The global consumer market of golf balls is project to reach $1.38 billion by 2025. 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.
Typically, a golf ball consists of a plastic cover, windings of rubber thread, and a core that contains gel, liquid or solid. 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:
- Raw Material Selection
- Formulation Decisions
- 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 RPD framework as a general guide for the modeling process. However, the analysis can vary 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:
Raw Material Database: 11 properties (molecular weight, density, etc.) on 30 rubber materials were recorded. Only 13 rubbers had been used in past formulations but 30 rubbers were characterized in order to potentially use them in the new /re-formulated products.
Formulation Matrix: the ratio of each component in the blend:
• 11 RX rubber properties – RX1 to RX11, calculated using mixing rules as shown below
• 4 polypropylene mass fractions – PP1 to PP4
• 1 oil mass fraction – Oil1
Process: The operation was constant for each blend and therefore were not included in this analysis.
Product Performance: The final quality of the blend was characterized by 7 measurements – Y1 to Y7
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 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: processing conditions, the choice of raw materials (and specifically their 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 biplot for the first two latent variables demonstrates the power of using PLS for this application.
The biplot highlights the correlations between the variables and observations in this dataset. The blue points show the distribution of observations (existing products) in the first two latent variables. Products located near each other are similar in both product characteristics and raw material and formulation properties.
In terms of relationships amongst the variables, Y1 to Y5 are positively correlated with RX1 and RX4, which is evident by the clustering of these variables. This cluster is negatively correlated with Y7 and Oil1 since these two clusters are on opposite sides of the plot.
This means that if the customer is mostly interested in improving the Y5 quality, a blend with a higher RX4 property and a lower oil fraction is desired. Visualizations associated with the generated model, such as the biplot, provide an improved understanding of the underlying chemistry and correlations and also forms the basis for developing new products or re-formulating existing ones.
Once the model was built and validated on the previous products, numerical optimization was applied to solve the product design problem of suggesting raw material selections and combinations that achieve the quality targets of 7 key properties at minimum cost.
A major advantage of this PLS model structure is the use of the mixture matrix that allows us to consider the new materials that have never been used in past formulations.
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.
The objectives of this project were achieved at the optimization stage with new and re-formulated golf ball cores developed at a minimum cost, therefore custom software was not required. However, this modeling approach could have been extended farther with custom software to allow manufacturers to custom-fit a golf ball for a players particular game, for weather conditions, and even specific course conditions.
Learn more about our recent success with Dow Chemicals through a product customization software tool that facilitates custom rapid product development using PLS models and constrained optimization.
- Golf Ball Market Size Worth $1.38 Billion by 2025 | CAGR: 2.7%. (2020). Retrieved 25 September 2020, from https://www.grandviewresearch.com/press-release/global-golf-ball-market
- Muteki, K.; MacGregor, J.F. Sequential design of mixture experiments for the development of new products. J. Chemometrics, 2007, 21, 496-505.
- How golf ball is made – material, manufacture, history, used, parts, procedure, steps, industry, machine, History. (2020). Retrieved 25 September 2020, from http://www.madehow.com/Volume-3/Golf-Ball.html