## 18. Computer Aided Engineering (CAE)

• One of the fundamental features of Engineering is to make trade-offs to get optimal designs

• If we over-design, then all designs become simple, but more expensive, and more difficult to manufacture

• If we under-design, then our design will not fulfill our requirements

• Therefore we use knowledge and tools to achieve designs which are ‘just right’.

• There are many physical factors which can affect the quality of a design,

Yield stress failure

Excessive deformation

Insufficient heat transfer

Kinematic interference

Too much/little air drag

Resonance at wrong frequency

Electromagnetic interference effects

Non uniform cooling effects (eg. warping in plastic parts)

etc.

18.1 Finite Element Analysis (FEA)

• Why?: When we have to find an effect (stress, strain, flux, etc) which is distributed throughout a volume, and is too difficult to calculate by hand.

• How: Break a part into discrete chunks (elements), Apply driving functions, constraints, etc., then solve for physical effects.

• Elements

different types of elements may be used in a FEM mesh

elements that are too deformed will yield poorer results

if a field variable will be subject to a large change over an area, then smaller elements should be used to improve the approximation.

• CAD systems will often allow a user to manually, and automatically mesh a part.

• Generative meshing algorithms will

mesh a part roughly,

solve the problem using the rough mesh,

identify elements with large errors,

reduce the element sizes in the critical areas,

resolve the problem to obtain a more accurate result.

• Errors of 10% or more are easy to get using FEA systems. Care must be taken when examining results.

• Boundary conditions used in FEA systems include,

x, y, and/or z positions fixed

x, y, and/or z axis rotations fixed.

applied force

applied moment

• Automeshing

Still a research topic, and many various methods are available

Generally the computer breaks geometry into subsections

18.2 Assembly and Kinematics

• It is difficult for the computer to distinguish between two or more parts, and how they are related

• Assemblies tend to have a hierarchy of sub-assemblies and parts

• Another important concept is an instance. For example, a bolt is a single part in a CAD system, but there may be 10 instances of the bolt in a product.

• Each instance of a part has,

a position

an orientation

a unique identification

other information the designer chooses to associate

• It is also important to define instances in an assembly as a chain of kinematic entities. Some common joints are,

slider

rotary

spherical

universal

ground (a special case for kinematic solutions)

• Assembly planning requires some representation of a precedence for assembly mating. The example that follows shows some of the data structures which may be used for describing an assembly.

#### 18.2.1 Tolerancing

• The real value of tolerancing becomes obvious when we begin to consider assemblies.

• The obvious methods of tolerancing are,

dimensional tolerancing

geometrical tolerancing

• There are many methods for dealing with tolerances when working by hand (eg. Maximum metal condition)

• The trade off to be handled by tolerancing is tighter tolerances increase quality, but they slow production, and increase cost.

• As tolerances are stacked up, accumulated errors occur. It is hard to predict what effects these errors will have.

• The ability to obtain a tolerance can also be effected by the manufacturing method chosen.

• A popular computer based method for tolerance analysis is the Monte Carlo simulation. In effect, each tolerance has a random distribution, and it is varied randomly. The effect is noted, and statistics are gathered from the model. The basic process is outlined below.

• Monte Carlo Tolerance Evaluation,

1. Generate a candidate instance of an as-manufactured part using a normal (or other) distribution random number generator to perturb the vertices of the part within the specified size tolerance zone.

2. Check if the part instance meets the specified form tolerances. This is needed because form tolerances may be tighter than size tolerances, and because normal distribution may, in rare cases, generate perturbations with standard deviations beyond the size tolerance zone.

3. If one or more of the vertices of the part instance are found out of zones of form tolerances, the part instance is rejected. If all vertices are inside the zone, the part instance may be accepted.

4. Repeat steps 1 to 3 for all other parts in the assembly.

5. Use the solid modeler to create the assembly instance using all the instances created in step 4. These instances are positioned relative to datums established by part features.

6. Check if the assembly instance from step 5 satisfies the design constraints. If yes, the assembly is accepted. If not, the assembly is rejected.

7. Repeat steps 1 to 6 as many times as the desired sample size (number of assembly instances) is used to calculate the statistics. The larger the sample size the better, and the more confidence we have in the results.

18.3 Assemblies

• While assemblies apparently look simple, they pose intersection problems

• The dilemma is that two points in a modeled assembly may occupy the same point in space, a physical impossibility.

• In some cases this may be simply ignored, but when doing interference checks, or joining models, the two assembled parts may become one part, then change the results when doing FEM, kinematic, and vibration analysis.

• Some methods to deal with this are,

Explicitly store, and manipulate parts of an assembly separately

To use complex graphics boundaries called s-sets (still research)

18.4 Optimization

• One of the most important aspects of engineering