whole process repeats until the final solution is found.

Detailed steps and algorithms are stated in Sections 5 and 6 respectively. It should be advised that Steps 1-5 are automatically done while Steps 6-7 still needs user inputs because automatic assembly sequence planning is still challenging. The conflict information hub archives all conflicts encountered in the process, and this conflict info can be retrieved for future usage, for example, recommendation of conflictsolving solutions. Once a given conflict is solved, the broken link can be restored and the whole process can be repetitively recalled to synthesize a new solution.

Table 3

 3 Scoring criteria based on interaction strength between components

	#	Strength	Value	Physical interaction	Description Functional interaction	Examples
	1	Very strong	1	Firm connection	Exchange of large force or torque	Tightly bolted connection
	2	Strong	0.8	Medium connection	Exchange of large force or torque	Multiple-bar mechanism
	3 Medium strong	0.6	Firm connection	Exchange of medium force or torque	Non-laden welded frame
	4	Medium	0.5	Medium connection	Exchange of medium force or torque; Exchange of energy	Cable and battery
	5 Medium weak	0.4	Loose connection	Exchange of low force or torque	Left and right casing
	6	Weak	0.2	No direct connection	Exchange of signal or material	Positioning/channel
	7	No	0	No	No

Table 4

 4

		node and edge physical attributes
	# Attribute name	CAD model	Data source Manual input	Calculated	Parent object* v	Associated rules
	1	Material					R2, R6
	2	Size					R5
	3	MaintFreq					R7
	4	IsStandard					R4
	5	Stack size					R5
	6 Material variance					R2
	7	MaintFreq diff					R7
	8 Relative motion					R1
	* object refers to the rule to be applied on

Table 5

 5 Component list and attributes

			pedal pins lever	Right case	Shaft	Bear -ing	Ret. ring	D-pin	Potl. meter	Rot. limit	Spring	Left case	Gasket
	#		C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13
	Volume	L W H	50 37 10	11 7 6.3	217 74 22	74 74 12.5	40 40 23	68 68 9	52 52 1.6	28 7.5 5.5	40 40 23	63 63 9	38 34 20	107 74 18	74 74 0.5
	Material	steel	steel steel	steel	steel	steel steel steel plastic	steel	steel	steel	rubber
	MaintFreq	H

Table 7

 7 Stack size of each group (Renishaw Ren 500M)

	#	Node group	Stacksize (L,W,H)
	1	(1,2)	270, 42.4, 20.2
	2	(4,5,6,10,9)	267.5, 122.3, 112.2
	3	(7,8,11)	314.8, 200, 149
	4	(13,14)	270, 42.4, 20.2
	5 (16,17,18, 19, 20, 21)	291, 249, 164.4
	6	(30)	425,129.6,118.2
	7	(12)	127,115,113
	8	(15)	435,130,118.2
	9	(22)	1585, 150, 135
	10	(23)	1585, 150, 135
	11	(24)	1585, 150, 135

Table 8

 8 Effective cut at each global iterations (Renishaw Ren 500M)

Table 1

 1 Comparison of existing PCCD strategies in DFAM

	Table 2	Conflict type code table
	Table 3	Scoring criteria based on interaction strength between components
	Table 4	node and edge physical attributes
	Table 5	Component list and attributes
	Table 6	Relative motion matrix
	Table 7	Stack size of each group (Renishaw Ren 500M)

Table 8

 8 Effective cut at each global iterations (Renishaw Ren 500M)

Table 1

 1 Comparison of existing PCCD strategies in DFAM

	Literature	Not discussed	strategy Heuristic rules	Point-to-face	Selected object	Modular degree	Scale*	Final #
	GE [5]				fuel nozzle	high	20	1
	Schmelzle et al. [4]				Hydraulic manifold	high	<17	1
	Gibson et al. [10]				air duct	high	16	1
	Dietrich and Cudney [6]				manifold duct	high	>9	1
	Klahn et al. [22]				sawdust blower	high	>4	1
	Lindemann et al. [24]				RW-bracket	low	4	2
	Kumke et al. [8]				housing cover assembly	high	2	1
	Yang et al. [23]				triple clamp	medium	6	3
	Prakash et al. [25]				flow control valve	medium	18	8
	GE aviation [7]				Helicopter Engine	high	<900	14

Table 8

 8 Effective cut at each global iterations (Renishaw Ren 500M)

	Iteration #	1	2	3	4	5	6	7	8	9
	Link	(14,15) (13,15) (13,16) (2,3) (1,3) (3,22) (3,23) (3,24) (15,22)
	Iteration #	10	11	12	13	14	15	16	17
	Link	(15,23) (15,24)	(1,4)	(1,6) (6,7) (6,8) (7,12) (9,11)

Acknowledgement

Constructive review comments from reviewers and editors are highly appreciated. Financial support from the National Sciences and Engineering Research Council of Canada Discovery Grant RGPIN 436055-2013 and McGill Engineering Doctoral Award (MEDA) is acknowledged with gratitude.

"GetStackSize(

)", which is to communicate with a CAD software to get the stack size of a node group. The number of elements within a node group can vary from 1 to n.

Kernel function

This section is dedicated to iteratively find the minimum grouping solution with respect to R5 with the input of the pair-wise feasible network ( ). The strategy of finding such a solution is to continuously break existing links according to connection strength rank until all node groups are feasible. Such a cycle is defined as one global iteration, and the very last broken link is defined as an effective cut. The solution obtained at this step may not be the optimal because the graph is broken into too fine groups. An extreme example is that each node is assigned as one group, which is definitely a feasible solution. To avoid this, the program begins to restore all the broken links except the effective cut. This kind of "break" and "restore" manner repeats until the number of node groups cannot be further minimized. The algorithm of this kernel function is detailed in Figure 5. The most important logic within the program is when to break and restore links.

Figure 6 shows a simple example of how it works. For Group 1, the program will first break (1, 2) and then [START_REF] Yang | Additive manufacturing-enabled design theory and methodology: a critical review[END_REF][START_REF] Schmelzle | Re) Designing for Part Consolidation: Understanding the Challenges of Metal Additive Manufacturing[END_REF] guarantee the conformance of R5. After the first global iteration, the solution is ((1), (2, 3), ( 4,

)). However, this may not be the optimal solution with the least number of node groups because node 1 is singled out in the first step. Instead, when the first solution is found, link (1, 2) should be restored and go for evaluation again. The final solution is ((1, 2), [START_REF] Yang | Additive manufacturing-enabled design theory and methodology: a critical review[END_REF][START_REF] Schmelzle | Re) Designing for Part Consolidation: Understanding the Challenges of Metal Additive Manufacturing[END_REF][START_REF]Additive Manufacturing Redefining What's Possible[END_REF]). In Group 2, assume the final solution is (( 6), [START_REF]An Epiphany Of Disruption: GE Additive Chief Explains How 3D Printing Will Upend Manufacturing[END_REF][START_REF] Kumke | A new methodological framework for design for additive manufacturing[END_REF], ( 9)). The "break and restore" scheme may be a little more complex because at each global iteration, it takes more than one step to break the graph into smaller groups. For example, breaking [START_REF] Kumke | A new methodological framework for design for additive manufacturing[END_REF][START_REF] Yang | A Generic Sustainability Assessment Model towards Consolidated Parts Fabricated by Additive Manufacturing Process[END_REF] cannot separate node 9 from other connected groups. & n is the total number of nodes or node groups and time cost varies from n-1 to 1 which depends on sequence of verification.