search.noResults

search.searching

saml.title
dataCollection.invalidEmail
note.createNoteMessage

search.noResults

search.searching

orderForm.title

orderForm.productCode
orderForm.description
orderForm.quantity
orderForm.itemPrice
orderForm.price
orderForm.totalPrice
orderForm.deliveryDetails.billingAddress
orderForm.deliveryDetails.deliveryAddress
orderForm.noItems
MOTORS, DRIVES & CONTROLS


BEARING FACTORS


DESIGN


Markus Raabe discusses the issues that influence shaft and bearing stiffness


eople often ask about stiffness values of bearings or shafts and it is not really clear what information they actually need. Te stiffness can be used for the calculation of critical speeds or natural frequencies or for the assessment of machine tools, which should only show little deformations under load. Bearing catalogues sometimes provide


P


values for axial and radial stiffness, but these are only values for one load direction without any information on the mounting state and without cross coupling between axial and radial deformation. If diagrams are shown the stiffness rises with the load. Fig. 1 shows the radial stiffness of a 7210 angular contact ball bearing with axial preload of 500N under increasing radial load. Does the stiffness increase with load? Why are there three curves and not only one?


What is a stiffness? To calculate stiffness, frequently force over deflection is used, but this is only correct for linear and for one-dimensional systems. More accurately the variation of force over variation of deflection ∆F/∆u (Difference quotient) or ∂F/∂u (partial derivative) should be used. Te result for a bearing with five position parameters (three displacements and two angles) and F(ux, uy, uz, ry, rz) a 5x5 stiffness matrix is shown in Table 1.


Te compliance is the variation of


deflection over variation of force ∆u/∆F (Difference quotient) or ∂u/∂F (partial derivative) and for a bearing with u(Fx, Fy, Fz, My, Mz) a 5x5 compliance matrix can be derived, as shown in Table 2.


48 www.engineerlive.com


FIG 1. Stiffness for a 7210 angular contact ball bearing with 15° contact angle and 500N axial preload


TABLE 1


Fx [N] Fy [N] Fz [N]


My [Nm] Mz [Nm]


TABLE 2 Fx [N]


ux [µm] uy [µm] uz [µm]


ry [mrad] rz [mrad]


0.01426 0 0 0 0


Fy [N] 0


0.081688 0 0


0.00763


Fz [N] 0 0


0.081688 -0.00763 0


My [Nm] 0 0


-7.624 0.7525 0


Mz [Nm] 0


7.624 0 0


0.7525


ux [μm] 41.112 0 0 0 0


uy [μm] 0


232.547 0 0


-2.360


uz [μm] 0 0


232.547 2.360 0


ry [mrad] 0 0


2356.015 25.242 0


rz [mrad] 0


-2356.015 0 0


25.242 Better modelling


results in better end products


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52