Understanding Beran's Fibre Support Index and Its Impact on Papermaking Efficiency

Dr. Robert Beran, in 1978, developed the Fibre Support Index (FSI) as a two-dimensional mathematical model to quantify a forming fabric's ability to support fibers during the paper sheet formation process. This single numerical value (FSI) allows for objective assessment and comparison of different forming fabric designs based on their resistance to fiber embedment. 

How FSI works

Beran's model calculates the probability of a unidimensional fiber falling onto a two-dimensional grid representing the forming fabric's structure.

The FSI value depends on: 

• Fabric Design: Specifically, the number of yarns running in the machine direction (MD) and cross-machine direction (CMD) on the paper-forming side of the fabric.

• Support Contribution: Coefficients ('a' and 'b') account for the contribution of support from yarns in both the machine and cross-machine directions. 

  
  

Significance and application

A higher FSI value indicates:

• Improved Fiber Support: The fabric offers better support to the fibers, preventing them from embedding within the fabric structure.

• Enhanced Retention: The forming fabric better retains fibers on its surface during the dewatering process.

• Reduced Two-Sidedness: The wire side of the paper sheet becomes more similar to the top side, minimizing two-sidedness.

• Better Paper Quality: Improved fiber support translates to enhanced paper sheet properties like flatness, smoothness, printability, and strength. 

  
  

The FSI is widely used in the paper industry to:

• Evaluate Fabric Performance: Assess the effectiveness of different forming fabric designs in supporting fibers and achieving desired sheet properties.

• Improve Paper Quality: Select fabrics with high FSI to produce paper with superior characteristics like smoothness, printability, and strength.

• Optimize Forming Fabric Design: Adjust fabric parameters like yarn density and weave patterns to achieve the desired FSI for specific paper grades and machine conditions.

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  Forming Fabric

  
  

  Calculation: FSI is calculated using the Beran equation, which considers the number of machine direction (MD) and cross-machine direction (CMD) yarns and their support characteristics. The formula emphasizes CMD support (weft yarns) by giving it double the weight of MD support (warp yarns), reflecting the greater influence of CMD yarns on fibre retention due to their orientation across the fabric surface.

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  Formula: 

  FSI = 2/3(a .Na + 2 . b. Nb}

  • Where:

    • Na

      : Number of machine direction (warp) yarns per unit length (e.g., yarns/inch).

    • Nb

      : Number of cross-machine direction (weft) yarns per unit length (e.g., yarns/inch).

    • a: MD support factor, related to the length of MD yarn knuckles or support points.

    • b: CMD support factor, related to the length of CMD yarn knuckles or support points.

    • The factor of 2 for CMD support reflects its greater contribution to fibre retention, and the division by 3 normalizes the result.

    Limitations: While FSI is effective for comparing fabrics, it does not account for the uniformity of support across the fabric surface, which is critical for consistent sheet quality. It was developed before multilayer forming fabrics became common, so it may need adaptation for modern complex weave designs.

    
    

  Who Was Dr. Robert Beran?

  Dr. Robert Beran was a statistician and researcher who contributed significantly to the field of papermaking through his development of the Fibre Support Index. While limited biographical information is available, Beran is recognized for his work in applying statistical methods to industrial processes, particularly in the pulp and paper industry.

  • Profession: Beran was a statistician with expertise in developing models to analyze and optimize industrial processes. His work extended beyond papermaking, as evidenced by his contributions to statistical methodologies, such as a nonparametric estimator of conditional survival functions in 1981 and publications on statistical methods for long-memory processes. These suggest a deep background in statistical modeling and data analysis.

  • Relevance to Papermaking: Beran’s development of the FSI demonstrates his ability to translate statistical principles into practical tools for industrial applications, specifically addressing the interaction between forming fabrics and fibre mats in paper machines.

  • Other Contributions: Beyond FSI, Beran published works in statistical theory, including a 1988 paper on prepivoting test statistics and contributions to long-range dependence in statistics, indicating a broad influence in statistical methodologies across industries.

    
    

  When Was FSI Introduced?

  The Fibre Support Index was introduced by Dr. Robert Beran in 1978. It was developed as a response to the need for a standardized metric to evaluate forming fabrics’ ability to support fibres, particularly as papermaking processes began to incorporate more recycled fibres with shorter lengths, which posed retention challenges. The FSI was established before the widespread adoption of multilayer forming fabrics, making it a foundational tool in the industry.

  
  

  Universal Use of FSI

  The Fibre Support Index remains a widely used metric in the papermaking and forming fabric manufacturing industries, despite being introduced nearly five decades ago. Its universal adoption is attributed to the following reasons:

  • Standardized Comparison: FSI provides a consistent, quantitative measure to compare different forming fabric designs across manufacturers and paper machines. It allows papermakers and fabric designers to assess fibre support potential objectively, regardless of specific weave patterns or materials.

  • Simplicity and Practicality: The FSI formula is straightforward, using measurable parameters (MD and CMD yarn counts and support factors), making it accessible for engineers and designers to apply in real-world settings.

  • Relevance to Fibre Retention: Fibre retention remains a critical challenge in papermaking, especially with the growing use of recycled fibres and high-speed machines. FSI directly addresses this by quantifying a fabric’s ability to retain fibres, making it a timeless tool for optimizing sheet quality and reducing waste.

  • Industry Standard: FSI has been adopted as an industry standard, referenced by major forming fabric manufacturers (e.g., Heimbach, Cristini) and technical associations like TAPPI. Its widespread acceptance ensures its continued use in fabric design specifications and performance evaluations.

  • Adaptability: While originally developed for single-layer fabrics, FSI is still applied to multilayer designs by adjusting support factors, ensuring its relevance across evolving fabric technologies.

    
    

  Relevance Despite Technological Changes:

  Papermaking and forming fabric manufacturing have undergone significant advancements since 1978, including the introduction of multilayer fabrics, high-speed machines, advanced materials (e.g., finer monofilaments), and modern coagulation chemistry for retention aids. Despite these changes, FSI remains relevant for the following reasons:

  • Core Principle Endures: Fibre retention continues to be a fundamental requirement in the forming section, regardless of technological advancements. FSI’s focus on the interaction between fabric weave and fibre mat remains critical, as it directly impacts sheet quality, retention efficiency, and machine performance.

  • Compatibility with Modern Fabrics: Although FSI was developed before multilayer fabrics, it can be adapted to evaluate complex designs by adjusting MD and CMD support factors. Manufacturers use FSI alongside other metrics (e.g., Drainage Index, fabric density) to optimize modern fabrics for specific paper grades.

  • Complementary to Chemistry: While modern coagulation chemistry (e.g., retention aids from companies like Nalco) plays a significant role in fibre retention, forming fabric design remains a primary factor. FSI helps manufacturers design fabrics that complement chemical retention systems, ensuring optimal performance.

  • Focus on Recycled Fibres: The increased use of recycled fibres, which are shorter and harder to retain, has made FSI even more relevant. Its ability to guide fabric design for improved fibre support is critical in addressing the challenges of modern furnish compositions.

  • Persistent Design Challenges: Technological advancements have not eliminated the need to balance fibre retention with drainage and sheet formation. FSI provides a reliable framework for navigating these trade-offs, even in high-speed, automated paper machines.

  • Industry Inertia and Trust: As an established metric, FSI is deeply embedded in industry practices, training, and technical literature. Its proven track record and ease of use make it a trusted tool, even as new metrics and technologies emerge.

In summary, the FSI, developed by Dr. Beran, provides a simple yet effective tool for characterising the fibre support capabilities of forming fabrics, ultimately contributing to the production of high-quality paper.