A presentation by mayank mishra on mechanics of forming process

1. Introduction to force
equilibrium method
A presentation by Mayank Mishra on Mechanics of forming process

2.  Types of Forming process and its mechanism
 Rolling
 Forging
 Drawing
 Deep drawing
 Bending
 Extrusion
Why we want to find and analyse forces applied
• A definite geometry can be produced
• Extent of Change in properties of material can be found
• It will make process economical as we are not going to apply more
than required force

3. Rolling

4. Mechanics of rolling operations
Here our goal is to find out
 The roll separating force
 Torque and power required to drive the belt
 Power losses in bearings
 For calculations of all these factors we make few assumptions
 The rolls are straight and rigid cylinder
 The width of strip is much larger then its thickness and no significant
widening takes place
 Coefficient of friction is low and constant
 Yield stress of material remains constant

6. 𝑝
2𝑘
=
2𝑦
𝑡
1 −
𝜎
2𝑘
ⅇ^µ(𝜆𝑗 − 𝜆)
𝑝
2𝑘
=
2𝑦
𝑡
1 −
𝜎
2𝑘
ⅇ^(µ𝜆)

8. Roll separating force
Drive torque and power

9. Forging
 Forging assumptions
 Forging F attains its maximum value at the end of operation
 Coefficient of friction remains constant
 Thickness of workpiece is small as compared to other dimensions
 The entire workpiece is in plastic state during the process

10. Total forging force per unit length of workpiece
𝐹 = 2
0
𝑥
𝑝1 𝑑𝑥 +
𝑥
𝑙
𝑃2 𝑑𝑥
 Forging of rectangular billet

11. Forging of disk

12. Drawing
Assumptions
 The coefficient of friction 𝜇 and half angle 𝛼 are same
 The yield stress 𝜎 𝑦 is constant
 −𝑝 & 𝜎 𝑥 are the principal stress
 𝜎 𝑥 doesn’t vary in radial direction

13. 𝐷 = 1 − (𝑑𝑖/𝑑 𝑓)2
∈= log 1 − 𝑑 −1
 Drawing of a cylindrical
rod
 Determination of drawing force and power
𝐹 = 𝜎 𝑥𝑓 𝐴 𝑓
𝑃 = 𝐹𝑉

14. Deep drawing

15. Objective of our analysis
 To correlate the initial and final dimension of job
 To estimate the drawing force F
𝐹 = 𝜎𝑧2𝜋𝑟𝑝 𝑡
𝜎𝑟
2𝑘
=
𝜇𝐹ℎ
2𝜋𝑡𝐾𝑟𝑗
+ log
𝑟𝑗
𝑟
At r=𝑟𝑑
𝜎𝑟
2𝑘
=
𝜇𝐹ℎ
2𝜋𝑡𝐾𝑟𝑗
+ log
𝑟𝑗
𝑟𝑑

16. Bending
In bending operations apart from determination of work load, an estimated
amount of elastic recovery is there So when final shape is prescribed a suitable
amount of overbending is required to take care of this spring back

17.  Details in bending
𝐹 𝑚𝑎𝑥 =
𝑀
𝐿
1 + cos tan−1 𝜇 + 𝜇 sin tan−1 𝜇

18. Extrusion
It is similar to drawing but here along with tensile
load at exit end a compressive load is also applied at
inlet

19.  Determination of work load from stress analysis
Frictional load during
extrusion
𝐹 =
𝜋
4
𝑑𝑖
2
𝜎𝑥𝐵𝐵 +
𝑑𝑖
3
𝑑𝑖 𝑙𝜎 𝑦