Target Cascading: A Design Process For Achieving Vehicle Targets

Transcription

1 Target Cascading: A Design Process For Achieving Vehicle Targets Hyung Min Kim and D. Geoff Rideout The University of Michigan May 24, 2000

2 Overview Systems Engineering and Target Cascading Hierarchical Optimization for Target Cascading Target Cascading Application to SUV Design Analysis Model Description Results and Future Work

3 Systems Engineering: Why Important? Design Targets Large-scale design Dynamics NVH Durability Safety Consistent design? Efficient process?

4 Systems Engineering Definitions (IEEE Standard 1220) -... The Systems Engineering Process is a generic problemsolving process, which provides the mechanisms for identifying and evolving the product and process definitions of a system.... A Hierarchical System Terminology (NASA) Supersystem System Element Subsystem Assembly Subassembly Part

5 Target Cascading in Systems Engineering Target Cascading enables quick target setting at the early stages of the system design process.

6 Two Approaches to Target Cascading Component Approach Systems Approach x Supersystem x Cascade Down x System x x Subsystem x x Component Rebalance Up x Issues: Complexity Design availability Design freedom Issues: Efficiency Design Feasibility Common Variables Model Availability

7 Target Cascading Problem Statements Given - a set of overall (supersystem) targets, - models for systems, subsystems and components, Determine system, subsystem and component targets by - partitioning the overall design problem, - satisfying feasibility/optimality of system, subsystem and component designs, - achieving overall targets.

8 Hierarchical Target Cascading Structure Target Cascading structure is composed of multiple levels. Linking variables and responses are identified. Supersystem Optimal Design Model Supersystem Level Analysis Model Analysis Model System Level System Optimal Design Model Analysis Analysis System Optimal Design Model Analysis Analysis Subsystem Level Subsystem Optimal Design Model Subsystem Optimal Design Model Subsystem Optimal Design Model Subsystem Optimal Design Model Analysis Analysis Analysis Analysis Analysis Analysis Analysis Analysis

9 Design vs. Analysis Models Design Models - Call for analysis models to make design decisions. - Are composed of design objective and constraints. - Can call multiple analysis models. Analysis Models - Take input design variables, parameters, and low-level responses. - Return responses for current design. - Are explicit functions, response surface models, simulations, or spreadsheets.

10 Hierarchical Optimization Vehicle Targets Vehicle System Subsystem Response & Linking Variable Targets Response & Linking Variable Targets Minimize Deviation between vehicle targets and responses subject to constraints for system responses, subsystem linking variables and vehicle Minimize Deviation between system targets and responses and between subsystem linking variable targets and variables subject to constraints for subsystem responses, component linking variables and system Minimize Deviation between subsystem targets and responses and between component linking variable targets and variables subject to constraints for subsystem Responses & Linking Variables Responses & Linking Variables

11 Mathematical Formulation Optimal design problem at i th level for j th partitioned element minimizes the deviations for responses and linking variables from the upper level U subject to responses and linking variables from the lower level L. Minimize x ( i+1) j,y (i+1) j,y (i+2)j,r (i+1) j R ij R U U ij + y (i+1) j y (i+1) j where R ij = r ij (i+1) j (R (i+1) j, x (i+1) j, y (i+1) j ) subject to L R (i+1) j R (i+1) j ε R + ε R + ε y L y (i+2)j y (i+2)j ε y g ij (i+1) j (R (i+1) j, x (i+1) j, y (i+1) j ) 0 h ij (i+1) j (R (i+1) j, x (i+1) j, y (i+1)j ) = 0

12 Application to Vehicle Design Vehicle - production SUV - Targets - heuristic ride and handling metrics Emphasis - Formal Target Cascading problem statement - Demonstration of T.C. potential to identify / study» Possible design goal incompatibilities» Compromise among competing objectives Goals for example problem - Meaningful, yet of manageable scope - Vehicle, system, and component levels; linking variables

13 Problem Schematic 9(+,&/(/(9(/ 9(+,&/(237,0$/'(6,*1352%/(0 T = [ω sf, ω sr, ω tf, ω tr, ω p, k us ] T ,))1( ,))1(66 )52175($5 7,5( 67,))1(66 )52175($5 &251(5,1* 67,))1(66 6<67(0/(9(/ ) (16,21 5($5 6863(16,21 7,5( 9(57,&$/ 67,))1(66,1)/$7,21 35(6685(6 7,5( &251(5,1* 67,))1(66 635,1* 67,))1(66 635,1* 67,))1(66 &20321(17/(9(/ )5217&2,/ 635,1* 5($5&2,/ 635,1*

14 Vehicle: Linear Half-Car Model Vertical b 0 V - θ a Targets front and rear ride frequencies ω sf, ω sr pitch natural frequency ω p K sr & VU K sf & VI wheel hop frequencies ω tf, ω tr 9 U W 0 XVU K tr 9 I W 0 XVI K tf Variables / Responses front and rear suspension, tire stiffnesses a, b

15 Lateral Vehicle: Bicycle Model δ f C αf )RUZDUG9HORFLW\X Targets a 5 understeer gradient k us b Variables / Responses C αr a, b δ f = L R + mb LC αf ma LC αr 2 u R tire cornering stiffness C α k us

16 System: Front, Rear Suspension Given a required suspension stiffness from the vehicle model, DOUBLE A-ARM - SUSPENSION Targets L o z suspension stiffness K sf, K sr K spring multi-body model (Hogland, 00) F Variables / Responses coil spring stiffness and free length spindle force applied, static deflection predicted - K sf, K sr

17 System: Tire Given a required tire stiffnesses from the vehicle model, Vertical Stiffness: [( P )F ] K T = 0.9 i m + K t Cornering Stiffness: C = [(-2.668x10 )Pi + (1.605x10 )Pi 3.86x10 ] F m C )URP:RQJ7KHRU\RI*URXQG9HKLFOHV ) \ ) P Stiffnesses are a function of - inflation pressure - load due to vehicle weight

18 Component: Suspension Springs Given a required coil spring properties from the suspension model, Use classic spring design equations (e.g. Shigley) - Static shear stress - Fatigue life - Stability Targets linear stiffness K LIN free length L o d D p Variables wire diameter, coil diameter, pitch (d, D, p)

19 Vehicle: Optimal Design R ~ x s S a = b K K K = K C C SF SR TF TR ) ) +$/)&$59(57,&$/ $1'&251(5,1* 02'(/ min T-R V +ε R +ε y Subject to constraints on: Min., max. a and b Convergence tolerances R S -R SL ε R 1/2( y SS -y SS3L + y SS -y SS4L ) ε y R V = k SF SR TF TR P US U R s1 L R s1 To / from front susp n T = target vector (given) R V = target values from vehicle model R S = responses from system models y SS = linking variables (tire pressures) To / from rear susp n U R s3 U y ss L R s3 L y ss3 To / from tire K t model To / from tire C α model

20 Problem Setup Set constraints and bounds at each level, e.g., - Fully laden static deflection (vertical and pitch) - Maximum allowable suspension travel - Spring dimensions Select targets based on ride/handling experience Initially, try to please everybody - Weight all targets equally in objective function

21 Results - First Run Vehicle Targets Targets Responses Ride frequency front [Hz] rear Wheel hop freq. front [Hz] rear Pitch frequency [Hz] Understeer gradient [rad/m/s 2 ] )URQW5LGH )UHT 5HDU5LGH )UHT )URQW 5HDU:KHHO :KHHO+RS +RS)UHT )UHT 3LWFK )UHTXHQF\ 8QGHU VWHHU *UDGLHQW Normalized Responses 1 represents exact target match

22 Results Consistent Design Compare i th -level target and i th -level response Linking variables also consistent Variables Optimal Lower Bounds Upper Bounds Vehicle Susp. Tire (Vert.) Tire (Lat.) Spring Front susp. stiffness [N/m] Front tire stiffness [N/m] Front cornering stiffness [N/rad] K SPRING [N/mm] Front susp. stiffness [N/m] Front Tire Pressure [kpa] Front Tire Vert. Stiffness [N/m] Front Tire Pressure [kpa] Front Cornering Stiffness [N/rad/m^2] Wire diameter [mm] Coil Diameter [mm] Pitch [mm] K SPRING [N/mm] 120.4

23 Results Not all targets met - Suppose Pitch Frequency of 0.87 Hz deemed unacceptable - OPTION A - Decrease target value try to pull Pitch Frequency down closer to 0.5 Hz» Change target value without changing feasible design space Results )URQW5LGH )UHT 5HDU5LGH )UHT )URQW 5HDU:KHHO 3LWFK 8QGHUVWHHU :KHHO+RS +RS)UHT )UHTXHQF\ *UDGLHQW )UHT 5XQ 237,21$

24 Results Changing target alone has little effect on Pitch Frequency - Design decision: expand design space by relaxing constraint/bound - Try increasing weight of target in objective function - OPTION B Increase target weight 10x, decrease lower bound on front coil spring stiffness Results )URQW5LGH )UHT 5HDU5LGH )UHT )URQW:KHHO +RS)UHT 5HDU:KHHO +RS)UHT 3LWFK )UHTXHQF\ 8QGHUVWHHU *UDGLHQW 5XQ 237,21$ 237,21%

25 Results Pitch frequency target not achieved after - Increasing its relative importance - Relaxing relevant variable bound Conclusion - Some targets cannot be achieved within current design space. - Discussion and decisions by design team required.» Change targets?» Relax constraints?» Relax bounds further?

26 Discussion and Conclusions Target cascading links different software tools, possibly in different locations via Internet Designs are concurrent design targets are updated and communicated to each department TC can unearth target incompatibilities early in design process

27 Future Work Implementation of Target Cascading process in Internetbased design environment Expansion of Target Cascading model hierarchy with more analysis models Model reduction techniques to achieve proper model fidelity at each level