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Forum index » Science and Technology » Engineering » Mechanics
Angle Calculation
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seanlisa@bigpond.net.au
science forum beginner


Joined: 14 Jun 2006
Posts: 1

PostPosted: Wed Jun 14, 2006 5:07 am    Post subject: Angle Calculation Reply with quote

I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
Anyone info would be much appreciated as I can not calculate this by
myself.
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eromlignod
science forum addict


Joined: 02 May 2005
Posts: 68

PostPosted: Wed Jun 14, 2006 2:15 pm    Post subject: Re: Angle Calculation Reply with quote

seanlisa@bigpond.net.au wrote:
Quote:
I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
Anyone info would be much appreciated as I can not calculate this by
myself.


We'll need to know what material the chocks are made from. Are they
steel on steel?

Don
Kansas City
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Jeff Finlayson
science forum Guru Wannabe


Joined: 02 May 2005
Posts: 142

PostPosted: Wed Jun 14, 2006 2:33 pm    Post subject: Re: Angle Calculation Reply with quote

seanlisa wrote:

Quote:
I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).

Anyone info would be much appreciated as I can not calculate this by
myself.

The wedges run the long dimension (400 mm) of the choke or the
short dimension?

Unless the blocks are lubed somehow, a low number for the
coef. of friction should be 0.1. That's for steel on steel.
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eromlignod
science forum addict


Joined: 02 May 2005
Posts: 68

PostPosted: Wed Jun 14, 2006 3:47 pm    Post subject: Re: Angle Calculation Reply with quote

Jeff Finlayson wrote:
Quote:
seanlisa wrote:

I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).

Anyone info would be much appreciated as I can not calculate this by
myself.

The wedges run the long dimension (400 mm) of the choke or the
short dimension?

Unless the blocks are lubed somehow, a low number for the
coef. of friction should be 0.1. That's for steel on steel.


It does not matter which direction the wedge runs, nor do the linear
dimensions matter at all. Friction is independent of surface area and
only depends on the coefficient of friction between the two surfaces
and the normal force applied.

In fact, in this case only the angle matters, independent of the
weight. If you do a free body diagram, the normal force on the wedge
is

N = w * cos A

where A is the wedge angle and w is the weight applied. The force
along the slope is

F = w * sin A

The resisting friction force f is

f = u * N = u * w * cos A

where u is the static coefficient of friction. The point at which the
wedge breaks free is when F > f, so

w * sin A > u * w * cos A

The weight w cancels out and we're left with

u < tan A

So the tangent of the wedge angle must be less than the coefficient of
friction to prevent sliding.

For clean steel on steel, u = 0.8 approximately and the critical angle
is

A = arctan (0.Cool = 38.7 deg.

But this is the critical point where the wedge comes loose. To be safe
we must have a smaller angle. Really, to be sure that the chock
doesn't slide even if it suffers a shock and breaks the static
friction, we should use the coefficient of kinetic friction, so that it
still can't slide.

So, u = .4 and A = 21.8 deg maximum.

If the wedge is in an oily environment, then u = .03 (kinetic) and

A = 1.72 deg. max., even if oiled.

Don
Kansas City
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Jeff Finlayson
science forum Guru Wannabe


Joined: 02 May 2005
Posts: 142

PostPosted: Wed Jun 14, 2006 5:07 pm    Post subject: Re: Angle Calculation Reply with quote

eromlignod wrote:
Quote:
Jeff Finlayson wrote:
seanlisa wrote:

I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).

Anyone info would be much appreciated as I can not calculate this by
myself.

The wedges run the long dimension (400 mm) of the choke or the
short dimension?

Unless the blocks are lubed somehow, a low number for the
coef. of friction should be 0.1. That's for steel on steel.

It does not matter which direction the wedge runs, nor do the linear
dimensions matter at all. Friction is independent of surface area and
only depends on the coefficient of friction between the two surfaces
and the normal force applied.

In fact, in this case only the angle matters, independent of the
weight. If you do a free body diagram, the normal force on the wedge
is

Yes it does! You need to know which length to use to go with the
height to determine the angle (or determine the height from the angle).

Quote:
N = w * cos A

where A is the wedge angle and w is the weight applied. The force
along the slope is

F = w * sin A

The resisting friction force f is

f = u * N = u * w * cos A

where u is the static coefficient of friction. The point at which the
wedge breaks free is when F > f, so

w * sin A > u * w * cos A

The weight w cancels out and we're left with

u < tan A

So the tangent of the wedge angle must be less than the coefficient of
friction to prevent sliding.

For clean steel on steel, u = 0.8 approximately and the critical angle
is

A = arctan (0.Cool = 38.7 deg.

But this is the critical point where the wedge comes loose. To be safe
we must have a smaller angle. Really, to be sure that the chock
doesn't slide even if it suffers a shock and breaks the static
friction, we should use the coefficient of kinetic friction, so that it
still can't slide.

So, u = .4 and A = 21.8 deg maximum.

If the wedge is in an oily environment, then u = .03 (kinetic) and

A = 1.72 deg. max., even if oiled.

Don
Kansas City
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eromlignod
science forum addict


Joined: 02 May 2005
Posts: 68

PostPosted: Wed Jun 14, 2006 6:04 pm    Post subject: Re: Angle Calculation Reply with quote

Jeff Finlayson wrote:
Quote:
Yes it does! You need to know which length to use to go with the
height to determine the angle (or determine the height from the angle).


He asked for the angle. You don't need any size dimensions to
determine the slip angle. When he machines the wedges he will set the
angle on his mill in degrees. The angle can go in either
direction...or even at a rotated gradient. The length and height of
the block are immaterial.

Don
Kansas City
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Jeff Finlayson
science forum Guru Wannabe


Joined: 02 May 2005
Posts: 142

PostPosted: Wed Jun 14, 2006 7:28 pm    Post subject: Re: Angle Calculation Reply with quote

eromlignod wrote:
Quote:
Jeff Finlayson wrote:

I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
....


Quote:
Yes it does. You need to know which length to use to go with the
height to determine the angle (or determine the height from the angle).

He asked for the angle. You don't need any size dimensions to
determine the slip angle. When he machines the wedges he will set the
angle on his mill in degrees. The angle can go in either
direction...or even at a rotated gradient. The length and height of
the block are immaterial.

That's all fine. But the design envelop was given. The choke's
max angle is 8.88-14 deg depending on which length dimension is used.
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Brian Whatcott
science forum Guru Wannabe


Joined: 09 May 2005
Posts: 267

PostPosted: Thu Jun 15, 2006 3:51 am    Post subject: Re: Angle Calculation Reply with quote

On 13 Jun 2006 22:07:13 -0700, seanlisa@bigpond.net.au wrote:

Quote:
I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
Anyone info would be much appreciated as I can not calculate this by
myself.

I liked Don's response, though it must be said he cast his net wide.

I have been chided in the past for offering an angle of 15 degrees as
providing non-loosening grip, from such things as taper pins.
People have mentioned more conservative values, less than 3 degrees if
I recall - but it stuck with me that someone offered the cautionary
note that no taper at all can be considered proof against vibration -
which can move the adjacent surfaces.

Brian Whatcott Altus OK
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Nude
science forum beginner


Joined: 15 Jun 2006
Posts: 2

PostPosted: Thu Jun 15, 2006 7:38 am    Post subject: Re: Angle Calculation Reply with quote

Yes they will be steel on steel with a machined finish

eromlignod wrote:
Quote:
seanlisa@bigpond.net.au wrote:
I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
Anyone info would be much appreciated as I can not calculate this by
myself.


We'll need to know what material the chocks are made from. Are they
steel on steel?

Don
Kansas City
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Nude
science forum beginner


Joined: 15 Jun 2006
Posts: 2

PostPosted: Thu Jun 15, 2006 7:44 am    Post subject: Re: Angle Calculation Reply with quote

The wedges run along the 400mm length


Jeff Finlayson wrote:
Quote:
seanlisa wrote:

I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).

Anyone info would be much appreciated as I can not calculate this by
myself.

The wedges run the long dimension (400 mm) of the choke or the
short dimension?

Unless the blocks are lubed somehow, a low number for the
coef. of friction should be 0.1. That's for steel on steel.
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hob
science forum addict


Joined: 03 Aug 2005
Posts: 50

PostPosted: Fri Jun 16, 2006 3:09 am    Post subject: Re: Angle Calculation Reply with quote

<seanlisa@bigpond.net.au> wrote in message
news:1150261633.354002.262320@y43g2000cwc.googlegroups.com...
Quote:
I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
Anyone info would be much appreciated as I can not calculate this by
myself.


rule of thumb for brakes and gears is self-engagement (no slip) at less than
3 degrees.

Mark's Handbook has details on it - brakes section.

>
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Jeff Finlayson
science forum Guru Wannabe


Joined: 02 May 2005
Posts: 142

PostPosted: Fri Jun 16, 2006 3:26 pm    Post subject: Re: Angle Calculation Reply with quote

Jeff Finlayson wrote:
Quote:
eromlignod wrote:
Jeff Finlayson wrote:

I need help in determining the angle at which slippage will not occur
at between two tapered wedges that make up an adjustable chock that
will sit under a machine. Each chock is 400 x 250mm. The height
need to
be 62.5+/-5mm. Each chock will be carrying 48T(metric).
....

Yes it does. You need to know which length to use to go with the
height to determine the angle (or determine the height from the angle).

He asked for the angle. You don't need any size dimensions to
determine the slip angle. When he machines the wedges he will set the
angle on his mill in degrees. The angle can go in either
direction...or even at a rotated gradient. The length and height of
the block are immaterial.

That's all fine. But the design envelop was given. The choke's
max angle is 8.88-14 deg depending on which length dimension is used.

That's based on 2 triangular wedges. Tapered pentagonal wedges
will yield a wider range of angles.
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