Manufacturing Process Workshop Technology: Analysis Of High-Speed Roller Bearings

Hertzian Contact Stress in High-Speed Roller Bearings

Question:

Discuss About The Manufacturing Process Workshop Technology?

Lightly loaded high-speed roller bearings are in most cases prone lubricant starvation and slip especially at the interface where the inner circle comes into contact with the rollers. The bearing life of the roller is affected therefore by these two factors, slip and starvation of the lubricant, as these factors affect the thickness of the film of oil. Of the most important life factor is the speed of the cage in the estimation of the contact pressure. This is because any modification that happens to the bearing-inner race interface is affected by the speed at which the cage moves (Weisenberger, 2013).

The stress developed when the two surfaces come into contact is defined by Hertzian contact stress. The extent of deformation on the point of contact when the two surface come together is dependent on the normal contact force, the elasticity modulus of the two surfaces coming into contact as well as the radii of curvature of the two surfaces that have come into contact. Using the equation , the maximum contact pressure between the two surfaces can be established (Singh, 2006).

Depending on the magnitude of the stress, there is deformation caused, either elastic or plastic to the surface of contact. A need thus arises to calculate the stress that is developed at the point of contact. Among the assumptions made while calculating the contact stress, include;

• Homogeneity of the materials that are in contact and that the yields stress is not surpasses
• A load, which is normal to the tangent of the contact plane, is responsible for the contact stress. This means there are no tangential forces that could be acting in between the two solids, which are intact(Castillo-León, 2014)
• The area of the contact is small in comparison with the dimensions of the solids whose surfaces are coming into contact
• Surface roughness has negligible effect on the overall contact stress
• The solids, which are coming into contact, are at equilibrium and at rest during the time of contact.

It is recommended that analysis of non-metallic components is done through nonlinear stress analysis as a result of the complexity of the relationships in load deformation (Committee, 2010). Finite element analysis can then be used in the calculation and estimation of the stresses and the displacement of the final products resulting from such operational loads as contact between surfaces, pressures, temperatures, accelerations or even forces. Multiphysics analysis can be performed from loads imported from simulation, thermal and flow studies.

Being that the roller bearings and the roller race are made of metallic components, the analysis of the components of this solid can be done using either linear or nonlinear stress analysis. The analysis chosen depends upon the extent of push that the design is to be taken. In cases where there is need to keep the geometry in a linear elastic range, then linear stress analysis would be deployed. Keeping the geometry of the design in a linear elastic range would mean the components would be able to regain their original shape upon the withdrawal of the load. This would occur for as long as the geometry of the components is relatively larger than the rotations and the displacements. Such analyses normally aim factor of safety (Engineers, 2005).

Linear and Nonlinear Stress Analysis of Roller Bearings

On the other hand, in cases where the pot-yield load cycles the geometry, nonlinear stress analysis is conducted to analyze the forces and the loads. Under such circumstances, the impact of permanent deformation and hardening of strain on the residual stresses are given a priority and thus the goals of the analysis. For the case of the presented problem, it is deducible that the geometry of the design is suitable. The boundary conditions of the components have clearly been defined, and from the provided information, the linear analysis would be deployed in the analysis of the forces of the components. The main aim of the design would be to ensure the roller bearings are able to contain the forces and the stress when it comes into contact with the roller race along the raceway (Lee, 2017).

Most of the metals that are used in the manufacture of components are ductile. This loosely means metals occasionally react with loads in a linear way when loaded to a point called the yield strength beyond which the metal would behave non-linearly thereby resisting a very small amount of load before it can finally hit its point of ultimate strength where it breaks. The point at which there is conversion from linearity to non-linearity is called the plastic zone. It is not mathematically and computationally possible to describe into details this region (Kotzalas, 2006).

Another limitation of this analysis is the stress concentration. In a bid to eliminate the plastic zone effects that result from non-linearity, Linear FEA version of computing is used in the simulation exercise. This version assumes that all materials used in the making of components would behave in a linear way even beyond the yield strength. Linear FEA tends to be inaccurate when it comes to stress concentrations. There tends to be very large stress over a very small area in a material at stress concentration (Gokhale, 2008). This is caused by abrupt changes in the geometry of the component and such areas are able to experience stress that is beyond the yield strength of the material. Due to this abrupt increase, linear FEA has been found to be inaccurate in the prediction of the possible effects that can come with these stress concentrations.

Despite stress concentrations being a common phenomenon in finite element analysis, it is not accurately portrayed what happens in these regions with the assumptions that are used in the linear finite element analysis. It not correct and precise that the failure of the entire component of the system to be pegged purely on stress concentration on a linear analysis. Experimental findings have determined that there exists an acceptable allowance for stress just before stress concentration can have a relatively significant impact on the entire strength of the structure (Castillo-León, 2014).

Limitations of Linear Stress Analysis

One of the simplest ways of determining the maximum contact stress of the roller bearings and the roller race in the component provided is by assuming that the bearings make contact with the race over its full circumference.  It is also assumed that as the roller moves along the raceway, the contact pressure over the area it moves remains constant throughout the time it moves (Esam, 2009). In so doing, contact pressure is created which is equivalent to the quotient of the loaded and the projected area of contact of the two surfaces

Since the roller does not make contact with the roller race over the whole diameter, the contact pressure will not be constant throughout the area of contact. Instead, in case there is no deformation the roller bearings would end up only contacting the roller race along a line down its thickness. The elastic deformation experienced between the roller bearings and the roller race can be calculated using Hertz analytic solution, mostly called Hertzian contact. This method of calculation would yield the stress that would account for the actual geometry of the component:

Conclusion

This experimental design of a cylindrical roller and race design is almost similar in characteristics and conditions with that of numerical and analytical models. In as much as the data and the signals used in the analysis of this model are seemingly borrowed from and almost similar to real known model (Dieter, 2013). This experimental design model is can be validated by the use of Harrison Jones’s analytical model with minimal differences observed between the two models. Any differences that can be noted between this model and Jones’ would be due to asymmetrical load zone of by the numerical dynamic. This experimental model provides an avenue for further exploration into the various possible events that may result into or can be termed as chaotic behaviour of elements the roller. Numerical models are capable of generating the geometry of the load zones, which are adaptive to the dynamism of the bearing elements that are in contact with the geometry. Such allows for prediction of the failure and location of critical areas as well as the behaviour of the various components (Schell, 2014).

References

Alawadhi, E. M. (2015). Finite Element Simulations Using ANSYS, Second Edition. London: CRC Press.

Castillo-León, J. (2014). Lab-on-a-Chip Devices and Micro-Total Analysis Systems: A Practical Guide. Oxford: Springer.

Committee, A. I. (2010). ASM Handbook, Volume 22, Part 1. Chicago: ASM International.

Dieter, G. E. (2013). Handbook of Workability and Process Design. Oxford: ASM International.

Engineers, A. S. (2005). Proceedings of DETC, Volume 3, Parts 1-2. New York: American Society of Mechanical Engineers.

Esam, A. (2009). Finite Element Simulations Using ANSYS. New York: CRC Press.

Gokhale, N. S. (2008). Practical Finite Element Analysis. Kansas: Finite To Infinite.

Kotzalas, M. N. (2006). Advanced Concepts of Bearing Technology,: Rolling Bearing Analysis, Fifth Edition. New York: CRC Press.

Lee, H.-H. (2017). Finite Element Simulations with ANSYS Workbench 17. Sydney: SDC Publications.

Schell, J. (2014). The Art of Game Design: A Book of Lenses, Second Edition. New York: CRC Press.

Singh, R. (2006). Introduction to Basic Manufacturing Process and Workshop Technology. Beijing: New Age International.

Weisenberger, N. (2013). Coasters 101: An Engineer's Guide to Roller Coaster Design. Macnhester: Nick Weisenberger.