Louis Lux
Application Engineer
SDRC
Milford, Ohio

Edited by Paul Dvorak

The solid model of the suspension shows accurately detailed   components. The stabilizer bar must snake through the maze from one side   of the frame to the other to add stiffness for better control. However,   sizing the bar is a bit more complex than just avoiding interference with   other components. In this example, finite-element, motion, and fatigue   analyses play roles.

The solid model of the suspension shows accurately detailed components. The stabilizer bar must snake through the maze from one side of the frame to the other to add stiffness for better control. However, sizing the bar is a bit more complex than just avoiding interference with other components. In this example, finite-element, motion, and fatigue analyses play roles.


<I>A design update<br>  </i>Lengthening the wheelbase (lower image) pushes the rear axle and stabilizer   bar into the spare tire's allotted volume. The interference is obvious.   But in some products, such as electronic equipment made of thousands of   components, interference is not readily visible after changes.

A design update
Lengthening the wheelbase (lower image) pushes the rear axle and stabilizer bar into the spare tire's allotted volume. The interference is obvious. But in some products, such as electronic equipment made of thousands of components, interference is not readily visible after changes.


Building the suspension with variational design features, called   VGX in SDRC I-DEAS, lets engineers examine the position extremes that   could be caused by a bumpy road. The blue dimensions are changed to show   the assembly moving.

Building the suspension with variational design features, called VGX in SDRC I-DEAS, lets engineers examine the position extremes that could be caused by a bumpy road. The blue dimensions are changed to show the assembly moving.


Only four connection points of the axle and frame, and   a handful of surfaces from surrounding components must be added to the   initial design to control the shape of the stabilizer bar. The red half-cylinder   is from a shock absorber and the basinlike surface is from the differential.   Critical connection points are represented by coordinate systems.

Only four connection points of the axle and frame, and a handful of surfaces from surrounding components must be added to the initial design to control the shape of the stabilizer bar. The red half-cylinder is from a shock absorber and the basinlike surface is from the differential. Critical connection points are represented by coordinate systems.


THE BAR'S PLANE OF MOTION<br>  The stabilizer started with a 2D wire frame that was extruded into an   open surface model. The solid stabilizer bar was then swept on these surfaces   to define its design envelope as well as the minimal controlling factors   effecting the shape from surrounding components. The stabilizer design   can float within these surfaces to avoid interference with neighboring   components. The detailed vertical undulations of the bar can now be defined   from a projection of lines from an arbitrary vertical plane.

THE BAR'S PLANE OF MOTION
The stabilizer started with a 2D wire frame that was extruded into an open surface model. The solid stabilizer bar was then swept on these surfaces to define its design envelope as well as the minimal controlling factors effecting the shape from surrounding components. The stabilizer design can float within these surfaces to avoid interference with neighboring components. The detailed vertical undulations of the bar can now be defined from a projection of lines from an arbitrary vertical plane.


HOW TWO DIMENSIONS AFFECT DISPLACEMENT<br>  Variational Analysis in I-DEAS provides a design surface that shows how   two design parameters affect displacement. Generating this type of result   is the reason for developing the analysis — to find and illustrate   relations between critical dimensions.

HOW TWO DIMENSIONS AFFECT DISPLACEMENT
Variational Analysis in I-DEAS provides a design surface that shows how two design parameters affect displacement. Generating this type of result is the reason for developing the analysis — to find and illustrate relations between critical dimensions.


Variation Analysis for two parameters shows that parameter   2 does not affect stress, a detail not obvious from a model of the suspension.   What's more, information such as this is not available from traditional   analysis.

Variation Analysis for two parameters shows that parameter 2 does not affect stress, a detail not obvious from a model of the suspension. What's more, information such as this is not available from traditional analysis.


A SUSPENSION ASSEMBLY AT WORK<br>  Integrated motion and stress analysis lets engineers apply a braking load   to study stresses and generate a modal analysis.

A SUSPENSION ASSEMBLY AT WORK
Integrated motion and stress analysis lets engineers apply a braking load to study stresses and generate a modal analysis.


Applying the brakes for one second produces high loads   on the system after a half second. These loads are transferred to a finite-element   model.

Applying the brakes for one second produces high loads on the system after a half second. These loads are transferred to a finite-element model.


The peak load from the brake test produces the exaggerated   deflections on the steering knuckle. Such an analysis would be difficult   with separate or nonintegrated programs.

The peak load from the brake test produces the exaggerated deflections on the steering knuckle. Such an analysis would be difficult with separate or nonintegrated programs.


Variational Analysis lets users see how stresses change   with several different lengths. Likewise, the bar could be given a larger   diameter to see how stresses change. Getting the same results from traditional   FEA would require separate analyses taking several hours. The lower image   shows results of a fatigue analysis.

Variational Analysis lets users see how stresses change with several different lengths. Likewise, the bar could be given a larger diameter to see how stresses change. Getting the same results from traditional FEA would require separate analyses taking several hours. The lower image shows results of a fatigue analysis.


Mention integrated CAD and FEA software to engineers and they think of transferring IGES files, or using some sort of custom interface. When designing assemblies, this weak integration reveals limitations soon after the first analysis begins. Questions that pop up include:

What happens when the assembly changes? Do I have to start all over with a new IGES file? (That could mean beginning the whole process of geometry abstraction, meshing, and defining boundary conditions.)

How will design changes affect surrounding components in an assembly? Position relationships exist in just about every product.

And what happens to the finite-element model of the part under analysis when a connection to a neighboring part moves or changes?

These questions raise important issues that should be considered before selecting software that claims it integrates design with simulation. Few modeling systems keep shape, position, and downstream analysis completely associative.

An actual industrial application reveals the overwhelming advantages of integrated CAD and analysis systems. This case uses I-DEAS Master Series to design a complex light-truck suspension, where a seemingly simple component, a stabilizer bar, provides a tough sizing and routing problem.

The example
Developing a stabilizer bar seems straightforward. The design requires a certain stiffness to resist rolling motions when the vehicle turns. The challenge is to make it serve its purpose and avoid interfering with other components in the tight space allocated.

The design begins by creating a suspension with as much detail as necessary to make design decisions. These include locating components, and controlling movement and articulation for fit and packaging studies. The assembly also has geometric constraints such as coincidence, tangent, parallel, and perpendicularily between curves, surfaces, and specific points on individual components. Then articulations are analyzed quantitatively in the computer with interference calculations, and visually on screen as well.

Design of the bar begins by capturing critical position and shape factors from other suspension components. This constrains the stabilizer in terms of shape and will change when the shape or position of surrounding components change. Fortunately, not all the detail of the surrounding components is needed for the stabilizer model. To define its shape, its model only needs connection points and a few selected surfaces from surrounding components. This simplifies associative modifications as the design changes. These associated changes are at the heart of smart assemblies. After completing a rough shape for the stabilizer bar, normal or expected design changes can be made with logical results.

Viewing the assembly from the top shows that the wheelbase is a controlling dimension. Suppose a design change calls for a 46-mm extension to the wheelbase. Entering the change, as has been done in A design update, makes all components in the assembly adjust in a logical fashion based on a smart-dimensioning feature that relates all assembly components.

The specialized CAD software can automatically calculate interference, alert the designer, and indicate the part's total volume with an option to save the interfering volume as a part that can later be used to help resolve the problem.

With regard to vertical motion, surfaces of the floor pan, springs, shocks, brakeline, and differential housing may be the only potential design concerns. The stabilizer's motion on a moving vehicle will be vertical, so the horizontal plane is extended vertically by extruding the shape into vertical surfaces, as it is in The bar's plane of motion. These vertical planar and cylindrical surfaces could be considered the space that belongs to the stabilizer. In other words, the bar should be able to slide anywhere along these surfaces when it's operating. Trimming additional space off with the floor-pan and cargo surfaces provides a more constrained range that the stabilizer bar design needs to consider. No other suspension components should intrude in this space. These vertical surfaces are removed later because they do not represent actual part geometry. However, they play an important role in design intent, so it's necessary to store them in the part's history.

Although the stabilizer bar is best designed as a solid model, the process here used traditional model methods: wire frame, surfaces, and solids. But solids provide a complete and unambiguous representation.

Now add FEA
Recent thinking on the use of finite-element analysis has it improving designs by optimizing performance goals, such as a least allowable mass, a particular natural frequency, or low static-stress levels. But FEA has not lived up to its potential because it can be difficult and time consuming.

To overcome the drawbacks, the auto companies have invested time and research developing equations that describe effects of changing the stabilizer's major dimensions: diameter and length between connection points. But the bar's surroundings contribute to its shape. It's unknown how these other dimensions contribute to stiffness because each vehicle is unique. The exact effects usually remain unknown unless a manager budgets time to run enough analyses and find them.

Better technology has emerged to address such drawbacks. At least one FEA program avoids the time consuming steps of manually remeshing and resolving, and is usable by designers. Called Variational Analysis, the software takes a single analysis to show the effects of changing dimensions on a loaded part.

Variation Analysis provides this information regardless of vehicle uniqueness, and from a single analysis using one finite-element model. The technology expands the design possibilities through analysis because structural performance possibilities are understood more completely. Variational Analysis also identifies a range of design variables that point to a more complete picture of the dimension effects. Traditional optimization software, on the other hand, narrows in on only one set of dimensional values.

Design guidance, for example, comes when the software shows the strong or weak influence of certain dimensions. How two dimensions affect displacement shows the complex interaction between two dimensions with respect to maximum displacement in the bar. The design surface makes it easy to pick off the dimensions that provide an allowable stress. More importantly, the plot is a parameter study that gives a better understanding of stress magnitudes that come with variations of these two dimensions. The analysis does not enforce a single solution but shows many possibilities with guidance, leaving considerations of other trade-offs not reflected in a single FEA alone. How two dimensions affect stress tells another tale. It shows that one dimension has little effect on stress, which means its value might be selected for lowest cost manufacturing.

Now add motion analysis
It's also possible to calculate mechanical loads on suspension components in various extreme conditions. Forces from these studies can be automatically transferred as static or transient loads to finite-element models of these parts. Better still, integrated design software transfers loads without introducing human error.

Integrated mechanism simulation provides useful information regarding assemblies with intrapart motion-design issues. Simulations for complex mechanisms can include bushings, rack-and-pinion operations, and contact, for example. In addition to movement, it may be more important to understand the forces transferred between assembly components. A suspension assembly at work, for instance, focuses on the steering knuckle, upper and lower-control arms, and the strut assembly. Motion of this assembly becomes complex when one adds steering loads, road irregularities, braking, turning, and speed variations. Many of these loading situations may need a separate analysis.

Let's look at how the knuckle behaves from a braking load. A plot of forces between the upper arm and knuckle during one second of braking indicates significant loads. Whether dynamic inertial effects need to be included in the stress analysis depend on the frequency comparison between the loading and the structure's natural frequencies.

The graph indicates that after nearly a half a second, a relatively long period, there are no vibrations near a previously calculated natural frequency's first mode of about 250 Hz. This means dynamic analysis would produce results similar to those from the static analysis.

Loads also arise from the tie rod, lower control arm, and tires. Well-integrated software would automatically transfer selected loads from the mechanism analysis to existing FE models. If the FE model doesn't exist for a part, the software automatically creates one.

Now add nonlinear and fatigue
Linear analysis easily handles small displacements. Large displacements and rotations are another matter. For example, extreme displacements from static loads produce stress-stiffening effects that a linear analysis cannot predict. The nonlinear effect means the structure's deformations have changed so significantly that the original mathematical model no longer represents it. The structure's stiffness must be recalculated in its updated state. In addition, the stiffness must be corrected to accommodate the stress of the structure because the stabilizer bar's stiffness changes as it distorts. As a result, an iterative algorithm in the software converges to an equilibrium state of negligible residual force, indicating an accurate analysis.

Fatigue presents additional design challenges. It becomes a potential problem when products are cyclically loaded for long periods. Suspensions in general are exposed to low-level vibrations from road conditions as well as occasional extreme impacts, as would happen when hitting speed bumps and potholes. Such loads can produce fatigue failure even when they are within the elastic yield-stress levels. This is where durability software comes in. It finds the number of cycles to failure from repetitive duty cycles that includes all loading conditions.

The bar's possible fatigue failure after millions of duty cycles raises additional concerns. Using various static and dynamic loads, engineers would define a duty cycle to establish stress levels the vehicle can tolerate over its design life. Engineers calculate fatigue-life estimates using cycle-to-failure or S-N curves for the bar's material (SAE 1090). Repeated loads well below the yield stress of the material also contribute to fatigue-crack initiation. Durability software can estimate potential crack initiation in terms of numbers of cycles to failure. Armed with the information, vehicle manufacturers might then set a target of 500 million cycles before fatigue cracks occur in the stabilizer bar.

Should a design does not measure up in the durability software, engineers might tweak a few dimensions to reduce weight. But which dimensions can be adjusted to keep the required stiffness and lower the weight? Variational analysis provides such guidelines.

Other analysis disciplines such as thermal, crash, and magnetic field also play vital roles in product design. Complete integration is critical to making these analyses useful. Certainly, it is possible to transfer geo-metric models from one software package to another. But is it possible to keep design intent and associativity between geometric design and analysis models without it? The simple answer is no. Integrated software is key. Finally, if integration is not deep within the geometric data structure of the software, users are unlikely to try to leverage analysis at all because the efficiencies from the integration are not available.