Design of Slideways for Stiffness

Stiffness is one of the significant parameters for designing slideways. The design of slideways for stiffness needs that the deflection of the cutting edge because of contact deformation of the slideway should not exceed specific permissible value. This value is specified from considerations of needed machining accuracy. For instance, in lathe machine, the vertical deflection of the tool or its horizontal deflection in the direction of feed motion has little influence on the dimensional accuracy of the machined workpiece. Though, diametrical error of 2 C occurs because of a deflection of the cutting edge by C in the radial direction. Therefore the lathe slideways are designed for stiffness along with a view to restrict their radial deflection. The suitable direction for stiffness design in several machine tools can be selected in each specific case from the above mentioned principle. In a bed using two flat slideways as displayed in diagram, the radial deflection occurs because of the contact deformation C_B of the vertical face of the slideway and rotation of the saddle because of unequal contact deformation C_A and C_C of the horizontal flat faces.

Therefore radial deflection is expressed by

((C_A - C_B) / C_C)). h

Therefore total radial deflection is given by

Equation

C_FF = ((C_B + C_A - C_C) / b.) h   

In the lathe bed by using a combination of flat and V slideways, the contact deformation of the flat slideways is displayed by lowering C_C. The faces of the V-slideways suffer a deformation of C_A and C_B. This results in:

(1) Vertical lowering of the V-slideway by

C_v = C_B sin λ+ C_A cos λ

(2) Horizontal displacement of the apex of the V-slideway by

C_h = C_B cos λ- C_A sin

This type of nature of deformation of flat and V-slideways results in:

(1) Radial deflection of the cutting edge by C_H and

(2) Rotation of the saddle because of unequal vertical lowering of the flat and V slideways that leads to radial deflection of the cutting edge by

((C_v - C_c) / b)) . h

After that the total radial deflection becomes

Equation

C_Fv = (C_h + (C_v-C_c) / b). h

The contact deformation is assumed proportional to the average pressure for the purpose of stiffness design. Coefficient of proportionality d is termed as contact compliance. This coefficient has to be determined for each pair of slideway materials. Though for approximate calculations, an average value of d = 1 × 10^{- 6} mm²/N may be utilized.

Eq. (24) and (25) can be rewritten as follows:

Equation

C_FF = d P_B + d (P_A - P_c /b) .h

Equation

C_Fv = d(P_B cos λ - P_A sin λ) +dh/b (P_B sin λ + P_A cos λ - P_c)

Later than calculating the total radial deflection of the cutting edge, the design for stiffness is performed in accordance with C_i = C_ip.