The Mathematics Behind Additive Manufacturing

In a compelling episode of the Additive Snack Podcast, host Fabian Alefeld speaks with Harshil Goel, founder and CEO of Dyndrite, about the pivotal role of mathematics in advancing additive manufacturing (AM).

Goel, who has a strong background in mathematics and mechanical engineering, shares his unexpected journey into the AM world and how Dyndrite is leveraging pure math to solve complex industry challenges. This episode unpacks Dyndrite's mission, its impact on empowering engineers, and its efforts to push the boundaries of AM.

From Outsider to Founder: Harshil’s Journey into the AM World

Goel brings a unique blend of academic rigor and entrepreneurial spirit to the AM industry. His scientific background is rooted in mathematics, specifically differential geometry and topology, which he describes as "doing calculus on surfaces." In mechanical engineering, his expertise lies in fluid mechanics, computational fluid mechanics, and continuum mechanics — essentially, "solving very difficult mathematics problems for engineering purposes."

Goel's journey into AM was unconventional; he himself confessed that he didn't really know what AM was until 2015-2016, when Boeing approached him with a challenge regarding the shortcomings of existing AM software. His ability to quickly conceptualize and deliver solutions led to the founding of Dyndrite in 2017, initially moving to Washington to be closer to early customers and employees.

Before founding Dyndrite, Goel taught MATLAB and Python at UC Berkeley, where he also completed his bachelor's, master's, and PhD programs. This teaching experience significantly influenced Dyndrite's software design, which subtly teaches users how to program.

Dyndrite's Core Concept and Industry Impact

Dyndrite's primary offering is software designed to guide customers from initial machine usage all the way to full-scale production in AM. Goel categorizes the customer journey into three levels of maturity:

1. Building preparation: This involves essential tasks such as importing geometry, orienting, nesting, labeling, supporting, and slicing parts for machine readiness. While not the "sexiest" aspect, it's a fundamental requirement. Dyndrite automates these processes significantly, as demonstrated by a customer saving $20,000 a week on labeling alone by automating the entire process.
2. Materials and process development: After producing a first part, customers aim to reliably create specific parts on specific machines with specific materials. Dyndrite's unique contribution here is developing strategies to instruct the machine on "where to do what when" to enhance part quality and machine productivity. An example includes applying a "skin parameter" for critical areas (e.g., 30-60 microns) and a "productivity parameter" for the core (e.g., 90-120 microns), potentially resulting in a two-fold improvement in build time. One propulsion customer, with no prior experience or simulation, was able to print Inconel parts in 1.5 weeks that they previously thought impossible, using Dyndrite's tools and basic math.
3. Qualification and traceability: Once parts are produced, ensuring repeatability, qualification, calibration, and traceability becomes paramount for production readiness. Dyndrite aims to simplify qualification processes, making it easier for companies to switch between software while maintaining compliance.

A key innovation in Dyndrite's software is its "turbo mode," which displays Python code in the background as users interact with the graphical user interface (GUI). This design choice stems from Goel's language learning approach, presenting the familiar GUI alongside the new programming language, thereby demystifying coding for mechanical engineers and encouraging them to codify their practices. This approach allows for advanced automation, such as automatically generating labels and supports based on CAD color metadata.

Industry Observations and Future Predictions

Goel notes that the AM industry is maturing significantly, with more sophisticated professionals asking more complex questions, driving innovation. Machine sizes and volumes continue to double every five to ten years, creating a need for more robust data processing capabilities for toolpath generation.

Regarding technological advancements, Goel highlights the crucial role of GPUs. While acknowledging the hype around AI, he believes the most significant impact of trends like Bitcoin, video games, and VR on AM is the increased investment in GPU development. This has dramatically accelerated computational geometry algorithms, allowing for faster and more complex toolpath generation for increasingly large machines. GPUs have seen a thousand-fold increase in speed, making advanced computing more accessible and affordable.

From a qualification standpoint, Goel identifies a loophole in existing frameworks: By translating traditional key performance variables (KPVs) like hatch distance, spacing, laser power, and speed into a new set of non-dimensional numbers (ratios), companies can gain more flexibility. For example, instead of qualifying a part based on a 60-micron layer height, qualifying it by volumetric energy density allows for adjustments in layer height (e.g., 120 microns or 30 microns) by proportionally adjusting laser power, without requiring requalification.

This approach dramatically accelerates the application of multiple parameters to a single part and enables faster printing.

Harshil Goel's insights underscore the transformative power of mathematics and strategic software in advancing additive manufacturing. His vision for streamlined qualification and enhanced productivity paves the way for AM to reach its full potential in industrial applications.

Connect and Learn More

For more insights into Harshil Goel's work and Dyndrite, you can explore the following resources:

• Learn more about Harshil Goel’s work at Dyndrite.
• Connect with Harshil Goel on LinkedIn.
• Read Harshil Goel's profile on Forbes.