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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 their 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.

ball bearing modeling software
ball bearing modeling software

UNique in the world

We do not rely on traditional or specific digital market modeling tools, which cannot guarantee access to the real equilibrium of the bearing. These tools do not remove some uncertainties. Nor do we rely on the 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, on a case-by-case basis, the kinematics and the dynamics of the balls. Whatever the operating conditions.



What is the core of your methods and tools?


The methods and tools developed by APO-GEE use fundaments 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 real 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, which leads to the real 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 dictated by any hypothesis, but by a demonstrated theory on the kinematics of the balls.

How would you qualify the functioning of Rose, your set of computational and modeling tools FOR BEARINGS?


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 wanted a new model to discover the physics behind cage instability. And we succeeded.


We know that a lot of research works have been performed on the subject, in order to improve the behavior on the cage. But our research and understanding of physics led to a specific geometry that constitutes even more than a major improvement. It does not reduce cage instability. It prevents cage instability to occur.



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


Our goal is not to replace the work performed by all the lubricant researchers all over the world. However, the question that we asked ourselves is this one: is an EHL (elastohydrodynamic lubrication) model necessary to achieve what we want to achieve?  Our goal is to understand how we can improve the working behavior of ball bearings. We do that by understanding the physics behind the deleterious phenomena, from one side, and by proposing innovative solutions based on these physical aspects, on the other. 


Let us for instance consider the cage instability problem. Our goal is not to precisely determine how the cage could behave with one lubricant or another. Our goal is to understand the effects of friction on the behavior of the cage. What is the impact of low friction (optimal lubrication)? What is the impact of high friction (bad or no lubrication)? Once we have a deep understanding of this, how can we act to solve the cage instability problem? If we attempt to bring a new solution based on the design, this approach does not necessarily require a dedicated EHL model. We have proved it.


The same observation can be made for high-speed bearings. Our goal is to find a way to understand how to significantly improve the behavior of high-speed ball bearings. If we can identify generic improvements, which are independent of the lubrication regime, a dedicated EHL model is not necessarily required either. We have also proved it.



Are you expert in material?


No! These are competences that we don’t have.  Our innovations are nevertheless perfectly compatible with the advances in materials sciences. For example, we have solved the instability problem with an innovative design. The most efficient materials for the cage can only contribute to an even better behavior.



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


Yes! On many occasions, both at the level of product development and in the context of application engineering.


For example, our modeling of cage behavior has been experimentally validated several times and at different levels: anticipation of stable or unstable behavior, control of stable or unstable behavior, definition of an unconditionally stable design. Each time, our understanding of physics and our ability to predict and model was validated.



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


No! If they are particularly adapted to take into account the harsh environment and operating conditions in aerospace & defense applications, they have also proven to be highly effective for specific applications in the automotive industry, medtechs or machine tools, for example.



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


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



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


No! Rose is dedicated to the understanding of bearing physics and works in combination with deep-knowledge and appropriate methodology. It is part of our competitive advantage to find concrete solutions for engineering applications challenges, and to develop innovative products. We are not a software editor company and do not want to become one. Innovative ball bearing engineering remains our focus. 


We are nevertheless available to provide you with help and support for your projects.



How would you summarize all of this?


Deep understanding of the physics of bearing leads to innovative products and appropriate solutions

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