Toner Density Inclination Calculation Using Patch Count
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Solution Overview
Problem
Existing techniques for calculating the electrical charge amount of toner in image forming apparatuses are inefficient, particularly due to reliance on measuring only two toner patches, which can lead to significant errors from accidental variations in developing current and toner amount, and lack consideration for the number of calculations required.
Innovation Solution
The proposed solution involves an image forming apparatus with a developing roller, photoconductor drum, density detector, and current detector, utilizing a controller to calculate the inclination of the relation between toner density and developing current by developing three or more toner patches, with different mathematical expressions used depending on whether three or four or more patches are formed, to reduce calculation times and errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If two toner patches are used to calculate the inclination, then the measurement process is simple, but the accuracy is low due to significant errors from accidental variations
Solution Approach 1:
The patent divides the measurement into multiple segments by using three or more toner patches instead of two. This segmentation allows for multiple data points to be collected, enabling more accurate statistical analysis and reducing the impact of accidental variations in any single measurement.
Solution Approach 2:
The patent changes the parameter of the number of toner patches from two to three or more. This parameter change fundamentally improves the accuracy of the inclination calculation by providing sufficient data points for reliable linear regression analysis, eliminating the significant errors associated with only two measurements.
2Measurement precision
If three or more toner patches are used to improve accuracy, then the measurement precision increases, but the calculation time and complexity increase
Solution Approach 1:
The patent uses a standardized mathematical model (linear regression) that can be efficiently copied and applied to multiple data points. By establishing a general formula for calculating the inclination with three or more patches, the system achieves high accuracy without proportionally increasing calculation time, as the same computational approach scales efficiently.
Solution Approach 2:
The patent optimizes the parameter of the number of patches to three or more, which is the minimum required for reliable linear regression. This parameter change balances accuracy improvement with calculation efficiency, avoiding the unnecessary time loss that would occur with excessively large numbers of patches while still eliminating the errors of two-patch methods.
3Productivity
If a uniform mathematical expression is used for all numbers of patches, then the calculation method is simple, but the efficiency is reduced due to unnecessary calculations
Solution Approach 1:
The patent implements a dynamic calculation method that adapts the mathematical expression based on the number of toner patches available. When three patches are used, one specific formula is applied; when four or more patches are used, a different optimized formula is applied. This dynamic adaptation maximizes calculation efficiency for each scenario without requiring a complex universal solution.
Solution Approach 2:
The patent applies different mathematical expressions tailored to specific cases (three patches vs. four or more patches). This local optimization ensures that each calculation scenario uses the most efficient formula for its specific conditions, improving overall productivity without significantly increasing the complexity of the calculation method.
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
This approach reduces the number of calculations and calculation time by using specific mathematical expressions based on the number of toner patches, enhancing the accuracy and efficiency of toner charge calculation.
Implementation Method 1
the photoconductor drum carries a toner patch on which an electrostatic latent image has been developed with the toner carried by the developing roller
Data Source
AI summary
An image forming apparatus includes a developing roller, a photoconductor drum, a density detector, a current detector, and a controller. The developing roller carries a toner. The photoconductor drum carries a toner patch. The density detector detects toner density of the toner patch. The current detector detects developing current flowing to the toner patch. The controller calculates an inclination of an approximate straight line approximating a relation between the toner density and the developing current. The developing roller develops three or more toner patches, different in toner density and different in developing current from one another, on the photoconductor drum. The controller calculates the inclination, using different mathematical expressions depending on whether three toner patches or four toner patches are provided.