BB20 is a ball bearing calculation program

• Angular contact ball bearing model, with 2, 3 or 4 contact points
• Quasi-static resolution with inertial effects taken into account
• Lubrication & friction forces
• Modelling of a rigid or flexible cage in quasi-dynamics
• Calculation of the stiffness matrix
• Calculation of power losses
• Balls-rings
• Balls-cage
• Cage-rings
• Windage
• Three resolution level : R1, R2 & R3 (rigid cage or flexible cage)
• Developped at LaMCoS and Mecalam for Safran

System of equations and unknowns (N being the number of balls) :

• Equations :
• Inner ring equilibrium (5 equations)
• Balls equilibrium (2N+4N equations)
• Geometrical equations (6N equations)
• Cage equilibrium (6/6N equations)
• Unknowns :
• Degrees of freedom of the inner ring (5 unknowns)
• Ball-ring contact angles (4N unknowns)
• Hertzian deformations at ball-ring contacts (4N unknowns)
• Axes of self rotation of balls (2N unknowns)
• Effective rolling radius at ball-ring contacts (2N unknowns)
• Degrees of freedom of the cage (6/6N unknowns)

Calculation assumptions :

• Geometry: Angular contact ball bearings with 2, 3 or 4 contact points
• Deformation of components :
• The components of the bearing are rigid bodies with a perfect geometry.
• R3 (flexible cage) : The cage is modelled as an assembly of deformable elements
• Tangential displacement of balls :
• R1, R2 : The cage maintains a constant angular distance between each ball
• R3 (rigid cage or flexible cage) : The balls can move tangentially in the cage
• Interactions with the cage :
• R1, R2 : Interactions with the cage are neglected
• R3 (rigid cage or flexible cage) : Interactions with the cage are taken into account:
• balls-cage : HD/EHD, barrel-plan & short journal bearing
• rings-cage : HD, short journal bearing
• Type of resolution: Quasi-static resolution (R1, R2) or quasi-dynamic resolution (R3 rigid cage or flexible cage) with centrifugal and gyroscopic effects taken into account
• Ball-ring contacts :
• Calculated sliding (elliptical contacts), enhanced Coulomb friction model
• Contacts considered as lubricated Hertzian contacts (Hamrock-Dowson)
• Equilibrium of ball moments :
• R1 : unresolved; balls self rotation angles β’ null & β calculated either by :
• Assumption of control by the outer ring
• Minimisation of the power dissipated at ball-ring contacts
• R2, R3 (rigid cage or flexible cage) : resolved

DYNAR is a cylindrical roller bearing calculation program

• Planar model of cylindrical roller bearings
• Static and dynamic resolution
• Lubrication & friction forces
• Interactions with cage taken into account
• Deformable rings and ability to model faults
• Calculation of power losses
• Rollers-rings (tracks & flanges)
• Rollers-cage (separators & flanges)
• Cage-ringss
• Windage
• Developped at LaMCoS and at Mecalam for Safran

System of equations and unknowns (N being the number of rollers) :

• Equations :
• Inner ring equilibrium (4 équations)
• Rollers equilibrium (3N équations)
• Geometrical equations (1N équations)
• Cage equilibrium (6 équations)
• Unknowns :
• Degrees of freedom and speed of the inner ring (4 unknowns)
• Degrees of freedom and speed of the cage (6 unknowns)
• Degrees of freedom and speed of the rollers (3N unknowns)
• Rollers loading (1N unknowns)

Calculation assumptions :

• Geometry: Cylindrical roller bearings only, 2D problem
• Deformation of components: Rollers are rigid bodies with perfect geometry, rings are deformable.
• Tangential displacement of rollers: The rollers can move tangentially in the cage.
• Interactions with the cage: Interactions with the cage are taken into account.
• rollers-cage : HD/EHD, journal bearing & friction torque
• rings-cage : HD, short journal bearing
• Type of resolution: Static and dynamic resolution
• Rollers equilibrium :
• Unresolved tilt equilibrium, pure radial loading, no misalignment
• Roller-ring contacts considered as lubricated Hertzian contacts (linear contacts, friction forces, resistive torque due to asymmetrical hydrodynamic pressure field)
• Consideration of the roller-flange contact on the side of the roller (lubricated Hertzian point contact)

This simplified model enables a rapid calculation of the overall equilibrium of the bearing and can be efficiently integrated into dynamic models of complete systems.

• Calculation assumptions :
• Geometry : Angular contact ball bearings with 2 contact points
• Deformation of components : The components of the bearing are rigid bodies with a perfect geometry.
• Tangential displacement of balls : The cage maintains a constant angular distance between each ball
• Interactions with the cage : Interactions with the cage are neglected
• Type of resolution: Static resolution, centrifugal and gyroscopic effects are neglected
• Balls-rings contacts :
• Rolling without sliding on ball-ring contacts
• Contacts considered as dry Hertzian contacts
• Objectives :
• Balls loading
• Inner ring displacement relative to outer ring
• Stiffness matrix

This simplified model enables a rapid calculation of the overall equilibrium of the bearing and can be efficiently integrated into dynamic models of complete systems.

• Calculation assumptions :
• Geometry : Tapered and cylindrical roller bearings
• Deformation of components : The components of the bearing are rigid bodies with a perfect geometry.
• Tangential displacement of rollers: The cage maintains a constant angular distance between each roller.
• Interactions with the cage : Interactions with the cage are neglected
• Type of resolution: Static resolution, centrifugal and gyroscopic effects are neglected
• Rollers equilibrium :
• The rollers are cut into slices along their length, and the contact of each slice with the rings is considered to be independent (dry linear Hertzian contacts), making it possible to solve roller equilibrium when tilting.
• Possible consideration of roller-inner ring flange contact on the side of the roller (dry Hertzian point contact)
• Objectives :
• Rollers loading
• Inner ring displacement relative to outer ring
• Stiffness matrix