Mass Properties Computation for Nonhomogeneous Objects
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Solution Overview
Problem
Existing design systems struggle to accurately compute mass properties such as mass, center of mass, and moments of inertia for objects with nonhomogeneous material density distributions, which is crucial for additive manufacturing and other advanced manufacturing processes.
Innovation Solution
The method involves tessellating the object's surface into triangles, constructing tetrahedrons with a reference point, determining material density at each vertex, and recursively splitting tetrahedrons to compute and aggregate mass properties using closed-form expressions for linearly varying density, ensuring computational efficiency and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the object is divided into many small tetrahedrons to improve computation accuracy, then the measurement precision of mass properties improves, but the device complexity and computation time increase
Solution Approach 1:
The object is divided into multiple tetrahedrons through surface tessellation into triangles and constructing tetrahedrons with a reference point. Each tetrahedron's mass properties are computed independently using closed-form expressions, then aggregated to obtain the total mass properties of the object. This segmentation enables accurate handling of nonhomogeneous density distributions while maintaining computational tractability.
2Measurement precision
If tetrahedrons are recursively split to reduce approximation errors, then the measurement precision improves, but the productivity and computation speed decrease
Solution Approach 1:
The system dynamically adjusts the level of tetrahedron subdivision based on local density variation criteria. Tetrahedrons are recursively split only when necessary (when density variation exceeds a threshold), rather than uniformly subdividing all tetrahedrons. This adaptive approach maintains high accuracy in regions with significant density changes while preserving computational efficiency in homogeneous regions.
3Productivity
If closed-form expressions are used for linearly varying density to improve computation efficiency, then the productivity improves, but the measurement precision may be compromised for non-linear density distributions
Solution Approach 1:
The object is segmented into sufficiently small tetrahedrons such that the density variation within each tetrahedron can be approximated as linear. This segmentation transforms the non-linear density problem into a series of linear approximation problems that can be solved using closed-form expressions, achieving both computational efficiency and acceptable accuracy.
Solution Approach 2:
The system performs partial linearization by applying closed-form expressions only to small enough tetrahedrons where linear approximation is valid. For larger tetrahedrons with significant non-linear density variations, recursive subdivision is performed until the linear approximation criterion is met, ensuring accuracy is not compromised.
Data Source
AI summary
Methods for product design and corresponding systems and computer-readable mediums. A method includes receiving a modeled object having a surface and a non-homogeneous density distribution. The method includes tessellating the surface of the object into a set of triangles defined by triangle vertices. The method includes selecting a reference point for the object. The method includes, for each triangle in the tessellation, constructing a tetrahedron, the tetrahedron defined by tetrahedron vertices that include the vertices of the corresponding triangle and the reference point, determining a material density at each of the tetrahedron vertices, and computing mass properties for the tetrahedron using the material density at each of the tetrahedron vertices. The method includes aggregating the mass properties of the tetrahedrons. The method includes storing the aggregated mass properties of the tetrahedrons as the mass properties of the object.