6th World Congresses of Structural and Multidisciplinary Optimization Rio de Janeiro, 30 May - 03 June 2005, Brazil

CAD-Based Design Optimization for Vehicle Performance Kuang-Hua Chang and Sung-Hwan Joo University of Oklahoma, Norman, OK 73019, USA [email protected], [email protected] Abstract This paper presents an open and integrated tool environment that enables engineers to effectively search, in a CAD solid model form, for a mechanism design with optimal kinematic and dynamic performance. In order to demonstrate the feasibility of such an environment, design parameterization that supports capturing design intents in product solid models must be available, and advanced modeling, simulation, and optimization technologies implemented in engineering software tools must be incorporated. In this paper, the design parameterization capabilities developed previously have been applied to support design optimization of engineering products, including a High Mobility Multi-purpose Wheeled Vehicle (HMMWV). In the proposed environment, Pro/ENGINEER and SolidWorks are supported for product model representation, DADS (Dynamic Analysis and Design System) is employed for dynamic simulation of mechanical systems including ground vehicles, and DOT (Design Optimization Tool) is included for a batch mode design optimization. In addition to the commercial tools, a number of software modules have been implemented to support the integration; e.g., interface modules for data retrieval, and model update modules for updating CAD and simulation models in accordance with design changes. Note that in this research, the overall finite difference method has been adopted to support design sensitivity analysis. Keywords: Design Optimization, Design Parameterization, Computer-Aided Design, Dynamic Simulation, Tool Integration 1.

Introduction Parametric modeling technology has been adopted in mainstream Computer-Aided Design (CAD) tools used by industry. This technology provides designers with tremendous flexibility to explore feasible design alternatives. In order to support design decisionmaking for trade-offs between product performance and cost, engineers often depend on Computer-Aided Engineering (CAE) tools to realize product performance. Kinematic and dynamic performance is one of the primary requirements for mechanical system design. A significant amount of work has been devoted to simulating dynamic performance of mechanical systems including ground vehicles. However, the mapping between physical geometry of mechanical components to simulation parameters of the motion models, such as mass properties and joint locations, are not available since most simulation models were created in an analysis instead of a design form. As shown in Figure 1a, four parts are assembled for a slider-crank mechanism in CAD. In the motion simulation model (Figure 1b), there are three movable bodies and a ground body. Any change in the crankshaft length d2:0 (or connecting rod length d3:2) will affect its own mass properties. The change will also move the position that connects to the next body (in this case, connecting rod), therefore, altering the kinematic and dynamic characteristics of the mechanism. The mass properties and joint location due to design changes have to be calculated in order to support design optimization for the mechanism. Piston

d3:2

Crankshaft Connecting Rod d2:0

Ground

Piston Pin d2:0

Slider (Piston)

Connecting Rod Crankshaft (a) CAD Solid Model Form

(b) Schematic View of Motion Model

Figure 1 A Slider-Crank Mechanism A number of efforts have been made, primarily in the commercial sector, in connecting motion analysis software tools to CAD. For example, Dynamic Designer developed based on ADAMS by Mechanical Dynamics, Inc. [1], has been integrated into SolidWorks [2], SolidEdge [3], and Autodesk [4]; DADS of LMS-CADSI [5] links to Pro/ENGINEER [6], SolidWorks (called DesignWorks), CATIA [7], and I-DEAS [8]; and Pro/MECHANICA Motion [9] of Parametric Technology immerses in Pro/ENGINEER. Among these, only Pro/MECHANICA Motion supports design [10], but links to Pro/ENGINEER only. Pro/MECHANICA Motion supports designers primarily to design for planar mechanisms. Serious analysis engineers quickly find that the kinematic and dynamic analysis capabilities in Pro/MECHANICA Motion are not up to the caliber of advanced motion analysis tools, such as ADAMS and DADS. An integrated system that supports engineers to conduct optimization for mechanical systems by taking advantage of parametric modeling capability in CAD and extensive analysis capabilities in advanced analysis codes is practically non-existing. The objective of this research is to develop and demonstrate the feasibility of an open and integrated tool environment that enables engineers to effectively search, in a CAD solid model form, for a mechanism design with optimal kinematic and dynamic

performance. Essentially, the environment aims at solving the following design optimization problem: Minimize: Subject to:

φ(b) ψi(b) ≤ ψiu

(1)

bjl ≤ bj ≤ bju where φ(b) is the objective function; b is the vector of design variables captured in CAD solid models; ψi(b) is the ith dynamic performance with its corresponding upper bound ψiu; and bjl and bju are the lower and upper bounds of the jth design variable, respectively. Note that it is essential to have an integrated system that supports engineers to conduct CAD-based mechanism optimization, taking full advantage of parametric modeling capability in CAD and extensive analysis capabilities in advanced analysis codes. An open system that links multiple feature-based and parametric CAD tools, and several motion analysis tools is needed. In addition, a unified design parameterization method that supports engineers to systematically capture design intents in multiple CAD systems must be employed. 2.

Design Parameterization A preliminary study has been conducted to investigate the parametric technology employed in Pro/ENGINEER and SolidWorks [11]. This study led to a set of design parameterization guidelines that support designers to systematically capture design intents in product solid models. In this research, the parameterization method and guidelines have been successfully applied to support design parameterization of a HMMWV (High Mobility Multi-purpose Wheeled Vehicle) in SolidWorks. Moreover, in support of an open system that incorporates multiple CAD tools for product modeling and parameterization, issues involved in solid model translation between CAD systems have also been investigated, and has been documented in [12]. 2.1

Axioms and Guidelines for Design Parameterization The preliminary study conducted is briefly summarized in the following. Design intent in the context of product design is a product performance measure that the designer desires to attain by changing geometric shape of parts (or assemblies) and their placements with respect to other parts (or assemblies) in a product. This geometric shape change is usually realized through change of geometric dimension values in CAD solid models. The design intent can be captured in product solid models by creating parts and assemblies following a set of guidelines proposed in Ref. 11. These guidelines have been developed following two important axioms [13]; Axiom 1: Axiom 2:

Maintain the independence of design intents, Minimize the information content of the design intents.

Axiom 1 implies that changing the value of dimension design variables has an effect only on the corresponding design intent. In other words, it is desirable to uncouple the design intents whenever possible. Axiom 2 states that the amount of information (number of dimensions) that is available to the engineer for capturing the design intent must be minimized. A simple slider-crank example shown in Figure 1a is presented to illustrate the axioms for design parameterization. This slider-crank mechanism consists of four parts; crankshaft, connecting rod, piston pin, and piston. Two design intents are defined in this example, (1) horizontal velocity of the piston increases 20% when the crankshaft is driven at a constant angular velocity, and (2) weight of the mechanism reduces 30%. The first intent can be captured by choosing lengths of the crank (d2:0) and rod (d3:2) as two independent design variables. However, changing either one will affect the second intent, weight of the mechanism. In this case, these two design intents are coupled. In order to reduce the coupling effect, additional design variables, such as width of the crankshaft or outer diameter of the piston, can be defined to support the second intent. Adding design variables for the second intent helps comply with Axiom 1. Moreover, geometric features in the crankshaft and connecting rod have been created with proper dimensions and references such that when their lengths are changed, the entire parts vary accordingly. At the assembly level, when either of the two design variables d2:0 or d3:2 is changed, the change must be propagated to the affected parts. The remaining parts must be kept unchanged, and the entire assembly must be maintained intact, as illustrated in Figure 2. d2:0 = 3

d3:2 = 8

(a) Design Variables d2:0 and d3:2

d2:0 = 4

d3:2 = 12

(b) d2:0 Changes to 4

(c) d3:2 Changes to 12

Figure 2 Change of Length Design Variables 2.2

Design Parameterization for HMMWV Suspension The vehicle track and wheelbase shown in Figure 3 are the two primary design variables defined for HMMWV. In order to support HMMWV design optimization, the suspension assembly must be parameterized in CAD. The design parameterization must be conducted at both part and assembly levels. At part level, design parameterization implies creating solid features and relating dimensions among or across solid features. At assembly level, design parameterization involves defining placement constraints and

relating dimensions across parts. Note that there are six degrees of freedom (dof) of each part brought into the assembly, three rotations and three translations. Placement constraints, such as surface mates, must be employed to define part position and orientation related to other parts in an assembly. Proper placement constraints must be chosen along with relations of dimensions across parts to capture design intents at the assembly level. Differential Steering Rack

Front Wheelbase: 128.6 in. Track: 77.4 in. (a) Vehicle Assembly

(b) Track and Wheel Base Design Variables

Figure 3 HMMWV Vehicle Assembly and Suspension Track Design Variable For the track design variable, two parts are involved, differential (Figure 4a) and steering rack (Figure 4b). Geometry of both parts is simple, and their width dimensions are to be related to capture the track design variable. The outer width of the differential d2@sketch1, as shown in Figure 4a, is chosen as an independent dimension. All the geometric features in the differential will be changed according to d2@sketch1 following the relations defined in Table 1. The relations show that d1@sketch2, d1@sketch3, and d1@sketch4 will be changed according to d2@sketch1. In addition, d2@sketch3 and d2@sketch2, and d2@sketch4 are fixed. Note that in the equations of Table 1, dimensions shown on the left hand side of the equal sign become dependent. Table 1 Relations Defined for Differential Equations d1@sketch2 = d2@sketch1–2×d2@sketch3 d1@sketch3 = d2@sketch1–2×d2@sketch2 d1@sketch4 = d2@sketch1–2×d2@sketch4

Design Intents d2@sketch1 is independent, d2@sketch3 = 2.0, and is fixed. d2@sketch1 is independent, d2@sketch2 = 4.0, and is fixed. d2@sketch1 is independent, d2@sketch4 = 3.0, and is fixed.

For the steering rack, dimension d1@sketch1 is chosen as independent, and d6@sketch1 will be changed with the same amount as d1@sketch1, as defined by the first equation listed in Table 2. Dimensions d1@sketch10 and d6@sketch10 are related to d1@sketch1 and d6@sketch1 via the last two equations shown in Table 2, respectively, with a fixed wall thickness d3@sketch10 = 0.530 in. d2@sketch3 = 2.0 in.

d2@sketch1 d2@sketch1

d1@sketch1

d1@sketch2

d1@sketch10

d2@sketch4 = 3.0 in.

d6@sketch1 d6@sketch10 d3@sketch10=0.530in.

d1@sketch3 d1@sketch4

Top View

d2@sketch2 = 4.0 in.

Bottom View

d2@sketch1 = 7.5 in.

Top View

(a) Design Parameterization for the Differential

Bottom View

(b) Design Parameterization for the Steering Rack

Figure 4 Design Parameterization for Track Design Variable at the Part Level Table 2 Relations Defined for Steering Rack Equations d6@sketch1 = d1@sketch1−2×d2@sketch1 d1@sketch10 = d1@sketch1−2×d3@sketch10 d6@sketch10 = d6@sketch1−2×d3@sketch10

Design Intents d1@sketch1 is independent, d2@sketch1 = 7.5 in., and is fixed d1@sketch1 is independent, wall thickness d3@sketch10 = 0.530 in. fixed Wall thickness d3@sketch10 = 0.53033 in. fixed.

At the assembly level, placement constraints are defined for the differential and both frame rails, as shown in Figure 5a. At first, side faces of the differential and frame are assembled using surface coincident (mate) constraints. In addition to surface coincident constraints, point coincident constraints are added between the corner points of the differential and points on the top edge of the frame rails. The steering rack is assembled to the tie-rod on each side, by using concentric (axis alignment) and surface

coincident (mate) constraints, as shown in Figure 5b. Next, the relationship between the width of the differential and width of the steering rack is defined at assembly level, as shown in Figure 5c. The relationship between dimensions d1@sketch1 in the steering rack and d2@sketch1 in the differential is defined; i.e., d1@sketch1@steering_rack.Part = d2@[email protected], so that widths of the steering rack and differential change simultaneously. Therefore, d2@[email protected] represents the track design variable which is independent. Note that d1@sketch1@steering_rack.Part and d2@[email protected] have the same numerical value. Surface Coincident

Point Coincident Concentric

Surface Coincident

Tie Rod

Point Coincident

Surface Coincident

Surface Coincident Point Coincident Front

Front Concentric

Tie Rod

Point Coincident

(a) Placement Constraints for Differential and Frame

(b) Placement Constraints Defined for Rack and Tie-Rods

Front d1@sketch1@steering_rack.Part

d2@[email protected]

(c) Relation between Widths of Differential and Steering Rack Figure 5 Design Parameterization for Track Design Variable at the Assembly Level

Front

Center Frame Rails

Point Coincident

Point Coincident

Rear Frame Rails

Point Coincident d1@sketch3@left_frame.Part

Surface Coincident Front

Front Frame Rails

Point Coincident Surface Coincident

(a) Relation Between Two Center Frame Rails (b) Placement Constraints Defined for the Center and Rear Frame Figure 6 Design Parameterization for Wheelbase Design Variable Wheelbase Design Variable Defining the wheelbase design variable is straightforward. It involves changing the length of the two center frame rails at the same time (Figure 6a). The center frame rails are assembled to the rear frame using surface coincident constraints as well as point coincident constraints at the end faces of the frame (Figure 6b). Similar constraints are defined for assembling the center frame rails to the front frame. A relation d1@sketch5@right_frame.Part = d1@sketch3@left_frame.Part is defined to capture the wheelbase

design variable represented by d1@sketch3@left_frame.Part. As a result, when d1@sketch3@left_frame.Part is increased, the rear portion of the vehicle gets pushed backwards, and vise versa. Note that when the track or wheelbase design variable is changed, both mass properties and joint locations of the HMMWV vehicle model are altered, therefore, varying the vehicle dynamic performance. In this case, both the track and wheelbase design variables are called global design variables. Thickness Design Variable There is another class of design variables, called local design variables, where only mass properties are affected when they are modified. In the HMMWV example, the only local design variable included is the thickness of the lower control arm (Figure 7). Since there are six pieces of sheet metal that form a hollow control arm and each piece has unique thickness, the thickness design variable is defined as the proportional change (or percentage change) in the thickness of individual pieces. In this case, the CAD model of the control arm does not have to be parameterized, instead, the change of mass properties is assumed to be proportional to the percentage change α of the individual thickness; i.e., ∆m ≈ ∆α and ∆I ≈ ∆α, where m and I are the total mass and moment of inertia of the control arm, respectively. Note that this assumption is valid only when the thickness is relatively small. 0.135 in. 0.156 in. Thickness 0.140 in. 0.135 in.

0.120 in.

0.135 in.

(a) Unexploded View

(b) Exploded View with Thicknesses

Figure 7 HMMWV Lower Control Arm 3.

CAD-Based Design Optimization System The proposed open system that supports CAD-based mechanism optimization is illustrated in Figure 8. The system consists of several essential modules, such as commercial CAD and motion analysis tools, as well as modules developed in this research that support design optimization and integration of commercial tools. In this system, engineers will create parts and assemblies of the product in a CAD tool. The solid model will be parameterized by properly generating part features and assembly constraints, as well as relating geometric dimensions to capture the design intents, as discussed in Section 2. These independent geometric dimensions are chosen so that their influence to the motion characteristics of the mechanical system is significant. Therefore, these variables will help engineers achieve the design objectives more effectively. Note that in CAD, parts may be assembled into subassemblies such that each individual part or subassembly represents a single body in the motion model. Materials are also defined in CAD. Another important entity that requires special attention is the coordinate system. In CAD, there is always a default coordinate system created for part and assembly. This default coordinate system serves as a reference along with datum planes for defining solid features in parts and assemblies. The mass properties provided by CAD are usually referred to the default coordinate system, unless specified otherwise. In this research, the default coordinate system of parts or subassemblies is chosen as the local coordinate system (LCS) of the respective body in the dynamic simulation model. Note that the LCS is referred to as the Non-Centroidal Body Frame (NCBF) in DADS. In addition to mass properties, joint locations must also be specified in CAD for the simulation model. In DADS, the joint locations are defined with respect to the body NCBF. Therefore, it is reasonable to define a joint location by creating a datum point in the CAD solid model, referring the datum point to the default coordinate system, and relating the datum point dimensions to independent design variables. The pre-processor supports design engineers in defining a complete motion model derived from the CAD solid model. Key steps include assigning a body local coordinate system (usually the default coordinate system in CAD), defining connections (or joints) between bodies, specifying initial conditions, and creating loads and drivers for dynamic and kinematic analyses. Commercial tools, such as Pro/MECHANICA Motion, have addressed this issue well, although the analysis capabilities are limited, especially for support of ground vehicle simulation. Design sensitivity analysis (DSA) calculates gradients of motion performance measures of the mechanical system with respect to dimension design variables in CAD. This is critical for optimization. The gradient information provides engineers with a valuable resource for making design decisions interactively. At the same time, it supports gradient-based optimization algorithms in searching for an optimal design. The gradient information and performance measure values are provided to the optimization algorithms in order to search for a better design during optimization iteration. The motion model must be updated after a new design is determined in the optimization iterations. Mass properties and joint locations of the new design must be recalculated according to the new design variable values. The new properties and locations will replace the existing values in the input data file or binary database of the motion model for motion analysis in the next design iteration. Note that the definition of the motion model is assumed unchanged in design iterations; i.e., no new body or joint can be added, driving condition cannot be altered, and the same road condition must be kept during design iterations. Only mass properties,

joint locations, and parameters that define forces or torque (such as spring constant) are expected to change during design iterations. In addition to the individual modules, commercial CAD and motion analysis tools, as well as the design parameterization, DSA, and optimization capabilities, must be integrated to support the proposed CAD-based mechanism optimization. Specifications or Design Objectives

CAD 2

CAD 1 Simulation Scenario

Define Motion Model (Preprocessor)

Motion Analysis Tool 1 Update CAD Model, then STOP Commercial Tool Data and Document Modules to Develop

CAD m

Yes

Tool 2

Optimal Design? No

Update Models

Tool n

Define Objective and Constraint Functions

Design Sensitivity Analysis (DSA) New Design Optimization

Figure 8 Overall Flow of the CAD-Based Mechanism Optimization 4.

Software Implementation The proposed system has been implemented. Both Pro/ENGINEER and SolidWorks have been incorporated for support of solid modeling and design parameterization. Currently DADS is employed for dynamic simulation. In addition, Design Optimization Tool (DOT) [14] is incorporated to support the gradient-based optimization. Interface programs have been developed for retrieving information from commercial CAD and analysis software via their respective Application Protocol Interfaces (APIs). Additional modules that are not available commercially, as shown in Figure 8, have also been developed. The entire system is integrated and functional. The environment is designed with a flexibility of incorporating additional CAD, motion analysis, and optimization tools. Key components that support the open system include: (1) Interface programs that retrieve design and simulation data from CAD and analysis codes; (2) Pre-processor that converts the CAD assembly into motion simulation model with user’s interaction (mostly for defining bodies and joints); (3) Design sensitivity analysis (DSA) for gradient calculations; (4) Model update that first regenerates CAD models, including both parts and assembly, in a batch mode; and then updates analysis input data file (or binary database) for mass properties and joint locations due to design changes determined during design iterations; (5) Data files that store design and analysis information external to the commercial tools. 4.1

Interface Programs Two types of interface programs are identified in this research, those that retrieve information from and to commercial codes. Interface programs are needed for CAD, motion analysis, and optimization software acquired commercially. For CAD systems, interface programs are developed using API. Data retrieved from CAD include mass properties, default coordinate systems, and locations of datum points that represent joints. For Pro/ENGINEER a C function called ProSolidMassPropertyGet available in Pro/Toolkit is employed for retrieving mass properties. Note that Pro/ENGINEER’s APIPro/Toolkit is a collection of C functions that allow programmers to interact with and add capabilities to Pro/ENGINEER. Note that ProGeomitemDistanceEval function is called to retrieve both locations of coordinate systems and datum points. SolidWorks’ API is a collection of C and Visual Basic functions. The Visual Basic function Part.GetMassPropeties is used for retrieving mass property data. Part.AndSelectByID is for retrieving information for coordinate systems and datum points. For motion analysis software, simulation results including position, velocity, and acceleration of bodies and joints, joint reaction forces and torque, etc., must be retrieved from its database after a motion analysis is completed. In DADS, user-defined subroutines which are similar to the API of CAD tools are provided. The user-defined subroutines provided by DADS are templates written in FORTRAN. The template subroutines can be modified, compiled, and linked to DADS to support users’ needs. There are three main subroutines in DADS, INUDF, FRCUDF, and RPTUDF. INUDF is called once by DADS at the start of the program

execution to gather model data. FRCUDF is called at each analysis time step to calculate the components of the user-defined force expressions. This is where the simulation results are retrieved from DADS and processed for calculating performance measure values to support design optimization. The third subroutine RPTUDF is to specify how and where the data is stored. Similarly, an interface program is needed to bring the objective and constraint function values as well as gradient information from data files to Design Optimization Tool (DOT). Note that DOT provides subroutines to allow users to bring external function values and gradient information into the numerical algorithms for design optimization. Note that when a new tool is added to the environment, for example ADAMS, additional interface programs must be developed. 4.2

The Pre-Processor The goal of the pre-processor is to support users converting CAD models to a simulation model. One pre-processor for one specific motion analysis tool is usually required since their input data formats are different. Basically, the mass properties, coordinate systems, and joint locations defined in CAD can be retrieved to support defining the simulation model. Users are expected to use the pre-processor to add information, such as joint type, driving torque, road profile, etc., to create a complete motion simulation model. In general, there are three possible ways for developing a pre-processor. First, a pre-processor can immerse into a CAD tool. This pre-processor provides users with a seamless connection to CAD, such as Pro/MECHANICA in Pro/ENGINEER, and DesignWorks in SolidWorks. Second, the pre-processor is embedded into simulation tools, such as the pre-processor of DADS. Third, the pre-processor can be a stand-alone application that supports multiple CAD and simulation tools. The third approach is the most general, but requires more development effort. In this research, both DesignWorks and DADS pre-processor are employed. No standalone pre-processor has been developed in this research. There are two possible scenarios in the integrated environment that support multiple CAD tools, (1) the entire model is created in one CAD, and (2) the CAD models are created using multiple CAD tools, however, parts are assembled into bodies. For scenario 2, users may convert all models into a single CAD tool or use corresponding interface programs to retrieve data from CAD databases to create a complete motion model. In this case, a consistent global coordinate system must be defined for all CAD models. In addition to the global coordinate system, consistent local coordinate systems must be ensured between solid models in CAD and bodies in simulation models. This is because the mass properties and joint location values calculated in CAD must refer to the body reference frames (NCBF in DADS) in simulation models in order to avoid mismatch or additional coordinate translations. 4.3

Design Sensitivity Analysis There are two methods for gradient calculation, the overall finite difference method and the analytical method. Using the overall finite difference method, the derivative of a motion performance ψ with respect to CAD design variables b can be expressed as, ∂ψ(b) ∆ψ(b) ψ(b + ∆b i ) − ψ(b) (2) ≈ = ∂b i ∆b i ∆b i where ψ(b) is the dynamic performance of the mechanical system at the current design, and ψ(b+∆bi) is the performance at the perturbed design with a design perturbation ∆bi. Note that the design perturbation ∆bi is usually very small.

For the analytical method, the derivative of a motion performance ψ with respect to CAD design variables b can be expressed as,

∂ψ(d, c) ∂ψ(d, c) ∂m ∂ψ(d, c) ∂p ∂ψ(d, c) = + + ∂b ∂m ∂d ∂p ∂d ∂c

(3)

where b = [d, c]T is the vector of design variables; d is the vector of dimension design variables captured in CAD solid models; c is a vector of coefficient parameters included in a load or a driver, such as the spring constant of a spring force created in the analysis model; m is the vector of mass property design variables, including mass center, total mass, and moment of inertia; and p is the vector of joint position design variables. Note that the calculation of derivatives ∂ψ/∂m, ∂ψ/∂p, and ∂ψ/∂c have been well established for general mechanism and 2-D vehicle models [15]. It is clear that the additional task is the calculation of the sensitivity of mass properties and joint locations with respect to CAD design variables; i.e., ∂m/∂d and ∂p/∂d. Through the chain rule of differentiation the overall sensitivity coefficients can be calculated using Eq. 3. However, more research is being conducted to expand the capabilities to support 3-D vehicle models, such as the HMMWV. Therefore, in this research, the overall finite difference method is adopted for gradient calculations. 4.4

Model Update For each design iteration in optimization, CAD solid models must be first regenerated for both parts and assembly according to the design changes in a batch mode. Such regeneration action will trigger calculations or updates for mass properties, coordinate systems, and datum points in CAD solid models. This regeneration is carried out in a batch mode by calling API functions. In Pro/ENGINEER two functions ProDimensionDimensionReset and ProSolidRegenerate are called to set the new dimension values and regenerate the parts and assembly, respectively. Similarly, in SolidWorks Part.Parameter(diemsnsionID).SystemValue and Part.EditRebuild are called for the same purposes. After the regeneration of CAD models is completed, the CAD interface programs will retrieve the model data at the new design and store them in external data files, which are then employed to update the dynamic simulation model. Update of analysis model can be done either by modifying the input data file in text form or rewriting binary data array in database of the analysis software. In this research, the user-defined modules FRCUDF written in FORTRAN language are called in DADS to modify the internal arrays instead of editing the ASCII input data file to simplify the implementation as well as gain efficiency in optimization iterations. Note that when a new CAD or analysis code is added to the system, the above modules must be developed by using its own API.

5.

HMMWV Design Example A High Mobility Multi-purpose Wheeled Vehicle (HMMWV) shown in Figure 3a is employed to show the effectiveness and general capabilities of the proposed system. The HMMWV CAD models are created in both Pro/ENGINEER and SolidWorks. The suspension is modeled in detail. A closer view of the front right suspension is shown in Figure 9a. Revolute Joint

Chassis Frame

S

R

Spherical Joint

7

8

9

R

S 6

Wheel Hub

Steering Rack

Translational Joint

Spherical

R

R

11 S

12 13 R R Upper 1 S S Control Arm Chassis R R 3 Chassis NCBF 4 5 T R Wheel Hub 15 S 2 Front S R Lower 18 16 17 Steering Rack Control Arm R 14 R S Wheel

Z

Lower Control Arm

z

x

X

Revolute Joint

(a) Front-Right Suspension

y

10

Y Global Coordinate System

(b) Schematic View of Vehicle Motion Model

Figure 9 HMMWV Dynamic Simulation Model The dynamic simulation model consists of 18 bodies and 21 joints, as shown in Figure 9b. The dynamic simulation has been conducted in DADS (Figure 10) with a total of 17 seconds and a time step of 0.001 second. A 100 by 100 ft terrain is used for simulation (see Figure 10). Note that the terrain is fairly bumpy. The maximum height of the bumps on the terrain is 7.78 inches. The vehicle vibrates significantly towards the later stage of the simulation due to the bumpy road conditions. An 18-body HMMWV DADS model was initially provided by the National Advanced Driving Simulator (NADS) Center [16]. In that model, the vehicle is “driven” by a torque applied at the four wheels with a prescribed steering function defined in time. The initial velocity is zero. With these conditions, the vehicle turns a U-shape of 714 by 982 in. (59.50 by 81.84 ft.) in a 17-second simulation, as shown in Figure 10. Note that the mass properties of the DADS model are calculated in CAD. It is later found that the torque-driven model will not follow the same path during design optimization iterations since mass properties of the vehicle are varying due to design changes. A heavier HMMWV model will move along a smaller U-path. An optimal design obtained while the vehicle is moving on a different path (a possibly less severe road condition) does not guarantee a better design. Therefore, instead of torque, a constant angular velocity is defined at all four wheels in order to ensure that the vehicle follow the same path during optimization iterations. After trial-and-error, a constant angular velocity of 1.53 rad/sec applied at the four wheels produce a path that is similar to the U-shape shown in Figure 10 and goes through bumpy areas. In this case, the vehicle is moving at a constant speed of 9.54 mile/hour. The design problem is defined as follows: Mininize : φ(b) =

1 T 2 ∫ [F(p( t ))] dt T 0

(

)

u Subject to : ψ α (b) = z w i ( t ) − 18 − h i ( t ) ≤ ψ α , α = 1,4

[(

)

]

ψ β (b) = − z w i ( t ) − 18 − h i ( t ) ≤ ψ βu , β = 1,4 ..

ψ 9 (b) = z ds ( t )

(4)

≤ ψ 9u

u ψ10 (b) = z ds ( t ) − z ch ( t ) ≤ ψ10

ψ γ (b) = z w i ( t ) − z ch ( t ) ≤ ψ uγ , γ = 1,4 b lj ≤ b j ≤ b uj , j = 1,3

where φ(b) represents energy absorption ability of the vehicle suspension at the driver seat; zwi(t) is the z-coordinate of the ith wheel center; hi(t) is the height of the road profile corresponding to the ith wheel at the given time t; zds(t) and &z& ds (t) are the driver seat position and acceleration, respectively, in the z-direction of the global coordinate system (vertical); zch(t) is the z-displacement of the chassis NCBF with respect to the global coordinate system (shown in Figure 9b). Note that in Eq. 4, ψα(b) and ψβ(b) essentially characterize deformation of the tires. ψ u simply represents the lower bound of the constraints ψα(b). Note that the tire radius is 18" β and zwi(t)−18 is zero if no deformation occurs in tire. ψγ(b) specifies the wheel center position with respect to the chassis in the vertical direction.

Figure 10 HMMWV Motion Simulation In Eq. 4, the function in the integrand F(p(t)) is defined as [17], F(p(t)) = p1(t) − 0.108 p4(t) + 0.25 p6(t) − p7(t), where pi(t) can be computed from the absorbed power equations p& 1 ( t )  − 29.8p1 ( t ) − 497.49&z&s ( t ) − 100.0p 2 ( t )  &    p 2 ( t ) 10.0p1 ( t )  p& 3 ( t )  1736.9p ( t ) − 108.0p ( t )  1 4     & p 4 ( t ) = 100.0p1 ( t ) − 35.19p 3 ( t ) − 39.1p 4 ( t )  &  − 315.7p ( t ) + 34.0956p ( t ) + 171.075p ( t ) p ( t ) 1 4 6 5     p& 6 ( t )  − 80.0p1 ( t ) − 91.36p 4 ( t ) − 30.28p 5 ( t )      p& 7 ( t ) p1 ( t ) − 0.108p 4 ( t ) + 0.25p 6 ( t ) − 6.0p 7 ( t ) 

(5)

for 0 ≤ t ≤ T, with initial conditions pi(0) = 0, i = 1, 7. Note that the initial conditions are reset at each time step during numerical calculation. Currently, Mathematica [18] is being used for the computation. As discussed before there are three design variables defined for the HMMWV. They are vehicle track, wheelbase, and percentage change in thickness of the lower control arm. Constraint function bounds are shown in Table 3. The constraint functions are evaluated at every 0.01 seconds during the total 17 second simulation period, except for the z-accelerations at the driver seat, where the step size is refined to 0.001 second since they directly contribute to the objective function. Therefore, there are 39,100 (13×100×17+1×1,000×17) constraint functions to process at each design iteration. Note that most of the constraint function values at the initial design are less than their respective upper bounds, except for a few time steps of driver seat acceleration ψ9(b) and driver seat position ψ10(b). Therefore, the initial design is infeasible. The optimization took 18 iterations to converge using Modified Feasible Direction algorithm. At the optimal design the objective function is reduced by 31.3%, and all performance constraints are satisfied. The track and wheelbase design variables increase by 17.7% and 14.6%, respectively. The percentage thickness of the lower control arm decreases by 17.9%, as summarized in Table 4. Table 3 Upper Bounds of Constraint Functions Performance Function ψαu ψβu ψ9u ψ10u ψγu

Description The jounce of each of the wheels The rebound of each of the wheels Driver’s seat acceleration Driver’s seat position w.r.t. the chassis Wheel center position w.r.t. the chassis

Upper Bound 1.25 in 3.5039 in 0.75 G 3.5 in 12.0 in

Table 4 Design Optimization of the HMMWV Dynamic Model Measure φ(b) b1 b2 b3

Initial Design 0.00595 Watts 21.68 in 50.69 in 100 % of original thickness

Optimal Design 0.00405 Watts 25.52 in 58.12 in 82.0 % of original thickness

% Change −31.3 +17.7 +14.6 −17.9

The optimization history graphs of the objective function and design variables are shown in Figures 11a and 11b, respectively. Note that the reduction of objective function value is due to the significant decreasing z-acceleration values at the driver seat. Also, the distance between the driver seat and the chassis in the z-direction has been significantly reduced. The rest constraint functions also indicate that the vehicle becomes smoother while moving along the same paths. This is due to the fact that both vehicle track and wheelbase are increased that contributes to a wider and longer chassis, therefore, more stable and less vibration.

Wheelbase (Blue)

Thickness (Green) Track (Red)

(a) Objective Function φ(b) (Unit: Watt)

(b) Design Variables

Figure 11 Design Optimization History 6.

Conclusions An integrated system that supports optimization of general mechanical systems, including ground vehicles, has been presented. This system supports engineers to effectively search, in a CAD solid model, for a mechanism design with optimal kinematic and dynamic performance. The system is open that allows engineers to add CAD and analysis software with a minimum effort. A HMMWV has been optimized to demonstrate the feasibility and the effectiveness of the proposed system. Although the overall finite difference method has been adopted in this research, the research team looks forward to incorporating analytical method for gradient calculations when the opportunity becomes available. Acknowledgements The authors would like to express their gratitude to the National Science Foundation for supporting the research through a grant EEC-0118091. The authors also appreciate the technical guidance provided by Professor E.J. Haug at the National Advanced Driving Simulator (NADS) Center, the University of Iowa, Iowa City, Iowa throughout this research. Also, the technical support on HMMWV simulation models provided by Mr. Horatiu German at the NADS center is highly appreciated. The authors would like to thank Mr. Bill Prescott at LMS-CADSI for providing the research team with DADS and DesignWorks software as well as support in installing and using the software throughout this research. References 1. Mechanical Dynamics Inc., Design Technologies Division, 2301 Commonwealth Boulevard, Ann Arbor, MI. http://www.designtechnologies.com 2. SolidWorks, SolidWorks Corporation, 300 Baker Avenue, Concord, MA 01742. http://www.solidworks.com/ 3. SolidEdge, UGS, 675 Discovery Dr., Suite 100 Huntsville, AL. 35806. http://www.solidedge.com 4. Autodesk, Autodesk, Inc., 111 McInnis Parkway, San Rafael, CA 94903. http://www.autodesk.com 5. DADS, Dynamic Analysis and Design System, Computer Aided Design Software, Inc., 2651 Crosspark Road, Coralville, IA. http://www.cadsi.com/ 6. Pro/ENGINEER, Parametric Technology, Inc., 128 Technology Drive, Waltham, MA. http://www.ptc.com/ 7. CATIA, Dassault Systems, 6320 Canoga Avenue, Trillium East Tower, Woodland Hills, CA. http://www.catia.com/ 8. I-DEAS, UGS, 5800 Granite Parkway, Suite 600, Plano, TX 75024. http://www.ugs.com/ 9. Pro/MECHANICA Motion, PTC, 140 Kendrick Street, Needham, MA 02494. http://www.ptc.com/ 10. Chang, K.H., Pro/MECHANICA Motion: Mechanism Design and Analysis, Schroff Development Corporation, P O Box 1334, Mission, KS 66222, ISBN: 1-58503-005-8, September 2000. 11. Silva, J.S. and Chang, K.H., "Design Parameterization for Concurrent Design and Manufacturing of Mechanical Systems," Concurrent Engineering Research and Applications (CERA) Journal, Vol. 10, pp. 3~14, March 2002. 12. Chang, K.H. and Joo, S-H., "Design Parameterization and Tool Integration for CAD-Based Mechanism Optimization," Advances in Engineering Software, Submitted, January 2005. 13. Suh, N.P., The Principles of Design, Oxford Series on Advanced Manufacturing, Oxford University Press, New York, NY, 1990. 14. DOT, Vanderplaats R&D, Inc., 1767 S. 8th Street, Suite. 100, Colorado Springs, CO 80906. 15. Haug, E.J., Wehage, R.A., and Mani, N.K., "Design Sensitivity Analysis of Large Scale Constrained Dynamic Mechanical Systems," Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 106, No. 2, Jun. 1984, pp. 156-162. 16. National Advanced Driving Simulator (NADS) Center, University of Iowa, Iowa City, Iowa. www.nads-sc.uiowa.edu 17. NATO Reference Mobility Model, Edition I, U.S. Tank-Automotive Research and Development Command, Technical Report No. 12503 for the North Atlantic Treaty Organization, October 1979. 18. Wolfram, S., Mathematica Book, Addison-Wesley Reading, 1998.