Analysis of causes and effects errors in calculation of rolling slewing bearings capacity

In the paper the basic design features and essentia l assumption of calculation models as well as the f actors influencing quality improvement and improvement of calcula tion process of bearing capacity of rolling slewing bearings are discussed. The aim of conducted research is the identi fication and elimination of sources of errors in de termining the characteristics of slewing bearing capacity. The result of the research aims atdeterminingthe risk of making mist akes and specifying tips for designers of slewing bearings. It is shown that ere is a necessity fora numerical method to be a pplied and that real conditions of bearing work must necessarily be taken int o account e.g. carrying structure deformations as t he first ones.


Introduction
Human desire to receive the best product has led to emergence of tools and methods of quality management that needs to monitor and act to strive for perfection of a product.The concept of quality is not limited to a product or service, it is a broader concept and can be applied everywhere (ULEWICZ R. 2013).
Alongsidewith the development of quality management, emerged many methods which have an impact on quality while sing data collected with the help of quality tools.Methods of quality management are more oriented on the analysis of collected data, however,tools have a more basic character and serve the collection of data concerning a given product.Animportant thing is the ability to see information contained in the methods and use of it to improve other processes or products (ULEWICZ R., JELONEK D., MAZUR M. 2016).
The article presents the factors that aim to improve the quality and process of slewing bearing load capacity calculation.The objective of conducted research is identification and elimination of sources of errors in determining characteristics of slewing bearing capacity.The result of the research is determination of risks of making mistakes and providing advice for designers of slewing bearings.

Factors influencing the capacity and durability of the slewing bearings
Slewing bearing is a subgroup of rolling element bearing commonly used in large industrial machineries such as turntable, steel mill cranes, offshore cranes, rotatable trolley, excavators, stackers, swing shovels, and ladle cars.A slewing bearing is basic with a gear wheel integrated in the inner or outer ring, which is subjected to a complex set of heavy loads.They typically support high axial Q ment M and high radial load H (Fig.  Slewing bearings are often critical production part.An unplanned downtime when a bearing breaks down can be very expensive due to the loss of production.Moreover, as replacement of large slewing bearing take several months to arrive due to long manufactu ing and delivery time; plants often carry spare bearing to guard against these unforeseen circumstances ad ing an extra cost.In order to prevent unplanned dow time, a condition monitoring and prognos needed (KRYNKE M. 2015, ŚPIEWAK There are many different types of slewing bearings depending on the number of rows and in the type of rolling elements.Thus, there are bearings with one, two and three rows, and the rolling elements c balls or cylindrical rollers (SMOLNICKI

Factors influencing the capacity and durability of the slewing bearings
Slewing bearing is a subgroup of rolling element bearing commonly used in large industrial machineries such as turntable, steel mill cranes, offshore cranes, rotatable trolley, excavators, stackers, swing shovels, and ladle cars.A slewing bearing is basically a bearing with a gear wheel integrated in the inner or outer ring, which is subjected to a complex set of heavy loads.
Load distributions in a slewing bearing.
Slewing bearings are often critical production part.An unplanned downtime when a bearing breaks down can be very expensive due to the loss of production.Moreover, as replacement of large slewing bearing can take several months to arrive due to long manufacturing and delivery time; plants often carry spare bearing to guard against these unforeseen circumstances adding an extra cost.In order to prevent unplanned downtime, a condition monitoring and prognosis method is PIEWAK S. 2016).There are many different types of slewing bearings depending on the number of rows and in the type of rolling elements.Thus, there are bearings with one, two and three rows, and the rolling elements can be MOLNICKI T. 2013).

Fig. 2. Factors influencing the capacity and durability of the
Slewing bearings designed and manufactured for a specific application requiring knowledge of the d sign of the device on which the bearing will work, the approximate dimensions of the bearings, the diameters of the bearing rings mounting screws locations, as well as all the types and magnitude of loads that are tran mitted through the bearing (Fig.

Calculation of slewing bearings carrying capacity
The load capacity of slewing bearings is dete mined by different calculation methods.Simple model calculations allow to determine the characteristics of the bearing under the condition of a number of fications.The consequence of the applied simplific tions is an inaccurate assessment of actual bearing capacity (KANIA L. KRYNKE of slewing bearing is dependent on a number of fa tors, such as (KRYNKE M., • the flexibility of the bearing rings, • the flexibility of fastening bolts on the bearing rings in the structure of the working machines, • the sizes of the contact areas of rolling el ments with raceways, • nominal angle of action of the forces transmi ted through the rolling elements, and its change under load bearings, • the coefficient of adhesion of beads to the raceways, • fill factor parts rolling around the circumf rence of the raceways of the bearing, • clearance of the bearing, • the flexibility of the supp Static load rating of slewing bearings presented in graphs, called characteristics.Generally it is the curve described by the function the maximum value of the tilting moment, imum axial force, and H load (Fig. 3).Component stant value, which is determined by the functions M(Q).Slewing bearings designed and manufactured for specific application requiring knowledge of the design of the device on which the bearing will work, the approximate dimensions of the bearings, the diameters of the bearing rings mounting screws locations, as well as all the types and magnitude of loads that are transmitted through the bearing (Fig. 2).

Calculation of slewing bearings carrying capacity
The load capacity of slewing bearings is determined by different calculation methods.Simple model calculations allow to determine the characteristics of the bearing under the condition of a number of simplifications.The consequence of the applied simplifications is an inaccurate assessment of actual bearing RYNKE M. 2013).Load capacity of slewing bearing is dependent on a number of fac-M., BORKOWSKI S. 2014): the flexibility of the bearing rings, the flexibility of fastening bolts on the bearing rings in the structure of the working machines, the sizes of the contact areas of rolling elements with raceways, nominal angle of action of the forces transmitthrough the rolling elements, and its change under load bearings, the coefficient of adhesion of beads to the fill factor parts rolling around the circumference of the raceways of the bearing, clearance of the bearing, the flexibility of the supporting structures.Static load rating of slewing bearings presented in graphs, called characteristics.Generally it is the curve described by the function M(Q, H), where M denotes the maximum value of the tilting moment, Q, the max-H is the radial component of the .Component H is often accepted as a constant value, which is determined by the functions Source: own study.

Quantitative assessment of the causes of errors in determining the bearing capacity
To determine the risk associated with the determ nation of the bearing capacity of rolling bearings, which are as a result of the simplifications adopted in models of computation, the FMEA method w This method analyzes the causes and consequences of errors.The purpose of this analysis-search for possible

Potential error
The effects of errors of the

the causes of errors in determining the bearing
To determine the risk associated with the determination of the bearing capacity of rolling bearings, which are as a result of the simplifications adopted in models of computation, the FMEA method was used.This method analyzes the causes and consequences of search for possible causes and effects of errors in the design stage and eliminate them before it becomes a finished product.It has also wide application at where there are already failures caused by errors in the implementation of products, that is, in the production process.This method is mainly used in project and research activities and production M. KNOP K. 2016).
In studies the risk was determined by identifying the criteria for selection of coefficients, i.e.: R risk of error, Z -the error value and W of accounting errors in the calculations.A number of priority risk was defined by using d In the FMEA analysis, it is assumed that the causes of the error estimation of the bearing capacity, where the number of priority 1 < RPN < 100, does not require the introduction of protection measures.But if the priority number RPN ≥ 100, you should take pr cautions for reasons arising out of errors in determi ing the bearing capacity.Tab. 1 factors and risks that are there, if not their relative in the calculations of the bearing capacity of rolli ing bearings.
The greatest risks related to incorrect evaluation of the slewing bearing capacity include ignoring susce tibility of bearing supporting structures for machine and bearing clearance.

R Z W RPN
The )/2016 causes and effects of errors in the design stage and eliminate them before it becomes a finished product.It the stage of operation where there are already failures caused by errors in the implementation of products, that is, in the production process.This method is mainly used in project and research activities and production (JAGUSIAK-KOCIK In studies the risk was determined by identifying the criteria for selection of coefficients, i.e.: R -the the error value and W -the difficulty of accounting errors in the calculations.A number of priority risk was defined by using dependencies: In the FMEA analysis, it is assumed that the causes of the error estimation of the bearing capacity, where the number of priority 1 < RPN < 100, does not require the introduction of protection measures.But if ≥ 100, you should take precautions for reasons arising out of errors in determing the bearing capacity.Tab. 1 shows the individual factors and risks that are there, if not their relative in the calculations of the bearing capacity of rolling slew-The greatest risks related to incorrect evaluation of the slewing bearing capacity include ignoring susceptibility of bearing supporting structures for machine Analysis of the causes and consequences of errors in the calculation of the bearing capacity of the slewing bearings.

Construction of numerical models using FEM
In numerical calculations the finite element method to model the bolts with beam elements with pretension In computational models, the balls should be replaced element special which allows, in particular, in accordance with the change in the angle of operation of the parts of rolling due to

Summary
The study analyzes the methods quality of calculating the slewing bearing static load capacity.In relation to the classical methods used currently are considered the main factors that formed the basis of a simplification of the classical methods of calculating the bearing capacity, namely: • the flexibility of the bearing rings, • the flexibility of the bolts securing the ring to the structures it is installed, • deformation and change of contact geometry in the contact zone of rolling elements contact with the raceways of the bearing, • flexibility and deformation of the supporting structure of the working machine caused by the load.In the light of the obtained results, when determining the bearing capacity of slewing bearings, located on load-bearing structures, do not have a corresponding stiffness, it is necessary to consider that flexibility is not only rings, bearings and bolts, as well as exposure to the entire load-bearing system of the working machine.