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# WHY US

WE TRULY UNDERSTAND BALL BEARING KINEMATICS AND ENERGETICS

## POWER criterion IS KEY

No method of calculation or modelling tool can properly approximate the effective behavior of the balls, let alone the bearing, via the Newton’s formalism. For this reason, all the methods used so far have shown their limitations or incompleteness.

We base our characterization on a new power criterion and a related original tool, Rose,  instead of the classic newtonian dynamics-based softwares,  to achieve the bearing equilibrium.

## UNique in the world

We do not rely on traditional or specific digital market modeling tools, which cannot guarantee access to the true equilibrium of the bearing. These tools do not eliminate some uncertainties. Nor do we rely on classic formalism used by bearing manufacturers to predict service life.

We follow a specific analytical approach, unique in the world, in conjunction with our original tool (Rose), to characterize the kinematics and dynamics of the balls on a case-by-case basis, regardless of the operating conditions.

# What is the core of your methods and tools?

The methods and tools developed by APO-GEE use fundamentals that take an opposite orientation compared to existing tools.

Most existing tools use a Newtonian formalism, which is based on the equilibrium of forces and moments. However, no method of calculation or modeling can properly approximate the effective behavior a ball bearing via the Newton’s formalism. For this reason, all the methods and classic newtonian dynamics based softwares, which are used so far to model ball bearing behavior, have shown limitations or incompleteness. They cannot guarantee the access to the true equilibrium of the bearing, because they rely on simplifying assumptions on balls kinematics.

The core of the approach developed by APO-GEE is made of a brand-new equilibrium criterion, which is based on the power. It has been the object of an in-depth mathematical demonstration. Indeed, it occurs that satisfying this criterion is equivalent to satisfying the Newton’s laws of motion. Nevertheless, contrary to the Newton’s approach, the use of the methodology of APO-GEE gives the possibility to completely compute the kinematics of the balls, leading to the true equilibrium of the ball bearing. Without approximation. No matter the working conditions that the bearing endures (loads, misalignment, speed, …).

# Do you rely on the A.B. Jones hypothesis?

A.B. Jones (1950’s) is definitely one of the pillars of modern bearing calculation. He formulated an hypothesis stating that the balls are rolling on one race of the bearing only (the so-called ‘‘race control’’).

It is important to note that most of the subsequent works on ball bearing modeling takes the Jones hypothesis as a theory! A lot of modern bearing calculation tools are still based on this hypothesis. Rose is not not bound by any hypothesis but by a demonstrated theory of ball kinematics.

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Rose relies on a newtonian quasi-static/quasi-dynamic formalism. But, contrary to the approach of Jones, we have developed a new variational method to remove the classic ‘‘race control’’ hypothesis of Jones.

Managing uncertainties and multiples input variables when studying a business case is very tricky if we want reliable results. What we’ve done is to remove the uncertainty on the kinematics of the balls. That’s why the core of Rose is the comprehensive computation of the kinematics of the balls, whatever the operating conditions.

So if we want to represent the functioning of Rose, it is based on the deep knowledge of the bearing equilibrium, that gives key information on internal bearing variables such as dissipated heat, speeds of balls, forces, … This allows to characterize specific phenomena in a reliable and robust way.

# Could others have done it too?

There are definitely bright and smart engineers and scientists all around the world, in universities, aerospace companies and ball bearings companies.

What made the difference is that we had the opportunity to study ball bearing physics, and the kinematics of the balls in particular, in a continuous effort of more that 10 years. It constitutes a R&D journey that is pretty unique. We did not have to stop or switch from one R&D project to another. We were able to focus on deep understanding of ball bearing physics, opening doors, closing others, testing new resolution methods, establishing new models and new geometries, right up to successful experimental validations.

It is only at the cost of this long, continuous effort that our innovations have been able to see the daylight.

# Does the accuracy of your modeling depend on the computing power of your computers?

No! Our position as APO-GEE is that modeling is a valuable tool, as long as it is preserved from excessive sophistication. Furthermore, it must be constantly confronted with reality, by feeding on precise experimental data. In this way, we develop advanced calculation tools that mainly focus on the specificities of the problems being addressed. We limit ourselves to what needs to be modeled, avoiding losing control and, above all, losing ourselves.

We do not seek to quantify at any cost, but rather to understand, surely. The opportunity to introduce indeed ever more refinement into a model is particularly attractive. But it is not without risk. Indeed, if it appears tempting to increase without limit the finesse of the laws that are used, constantly increasing the number of parameters means also multiplying the difficulties and the uncertainties accordingly.

We rely on understanding of ball bearing physics and phenomena, appropriate methodology and original computational tools to find solutions. In that order.

# Do you have a dedicated computational tool to model cage behavior ?

Yes! One module of Rose is specifically dedicated to cage dynamics analysis. In particular, this model aims at identifying sudden increase in bearing friction torque due to cage misbehavior (cage instability, ball speed variation,…). The model takes into account all the relevant parameters of the bearing (dimensions, material, tribological conditions, working conditions,...).

# A lot of cage models exist, why yours would be so different?

We did not attempt to develop another cage model to compete with others, we aimed to create a new model to to uncover the physics behind cage instability. And we succeeded.

We know that extensive research has been conducted on this subject to enhance cage behavior. However, our research and understanding of physics led to a specific geometry that represents more than just a major improvement. It not only reduces cage instability but also prevents it from occurring.

# How do you take lubrication into account, do you use EHL model?

Our goal is not to replace the work done by lubricant researchers worldwide. Instead, we asked ourselves: Is an EHL (elastohydrodynamic lubrication) model necessary to achieve our objectives?

Our aim is to understand how we can improve the operational behavior of ball bearings by comprehending the physics behind detrimental phenomena and proposing innovative solutions based on these physical aspects.

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Consider the cage instability problem, for instance. Our goal is not to precisely determine how the cage behaves with one lubricant or another, but to understand the effects of friction on cage behavior. What impact does low friction (optimal lubrication) have? What about high friction (poor or no lubrication)? Once we deeply understand this, how can we address the cage instability problem? Our approach to developing new solutions based on design does not necessarily require a dedicated EHL model, and we have proven this.

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The same principle applies to high-speed bearings. Our objective is to significantly enhance the behavior of high-speed ball bearings. If we can identify general improvements that are independent of the lubrication regime, a dedicated EHL model may not be necessary, and we have demonstrated this as well.

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# Are you expert in material?

No! These are competences that we don’t have.  However, our innovations are fully compatible with advancements in materials science. For instance, we have resolved instability issues through innovative design, and utilizing the most efficient materials for the cage can further improve performance.

# Does it works (have you actually proven that your methods and tools work)?

Yes, on many occasions, both in product development and application engineering.

For example, our modeling of cage behavior has been experimentally validated multiple times at various levels: anticipating stable or unstable behavior, controlling stable or unstable behavior, and defining unconditionally stable designs. Each time, our understanding of physics and our predictive capabilities have been validated.

# Do your tools & methods apply only in the aerospace & defense applications?

No, while they are particularly suited to handle the demanding environments and operating conditions in aerospace and defense, they have also proven highly effective in specific applications within the automotive industry, medical technology, and machine tools, among others.

# Can you find solutions where it is not possible with existing commercially distributed software ?

Yes! That’s what experience has shown us lately, both in product development and application engineering.

# Do you commercially distribute Rose, your original set of tools?

No! Rose is dedicated to understanding bearing physics and works in tandem with deep knowledge and appropriate methodology. Our focus remains on innovative ball bearing engineering rather than software distribution.

Nonetheless, we are available to provide assistance and support for your projects.

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# How would you summarize all of this?

A profound understanding of bearing physics leads to innovative products and effective solutions.

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