A 75 mm diameter, 15 mm wide A80-M12V grinding wheel is used for traverse surface grinding of a 75 mm by 75 mm 1040 steel workpi
ece. The workpiece traverse speed is 1 mm/sec, the radial depth of grind is 1.5 mm, the (axial) intermittent cross-feed is 10 mm/stroke, and the wheel surface speed is 314 mm/sec. Estimate the required amount of grinding time (without spark-out) and the spindle power.
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Answer:
the angle of twist of B with respect to D is -1.15°
the angle of twist of C with respect to D is 1.15°
Explanation:
The missing diagram that is supposed to be added to this image is attached in the file below.
From the given information:
The shaft is made of A992 steel. It has a diameter of 1 in and is supported by bearing at A and D.
For the Modulus of Rigidity G = 11 × 10³ Ksi = 11 × 10⁶ lb/in²
The objective are :
1) To determine the angle of twist of B with respect to D
Considering the Polar moment of Inertia at the shaft
shaft =
where ;
r = 1 in /2
r = 0.5 in
shaft =
shaft = 0.098218
Now; the angle of twist at B with respect to D is calculated by using the expression
where;
are the torques at segments CD and length at segments CD
are the torques at segments BC and length at segments BC
Also ; from the diagram; the following values where obtained:
= 2.5 in
= 0.098218
G = 11 × 10⁶ lb/in²
= -60 lb.ft
= 0 lb.ft
= 5.5 in
− 0.02 rad
To degree; we have
Since we have a negative sign; that typically illustrates that the angle of twist is in an anti- clockwise direction
Thus; the angle of twist of B with respect to D is 1.15°
(2) Determine the angle of twist of C with respect to D.Answer unit: degree or radians, two decimal places
For the angle of twist of C with respect to D; we have:
0.02 rad
To degree; we have
