Answer:
r=0.31
Ф=18.03°
Explanation:
Given that
Diameter of bar before cutting = 75 mm
Diameter of bar after cutting = 73 mm
Mean diameter of bar d= (75+73)/2=74 mm
Mean length of uncut chip = πd
Mean length of uncut chip = π x 74 =232.45 mm
So cutting ratio r
r=0.31
So the cutting ratio is 0.31.
As we know that shear angle given as
Now by putting the values
\
Ф=18.03°
So the shear angle is 18.03°.
Explanation:
There are two ways to find out the equivalent impulse response of the system.
1. Convolution in time domain
2. Simple multiplication in Laplace domain
2nd method is efficient, easy and is less time consuming.
Step 1: Take the Laplace transform of the given three impulse response functions to convert time domain signals into s-domain
Step 2: Once we get signals in s-domain, multiply them algebraically to get the equivalent s-domain response.
Step 3: Take inverse Laplace transform of the equivalent impulse response to convert from s-domain into time domain.
Solution using Matlab:
Step 1: Take Laplace Transform
Ys1 = 1/(s + 1)
Ys2 = 1/s - exp(-s/2)/s
Ys3 = exp(-3*s)
Step 2: Multiplication in s-domain
Y = (exp(-(7*s)/2)*(exp(s/2) - 1))/(s*(s + 1))
Step 3: Inverse Laplace Transform (Final Solution in Time Domain)
h = heaviside(t - 7/2)*(exp(7/2 - t) - 1) - heaviside(t - 3)*(exp(3 - t) - 1)
