Machining time and power estimation

MACHINING TIME AND POWER ESTIMATION

Machining time depends on the various process parameters such as workpiece material, tool material, cutting speed, feed, depth of cut etc. and hence, it is necessary to select the proper process parameters in right combination for optimum process conditions. Various process parameters useful in estimation of machining time and power are given as follows:

(a) Cutting speed (V):

Cutting speed in lathe refers to the number of metres measured on the circumference of a rotating job that passes the cutting edge of the tool in one minute. It is the surface speed of the workpiece. The length of the chip removed per minute is its measure.

where

D = Diameter of the workpiece in mm

N = Speed of rotation of the workpiece in rpm.

There are recommended specific 'average cutting speed’ for performing various machining operations on different materials using a tool made of a particular material. The cutting speed will be different for different operations. Maintaining correct cutting speed increases the tool life to the maximum.

(b) Feed (f):

Feed is the amount of advancement of tool parallel to the surface being machined per revolution of the job. It is usually given in mm/rev of the job. The amount of feed depends on the surface finish required, depth of cut and the rigidity of the machine tool. Feed may be calculated using the following formula.

where L = length of travel of the tool per pass, mm

N = speed of rotation of workpiece in rpm

Tm = cutting/machining time, min

(c) Depth of cut (d):

The depth of cut is the advancement of the tool in the job in a direction perpendicular to the surface being machined. It may be expressed as the thickness of the chip of metal removed by the tool in one cut in mm. The depth of cut depends on the amount of metal to be removed, tool material and power and rigidity of machine tool. It can be calculated using the following formula.

where D1 = Initial diameter of the workpiece.

D2 - Final diameter of the workpiece after machined.

1. Metal Removal Rate (MRR)

The metal removal rate is the volume of material removed per unit time. The volume of metal removed is a function of speed, feed and depth of cut. As the higher values of these parameters are, the higher will be the metal removal rate.

Metal removed / rev. = Volume of chip having length π D1 × Uncut chip area (Ac)

Hence volume of metal removed/rev., = π . D1 . Ac mm3

Then,

MRR = π. D1. Ac. N mm3/min

MRR = 1000 Ac. V mm3/min

The uncut chip area can be calculated as follows:

Uncut chip area, Ac = Width of chip (b) × Thickness of uncut chip (t).

= Feed (ƒ) × Depth of cut (d)

Therefore,

MRR = 1000 f d V in mm3/min

2. Estimation of Machining Time (Tm)

Machining time is the time required for turning one pass on the metal.

where L = length of travel of the tool per pass.

For turning operation,

L = Length of machining surface + Length of Tool approach + Length of tool over travel

where

D1 = Initial diameter of the workpiece.

D2 = Final diameter of the workpiece after machined.

Material removed per cut = Depth of cut (d)

Total machining time, Ttotal = Tm × n

3. Estimation of Power

Power is the product of cutting force and velocity. In machining process, the force component is the force in the direction of cutting speed. Force in the direction of feed and depth are too small when compared to force in the direction of cutting speed. So, these two are negligible.

Force involved in orthogonal cutting is the force component in the direction of cutting speed. Example: Turning, facing, parting-off operations etc.

So, the power required, P = Cutting force (Fc) × Velocity of cutting or cutting speed (V)

P = Fc × V

Power required depends on the cutting force which is calculated by using the following equation.

Cutting force,

Fc = K × d × f

where K is a constant depending upon the workpiece material.

⸫ Power required, P = K × d × f × V

Due to shear and friction, the total power is divided into components. They are as follows.

1. Power due to shear

2. Power due to friction

So,

Total power = Power due to shear + Power due to friction

P = Ps + Pƒ

⸫ Fc × V = Fs × Vs + Fƒ × Vƒ 

where

Fs = Shear force

Vs = Velocity of shear

Ff = Friction force.

Vf = Velocity due to friction

In oblique cutting, the resultant cutting force is calculated by considering the forces acting in three directions. Example: Milling, drilling, grinding operations etc.,

where

Fx = Force acting on X-X direction

Fy = Force acting on Y-Y direction

Fz = Force acting on Z-Z direction.