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Problem with a fan controling by the inverter ;/
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Jerry Avins
science forum Guru


Joined: 03 May 2005
Posts: 534

PostPosted: Mon Jun 26, 2006 7:04 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Micha³ wrote:
Quote:
Hi!
I've got, I believe, an easy problem that I can't solve ;/ My
situation look like this: an air flow through the fan is controlled now
by the guide ring. A fan works in its normal rotation, pressure and
flow. I need to change control by the guide ring on inverter connected
with the fan. And here appear my first problem. When I use an inverter,
I'll be able to change a rotation then I'll decrease pressure to the
level that I have already (when I have a guide ring open to the 20-30%).
And then I'll decrease also a flow - and this is my unfavorable
situation, because I can't change an air flow. It must be constant.
So - how to solve it? How to control (by the inverter) a fan to get
a stable flow and less than normal pressure? It is possibile?

I once lent a colleague a power supply that had both an adjustable
output voltage and an adjustable current limit. He connected it to a
fixed resister, and concluded from his inability to adjust voltage and
current independently that the power supply was defective.

He was a physicist, not an engineer, but it I was nevertheless surprised
that it took 15 minutes of equations and graphs on the blackboard to
show him why the supply necessarily behaved as it did.

Where is the pressure measured? Flow? Once you leave the fan chamber,
the relation between pressure and flow depends only on down-stream
conditions.

Jerry
--
Engineering is the art of making what you want from things you can get.
???????????????????????????????????????????????????????????????????????
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Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Mon Jun 26, 2006 7:51 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Jerry Avins wrote:
Quote:
Micha³ wrote:

Hi!
I've got, I believe, an easy problem that I can't solve ;/ My
situation look like this: an air flow through the fan is controlled
now by the guide ring. A fan works in its normal rotation, pressure
and flow. I need to change control by the guide ring on inverter
connected with the fan. And here appear my first problem. When I use
an inverter, I'll be able to change a rotation then I'll decrease
pressure to the level that I have already (when I have a guide ring
open to the 20-30%). And then I'll decrease also a flow - and this is
my unfavorable situation, because I can't change an air flow. It must
be constant.
So - how to solve it? How to control (by the inverter) a fan to
get a stable flow and less than normal pressure? It is possibile?


I once lent a colleague a power supply that had both an adjustable
output voltage and an adjustable current limit. He connected it to a
fixed resister, and concluded from his inability to adjust voltage and
current independently that the power supply was defective.

He was a physicist, not an engineer, but it I was nevertheless surprised
that it took 15 minutes of equations and graphs on the blackboard to
show him why the supply necessarily behaved as it did.

Where is the pressure measured? Flow? Once you leave the fan chamber,
the relation between pressure and flow depends only on down-stream
conditions.

Jerry

Perhaps he was a _theoretical_ physicist?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Mon Jun 26, 2006 8:29 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Jerry Avins w liscie z dnia 2006-06-26 21:04
napisala nastepujace slowa:

(...)
Quote:

Where is the pressure measured? Flow? Once you leave the fan chamber,
the relation between pressure and flow depends only on down-stream
conditions.

I measure only pressure after the fan...

Hmm.. I read your text about a physicist.. And.. And I see some
connection to my problem but.. but it's very far :P

I need to keep constant flow.. I control a fan speed.. And I need to
keep a pressure about 20-30% of the nominal pressure fan. I know from
the characteristic of the fan that it isn't possible. But.. Maybe you
have an idea how to change some part of the system to reach this parameters?

--
Best regards,
Michal
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Jerry Avins
science forum Guru


Joined: 03 May 2005
Posts: 534

PostPosted: Mon Jun 26, 2006 9:21 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Micha³ wrote:
Quote:
Osoba nazywajaca sie Jerry Avins w liscie z dnia 2006-06-26 21:04
napisala nastepujace slowa:

(...)

Where is the pressure measured? Flow? Once you leave the fan chamber,
the relation between pressure and flow depends only on down-stream
conditions.

I measure only pressure after the fan...

Hmm.. I read your text about a physicist.. And.. And I see some
connection to my problem but.. but it's very far :P

I need to keep constant flow.. I control a fan speed.. And I need to
keep a pressure about 20-30% of the nominal pressure fan. I know from
the characteristic of the fan that it isn't possible. But.. Maybe you
have an idea how to change some part of the system to reach this
parameters?

The flow you want may not be possible with the pressure you need to
keep. Think of the outlet duct as a resistor, with pressure analogous to
voltage and flow analogous to current. Although the flow through it is
not linearly proportional to pressure, they rise and fall together.
Maybe if you tell us more about your constraints and the reasons for
them, we'll be better able to offer specific suggestions.

I congratulate you on your command of English. It certainly is up to the
task.

Jerry
--
Engineering is the art of making what you want from things you can get.
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Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Mon Jun 26, 2006 10:00 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Micha³ wrote:

Quote:
Hi!
I've got, I believe, an easy problem that I can't solve ;/ My
situation look like this: an air flow through the fan is controlled now
by the guide ring. A fan works in its normal rotation, pressure and
flow. I need to change control by the guide ring on inverter connected
with the fan. And here appear my first problem. When I use an inverter,
I'll be able to change a rotation then I'll decrease pressure to the
level that I have already (when I have a guide ring open to the 20-30%).
And then I'll decrease also a flow - and this is my unfavorable
situation, because I can't change an air flow. It must be constant.
So - how to solve it? How to control (by the inverter) a fan to get
a stable flow and less than normal pressure? It is possibile?


Best regards,
Michal

I'm not sure what you mean here by 'guide ring'.

If you have a fixed mechanical arrangement with a fan blowing into a
plenum, and your only degree of freedom is to adjust the fan speed, then
you will, of necessity, adjust the pressure inside the plenum and the
flow simultaneously -- there's no other way.

Is the 'guide ring' you're talking about some movable device that
changes the airflow somehow? If so, and if you want to adjust things
for an airflow and pressure, then you'll need to adjust the fan and ring
independently, and have some fun making a responsive, stable system.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
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Herman Family
science forum Guru Wannabe


Joined: 14 Jun 2005
Posts: 173

PostPosted: Tue Jun 27, 2006 4:05 am    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

"Micha³" <mw099@gazeta.pl> wrote in message
news:e7pa01$d6h$1@news.onet.pl...
Quote:
Hi!
I've got, I believe, an easy problem that I can't solve ;/ My situation
look like this: an air flow through the fan is controlled now by the guide
ring. A fan works in its normal rotation, pressure and flow. I need to
change control by the guide ring on inverter connected with the fan. And
here appear my first problem. When I use an inverter, I'll be able to
change a rotation then I'll decrease pressure to the level that I have
already (when I have a guide ring open to the 20-30%). And then I'll
decrease also a flow - and this is my unfavorable situation, because I
can't change an air flow. It must be constant.
So - how to solve it? How to control (by the inverter) a fan to get a
stable flow and less than normal pressure? It is possibile?


Best regards,
Michal

Just how many groups are you posting this to? Typically one active group
will get you an answer.

Michael
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Tue Jun 27, 2006 6:19 am    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Herman Family w liscie z dnia 2006-06-27 06:05
napisala nastepujace slowa:

Quote:

Just how many groups are you posting this to? Typically one active group
will get you an answer.

I'm looking for the many points of view at my problem. I'm very sorry if
I made something wrong ;/


--
Michal
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Tue Jun 27, 2006 6:48 am    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Jerry Avins w liscie z dnia 2006-06-26 23:21
napisala nastepujace slowa:

Quote:

The flow you want may not be possible with the pressure you need to
keep.

Yes. I know that. But if we make an assumption that it is possible, what
I need to control my pressure with keeping stable air flow? Maybe some
chamber before the fan (in place where is already a guide ring)? Then I
can try to keep constant air flow.


Quote:
Think of the outlet duct as a resistor, with pressure analogous to
voltage and flow analogous to current. Although the flow through it is
not linearly proportional to pressure, they rise and fall together.


Quote:
Maybe if you tell us more about your constraints and the reasons for
them, we'll be better able to offer specific suggestions.

Ok. I'll try to describe my problem more precisely :)

Already my system looks like this:

--- oven -----> guide ring ---> fan ---
| |
------<-----------burner---<-----------

I measure a pressure drop and a temperature (but it's not the case in
this situation) in the oven. To keep needful parameters in oven I must
control an air flow in a fan. Nowadays I control it by opening or
closing a guide ring. It's not ease to control and very not optimized
system.


Future:
I need to dismount a guide ring and replace it by the inverter connected
to the fan. But I know if I do it I won't be able to keep constant air
flow, because if I decrease a fan speed to some level of pressure
(pressure necessary to continue all technological process in the oven)
then my air flow also decrease.



Quote:

I congratulate you on your command of English. It certainly is up to the
task.

Pardon? I think that I don't understand you.. Well my English -- I still
learning that language and I know that I make many mistakes but I
believe that you'll have understanding for me and nevertheless you won't
leave me alone with my question :)


--
Michal
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Tue Jun 27, 2006 8:04 am    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Tim Wescott w liscie z dnia 2006-06-27 00:00
napisala nastepujace slowa:

Quote:
Micha³ wrote:

Hi!
I've got, I believe, an easy problem that I can't solve ;/ My
situation look like this: an air flow through the fan is controlled
now by the guide ring. A fan works in its normal rotation, pressure
and flow. I need to change control by the guide ring on inverter
connected with the fan. And here appear my first problem. When I use
an inverter, I'll be able to change a rotation then I'll decrease
pressure to the level that I have already (when I have a guide ring
open to the 20-30%). And then I'll decrease also a flow - and this is
my unfavorable situation, because I can't change an air flow. It must
be constant.
So - how to solve it? How to control (by the inverter) a fan to
get a stable flow and less than normal pressure? It is possibile?


Best regards,
Michal

I'm not sure what you mean here by 'guide ring'.

Guide ring is a fixed mechanical element that can control an airflow.

Quote:

If you have a fixed mechanical arrangement with a fan blowing into a
plenum, and your only degree of freedom is to adjust the fan speed, then
you will, of necessity, adjust the pressure inside the plenum and the
flow simultaneously -- there's no other way.

Ok. I understand.


Quote:

Is the 'guide ring' you're talking about some movable device that
changes the airflow somehow? If so, and if you want to adjust things
for an airflow and pressure, then you'll need to adjust the fan and ring
independently, and have some fun making a responsive, stable system.

Yes. You right. But my boss want's to dismount a guide ring, and control
a fan only through a inverter.

If we mount a big chamber, before a fan, which can keep constant flow, a
decrease a pressure, what will be?



--
Michal
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Jerry Avins
science forum Guru


Joined: 03 May 2005
Posts: 534

PostPosted: Tue Jun 27, 2006 1:18 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Micha³ wrote:
Quote:
Osoba nazywajaca sie Jerry Avins w liscie z dnia 2006-06-26 23:21
napisala nastepujace slowa:

...

Quote:
Maybe if you tell us more about your constraints and the reasons for
them, we'll be better able to offer specific suggestions.

Ok. I'll try to describe my problem more precisely :)

Already my system looks like this:

--- oven -----> guide ring ---> fan ---
| |
------<-----------burner---<-----------

It seems that the air is circulating in a loop.

Quote:
I measure a pressure drop and a temperature (but it's not the case in
this situation) in the oven. To keep needful parameters in oven I must
control an air flow in a fan. Nowadays I control it by opening or
closing a guide ring. It's not ease to control and very not optimized
system.


Future:
I need to dismount a guide ring and replace it by the inverter connected
to the fan. But I know if I do it I won't be able to keep constant air
flow, because if I decrease a fan speed to some level of pressure
(pressure necessary to continue all technological process in the oven)
then my air flow also decrease.

I don't know what you mean by "inverter". Is the pressure in the oven
too high, or too low when the flow is right? If it is too low, throttle
the oven's outlet. If it is too high, throttle the oven's inlet. Either
way, adjust the fan speed to maintain the needed flow.

Quote:
I congratulate you on your command of English. It certainly is up to
the task.

Pardon? I think that I don't understand you.. Well my English -- I still
learning that language and I know that I make many mistakes but I
believe that you'll have understanding for me and nevertheless you won't
leave me alone with my question Smile

I mean that you write English better than merely well enough to
communicate your problem. I salute you!

Jerry
--
Engineering is the art of making what you want from things you can get.
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Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Tue Jun 27, 2006 2:23 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Micha³ wrote:
Quote:
Osoba nazywajaca sie Herman Family w liscie z dnia 2006-06-27 06:05
napisala nastepujace slowa:


Just how many groups are you posting this to? Typically one active
group will get you an answer.


I'm looking for the many points of view at my problem. I'm very sorry if
I made something wrong ;/


Generally if you're going to post a question to multiple groups you

should cross-post it -- that is, post it all in one message so that
replies go to all the groups. This lets everyone see all the answers,
getting you a better quality of answer and keeping me from giving you
duplicate answers. Even so, you should limit yourself to just a few
newsgroups.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
Back to top
Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Tue Jun 27, 2006 2:37 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Micha³ wrote:

Quote:
Osoba nazywajaca sie Tim Wescott w liscie z dnia 2006-06-27 00:00
napisala nastepujace slowa:

Micha³ wrote:

Hi!
I've got, I believe, an easy problem that I can't solve ;/ My
situation look like this: an air flow through the fan is controlled
now by the guide ring. A fan works in its normal rotation, pressure
and flow. I need to change control by the guide ring on inverter
connected with the fan. And here appear my first problem. When I use
an inverter, I'll be able to change a rotation then I'll decrease
pressure to the level that I have already (when I have a guide ring
open to the 20-30%). And then I'll decrease also a flow - and this is
my unfavorable situation, because I can't change an air flow. It must
be constant.
So - how to solve it? How to control (by the inverter) a fan to
get a stable flow and less than normal pressure? It is possibile?


Best regards,
Michal


I'm not sure what you mean here by 'guide ring'.


Guide ring is a fixed mechanical element that can control an airflow.


If you have a fixed mechanical arrangement with a fan blowing into a
plenum, and your only degree of freedom is to adjust the fan speed,
then you will, of necessity, adjust the pressure inside the plenum and
the flow simultaneously -- there's no other way.


Ok. I understand.



Is the 'guide ring' you're talking about some movable device that
changes the airflow somehow? If so, and if you want to adjust things
for an airflow and pressure, then you'll need to adjust the fan and
ring independently, and have some fun making a responsive, stable system.


Yes. You right. But my boss want's to dismount a guide ring, and control
a fan only through a inverter.

If we mount a big chamber, before a fan, which can keep constant flow, a
decrease a pressure, what will be?



I assume that by "inverter" you mean drive? "Guide ring" sounds like

something that, well, guides, where you must be talking about a variable
orifice.

Whether you have a fan running at fixed drive with the airflow
controlled by an orifice or a fixed orifice with the airflow controlled
by the fan drive you're still controlling pressure and flow
simultaneously. It seems that what your concern should be (and perhaps
is) is whether you can adequately control your airflow by controlling
drive to the fan.

Ultimately you'll have to answer this question on your own, because it
depends a lot on the type of fan, the type of motor, the type of drive
you select ('inverter' covers a lot of territory) and your performance
requirements.

How are you controlling your orifice now? Does your temperature control
loop generate a position command for a position loop around the orifice,
or does the temperature control generate a speed command for the
orifice, which then runs open loop? How much fluctuation can you stand
in your flow?

Assuming that your fan will have a well behaved flow vs. drive
characteristic, it seems like you'd have a pretty good chance of putting
it in and having it work. So the real question you need to ask is what
fan and motor combination do you need to achieve a flow vs. drive
characteristic that's as good as the fan, motor and variable orifice
combination you have now.

If it were _me_, I'd be saying how big the motor is, what kind of fan it
is (squirrel cage, axial, waving palm leaves, whatever), and what kind
of motor/drive technology (brushed DC with amplifier, brushless DC with
brushless amplifier, induction motor with variable frequency drive).
Then I'd sit back and hope some of the folks on this group who know more
about this sort of thing than I do tell me what's right or wrong about
the proposed choices.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Tue Jun 27, 2006 3:39 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Tim Wescott w liscie z dnia 2006-06-27 16:23
napisala nastepujace slowa:

Quote:

Generally if you're going to post a question to multiple groups you
should cross-post it -- that is, post it all in one message so that
replies go to all the groups. This lets everyone see all the answers,
getting you a better quality of answer and keeping me from giving you
duplicate answers.

Thanks you for information. Next time I will do that.


Quote:
Even so, you should limit yourself to just a few
newsgroups.

I send my message to one polish group and 4 english language.. So.. - in
my opinion - I send it 'to just a few newsgroups' Smile))


--
Michal
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Tue Jun 27, 2006 3:51 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Jerry Avins w liscie z dnia 2006-06-27 15:18
napisala nastepujace slowa:

Quote:
Micha³ wrote:
Osoba nazywajaca sie Jerry Avins w liscie z dnia 2006-06-26 23:21
napisala nastepujace slowa:

...

Maybe if you tell us more about your constraints and the reasons for
them, we'll be better able to offer specific suggestions.

Ok. I'll try to describe my problem more precisely :)

Already my system looks like this:

--- oven -----> guide ring ---> fan ---
| |
------<-----------burner---<-----------

It seems that the air is circulating in a loop.


Right. About 80-90% of the air is still the same. 10-20% is a 'fresh'
air, which contain oxygen (burner needs it).


[...]
Quote:

I don't know what you mean by "inverter". Is the pressure in the oven
too high, or too low when the flow is right? If it is too low, throttle
the oven's outlet. If it is too high, throttle the oven's inlet. Either
way, adjust the fan speed to maintain the needed flow.


Well... Word 'inverter' I found in a dictionary. In polish this element
is called as 'falownik'. In english, inverter is a electric device that
can control for an example a rotary speed of the engiine, by the
controlling frequency of the current - ehh.. it's difficult to explain
that - but I believe that you will understand me ;)

Right. I must adjust a pressure in the oven when the flow is still
constant. So - solve of the problem could be mounting a throttle after
and before the oven? Throttles can be connected with the inverter (which
control speed of the fan) by the feedback loop. Am I right?


[...]
Quote:

I mean that you write English better than merely well enough to
communicate your problem. I salute you!

Thanks you ;)

--
Michal
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Micha³
science forum beginner


Joined: 21 May 2005
Posts: 14

PostPosted: Tue Jun 27, 2006 6:31 pm    Post subject: Re: Problem with a fan controling by the inverter ;/ Reply with quote

Osoba nazywajaca sie Tim Wescott w liscie z dnia 2006-06-27 16:37
napisala nastepujace slowa:

Quote:
I assume that by "inverter" you mean drive? "Guide ring" sounds like
something that, well, guides, where you must be talking about a variable
orifice.

Inverter - electrical element which can control a drive by changing
current frequency :)

Guide ring - let's tell that's someting similar to orifice.


Quote:
Whether you have a fan running at fixed drive with the airflow
controlled by an orifice or a fixed orifice with the airflow controlled
by the fan drive you're still controlling pressure and flow
simultaneously.

Yes. And this situation was. Now, I'll control a fan speed (by changing
his current frequency) and then I'll be able to control only flow. But I
need to control also a pressure. But how? It this is the main point of
the problem.



Quote:
It seems that what your concern should be (and perhaps
is) is whether you can adequately control your airflow by controlling
drive to the fan.


Correct. That's right.

Quote:

Ultimately you'll have to answer this question on your own, because it
depends a lot on the type of fan, the type of motor, the type of drive
you select ('inverter' covers a lot of territory) and your performance
requirements.

How are you controlling your orifice now?

Manualy. And I need to change it. I need to control flow and pressure
automaticaly - so I want to dismount an orifice and mount an 'inverter'
(connected to the drive of the fan).


Quote:
Does your temperature control
loop generate a position command for a position loop around the orifice,
or does the temperature control generate a speed command for the
orifice, which then runs open loop?

Already I only see temperature on the digital indicator. When the
temperature is too high, worker needs to go down and more turn an orifice.



Quote:
How much fluctuation can you stand
in your flow?

I determin that flow must be about 2 m^3/s, and pressure drop in the
oven form about 800 Pa to 1500 Pa.

Parameters of the fan: V = 10 m^3/s, p = 5kPa.

Now a fan works in his 100% of power. And my parameters (V=2m^3/s and
p=800-1500Pa) are setting up by the orifice. Changing this all I want
to save an electric power (decreasing supply of power to the motor of
the fan) and controll my parametres directly from the fan.


Quote:

Assuming that your fan will have a well behaved flow vs. drive
characteristic, it seems like you'd have a pretty good chance of putting
it in and having it work. So the real question you need to ask is what
fan and motor combination do you need to achieve a flow vs. drive
characteristic that's as good as the fan, motor and variable orifice
combination you have now.

If it were _me_, I'd be saying how big the motor is, what kind of fan it
is (squirrel cage, axial, waving palm leaves, whatever), and what kind
of motor/drive technology (brushed DC with amplifier, brushless DC with
brushless amplifier, induction motor with variable frequency drive).
Then I'd sit back and hope some of the folks on this group who know more
about this sort of thing than I do tell me what's right or wrong about
the proposed choices.

Fan parameters:
n=1460 rpm
V=10,8 m^3/s
P=5300 Pa

type: radial

control: now: motor connected directly to the fan; future: motor
controled by the inverter (electric element which is able to change the
frequency of the current Smile connected to the fan.



I know that motor and fan are redimensioned. As I sad earlier, I only
about 20-30% power of the fan. I can't replace fan to the new - so I
must apply some way to decrease fan power keeping air flow at the level
from the 100% fan power.


--
Michal
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No new posts Mod computer problem William Elliot Math 4 Fri Jul 21, 2006 12:07 pm
No new posts Divine apparitions in the tethered goat problem? jpalmour@gmail.com Math 6 Thu Jul 20, 2006 8:26 pm
No new posts possible to use Generalized Method of Moments for this pr... comtech Math 1 Thu Jul 20, 2006 12:49 am

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