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A framework for optimal design of complex products
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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 70 (2018) 416–421 www.elsevier.com/locate/procedia
28th 28th CIRP CIRP Design Design Conference, Conference, May May 2018, 2018, Nantes, Nantes, France France
A optimal design of products A framework framework for optimal design of complex complex products 28th CIRP for Design Conference, May 2018, Nantes, France a,
a
Deyi a,*, David Imaniyana Deyi Xue Xue *,functional David Imaniyan A new methodology to analyze the and physical architecture of Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4 of Mechanical and Manufacturing Engineering, University ofproduct Calgary, Calgary, Alberta, Canada T2N 1N4 existing Department products for an assembly oriented family identification * Corresponding author. Tel.: +1-403-220-4168; fax: +1-403-282-8406. E-mail address: [email protected] a a
* Corresponding author. Tel.: +1-403-220-4168; fax: +1-403-282-8406. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
Abstract École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France Abstract many author. design methodologies and [email protected] developed, the presently achieved research results are not effective for design of *Despite Corresponding +33 3 87 37 54 30;tools E-mailhave address: Despite many designTel.: methodologies and tools have been developed, the presently achieved research results are not effective for design of
complex products when various methods and tools in different schemes have to be employed. A new framework for optimal design of complex complex products when various methods and tools in different schemes have to be employed. A new framework for optimal design of complex products is introduced in this research considering modeling, simulation and optimization aspects. First, a hybrid scheme is developed for products is introduced in this research considering modeling, simulation and optimization aspects. First, a hybrid scheme is developed for integrated modeling of complex products. In this hybrid scheme, descriptions of a generic product are modeled by an AND-OR tree. Feasible integrated modeling of complex products. In this hybrid scheme, descriptions of a generic product are modeled by an AND-OR tree. Feasible design candidates are created from the AND-OR tree through tree-based search. Geometric descriptions in a design candidate are associated Abstract design candidates are created from the AND-OR tree through tree-based search. Geometric descriptions in a design candidate are associated with a CAD system. Second, a hybrid simulation method is developed for evaluation of different product aspects with different simulation tools with a CAD system. Second, a hybrid simulation method is developed for evaluation of different product aspects with different simulation tools arebusiness integrated by the hybrid scheme. Simulations with geometric descriptions are conducted functions the of the CAD Inwhich today’s environment, themodeling trend towards more product variety and customization is unbroken. Due by to analysis this development, need of which are integrated by the hybrid modeling scheme. Simulations with geometric descriptions are conducted by analysis functions of the CAD system. Simulations withproduction non-geometric descriptions arecope conducted by theproducts knowledge-based systems. Third, a hybridand optimization method is agile and reconfigurable systems emerged to with various and product families. To design optimize production system. Simulations with non-geometric descriptions are conducted by the knowledge-based systems. Third, a hybrid optimization method is developed to identify the optimal design of the complex product. each design candidate, parameter optimization conducted to obtain systems as well as to choose the optimal product matches, productFor analysis methods are needed. Indeed, most of theis methods aim the to developed to identify the optimal design of the complex product. For each design candidate, parameter optimization is known conducted to obtain the optimalaparameter values. The optimal design solution level. is identified from all design candidates through configuration optimization. analyze product or one product family on the physical Different product families, however, may differ largely in terms of the number and optimal parameter values. The optimal design solution is identified from all design candidates through configuration optimization. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production © 2018 Authors. Published by Ltd. is an open access CC BY-NC-ND license 2017AThe Authors. Published by Elsevier B.V.This system. new methodology is proposed to analyze existing products in article view ofunder theirthe functional and physical architecture. The aim is to cluster © 2017 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review responsibility of the scientific committee of the 28th CIRPofDesign Conference 2018.and the creation of future reconfigurable these productsunder in new assembly oriented product families for the optimization existing assembly lines Peer-review under responsibility of the scientific scientific committee of of the 28th 28th CIRP CIRP Design Design Conference Conference 2018. 2018. assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and modeling; simulation;a optimization aKeywords: functionalComplex analysisproducts; is performed. Moreover, hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the Keywords: Complex products; modeling; simulation; optimization similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. Introduction geometric descriptions, modeling of non-geometric design ©1. The Authors. Published by Elsevier B.V. 1.2017 Introduction geometric descriptions, modeling of non-geometric design information and other product life-cycle information such as Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. information and other product life-cycle information such as
With the advances in design research and computer manufacturing and operation/use has also been studied [1]. In With the advances in design research and computer manufacturing and operation/use has also been studied [1]. In such as simulation/evaluation aspect, a design is usually evaluated by technology, many design methodologies and tools, such as simulation/evaluation aspect, a design is usually evaluated by knowledge-based design and computer aided design, have measures in different product life-cycle aspects such as knowledge-based design and computer aided design, have measures in different product life-cycle aspects such as been developed for improving quality and efficiency of manufacturing [4] and services [5] in addition to functional been developed for improving quality and efficiency of manufacturing [4] and services [5] in addition to functional product design [1]. Due to the increase of complexity in performances. Sophisticated simulation/evaluation tools, such design [1]. Due to the increase of complexity in of performances. Sophisticated simulation/evaluation tools, such 1.product Introduction the product range and characteristics manufactured and/or products, methods and tools for design of complex products as finite element analysis (FEA) and computational fluid products, methods and tools for design of complex products assembled as finite in element analysis (FEA) and the computational fluid this system. In this context, main challenge in and systems need to be developed [2]. dynamics (CFD) systems, are also employed to evaluate the and systems be developed [2]. in the domain of dynamics and (CFD) systems, are also employed to evaluate the Due to need the to fast development modelling analysis is now not only to cope with single The term of complex system was originated in information design. In optimization aspect, multi-objective optimization The term of complex originated in information design. Ina limited optimization multi-objective optimization communication and an system ongoingwas trend of digitization and products, productaspect, range or existing product families, science when a network was used to associate the [6] is often used to achieve the optimal design considering science whenmanufacturing a network enterprises was usedaretofacing associate the but [6] also is often achieveand theto optimal considering digitalization, important to be used able totoanalyze comparedesign products to define heterogeneous components into the same environment [3]. different product life-cycle evaluation measures. Various heterogeneous components intoenvironments: the same environment [3]. new different product life-cycle measures. Various challenges in today’s market a continuing product families. It can be evaluation observed that classical existing Among various aspects of complexity in design of products global optimization techniques [7] were also developed to Among various aspects of of complexity in design oftimes products global families optimization techniques [7] wereof also developed to tendency towards reduction product development and product are regrouped in function clients or features. and systems such as the number of components and the effort improve the quality and efficiency of optimization. and systems such lifecycles. as the number of components andincreasing the effort However, improve the qualityoriented and efficiency offamilies optimization. shortened product In addition, there is an assembly product are hardly to find. in manufacturing, a complex product or system in this Despite of the progress, these achieved research results are in manufacturing, a complex atproduct or time system this Despite of the progress, theseproducts achieveddiffer research results are demand same intechniques a in global the product family of level, mainly in two researchofiscustomization, considered as being the one the where multiple notOneffective for design complex products where various research is with considered as the all oneover where multiple techniques not effective for design ofnumber complex products where various competition competitors the world. This trend, main characteristics: (i) the of components and (ii) the are required for modeling, simulation and optimization. This methods and tools in different schemes have to be employed. are required for modeling, simulation from and optimization. This type methods and tools in different schemes have to be employed. which is focuses inducing development to micro of components (e.g. mechanical, electrical, research onthemodeling, simulation macro and optimization A new framework is introduced in this researchelectronical). for design of research results focusesinondiminished modeling,lot simulation and optimization A Classical new framework is introduced in thismainly research for products design of markets, sizes due to augmenting methodologies considering single aspects in design of complex products. complex products considering modeling, simulation and aspects varieties in design(high-volume of complex products. complex products considering modeling, simulation and product to low-volume production) [1]. or solitary, already existing product families analyze the In modeling aspect, in addition to CAD-based product optimization aspects. In modeling in addition to well CAD-based product optimization aspects. To cope with this aspect, augmenting variety as as to be able to product structure on a physical level (components level) which identify potentials in the existing causes difficulties regarding an efficient definition and 2212-8271possible © 2017 The optimization Authors. Published by Elsevier B.V. 2212-8271 ©system, 2017 TheitAuthors. Published Elsevier B.V. knowledge production is important tobyhave a precise comparison of different product families. Addressing this Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. Keywords: Assembly; method; Family identification technology, manyDesign design methodologies and tools,
Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 28thDesign CIRP Conference Design Conference Peer-review under responsibility of the committee of the of 28th 2018. 2018. 10.1016/j.procir.2018.02.038
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Deyi Xue et al. / Procedia CIRP 70 (2018) 416–421 Deyi Xue / Procedia CIRP 00 (2018) 000–000
2. A framework The framework for design of complex products considering modeling, simulation and optimization aspects is shown in Fig. 1. D2
D1
3. Design of complex products considering non-geometric descriptions and geometric descriptions 3.1. System architecture In this work, a system is proposed for design of complex products considering non-geometric descriptions in conceptual design and geometric descriptions in detailed design. Fig. 2 shows the system architecture. Knowledge Based Design System
……
……
Parameter Optimization Optimize F(X1)
Candidate Optimization Optimize Di
Attribute Relation Maintenance System
Symbolic Product Modeling Scheme
Relation
Modeling Scheme
Simulation System
Design Candidate Fig. 1. Framework for design of complex products
In this framework, multiple design solution candidates, Di (i=1,2,…,n), are created to achieve the same design requirements. Since different design candidates are composed of different components, each of these design candidates is also called a product design configuration. For each design candidate Di, the complex product is modeled by m different schemes, Mij (i=1,2,…,n; j=1,2,…,m). In each scheme, the product is modeled by product descriptions and their relations. Product descriptions in different schemes are associated by their relations. When a product description in one scheme is modified, this change should be propagated to other schemes automatically through the relations. Each product modeling scheme in a design candidate, Mij (i=1,2,…,n; j=1,2,…,m), is associated with a number of simulation systems, Sijk (i=1,2,…,n; j=1,2,…,m; k=1,2,…,p). A simulation system can be used to create, delete and modify product descriptions in that scheme. A simulation system can also be used to obtain the evaluation measures of the design. For each design candidate, a number of quantitative design parameters can be selected as design variables, Xi (i=1,2,…,n). The evaluation measure achieved by the simulation systems can be modeled as a numerical function of the selected design variables, F(Xi). The optimal design is achieved through multi-level optimization [8]. First parameter optimization, Optimize F(Xi) (i=1,2,…,n), is conducted to obtain the optimal values of the design variables Xi* and the corresponding best evaluation measure F(Xi*) for each design candidate Di (i=1,2,…,n). Among all n design candidates, configuration optimization, Optimize Di, is conducted to obtain the best design candidate Di* (i=1,2,…,n).
Motion Analysis System
Finite Element Analysis System
CAD Product Modeling Scheme
Multi-level Optimization System Modeling Scheme
Design Description
417
Simulation System
Fig. 2. Architecture of the complex product design system
In this system, the conceptual design descriptions are modeled using the symbolic product modeling scheme, while the detailed design descriptions are modeling using the CAD product modeling scheme. The geometric descriptions in the symbolic product modeling scheme are associated with the geometric descriptions in the CAD product modeling scheme. The symbolic product model is created and manipulated by the knowledge based design system. The consistency of the quantitative attribute values is maintained by the attribute relation maintenance system [9]. The CAD product model is created from the geometric descriptions in the symbolic product model and manipulated by the CAD system. The motion analysis system and the finite element analysis system are used for various types of analysis and evaluation to the CAD product model. Optimization is conducted to achieve the best design configuration candidate and its best parameter values. Optimization is conducted at two different levels: configuration optimization level and parameter optimization level. First different design candidates are created from the design requirements, and each of these design candidates is modeled by a product configuration. Parameter optimization is conducted to obtain the optimal parameter values for each product design configuration. Among all design candidates, the optimal one is identified through configuration optimization. 3.2. Modeling of complex products A complex product is described in both the symbolic product modeling scheme and the CAD product modeling scheme. In the symbolic product model, a complex product is defined by a tree with component nodes and assembly nodes as shown in Fig. 3. An assembly object with sub-nodes is
Deyi Xue et al. / Procedia CIRP 70 (2018) 416–421 Author name / Procedia CIRP 00 (2017) 000–000
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defined by a name (e.g., mech1), sub-objects including assemblies and components (e.g., m1, gp1), attributes in the form of attribute[object] (e.g., ratio[gp1]), qualitative facts in the form of (description, object-1, object-2, …) (e.g., (pair,g1,g2)), quantitative attribute relations in the form of numerical functions where each function is defined by several input attributes and one output attribute (e.g., ratio[gp1]:=z[g1]/z[g2]), and geometric descriptions. A component object at the bottom of the tree is defined by a name, attributes, qualitative descriptions, quantitative relations among attributes, and geometric descriptions. s2
s1
g1
g2
mech1: Mechanism
m1: Motor gp1: Gear-Pair
m1 (a). A mechanism Assembly: mech1 Sub-objects: m1, gp1 …… Component: m1 Attributes: h[m1]=30, d[m1]=20, n[m1]=500 Geometry: (cylinder, d[m1], h[m1]) …… Component: s1 Attributes: h[s1]=100, d[s1]=10, n[s1]=500 Geometry: (cylinder, d[s1], h[s1]) …… Component: s2 Attributes: h[s2]=100, d[s2]=10, n[s2]=250 Geometry: (cylinder, d[s2], h[s2]) ……
g1: Gear g2: Gear s1: Shaft s2: Shaft
(b). A tree Assembly: gp1 Sub-objects: g1, g2, s1, s2 Facts: (pair,g1,g2) Attributes: ratio[gp1]=0.5 Attribute Relations: ratio[gp1]:=z[g1]/z[g2], n[g2]:=n[g1]*ratio[gp1] …… Component: g1 Attributes: h[g1]=10, d[g1]=60, m[g1]=2, z[g1]=30, n[g1]=500 Attribute Relations: d[g1]:=m[g1]*z[g1] Geometry: (cylinder, d[g1], h[g1]) …… Component: g2 Attributes: h[g2]=10, d[g2]=120, m[g2]=2, z[g2]=60, n[g2]=250 Attribute Relations: d[g2]:=m[g2]*z[g2] Geometry: (cylinder, d[g2], h[g2]) ……
m: module (mm), z: tooth number, n: rotational speed (rpm), h: height (mm), d: diameter (mm) (c). Assembly and component objects Fig. 3. A mechanism in symbolic product modeling scheme
The symbolic geometric descriptions are defined by predicates for 2-D geometry creation (e.g., line and arc), 3-D geometry creation (e.g., cylinder and pyramid), 3-D feature creation from 2-D objects (e.g., extrusion and revolution), transformation operations (e.g., translation and rotation), and Boolean operations (e.g., union and subtraction). In the example shown in Fig. 3, the geometries of motor, gear, and shaft components are defined by cylinders. For each component or assembly, the position (i.e., location and orientation) of the local coordinate system in the global coordinate system is defined by 6 built-in position attributes: x, y, z, rx, ry and rz. Relations between two coordinate systems of two sub-objects can be defined by attribute relations in the parent assembly object. When one
3
position attribute is changed, the change should be propagated to other position parameters automatically. The geometric descriptions in the symbolic product model are converted into and associate with the geometric model in the CAD product modeling scheme through API (Application Programming Interface) of the CAD system. In this work, SolidWorks is selected as the CAD system. The geometric descriptions in the symbolic product model are used as the product geometry construction descriptions to build the SolidWorks parts and assemblies. In a SolidWorks part created from a component in the symbolic product model, the geometry construction descriptions are organized in the form of feature construction descriptions based on the data structure of constructive solid geometry (CSG). The actually created geometry in a SolidWorks part is described by the boundary representation (B-rep) model. In a SolidWorks assembly created from an assembly in the symbolic product model, constraints are used to define the relation between the coordinate system of a sub-part or sub-assembly and the coordinate system of the parent assembly. The dimensions in the CAD product model and the attributes in the symbolic product model are mutually associative. A change of the value in one model can be propagated to the other model automatically. 3.3. Simulation of complex products For the symbolic product model used in conceptual design, the simulation systems, including a knowledge based design system and an attribute relation maintenance system, are used to manipulate the product descriptions in this product modeling scheme. In the knowledge based design system, knowledge is modeled by IF-THEN rules. Both the condition part and result part of a rule are described by predicates with constant and variable terms linked with logic AND relation (e.g., IF (gear, ?X) & (gear, ?Y) & (pair, ?X, ?Y) THEN (gear-pair, ?X, ?Y)). In rule-based reasoning, the condition parts of all the rules are first checked. Among all the rules whose condition parts are satisfied, one of these rules is selected and result part of this rule is executed. This process is continued until no more conditions of rules are satisfied. When the rules are not in contradiction, different sequences of the rules can lead to the same reasoning results. The numerical relations among attributes are used to form attribute relation networks [9] as shown in Fig. 4. An attribute relation network is composed of two types of nodes: attribute nodes and relation nodes. Each attribute node is associated with an attribute value. Each relation node is linked with one or several input attribute nodes and one output attribute node. When an attribute value is changed, the relations that use this attribute node as the input attribute node are then activated to update this change to the relevant output attribute nodes. The attribute value propagation process is continued until no attribute change is required. When the attribute relations are not in contradiction, consistency of the attribute relations can be maintained. In the example shown in Fig. 4, when the value of z[g1] is modified, this change is then propagated to d1[g1], ratio[gp1] and n[g2] through relations of R1, R3 and R4, respectively. The attribute relation maintenance system is used to calculate the position attributes of the coordinate systems for component and assembly objects.
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s1
s2
g1
g2
d[g2]=120
R1 z[g1]=30 n[g1]=500
mechanism-1
(b). Attribute relations d[g1]=60
m[g1]=2
nodes should be selected. (3) When a node is selected, and its sub-nodes are associated with an OR relation, only one of these sub-nodes should be selected. Fig. 5(b) shows two product configurations created from the AND-OR tree given in Fig. 5(a).
R1: d[g1]:=m[g1]*z[g1] R2: d[g2]:=m[g2]*z[g2] R3: ratio[gp1]:=z[g1]/z[g2] R4: n[g2]:=n[g1]*ratio[gp1]
(a). A gear pair
ratio[gp1]=0.5
R3 R4
z[g2]=60
m: module (mm) z: tooth number n: rotational speed (rpm) d: diameter (mm)
pulley-belt-pair-1
gear-pair-1
gear-1 gear-2 shaft-1 shaft-2 pulley-1 pulley-2 shaft-1 shaft-2 belt-1 (a). An ANR-OR tree
n[g2]=250
mechanism-1
mechanism-1
(c). An attribute relation network g1: gear g2: gear s1: shaft s2: shaft
rotation-to-rotation-1
motor-1 m[g2]=2
R2
419
An attribute
motor-1 rotation-to-rotation-1
Fig. 4. Maintenance of attribute relations
Many simulation functions in the CAD system can be used to manipulate the CAD model. Typical simulation functions in SolidWorks include motion analysis function to calculate the position, velocity and acceleration attributes at the selected points on the parts of the designed mechanism at different time points, finite element analysis (FEA) function to calculate the stress, strain and displacement attributes at the selected points on the parts of the designed structure, and computational fluid dynamics (CFD) function to calculate the pressure, flow velocity and temperature attributes at the selected locations of the fluid. 3.4. Optimization of complex products The optimization is conducted at two different levels: configuration optimization level and parameter optimization level. First various design solution candidates are modeled by different configurations, and each of these design configurations is described by a tree with assembly nodes and component nodes in the symbolic product model which is associated with a CAD model. For each configuration, parameter optimization is conducted to obtain the best values of the selected attribute variables to achieve the best overall evaluation index. From all the feasible design solution candidates modeled by configurations, configuration optimization is conducted to obtain the best design solution. The variations of product configurations based on design requirements are first modeled by an AND-OR tree as shown in Fig. 5. A node in this tree is either an assembly, a component, or a function which can be achieved by alternative design sub-nodes. When all sub-nodes need to be selected to support a parent node, these sub-nodes are associated with an AND relation. When only one of the subnodes needs to be selected to support a parent node, these subnodes are associated with an OR relation. A design solution modeled by a product configuration is created from the ANDOR tree based on the following 3 rules. (1) The root node should be selected first. (2) When a node is selected, and its sub-nodes are associated with an AND relation, all these sub-
pulley-belt-pair-1
gear-pair-1
A relation
rotation-to-rotation-1
motor-1
gear-1 gear-2 shaft-1 shaft-2 pulley-1 pulley-2 shaft-1 shaft-2 belt-1 shaft-2
shaft-1 motor-1
gear-1
gear-2
shaft-2
shaft-1 motor-1
pulley-1
pulley-2
belt-1
(b). Two design configurations AND relation
OR relation
Fig. 5. Creation of design candidates modeled by product configurations
For each design candidate, parameter optimization is conducted to achieve the best values of the selected attribute variables. The attribute variables can be selected (1) only from the symbolic product model, (2) only from the CAD product model, or (3) both from the symbolic product model and the CAD product model. When vector of the selected attribute variables for the i-th design candidate is described by Xi, its evaluation measures can be modeled by Ej(Xi) (i=1,2,…,n; j=1,2,…,m). Since the different evaluation measures are usually in different units, these measures should be converted into comparable evaluation indices Ij(Xi) based on the non-linear relations between the evaluation measures and evaluation indices [10]. Ij(Xi) = Ij[Ej(Xi)], j=1, 2, ..., m
(1)
The overall evaluation index, I(Xi), is defined by: m
I( X i ) =
∑ [W I
j j(
j =1
(2)
m
∑W
]
Xi )
j
j =1
where Wj is the weighting factor between 0 and 1 representing the importance of the j-th evaluation aspect. The optimal attribute values are obtained through numerical optimization.
et al. / Procedia (2018) 416–421 AuthorDeyi nameXue / Procedia CIRP 00 CIRP (2017)70000–000
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max I ( X i )
w .r .t . X i
s .t . X i(L) ≤ X i ≤ X i( U )
(3)
hik ( X i ) ≥ 0, k = 1,2 ,...
gik ( X i ) = 0, k = 1,2 ,...
The configuration optimization is conducted to obtain the best design candidate from all design candidates. When the number of design candidates is small, exhaustive method is used by investigating all design candidates. When the number of design candidates is large, generic programming has to be employed [11]. 4. A case study A simple case study is illustrated to demonstrate the potential application of the complex product design system which is under development. The requirement for this design is to convert a high-speed rotational motion of a motor into a low-speed translational motion to drive a piston as shown in Fig. 6. design-1 piston-1
high-rotation-to-low-translation-1
motor-1
high-rotation-to-low-rotation-1
…… low-rotation-to-low-translation-1
gear-1 gear-2 shaft-1 shaft-2
link-1 link-2
slider-1
motion into the low-speed rotational motion. A crank-slider mechanism is considered to transform the low-speed rotational motion into the low-speed translational motion. The AND-OR tree for this design is given in Fig. 6(a). Two design candidates, as shown in Fig. 6(b), can be created from the AND-OR tree. In the symbolic product model, a design candidate is described as a product configuration. The symbolic product model is used to create a CAD product model in the SolidWorks CAD system. The symbolic product model and the CAD product model for a design candidate are mutually associative. Change in one model can be propagated to the other model automatically. The attribute relation maintenance system is primarily used to maintain the relations between position parameters of coordinate systems. The relations among motion attributes are used for motion analysis in the CAD model. Optimization is conducted at two different levels: configuration optimization level and parameter optimization level. First parameter optimization is conducted for each of the two design candidates. Configuration optimization is simply carried out by selecting the best design candidate from the two design candidates. For the first design candidate with the gear pair, the length of the link-2, l[link-2] (250 mm ≤ l[link-2] ≤ 350 mm), is selected as the design variable. Major selected attribute values for this design candidate are summarized in Table 1. Since the stroke of the piston is required to be 200 mm, length of the link-1, l[link-1], is selected as 100 mm. Table 1. Major attribute values for the first design candidate.
crank-slider-1
gear-pair-1
slot-1
pulley-belt-pair-1
Object
Attribute
Symbol
Value
motor-1
rotational speed
n
120 rpm
gear-1
tooth number
z
30
module
m
2 mm
diameter
d
60 mm
rotational speed
n
120 rpm
tooth number
z
120
module
m
2 mm
diameter
d
240 mm
rotational speed
n
30 rpm
length
l
100 mm
rotational speed
n
30 rpm
pulley-1 pulley-2 shaft-1 shaft-2 belt-1 OR relation
AND relation (a). A partial AND-OR tree shaft-1 motor-1
shaft-2
gear-2
slot-1 link-1
gear-1
gear-2
link-1 link-2
shaft-1 shaft-2 motor-1
pulley-1 belt-1 pulley-2
slider-1 slot-1
link-1 link-2
5
slider-1
(b). Two design configurations Fig. 6. Creation of design candidates in the case study example
Due to the high speed of the motor, this high-speed rotational motion needs to be transformed into a low-speed rotational motion, and this low-speed rotational motion is further transformed into a low-speed translational motion. Two alternative mechanisms, a gear pair and a pulley-belt pair, are considered to transform the high-speed rotational
When l[link-2] is assigned a value between 250 mm and 350 mm, the motion analysis function in SolidWorks is then used to calculate the displacement, velocity and acceleration attributes of the slider-1. Fig. 7 shows the position, velocity and acceleration attributes of the slider-1 when l[link-2] is selected as 250 mm. In this case study, the maximum acceleration of the slider-1 is selected as the measure to evaluate the created design. As shown in Fig. 7(c), two maximum acceleration values, 700 mm/s2 and -1382 mm/s2, can be obtained considering the positive and negative directions. The maximum acceleration of the slider-1 is defined as maximum-acceleration[slider-1]. Since different values of l[link-2] can lead to different values of maximumacceleration[slider-1], it is expected that the best l[link-2] value is selected, such that the maximum-acceleration[slider1] is minimized. The optimization problem is formulated as:
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min
w .r .t . l [ link − 2 ]
max imum − accleration [ slider − 1 ]
s .t . 250 mm ≤ l [ link − 2 ] ≤ 350 mm
421
(4)
(a). Displacement of the slider-1
(a). Maximum acceleration of the slider-1 in positive direction (b). Velocity of the slider-1
(c). Acceleration of the slider-1 Fig. 7. Results in motion analysis
Through motion analysis, the maximum acceleration measures in positive and negative directions with different length values of the link-2 are achieved as shown in Fig. 8. When the maximum acceleration in the positive direction is selected as the optimization objective function, the best length of the link-2 is obtained as l[link-2] = 280 mm. When the maximum acceleration in the negative direction is selected as the optimization objective function, the best length of the link2 is obtained as l[link-2] = 350 mm. Parameter optimization for the design candidate 2 can be conducted in the same manner. Since the gear pair mechanism is better than the pulley-belt pair mechanism considering the accuracy of the rotational motion transformation ratio, the design candidate 1 is selected as the best configuration. 5. Conclusions Advantages of this new framework for optimal design of complex products considering modeling, simulation and optimization aspects are summarized as follows. 1. The multiple modeling schemes allow both the conceptual design and detailed design of the same product to be described by the symbolic model and the CAD model. 2. The multiple simulation schemes allow both the conceptual design activities and the detailed design activities to be conducted simultaneously. 3. The multiple optimization schemes are effective to identify both the best design configuration and its best parameter values. Acknowledgements Financial support from the Natural Sciences and Engineering Research Council (NSERC), Canada is acknowledged.
(b). Maximum acceleration of the slider-1 in negative direction Fig. 8. Maximum acceleration measures with different lengths of link-2
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Lyu G, Chu X, Xue D. Product modeling from knowledge, distributed computing and lifecycle perspectives: a literature review. Computers in Industry 2017; 84:1-13. [2] Bhise VD. Designing complex products with systems engineering processes and techniques. CRC Press; 2014. [3] Mobus GE, Kalton MC. Principles of systems science - understanding complex systems. Springer; 2015. [4] Shukor SA, Axinte DA. Manufacturability analysis system: issues and future trends. International Journal of Production Research 2009; 47(5):1369-1390. [5] Giudice F, Fargione G. Disassembly planning of mechanical systems for service and recovery: a genetic algorithms based approach. Journal of Intelligent Manufacturing 2007; 18(3):313-329. [6] Collette Y, Siarry P. Multiobjective optimization: principles and case studies. Springer; 2013. [7] Younis A, Dong, Z. Trends, features, and tests of common and recently introduced global optimization methods. Engineering Optimization 2010; 42(8):691-718. [8] Xue D. A multi-level optimization approach considering product realization process alternatives and parameters for improving manufacturability. Journal of Manufacturing Systems 1997; 16(5):337351. [9] Xue D, Xu Y. Web-based distributed system and database modeling for concurrent design. Computer-Aided Design 2003; 35(5):433-452. [10] Yang H, Xue D, Tu YL. Modeling of the non-linear relations among different design and manufacturing evaluation measures for multiobjective optimal concurrent design. Concurrent Engineering: Research & Applications 2006; 14(1):43-53. [11] Koza JR. Genetic programming: on the programming of computers by means of natural selection. The MIT Press; 1992.
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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 70 (2018) 416–421 www.elsevier.com/locate/procedia
28th 28th CIRP CIRP Design Design Conference, Conference, May May 2018, 2018, Nantes, Nantes, France France
A optimal design of products A framework framework for optimal design of complex complex products 28th CIRP for Design Conference, May 2018, Nantes, France a,
a
Deyi a,*, David Imaniyana Deyi Xue Xue *,functional David Imaniyan A new methodology to analyze the and physical architecture of Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4 of Mechanical and Manufacturing Engineering, University ofproduct Calgary, Calgary, Alberta, Canada T2N 1N4 existing Department products for an assembly oriented family identification * Corresponding author. Tel.: +1-403-220-4168; fax: +1-403-282-8406. E-mail address: [email protected] a a
* Corresponding author. Tel.: +1-403-220-4168; fax: +1-403-282-8406. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
Abstract École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France Abstract many author. design methodologies and [email protected] developed, the presently achieved research results are not effective for design of *Despite Corresponding +33 3 87 37 54 30;tools E-mailhave address: Despite many designTel.: methodologies and tools have been developed, the presently achieved research results are not effective for design of
complex products when various methods and tools in different schemes have to be employed. A new framework for optimal design of complex complex products when various methods and tools in different schemes have to be employed. A new framework for optimal design of complex products is introduced in this research considering modeling, simulation and optimization aspects. First, a hybrid scheme is developed for products is introduced in this research considering modeling, simulation and optimization aspects. First, a hybrid scheme is developed for integrated modeling of complex products. In this hybrid scheme, descriptions of a generic product are modeled by an AND-OR tree. Feasible integrated modeling of complex products. In this hybrid scheme, descriptions of a generic product are modeled by an AND-OR tree. Feasible design candidates are created from the AND-OR tree through tree-based search. Geometric descriptions in a design candidate are associated Abstract design candidates are created from the AND-OR tree through tree-based search. Geometric descriptions in a design candidate are associated with a CAD system. Second, a hybrid simulation method is developed for evaluation of different product aspects with different simulation tools with a CAD system. Second, a hybrid simulation method is developed for evaluation of different product aspects with different simulation tools arebusiness integrated by the hybrid scheme. Simulations with geometric descriptions are conducted functions the of the CAD Inwhich today’s environment, themodeling trend towards more product variety and customization is unbroken. Due by to analysis this development, need of which are integrated by the hybrid modeling scheme. Simulations with geometric descriptions are conducted by analysis functions of the CAD system. Simulations withproduction non-geometric descriptions arecope conducted by theproducts knowledge-based systems. Third, a hybridand optimization method is agile and reconfigurable systems emerged to with various and product families. To design optimize production system. Simulations with non-geometric descriptions are conducted by the knowledge-based systems. Third, a hybrid optimization method is developed to identify the optimal design of the complex product. each design candidate, parameter optimization conducted to obtain systems as well as to choose the optimal product matches, productFor analysis methods are needed. Indeed, most of theis methods aim the to developed to identify the optimal design of the complex product. For each design candidate, parameter optimization is known conducted to obtain the optimalaparameter values. The optimal design solution level. is identified from all design candidates through configuration optimization. analyze product or one product family on the physical Different product families, however, may differ largely in terms of the number and optimal parameter values. The optimal design solution is identified from all design candidates through configuration optimization. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production © 2018 Authors. Published by Ltd. is an open access CC BY-NC-ND license 2017AThe Authors. Published by Elsevier B.V.This system. new methodology is proposed to analyze existing products in article view ofunder theirthe functional and physical architecture. The aim is to cluster © 2017 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review responsibility of the scientific committee of the 28th CIRPofDesign Conference 2018.and the creation of future reconfigurable these productsunder in new assembly oriented product families for the optimization existing assembly lines Peer-review under responsibility of the scientific scientific committee of of the 28th 28th CIRP CIRP Design Design Conference Conference 2018. 2018. assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and modeling; simulation;a optimization aKeywords: functionalComplex analysisproducts; is performed. Moreover, hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the Keywords: Complex products; modeling; simulation; optimization similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. Introduction geometric descriptions, modeling of non-geometric design ©1. The Authors. Published by Elsevier B.V. 1.2017 Introduction geometric descriptions, modeling of non-geometric design information and other product life-cycle information such as Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. information and other product life-cycle information such as
With the advances in design research and computer manufacturing and operation/use has also been studied [1]. In With the advances in design research and computer manufacturing and operation/use has also been studied [1]. In such as simulation/evaluation aspect, a design is usually evaluated by technology, many design methodologies and tools, such as simulation/evaluation aspect, a design is usually evaluated by knowledge-based design and computer aided design, have measures in different product life-cycle aspects such as knowledge-based design and computer aided design, have measures in different product life-cycle aspects such as been developed for improving quality and efficiency of manufacturing [4] and services [5] in addition to functional been developed for improving quality and efficiency of manufacturing [4] and services [5] in addition to functional product design [1]. Due to the increase of complexity in performances. Sophisticated simulation/evaluation tools, such design [1]. Due to the increase of complexity in of performances. Sophisticated simulation/evaluation tools, such 1.product Introduction the product range and characteristics manufactured and/or products, methods and tools for design of complex products as finite element analysis (FEA) and computational fluid products, methods and tools for design of complex products assembled as finite in element analysis (FEA) and the computational fluid this system. In this context, main challenge in and systems need to be developed [2]. dynamics (CFD) systems, are also employed to evaluate the and systems be developed [2]. in the domain of dynamics and (CFD) systems, are also employed to evaluate the Due to need the to fast development modelling analysis is now not only to cope with single The term of complex system was originated in information design. In optimization aspect, multi-objective optimization The term of complex originated in information design. Ina limited optimization multi-objective optimization communication and an system ongoingwas trend of digitization and products, productaspect, range or existing product families, science when a network was used to associate the [6] is often used to achieve the optimal design considering science whenmanufacturing a network enterprises was usedaretofacing associate the but [6] also is often achieveand theto optimal considering digitalization, important to be used able totoanalyze comparedesign products to define heterogeneous components into the same environment [3]. different product life-cycle evaluation measures. Various heterogeneous components intoenvironments: the same environment [3]. new different product life-cycle measures. Various challenges in today’s market a continuing product families. It can be evaluation observed that classical existing Among various aspects of complexity in design of products global optimization techniques [7] were also developed to Among various aspects of of complexity in design oftimes products global families optimization techniques [7] wereof also developed to tendency towards reduction product development and product are regrouped in function clients or features. and systems such as the number of components and the effort improve the quality and efficiency of optimization. and systems such lifecycles. as the number of components andincreasing the effort However, improve the qualityoriented and efficiency offamilies optimization. shortened product In addition, there is an assembly product are hardly to find. in manufacturing, a complex product or system in this Despite of the progress, these achieved research results are in manufacturing, a complex atproduct or time system this Despite of the progress, theseproducts achieveddiffer research results are demand same intechniques a in global the product family of level, mainly in two researchofiscustomization, considered as being the one the where multiple notOneffective for design complex products where various research is with considered as the all oneover where multiple techniques not effective for design ofnumber complex products where various competition competitors the world. This trend, main characteristics: (i) the of components and (ii) the are required for modeling, simulation and optimization. This methods and tools in different schemes have to be employed. are required for modeling, simulation from and optimization. This type methods and tools in different schemes have to be employed. which is focuses inducing development to micro of components (e.g. mechanical, electrical, research onthemodeling, simulation macro and optimization A new framework is introduced in this researchelectronical). for design of research results focusesinondiminished modeling,lot simulation and optimization A Classical new framework is introduced in thismainly research for products design of markets, sizes due to augmenting methodologies considering single aspects in design of complex products. complex products considering modeling, simulation and aspects varieties in design(high-volume of complex products. complex products considering modeling, simulation and product to low-volume production) [1]. or solitary, already existing product families analyze the In modeling aspect, in addition to CAD-based product optimization aspects. In modeling in addition to well CAD-based product optimization aspects. To cope with this aspect, augmenting variety as as to be able to product structure on a physical level (components level) which identify potentials in the existing causes difficulties regarding an efficient definition and 2212-8271possible © 2017 The optimization Authors. Published by Elsevier B.V. 2212-8271 ©system, 2017 TheitAuthors. Published Elsevier B.V. knowledge production is important tobyhave a precise comparison of different product families. Addressing this Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. Keywords: Assembly; method; Family identification technology, manyDesign design methodologies and tools,
Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 28thDesign CIRP Conference Design Conference Peer-review under responsibility of the committee of the of 28th 2018. 2018. 10.1016/j.procir.2018.02.038
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Deyi Xue et al. / Procedia CIRP 70 (2018) 416–421 Deyi Xue / Procedia CIRP 00 (2018) 000–000
2. A framework The framework for design of complex products considering modeling, simulation and optimization aspects is shown in Fig. 1. D2
D1
3. Design of complex products considering non-geometric descriptions and geometric descriptions 3.1. System architecture In this work, a system is proposed for design of complex products considering non-geometric descriptions in conceptual design and geometric descriptions in detailed design. Fig. 2 shows the system architecture. Knowledge Based Design System
……
……
Parameter Optimization Optimize F(X1)
Candidate Optimization Optimize Di
Attribute Relation Maintenance System
Symbolic Product Modeling Scheme
Relation
Modeling Scheme
Simulation System
Design Candidate Fig. 1. Framework for design of complex products
In this framework, multiple design solution candidates, Di (i=1,2,…,n), are created to achieve the same design requirements. Since different design candidates are composed of different components, each of these design candidates is also called a product design configuration. For each design candidate Di, the complex product is modeled by m different schemes, Mij (i=1,2,…,n; j=1,2,…,m). In each scheme, the product is modeled by product descriptions and their relations. Product descriptions in different schemes are associated by their relations. When a product description in one scheme is modified, this change should be propagated to other schemes automatically through the relations. Each product modeling scheme in a design candidate, Mij (i=1,2,…,n; j=1,2,…,m), is associated with a number of simulation systems, Sijk (i=1,2,…,n; j=1,2,…,m; k=1,2,…,p). A simulation system can be used to create, delete and modify product descriptions in that scheme. A simulation system can also be used to obtain the evaluation measures of the design. For each design candidate, a number of quantitative design parameters can be selected as design variables, Xi (i=1,2,…,n). The evaluation measure achieved by the simulation systems can be modeled as a numerical function of the selected design variables, F(Xi). The optimal design is achieved through multi-level optimization [8]. First parameter optimization, Optimize F(Xi) (i=1,2,…,n), is conducted to obtain the optimal values of the design variables Xi* and the corresponding best evaluation measure F(Xi*) for each design candidate Di (i=1,2,…,n). Among all n design candidates, configuration optimization, Optimize Di, is conducted to obtain the best design candidate Di* (i=1,2,…,n).
Motion Analysis System
Finite Element Analysis System
CAD Product Modeling Scheme
Multi-level Optimization System Modeling Scheme
Design Description
417
Simulation System
Fig. 2. Architecture of the complex product design system
In this system, the conceptual design descriptions are modeled using the symbolic product modeling scheme, while the detailed design descriptions are modeling using the CAD product modeling scheme. The geometric descriptions in the symbolic product modeling scheme are associated with the geometric descriptions in the CAD product modeling scheme. The symbolic product model is created and manipulated by the knowledge based design system. The consistency of the quantitative attribute values is maintained by the attribute relation maintenance system [9]. The CAD product model is created from the geometric descriptions in the symbolic product model and manipulated by the CAD system. The motion analysis system and the finite element analysis system are used for various types of analysis and evaluation to the CAD product model. Optimization is conducted to achieve the best design configuration candidate and its best parameter values. Optimization is conducted at two different levels: configuration optimization level and parameter optimization level. First different design candidates are created from the design requirements, and each of these design candidates is modeled by a product configuration. Parameter optimization is conducted to obtain the optimal parameter values for each product design configuration. Among all design candidates, the optimal one is identified through configuration optimization. 3.2. Modeling of complex products A complex product is described in both the symbolic product modeling scheme and the CAD product modeling scheme. In the symbolic product model, a complex product is defined by a tree with component nodes and assembly nodes as shown in Fig. 3. An assembly object with sub-nodes is
Deyi Xue et al. / Procedia CIRP 70 (2018) 416–421 Author name / Procedia CIRP 00 (2017) 000–000
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defined by a name (e.g., mech1), sub-objects including assemblies and components (e.g., m1, gp1), attributes in the form of attribute[object] (e.g., ratio[gp1]), qualitative facts in the form of (description, object-1, object-2, …) (e.g., (pair,g1,g2)), quantitative attribute relations in the form of numerical functions where each function is defined by several input attributes and one output attribute (e.g., ratio[gp1]:=z[g1]/z[g2]), and geometric descriptions. A component object at the bottom of the tree is defined by a name, attributes, qualitative descriptions, quantitative relations among attributes, and geometric descriptions. s2
s1
g1
g2
mech1: Mechanism
m1: Motor gp1: Gear-Pair
m1 (a). A mechanism Assembly: mech1 Sub-objects: m1, gp1 …… Component: m1 Attributes: h[m1]=30, d[m1]=20, n[m1]=500 Geometry: (cylinder, d[m1], h[m1]) …… Component: s1 Attributes: h[s1]=100, d[s1]=10, n[s1]=500 Geometry: (cylinder, d[s1], h[s1]) …… Component: s2 Attributes: h[s2]=100, d[s2]=10, n[s2]=250 Geometry: (cylinder, d[s2], h[s2]) ……
g1: Gear g2: Gear s1: Shaft s2: Shaft
(b). A tree Assembly: gp1 Sub-objects: g1, g2, s1, s2 Facts: (pair,g1,g2) Attributes: ratio[gp1]=0.5 Attribute Relations: ratio[gp1]:=z[g1]/z[g2], n[g2]:=n[g1]*ratio[gp1] …… Component: g1 Attributes: h[g1]=10, d[g1]=60, m[g1]=2, z[g1]=30, n[g1]=500 Attribute Relations: d[g1]:=m[g1]*z[g1] Geometry: (cylinder, d[g1], h[g1]) …… Component: g2 Attributes: h[g2]=10, d[g2]=120, m[g2]=2, z[g2]=60, n[g2]=250 Attribute Relations: d[g2]:=m[g2]*z[g2] Geometry: (cylinder, d[g2], h[g2]) ……
m: module (mm), z: tooth number, n: rotational speed (rpm), h: height (mm), d: diameter (mm) (c). Assembly and component objects Fig. 3. A mechanism in symbolic product modeling scheme
The symbolic geometric descriptions are defined by predicates for 2-D geometry creation (e.g., line and arc), 3-D geometry creation (e.g., cylinder and pyramid), 3-D feature creation from 2-D objects (e.g., extrusion and revolution), transformation operations (e.g., translation and rotation), and Boolean operations (e.g., union and subtraction). In the example shown in Fig. 3, the geometries of motor, gear, and shaft components are defined by cylinders. For each component or assembly, the position (i.e., location and orientation) of the local coordinate system in the global coordinate system is defined by 6 built-in position attributes: x, y, z, rx, ry and rz. Relations between two coordinate systems of two sub-objects can be defined by attribute relations in the parent assembly object. When one
3
position attribute is changed, the change should be propagated to other position parameters automatically. The geometric descriptions in the symbolic product model are converted into and associate with the geometric model in the CAD product modeling scheme through API (Application Programming Interface) of the CAD system. In this work, SolidWorks is selected as the CAD system. The geometric descriptions in the symbolic product model are used as the product geometry construction descriptions to build the SolidWorks parts and assemblies. In a SolidWorks part created from a component in the symbolic product model, the geometry construction descriptions are organized in the form of feature construction descriptions based on the data structure of constructive solid geometry (CSG). The actually created geometry in a SolidWorks part is described by the boundary representation (B-rep) model. In a SolidWorks assembly created from an assembly in the symbolic product model, constraints are used to define the relation between the coordinate system of a sub-part or sub-assembly and the coordinate system of the parent assembly. The dimensions in the CAD product model and the attributes in the symbolic product model are mutually associative. A change of the value in one model can be propagated to the other model automatically. 3.3. Simulation of complex products For the symbolic product model used in conceptual design, the simulation systems, including a knowledge based design system and an attribute relation maintenance system, are used to manipulate the product descriptions in this product modeling scheme. In the knowledge based design system, knowledge is modeled by IF-THEN rules. Both the condition part and result part of a rule are described by predicates with constant and variable terms linked with logic AND relation (e.g., IF (gear, ?X) & (gear, ?Y) & (pair, ?X, ?Y) THEN (gear-pair, ?X, ?Y)). In rule-based reasoning, the condition parts of all the rules are first checked. Among all the rules whose condition parts are satisfied, one of these rules is selected and result part of this rule is executed. This process is continued until no more conditions of rules are satisfied. When the rules are not in contradiction, different sequences of the rules can lead to the same reasoning results. The numerical relations among attributes are used to form attribute relation networks [9] as shown in Fig. 4. An attribute relation network is composed of two types of nodes: attribute nodes and relation nodes. Each attribute node is associated with an attribute value. Each relation node is linked with one or several input attribute nodes and one output attribute node. When an attribute value is changed, the relations that use this attribute node as the input attribute node are then activated to update this change to the relevant output attribute nodes. The attribute value propagation process is continued until no attribute change is required. When the attribute relations are not in contradiction, consistency of the attribute relations can be maintained. In the example shown in Fig. 4, when the value of z[g1] is modified, this change is then propagated to d1[g1], ratio[gp1] and n[g2] through relations of R1, R3 and R4, respectively. The attribute relation maintenance system is used to calculate the position attributes of the coordinate systems for component and assembly objects.
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Deyi Xue et al. / Procedia CIRP 70 (2018) 416–421 Deyi Xue / Procedia CIRP 00 (2018) 000–000
s1
s2
g1
g2
d[g2]=120
R1 z[g1]=30 n[g1]=500
mechanism-1
(b). Attribute relations d[g1]=60
m[g1]=2
nodes should be selected. (3) When a node is selected, and its sub-nodes are associated with an OR relation, only one of these sub-nodes should be selected. Fig. 5(b) shows two product configurations created from the AND-OR tree given in Fig. 5(a).
R1: d[g1]:=m[g1]*z[g1] R2: d[g2]:=m[g2]*z[g2] R3: ratio[gp1]:=z[g1]/z[g2] R4: n[g2]:=n[g1]*ratio[gp1]
(a). A gear pair
ratio[gp1]=0.5
R3 R4
z[g2]=60
m: module (mm) z: tooth number n: rotational speed (rpm) d: diameter (mm)
pulley-belt-pair-1
gear-pair-1
gear-1 gear-2 shaft-1 shaft-2 pulley-1 pulley-2 shaft-1 shaft-2 belt-1 (a). An ANR-OR tree
n[g2]=250
mechanism-1
mechanism-1
(c). An attribute relation network g1: gear g2: gear s1: shaft s2: shaft
rotation-to-rotation-1
motor-1 m[g2]=2
R2
419
An attribute
motor-1 rotation-to-rotation-1
Fig. 4. Maintenance of attribute relations
Many simulation functions in the CAD system can be used to manipulate the CAD model. Typical simulation functions in SolidWorks include motion analysis function to calculate the position, velocity and acceleration attributes at the selected points on the parts of the designed mechanism at different time points, finite element analysis (FEA) function to calculate the stress, strain and displacement attributes at the selected points on the parts of the designed structure, and computational fluid dynamics (CFD) function to calculate the pressure, flow velocity and temperature attributes at the selected locations of the fluid. 3.4. Optimization of complex products The optimization is conducted at two different levels: configuration optimization level and parameter optimization level. First various design solution candidates are modeled by different configurations, and each of these design configurations is described by a tree with assembly nodes and component nodes in the symbolic product model which is associated with a CAD model. For each configuration, parameter optimization is conducted to obtain the best values of the selected attribute variables to achieve the best overall evaluation index. From all the feasible design solution candidates modeled by configurations, configuration optimization is conducted to obtain the best design solution. The variations of product configurations based on design requirements are first modeled by an AND-OR tree as shown in Fig. 5. A node in this tree is either an assembly, a component, or a function which can be achieved by alternative design sub-nodes. When all sub-nodes need to be selected to support a parent node, these sub-nodes are associated with an AND relation. When only one of the subnodes needs to be selected to support a parent node, these subnodes are associated with an OR relation. A design solution modeled by a product configuration is created from the ANDOR tree based on the following 3 rules. (1) The root node should be selected first. (2) When a node is selected, and its sub-nodes are associated with an AND relation, all these sub-
pulley-belt-pair-1
gear-pair-1
A relation
rotation-to-rotation-1
motor-1
gear-1 gear-2 shaft-1 shaft-2 pulley-1 pulley-2 shaft-1 shaft-2 belt-1 shaft-2
shaft-1 motor-1
gear-1
gear-2
shaft-2
shaft-1 motor-1
pulley-1
pulley-2
belt-1
(b). Two design configurations AND relation
OR relation
Fig. 5. Creation of design candidates modeled by product configurations
For each design candidate, parameter optimization is conducted to achieve the best values of the selected attribute variables. The attribute variables can be selected (1) only from the symbolic product model, (2) only from the CAD product model, or (3) both from the symbolic product model and the CAD product model. When vector of the selected attribute variables for the i-th design candidate is described by Xi, its evaluation measures can be modeled by Ej(Xi) (i=1,2,…,n; j=1,2,…,m). Since the different evaluation measures are usually in different units, these measures should be converted into comparable evaluation indices Ij(Xi) based on the non-linear relations between the evaluation measures and evaluation indices [10]. Ij(Xi) = Ij[Ej(Xi)], j=1, 2, ..., m
(1)
The overall evaluation index, I(Xi), is defined by: m
I( X i ) =
∑ [W I
j j(
j =1
(2)
m
∑W
]
Xi )
j
j =1
where Wj is the weighting factor between 0 and 1 representing the importance of the j-th evaluation aspect. The optimal attribute values are obtained through numerical optimization.
et al. / Procedia (2018) 416–421 AuthorDeyi nameXue / Procedia CIRP 00 CIRP (2017)70000–000
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max I ( X i )
w .r .t . X i
s .t . X i(L) ≤ X i ≤ X i( U )
(3)
hik ( X i ) ≥ 0, k = 1,2 ,...
gik ( X i ) = 0, k = 1,2 ,...
The configuration optimization is conducted to obtain the best design candidate from all design candidates. When the number of design candidates is small, exhaustive method is used by investigating all design candidates. When the number of design candidates is large, generic programming has to be employed [11]. 4. A case study A simple case study is illustrated to demonstrate the potential application of the complex product design system which is under development. The requirement for this design is to convert a high-speed rotational motion of a motor into a low-speed translational motion to drive a piston as shown in Fig. 6. design-1 piston-1
high-rotation-to-low-translation-1
motor-1
high-rotation-to-low-rotation-1
…… low-rotation-to-low-translation-1
gear-1 gear-2 shaft-1 shaft-2
link-1 link-2
slider-1
motion into the low-speed rotational motion. A crank-slider mechanism is considered to transform the low-speed rotational motion into the low-speed translational motion. The AND-OR tree for this design is given in Fig. 6(a). Two design candidates, as shown in Fig. 6(b), can be created from the AND-OR tree. In the symbolic product model, a design candidate is described as a product configuration. The symbolic product model is used to create a CAD product model in the SolidWorks CAD system. The symbolic product model and the CAD product model for a design candidate are mutually associative. Change in one model can be propagated to the other model automatically. The attribute relation maintenance system is primarily used to maintain the relations between position parameters of coordinate systems. The relations among motion attributes are used for motion analysis in the CAD model. Optimization is conducted at two different levels: configuration optimization level and parameter optimization level. First parameter optimization is conducted for each of the two design candidates. Configuration optimization is simply carried out by selecting the best design candidate from the two design candidates. For the first design candidate with the gear pair, the length of the link-2, l[link-2] (250 mm ≤ l[link-2] ≤ 350 mm), is selected as the design variable. Major selected attribute values for this design candidate are summarized in Table 1. Since the stroke of the piston is required to be 200 mm, length of the link-1, l[link-1], is selected as 100 mm. Table 1. Major attribute values for the first design candidate.
crank-slider-1
gear-pair-1
slot-1
pulley-belt-pair-1
Object
Attribute
Symbol
Value
motor-1
rotational speed
n
120 rpm
gear-1
tooth number
z
30
module
m
2 mm
diameter
d
60 mm
rotational speed
n
120 rpm
tooth number
z
120
module
m
2 mm
diameter
d
240 mm
rotational speed
n
30 rpm
length
l
100 mm
rotational speed
n
30 rpm
pulley-1 pulley-2 shaft-1 shaft-2 belt-1 OR relation
AND relation (a). A partial AND-OR tree shaft-1 motor-1
shaft-2
gear-2
slot-1 link-1
gear-1
gear-2
link-1 link-2
shaft-1 shaft-2 motor-1
pulley-1 belt-1 pulley-2
slider-1 slot-1
link-1 link-2
5
slider-1
(b). Two design configurations Fig. 6. Creation of design candidates in the case study example
Due to the high speed of the motor, this high-speed rotational motion needs to be transformed into a low-speed rotational motion, and this low-speed rotational motion is further transformed into a low-speed translational motion. Two alternative mechanisms, a gear pair and a pulley-belt pair, are considered to transform the high-speed rotational
When l[link-2] is assigned a value between 250 mm and 350 mm, the motion analysis function in SolidWorks is then used to calculate the displacement, velocity and acceleration attributes of the slider-1. Fig. 7 shows the position, velocity and acceleration attributes of the slider-1 when l[link-2] is selected as 250 mm. In this case study, the maximum acceleration of the slider-1 is selected as the measure to evaluate the created design. As shown in Fig. 7(c), two maximum acceleration values, 700 mm/s2 and -1382 mm/s2, can be obtained considering the positive and negative directions. The maximum acceleration of the slider-1 is defined as maximum-acceleration[slider-1]. Since different values of l[link-2] can lead to different values of maximumacceleration[slider-1], it is expected that the best l[link-2] value is selected, such that the maximum-acceleration[slider1] is minimized. The optimization problem is formulated as:
6
Deyi Xue et al. / Procedia CIRP 70 (2018) 416–421 Deyi Xue / Procedia CIRP 00 (2018) 000–000
min
w .r .t . l [ link − 2 ]
max imum − accleration [ slider − 1 ]
s .t . 250 mm ≤ l [ link − 2 ] ≤ 350 mm
421
(4)
(a). Displacement of the slider-1
(a). Maximum acceleration of the slider-1 in positive direction (b). Velocity of the slider-1
(c). Acceleration of the slider-1 Fig. 7. Results in motion analysis
Through motion analysis, the maximum acceleration measures in positive and negative directions with different length values of the link-2 are achieved as shown in Fig. 8. When the maximum acceleration in the positive direction is selected as the optimization objective function, the best length of the link-2 is obtained as l[link-2] = 280 mm. When the maximum acceleration in the negative direction is selected as the optimization objective function, the best length of the link2 is obtained as l[link-2] = 350 mm. Parameter optimization for the design candidate 2 can be conducted in the same manner. Since the gear pair mechanism is better than the pulley-belt pair mechanism considering the accuracy of the rotational motion transformation ratio, the design candidate 1 is selected as the best configuration. 5. Conclusions Advantages of this new framework for optimal design of complex products considering modeling, simulation and optimization aspects are summarized as follows. 1. The multiple modeling schemes allow both the conceptual design and detailed design of the same product to be described by the symbolic model and the CAD model. 2. The multiple simulation schemes allow both the conceptual design activities and the detailed design activities to be conducted simultaneously. 3. The multiple optimization schemes are effective to identify both the best design configuration and its best parameter values. Acknowledgements Financial support from the Natural Sciences and Engineering Research Council (NSERC), Canada is acknowledged.
(b). Maximum acceleration of the slider-1 in negative direction Fig. 8. Maximum acceleration measures with different lengths of link-2
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