Carbon Concentration Calculation in Pulse Carburizing
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Solution Overview
Problem
Current methods for calculating carbon concentration distribution in vacuum low-pressure carburizing are inefficient, time-consuming, and lack real-time accuracy, particularly in pulse carburizing processes, which are essential for controlling the process and reducing carbon deposits.
Innovation Solution
A method utilizing Fourier series expansion and Green's function integral equation to calculate carbon concentration distribution, incorporating different boundary conditions for boost and diffusion processes, enabling rapid and accurate determination of surface carbon concentration and carburized layer depth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a numerical calculation method (finite element method or finite difference method) is used to calculate carbon concentration distribution, then the calculation can be performed, but the calculation time is long and calculation resources are excessive, preventing real-time results
Solution Approach 1:
The patent transforms the partial differential equation into an integral equation with separable variables by introducing a new parameter representation. This parameter transformation allows the solution to be expressed as a product of functions of single variables, enabling rapid calculation without requiring extensive computational resources while maintaining accuracy.
Solution Approach 2:
The patent replaces the traditional numerical calculation approach (finite element/finite difference methods) with an analytical integral equation method. This substitution eliminates the need for discrete meshing and iterative numerical solving, dramatically reducing calculation time and resource requirements while providing real-time results.
2Productivity
If a numerical calculation method is used, then carbon concentration distribution can be obtained, but systemic errors are produced due to mathematical simplification, resulting in low calculation accuracy
Solution Approach 1:
The patent replaces approximate numerical methods with an exact analytical integral equation approach. This substitution eliminates systematic errors inherent in numerical discretization while maintaining high calculation speed, achieving both accuracy and efficiency simultaneously.
Solution Approach 2:
The patent segments the solution into separate functions of individual variables through the integral equation formulation. This segmentation allows each variable to be handled independently, reducing mathematical complexity and eliminating coupling errors that cause systematic deviations in traditional numerical methods.
3Manufacturing precision
If traditional calculation methods are used, then carbon concentration distribution can be calculated, but real-time control cannot be achieved due to lack of real-time data feedback
Solution Approach 1:
The patent replaces time-consuming numerical calculation systems with a rapid analytical calculation system based on integral equations. This substitution enables real-time computation of carbon concentration distribution, providing immediate data feedback for process control and eliminating the time delay that prevents real-time adjustments.
4Object-affected harmful factors
If vacuum low-pressure carburizing is used to reduce carbon black production, then environmental performance is improved, but real-time measurement and control become impossible without oxygen probe
Solution Approach 1:
The patent introduces a mathematical model (integral equation) as an intermediary to indirectly determine carbon concentration distribution. Since direct measurement tools like oxygen probes cannot be used in vacuum, the model serves as a mediator that calculates carbon concentration from process parameters, enabling control without physical measurement instruments.
Solution Approach 2:
The patent replaces physical measurement instruments (oxygen probes) with a mathematical calculation system. This substitution enables carbon potential determination in vacuum conditions where physical sensors cannot operate, maintaining the environmental benefits of vacuum carburizing while restoring measurement and control capabilities.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method achieves high calculation accuracy and efficiency, allowing real-time control of the carburizing process, reducing carbon deposits, and optimizing gas utilization, thus enhancing the clean and green characteristics of vacuum low-pressure carburizing.
Implementation Method 1
expanding a piecewise function composed of the auxiliary function and an initial carbon concentration distribution into a Fourier series
Implementation Method 2
substituting M(z) into an integral equation of Green's function method for integral calculation of a carbon concentration distribution
Data Source
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AI summary
A method for calculating a carbon concentration distribution in a pulse carburizing process is provided. The method can calculate a carbon concentration distribution at a certain time in each process (a boost process or a diffusion process) during a pulse carburizing process, accurately describe a vacuum low-pressure carburizing process, and present a varying process of a surface carbon concentration and a carburized depth in the vacuum low-pressure carburizing process over time. Based on the method, a relationship of a surface transfer coefficient and a diffusion coefficient of a material with a carbon concentration distribution of a workpiece after carburizing may be established, whereby the surface transfer coefficient and the diffusion coefficient of a material can be calculated according to the performance of the workpiece after vacuum low-pressure carburizing. The method may further realize accurate control on a pulse carburizing process, reduce carbon deposit production, increase a carbon utilization ratio of a carburizing gas, and improve and give full play to clean, green, and efficient technical characteristics of vacuum low-pressure carburizing.