Developing the Srixon Golf Ball Core

The global consumer market of golf balls is project to reach $1.38 billion by 2025[1]. With an industry that large, competition is fierce as manufacturers endeavor to establish, maintain and grow their market share. Product development plays a critical role in differentiating one company from another, by facilitating the consistent release of new and improved products, and maintaining low manufacturing costs.

Project Details

The Challenge

Typically, a golf ball consists of a plastic cover, windings of rubber thread, and a core that contains gel, liquid or solid[3]. The goal of this analysis was to develop new core formulations composed of 2-5 rubbers (including ones that had not been previously used by Mitsubishi), the amount of oil, and the amount of each of 4 polyolefins.

A common complexity in product development is that there are more decisions to be made beyond selection of materials. In fact, there are three decision categories for developing a new product or reformulating an existing one:

1. Raw Material Selection
2. Formulation Decisions
3. Manufacturing Conditions

Traditional product development methods often address these decisions separately or sequentially, failing to account for the high degree of interaction between them. This leads to iterative, time-consuming product development.

The ProSensus Approach

Applying the RPD framework, which is based on multivariate modeling, allowed Mitsubishi Chemical to simultaneously model the interactive effects of these three sets of decision variables in order to develop high-performance rubber compounds for use in the golf ball cores.

The Mitsubishi Chemical case study is an excellent example to demonstrate the benefit of such framework.

The ProSensus Rapid Product Development Framework

ProSensus uses this framework for modeling product development data, and FormuSense users are guided through this workflow.

It should be noted that the analysis can vary somewhat for each project depending on the client’s application and the available dataset.

In many cases, clients do not start with “good” databases since past product design experimental data is often collected over many years, by many individuals, and without a planned format. Therefore, ProSensus often recommends a data audit as an initial step to investigate the suitability and structure of the data for multivariate modeling.

Suitability and Structure of Historical Data

A key goal in this Mitsubishi project was exploring possible formulations with new materials that had previously not been used, therefore, the availability of raw material properties was critical in order to model the impact of raw material properties on product quality.

A total of 111 previous formulations (products) had been recorded in the historical database. These were produced from blending 13 different rubbers, 1 oil and 4 polypropylenes.

The following data blocks were available:

The raw material properties and mass fractions were combined through ideal mixing rules to calculate the property of the blend. For example, if we assume that the ideal mixing rule holds for the weight-averaged molecular weight of a blend of material A with material B, then for a blend of 60% A with 40% B we have the blended molecular weight as:

The Results

Multivariate Modeling

The PLS model structure is shown with the key data blocks for this analysis. This is a powerful model structure since it simultaneously captures the interactive effects of the three data blocks on the final product properties.

The data blocks include: the formulation matrix (ingredient selections and the associated properties) and finally, what mass or molar ratios they were combined in.

The PLS model summarized the 16 input X-variables with 7 latent variables and a model fit over 90%.

The following FormuSense plots demonstrate the power of using PLS for this application.

The score plot (top left) shows the distribution of formulations (existing products) in the first two latent variables. Products located near each other on the score plot are similar in both raw material and formulation properties (X) as well as in performance properties (Y) .

The W*C plot (bottom left) highlights the correlations between the X (orange) and Y (blue) variables in this dataset.  Variables clustered together (such as  Y1-Y5, RX01, RX04, RX07 and PP1) are positively correlated with one another, while variables on the opposite side of the plot (such as Y7, Oil1, RX09, RX10 and RX11) are negatively correlated with the first cluster.

By selecting formulations with high Y5 values on the observed vs predicted plot (top right), it is observed that these formulations are located on the far right of the score plot. This is an expected result, recalling that Y5 is located in the same corresponding area of the W*C plot.

The coefficient plot indicates that if the customer is mostly interested in improving the Y5 quality, a blend with lower Oil1 content and PP4 content, and with higher PP1 content, RX01 and RX07 is desired.

Clearly, visualizations associated with the generated model, such as above, provide an improved understanding of the underlying chemistry and correlations and also forms the basis for developing new products or re-formulating existing ones.

Simulation

Once the model was built and validated on the existing products, digital simulation was used to rapidly reformulate an existing product. The goal of this reformulation was to reduce costs, while maintaining quality.

The impact of replacing an existing rubber ingredient (Rub05) with one of three candidates (RubNew01, RubNew02, Rub01) was predicted by applying the developed model in a forward direction for several formulation scenarios, as illustrated below. The candidate rubbers were selected by domain experts, based on their lower cost, and expected functionality.

While all three simulation scenarios resulted in a reduction in overall cost (summarized in the “★ Results” table below), the final product quality was unacceptable when RubNew01 and RubNew02 were used in place of Rub05. The discrepancy in product quality is visualized below in terms of the number of standard deviations from the model average, for each of the 7 quality variables and each simulation scenario.

Furthermore, the scenario using RubNew02 violates the SPEX model validity limit, indicating that the configured simulation scenario is inconsistent with the correlation structure of the historical dataset. This violation is indicated by the red colored cell in the ★ Results table. Although quality predictions are still provided for this scenario, results should be interpreted with caution, and not necessarily trusted, and are hence also colored red.

Fortunately, the scenario using Rub01 in place of Rub05 predicted relatively similar product quality with more than a 5% cost savings. As a result, Rub01 was selected as the best candidate to move forward with further investigation such as optimization and physical experiments.

Optimization

While simulation is a very helpful tool, a major advantage of the PLS model structure is the ability to invert the model and apply numerical optimization to reformulate products that maintain specified quality properties.

Following this approach, as existing product that used Rub06 was reformulated with different rubber and polypropylene ingredients to maintain the original product quality.

 
The reformulated product was obtained by specifying targets for all 7 quality variables that match the existing product quality. Deviation from these targets is included as part of the optimization objective function, in addition to other terms such as minimizing cost.

Several optimizations were performed with a variety of goals. One optimization resulted in reformulating an existing product with a material cost savings of 5% cheaper, by selecting to use a new rubber material. Another optimization resulted in the development of an entirely new product – the Srixon golf ball core.

FormuSense Software

FormuSense software was used to demonstrate the workflow and achieving the objectives of this project, including building a predicting model and applying that model in both a forward (simulation) and backward (optimization) direction to develop new and re-formulated golf ball cores developed at a minimum cost. 
 
Learn more about FormuSense, or our success with Dow Chemicals through a product customization software tool that facilitates custom rapid product development using PLS models and constrained optimization.