Deforming Geometric Solids via Computer Graphics for Precision Mating
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Solution Overview
Problem
Current technologies face challenges in manufacturing geometric solids with complex shapes that mate smoothly and precisely as they move relative to each other, particularly in achieving surface roughness of up to 10 micrometers, which is essential for efficient operation but difficult with existing machine tools and mathematical laws.
Innovation Solution
A computer graphics system is used to model and deform the shape of geometric solids, allowing for the precise calculation and production of mating surfaces by simulating the movement of the solids relative to each other, using polynomial laws to generate geometric data for each point on the surfaces, and applying Boolean logic to ensure accurate deformation and production.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing machine tools with numerical control (NC) are used to manufacture geometric solids with complex mating surfaces, then general-purpose manufacturing capability is maintained, but manufacturing precision of mating surfaces deteriorates (cannot achieve 10 micrometer roughness)
Solution Approach 1:
The patent creates a digital copy of the target geometric solid with its complex mating surface in a computer graphics system. This digital model serves as a template that can be repeatedly used to generate machining paths without requiring physical prototypes or specialized fixtures for each new design, thereby achieving high precision while maintaining ease of manufacture.
Solution Approach 2:
The patent replaces specialized mechanical machining systems with a computer-graphics-based system that uses polynomial mathematical laws to define surfaces and generates NC code automatically. This substitution eliminates the need for specialized machine tools and manual programming, achieving both high precision and ease of manufacture.
2Manufacturing precision
If specialist machine tools are developed to manufacture specific mating pairs of geometric solids, then manufacturing precision is improved, but device complexity and labor intensity increase significantly
Solution Approach 1:
The patent creates a universal computer graphics system that can handle any geometric solid with complex mating surfaces by using polynomial mathematical laws and automated NC code generation. This single system replaces multiple specialized machine tools, achieving high precision while reducing device complexity and enabling one tool to perform many different functions.
3Manufacturing precision
If manual development of mathematical laws is performed for each new geometry, then manufacturing precision can be achieved, but loss of time and labor intensity increase
Solution Approach 1:
The patent uses polynomial mathematical laws where coefficients represent geometric parameters of the mating solids. By changing these parameters, the system can adapt to different geometries without developing new mathematical laws from scratch, thereby maintaining precision while significantly reducing the time required.
Solution Approach 2:
The patent pre-establishes the polynomial mathematical framework and the relationship between polynomial coefficients and geometric parameters. This preliminary setup allows for rapid adaptation to new geometries by simply modifying parameters rather than developing entirely new mathematical models, reducing time loss while maintaining precision.
4Ease of manufacture
If gaps are allowed between mating surfaces, then ease of manufacture is improved, but reliability of the mating solids deteriorates
Solution Approach 1:
The patent replaces manual machining processes that cannot achieve tight tolerances with a computer-graphics-based system that uses polynomial surfaces and automated NC code generation. This substitution enables achievement of 10 micrometer surface roughness, ensuring reliable mating without gaps while keeping the manufacturing process simple through automation.
Data Source
AI summary
The proposed method for using a computer graphics system for changing the shape of models of geometric solids with the aid of deformation is characterized in that it is used for producing geometric solids which mate with one another as they were relative to one another and have mating surfaces, which require manufacture with precision accuracy (up to 10 micrometers), for example toothed screws (cylindrical, conical) of a screw compressor unit, gear trains, gears of a gear pump and similar mating pairs of geometric solids. The proposed method consists in that deformation of a model (3) of a semifinished product (3) of a first mating solid (1) is performed with the aid of a model (7) of a first tool (7), whose surface is automatically calculated using several mathematical laws, each of which is a polynomial in which at least one of the coefficients represents one of several characteristics defining the geometry of the shape of the surface of the second geometric solid (2). Deformation of a model (4) of a semifinished product (4) of a second mating solid (2) is performed with the aid of a model (10) of a second tool (10), which represents a deformed target model (8) of the first solid (1). Furthermore, said deformation is performed in accordance with a law for a movement imitating the movement of the geometric solids (1), (2) which mate with one another during use relative to one another. The proposed device is capable of implementing the proposed method.