Summary Flashcards
Three aspects that has to be included in assembly modeling
1) Hierarchical relations
- assembly -> subassembly –> part
2) Mating conditions
- geometrical restrictions, etc.
3) Mechanical degrees of freedom
Advantages and disadvantages with component based assembly modeling
+ simple
+ doesn’t require feature information
- changes in parts doesn’t show on assembly level
What is component based assembly modeling?
Position determined by global or relative coordinate systems
What is feature based assembly modeling?
- form features are associated on different parts
- Restricts form, position, orientation, etc between mating form features
Advantages and disadvantages with feature based assembly modeling
+ Assembly modeling can be done at a higher level
+ Restrictions are between features dimensions rather than between surfaces
+ Design changes are allowed to spread between parts
- Might be forced to build a chain of relations that can be hard to apply structural changes on
Boundary representation in Geometry modeling
- Parametric solids (representation surfaces)
- Fully parametric takes too long computation time
Curves in geometry modeling
A higher order of the curve gives increased precision, but also longer calculation times and risk of corrupt curves.
3rd order curves are most common
What are the three different curve types?
- Bezier Curves
- B-splines
- Rational parametric curves (NURBS Non-Uniform-Rational-B-Splines
Describe Beizer curves
Applied to automotive bodies
An approximate curve where a number of control points defines a characteristic polygon
Mathematical definition: P(u) = sum(p_i, B_i,n(u)), where 0 < u <= 1
- B_i,n : how the control points affect the curve
- p_i : control points
- n : degree of polynomial
- n + 1 : number of control points
Describe B-splines
- Developed from Beizer curves
- Improved local control
- Possible to add control points without increasing polynomial degree
- Easier defined joined curve segments
- Each segment controlled by 4 closest control points
Describe Rational parametric curves (NURBS Non-Uniform-Rational-B-Splines
- Can represent conical and circular forms exactly (which Beizer curves and B-splines cannot do)
- Requires use of homogenous coordinates
- Most commonly used curve type in modern CAD systems
Continuity in geometric modeling
- C0: curves joint without constraints
- C1: curves have same direction at common point
- C2: curves have same curvature at common point
Coordinates in geometric modeling
- Cartesian, P = [x, y, z]
- Homogenous, P = [hx, hy, hz, h]. This enables easier use of some mathematical operations and advanced curve types
Describe parametric surfaces in geometric modeling
Like parametric curves but in two directions (u and v)
P(u, v) = [x(u, v), y(u, v), z(u, v)]
- Defined in 2D parametric space
- Consists of inner trim curves (holes), and outer trim curves (boundaries)
- Trimmed parametric surfaces are transformed to 3D, ex thick, closed surface
What are two advantages of using solid modeling instead of surface modeling?
Solid models support higher levels of functionality (ex calculations of mass, inertia, etc) and automation than surface models
Solid models allow the designer to work with higher level objects rather than points, curves and surfaces
How is solid modeling with CSG (Constructive Solid Geometry) created?
Created by manipulating primitives with Boolean operators (union, sections and subtractions) (“Lego”)
What are the 3 types of solid models?
Decomposition models
- Voxel: consisting of cubes or octants (ex. x-ray) - Cell based models (finite elements mesh)
Constructive models
- Created by manipulating primitives with boolean operations - Half spaces: Analytical functions f(x, y, z) defines ex a cylinder or a plane - CSG models: solid models created by combining sub-solids
Boundary representations
- Solid defined with points, curves, surfaces and definition of what is inside - Uses graphical methods, ex sweep and rotate - Can use parametric surfaces and boolean operations
Describe half spaces
Real analytical functions f(x, y, z) defined in 3D that splits the space in two half-spaces:
- One half-space where f(x, y, z) > 0 - One half-space where f(x, y, z) < 0
Example cylindrical half-space x^2 + y^2 - r^2 < 0
Solid primitives are created by combining half spaces with Boolean operators.
H2: z > 0
H3: z-h < 0
How do you create a solid model using surface modeling
- Create wireframe elements, ex. points, planes, and curves in 3D or sketches
- Create surfaces from the wireframe geometries (sweep, revolve)
- Trim surfaces together
- Join surfaces together to a uniform element
- Transform into a solid (thick, closed surface)
( - Add fillets)
What are features in geometry modeling?
- A physical part or detail
- Engineering role (ex. function or manufacturing method)
- Linked to generic form
- Predictable properties
Digital Mock-Up (DMU)
- Assemblies with over 1000 parts
- Assemblies with parts from different CAD systems
- Used for visualization, packaging studies, assembly simulations
- Not used for mass calculations
Geometry representation: Triangulated surface modeling
Standards for geometry exchange
- IGES - mathematical
- STEP - mathematical
- JT - mathematical and triangulated
- VRML - triangulated
- STL - triangulated
Off-Line programming
- To simulate robots, NC machines or CMM (Coordinates Measurements Machines)
- Done before implementation:
- Avoid expensive mistakes
- Not shut down production for testing
- Faster and more efficient programming
- Test more variation of programs
Examples of geometry models
- CAD model: defines geometry
- Mechanical model: evaluate mechanical behavior
- Visual model: show product, used by marketing
- Ergonomic model: view the ergonomics, used for assembly and serviceability
What are the benefits of geometry models?
- Minimizing the need for costly physical prototypes
- Finding problems as early as possible in the development process (easier and cheaper to fix)
- Faster development process with efficient tools (time to market)
What are multi-body systems?
A generic tool for analysis of forces and motions of a mechanical system. Must include:
- Rigid bodies
- Constraints (joints and motions)
- Forces (loads, forces, gravity, friction)
What is geometry assurance?
Using computer tools to perform geometry assurance tasks on virtual product models.
Ex. gap, flush, parallelism
What are the three types of tolerance analysis?
- Variation analysis (Monte Carlo)
- Contribution analysis
- Stability analysis
What is variation analysis (Monte Carlo)?
Calculates a statistical prediction of the variation in critical measures
- Statistical method - random data
- Tolerances on parts (inputs) are randomly generated within defined distributions, tolerances and Cp
- Distributions for critical measures (outputs) are generated from thousands of iterations
- All kinematical relations and sensitivities are captured in a 3D assembly model
What is contribution analysis?
It is used to calculate a ranked list of how all input tolerances contributes to the variation in the critical measures.
- All input parameters are varied (one at a time) within their tolerances on 3 levels
- Max output is registered
- Contribution is calculated in percentage
What is stability analysis?
- Can be used to analyze the influence of each part locating scheme on:
- Variation amplification, color coding
- Position of stability parts
- Critical product dimensions (Measures)
- It is done by distributing each locating point with a unit disturbance and summarizing their contributions with RSS
- Often used to evaluate different positioning systems
How does Monte Carlo variation simulations work?
Model consists of:
- 3D assembly model with defined locating schemes
- Input tolerances with range and type of distributions
- Critical measures
Simulation:
1) Randomly assign one value for each input within its defined tolerances
2) Assemble the model according to the defined locating schemes
3) Calculate the critical measures and store the results for each iteration
4) Repeat this at least 1000 times
5) Calculate the distribution of the critical measures
What are the requirements and procedures for contribution analysis?
Model consists of:
- 3D assembly with defined locating schemes
- Input tolerances with range and type of distributions
- Critical measures
Simulation:
- All input parameters are varied (one at a time) within their tolerances on 3 levels
- Max output is registered for all measures
What is the procedure for stability analysis?
It is used to identify sensitive areas and sensitivity factors and guides optimization of locator position
Simulation:
- Each locating point is disturbed with a unit disturbance
- The amplification to the output, color-coding, part position or critical product dimension, is calculated
- The amplification for each individual locating point is summarized with RSS to give a value for the locating scheme
What can the method of influence be used for?
Perform Monte Carlo variation simulations on non-rigid parts
Since at least 1000 iterations has to be done, traditional FE methods would take too long. FE solver is used to create a linearized model of the assembly. The linearized model is used in the simulations. This gives a very large reduction of the simulation time (by a factor of 1000). If the locators or support points are moved, a new linearization has to be done.
