MNF1_HW002 Homework 2

	סטודנט א’	סטודנט ב’
שם	עידו פנג בנטוב	ניר קרל
ת”ז	CLASSIFIED	CLASSIFIED
דואר אלקטרוני	CLASSIFIED	CLASSIFIED

Question 1

Part a

We know that the maximum cutting speed is given by:

Therefore the rotational speed is .
Substituting the given maximum allowed cutting speed, and its appropriate diameter of the workpiece, we get the following rotational speed:

Part b

For the minimal diameter, , and the same cutting speed , the rotational speed would need to be:

Therefore, the machine needs to allow rotational speeds in the following range:

By allowing the rotational speed to vary, we get shorter cutting time:

Part c

From the drawings, we can see that the required surface finish is .
We also know that:

Substituting and , we get:

Part d

The power required is given by:

In both cases, the maximal power would be when is the largest. Substituting given parameters:

If varies, the power stays constant in this value for the whole process. If stays constant, the cutting speed is at its maximum only in the beginning, meaning that the calculated power is true only for that time period.

Part e

The cutting is given by:

In the more general case:

If is constant:

If varies ( is constant):

Therefore:

Question 2

Part a

The angle between each tooth is:

Part b

Definition of - the total arc angle that the tooth is in the material

Some trigonometry:

Geometry of the problem

From the figure above, we can see that:

Part c

The number of teeth is given by:

Part d

The cutting force is per tooth is given by:

Since there are 3 teeth in the material at any given time, we know that the total force would be

as long as the angles are bounded by:

or, in short:

The angle of each tooth in the material

We can see that the maximum will be at . Substituting the given parameters, we get:

Part e

We can see that the minimum will be at . Substituting the given parameters, we get:

Part f

The average force is given by:

Therefore:

Part g

The average power would be:

Therefore:

Part h

The total milling time (if ) is given by:

Therefore: