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A 25 mm round bar (cylindrical) rests in a Vee-Groove and has a clearance of 10 mm from the circumference of the bar to a flat at the bottom of the groove.
If a 26 mm bar is placed in the groove instead, what will be the clearance distance to the flat?.
The Vee-Groove is not vee-ed out to a sharp point but has a flat at the bottom of the Vee-Groove.
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Round Bar in V-Groove
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Re: Round Bar in V-Groove
by Guest » Fri Mar 21, 2014 4:27 pm
Sorry...omission above:-
The angle of the Vee_Groove is 30 degrees
The angle of the Vee_Groove is 30 degrees
- Guest
Re: Round Bar in V-Groove
by Guest » Fri Apr 04, 2014 5:48 am
Can somebody help do this question......??
- Guest
- Guest
Re: Round Bar in V-Groove
by Guest » Thu Apr 17, 2014 5:13 am
I'm assuming the V-groove is symmetrical and when the slanted sides are extended they meet at a point at an angle of 30 degrees.
Draw a diagram of the cross-section. You should have a circle, whose origin we'll label O, and whose radius just touches the slanted sides of the V-groove at points we'll label A and B. If you draw the radius OA you should find the angle between OA and the slanted side is 90 degrees (because the slanted side is tangent to the circle). Draw in both OA and OB and extend the slanted sides so they meet at a point which we'll label X (angle AXB should be 30 degrees). Now draw the line OX, this creates two congruent right angle triangles OAX and OBX. Because they are congruent we know the angle OXA is 15 degrees. This means the length of OX = r/sin 15 where r = radius of the circle (or equivalently OA). The length of OX could also be expressed as r+c+d where c = clearance of the bar to the flat bottom of the groove, and d = distance of flat bottom to X.
This means
r+c+d = r/sin 15
The question gives you r and c for a bar which allows you to work out d. Then using d and a new r for a second bar you can work out the new c.
Hope this helped,
R. Baber.
Draw a diagram of the cross-section. You should have a circle, whose origin we'll label O, and whose radius just touches the slanted sides of the V-groove at points we'll label A and B. If you draw the radius OA you should find the angle between OA and the slanted side is 90 degrees (because the slanted side is tangent to the circle). Draw in both OA and OB and extend the slanted sides so they meet at a point which we'll label X (angle AXB should be 30 degrees). Now draw the line OX, this creates two congruent right angle triangles OAX and OBX. Because they are congruent we know the angle OXA is 15 degrees. This means the length of OX = r/sin 15 where r = radius of the circle (or equivalently OA). The length of OX could also be expressed as r+c+d where c = clearance of the bar to the flat bottom of the groove, and d = distance of flat bottom to X.
This means
r+c+d = r/sin 15
The question gives you r and c for a bar which allows you to work out d. Then using d and a new r for a second bar you can work out the new c.
Hope this helped,
R. Baber.
- Guest
Re: Round Bar in V-Groove
by Guest » Thu Apr 17, 2014 3:40 pm
Thanks, good reasoning....
O= centre on the bar
X= point of Vee
OX1 = 12.5/Sin15
OX2 = 13.0/sin15
OX2 - OX1 = 0.5/sin15
OX2 - OX1 = 1.932 so centre of 26mm bar is 1.932 further from X than the 25 mm bar centre was.
But diameter of 26 mm bar is 0.5 mm bigger
Net clearance difference is 1.932 - 0.5 = 1.432 mm
So new clearance is 11.432 mm
Does that sound reasonable......
O= centre on the bar
X= point of Vee
OX1 = 12.5/Sin15
OX2 = 13.0/sin15
OX2 - OX1 = 0.5/sin15
OX2 - OX1 = 1.932 so centre of 26mm bar is 1.932 further from X than the 25 mm bar centre was.
But diameter of 26 mm bar is 0.5 mm bigger
Net clearance difference is 1.932 - 0.5 = 1.432 mm
So new clearance is 11.432 mm
Does that sound reasonable......
- Guest
Re: Round Bar in V-Groove
by Guest » Thu Apr 17, 2014 9:10 pm
....error in last post.......But diameter of 26 mm bar is 0.5 mm bigger......
....... I meant.....But radius of 26 mm bar is 0.5 mm bigger
..........................
....... I meant.....But radius of 26 mm bar is 0.5 mm bigger
..........................
- Guest
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