Deflection of Spindle Axis due to Compliance of Spindle Supports Assignment Help

Design of Spindle - Deflection of Spindle Axis due to Compliance of Spindle Supports

Deflection of Spindle Axis due to Compliance of Spindle Supports

Let δE and δG present the displacement of the rear and front support respectively. Owing to compliance support, the spindle deflects are displayed in figure. From similarity of triangles OHH' and OGG'.

Equation

d2 / m + x = δG / x

 ∴ d2 = (1 + (m / x)) δG

1880_Deflection of Spindle Axis due to Compliance of Spindle Supports 1.png

Figure: Deflection of the Spindle due to Compliance of Support

From similarity of triangles OEE' and OGG', we acquire

δG / x = δE / (a - x)

x = aδG / (δE + δG)

On substituting these values of x in Equation, d2 changes to,

Equation

d2 = (1+ (m/a)) δG + δE (m /a)

Therefore it is clear from above equation that displacement δG of the front bearing has greater affect on deflection d2 of spindle nose than displacement δE of the rear bearing.

Displacement  δE =   RE /SE

And δG = RG / SG                   

In which RE and RG are the support reactions at E and G correspondingly.

SE and SG are stiffness at E and G respectively.

At equilibrium,

∑M E = 0

∴ RG a - F2 k + M r - F1 (m + a) = 0

∴ R G = F2 k - M r + F1 (m + a) / a

Similarly          ∑ M G = 0

∴ RE a - F2 b - M r + F1 m = 0

∴ RE = (F2 b + M r - F1 m) /a

Equation

1396_Deflection of Spindle Axis due to Compliance of Spindle Supports 2.png

Therefore total deflection d (displayed in below diagram) is obtained as

d = d1 + d2

1407_Deflection of Spindle Axis due to Compliance of Spindle Supports 3.png

Figure: Total Deflection of Spindle Axis


Expertsmind’s world class education services

We at www.expertsmind.com offer email based assignment help – homework help and projects assistance from k-12 academic level to college and university level and management and engineering studies. Our experts are helping students in their studies and they offer instant tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.

- Quality assignment help assistance 24x7 hrs
- Best qualified tutor’s network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work