Designing a Cam

[LeonOfTheDead]

So Rasmus went nuts, and asked me for the holy terror of all the students at the following mechnical engineering in Modena.
This is the course why people don't get their degree, and this is one of the toughest exercise you have to do to being accepted at the exam.
No one really does it, they/we all copy it from previous years changing the data with ours.
The data change with the uni's ID, but that not the point.

Let's talk about the design of a cam.
A few info as background, not only to the argument, but to the exercise itself, on which I'm going to base my discussion.
Here is the link to the only material we are provided for this subject (to large to be attached).
https://www.ing.unimo.it/campusone/v...7213/MdA89.pdf
Consider the cam-valve sketch at page 31, (FIG 1)

Cam= body 1
Valve = body 3
Spring = body 4
Engine head = body 5

Body 2 is considered the same as body 3.

When the valve is open the contact is between 2 (from now on 3) and 1
When the valve is closed the contact is between 3 and 5.
4 guarantees the contact both between 3 and 1 and between 3 and 5.
Hence the position of the valve is defined by the contact 1-3 during the opening and by the contact 3-5 when it's closed.
Therefore the contact has to be moved from 1-3 to 3-5 during the closing/opening of the valve.

Since the cam has to be far from the valve when the valve itself is closed, there has to be a gap. The gap is designed considering the dimensions of the bodies when they are cold, and calculating their deformations during the functioning of the engine with the generated heat.
In order to be sure of the presence of this gap even with higher temperatures of those calculated, this gap has to be "over dimensioned".

That means the cam has a profile with a section, the "ramp", in which the contact between 1 and 3 begins.
The contact may begin at the beginning of the ramp, in the middle, or even near the end, we can't know for sure.
This ramp stand for the linear part of the second graph on page 31 (FIG 2) where the graph is negative (both in Y and in THETA).

That graph stands for the hypothetical position (Y) of the valve if it was following the cam.
Actually the valve enters in contact with the cam during this ramp.
before of it, the valve is closed, therefore standing, and therefore it was at a constant height H1<Y<0, using the symbols of the graph.
We don't know the exact position of the valve, but it's between those two values.
Once they enter in contact, the valve starts following the profile of the cam.

It's obvious that there is a hit between valve and cam, and that's proportional to the slope of the ramp. With a very long ramp, the slope would be minimal, the hit inexistent, and the cam huge. Not possible.

The same argument about the ramp is good for the beginning of the contact between 3 and 5 when the valve is closing.


Everything ok up to now?

[Rasmus]

Makes perfect sense.

What are the characteristics of different lobe profiles? I mean, from ramp, flank, nose, closing flank and then closing ramp?

I understand it depends on the application, but won't you generally look for the most lift without risking coil bind or valve bounce?

(Yes, I'm thinking of upgrading my cams, but I need to know more first)

[LeonOfTheDead]

Makes perfect sense.

What are the characteristics of different lobe profiles? I mean, from ramp, flank, nose, closing flank and then closing ramp?

I understand it depends on the application, but won't you generally look for the most lift without risking coil bind or valve bounce?

(Yes, I'm thinking of upgrading my cams, but I need to know more first)

That depends on what it's happening, or better, what you want to happen, inside of the combustion chamber, which is a whole different subject.
First you have to decide what you want as a result, which is probably moar powa.
Then you should study the fluid and thermo dynamics of your cylinder, in order to design a proper air/fuel mixture (since we are talking about your Mustang which doesn't adopt direct injection) to obtain the result you wanted.
And then the cam is designed accordingly.

Now, all of this, it's something I'll learn during the next two year or so.
I feel sick at the idea of studying for another two years, if not three.

So, what I'm going to write here doesn't depends strictly on the behavior you are aiming at. We are supposing to have it already decided it.

Now, to answer to you questions, obviously the ramp should be short if not inexistent.
In that way the cam could open faster, and therefore there would be more time, or better, more portion of the angular rotation of the cam, available for filling the combustion chamber with the valve full opened, which surely better since it allows for a better flux of the mixture at the maximum speed.

It isn't possible though.
We already stated there has to be a gap between the valve and the cam when the valve is closed. Why?
Because with the thermal deformation of the valve, it becomes longer, therefore even with the spring pushing back (towards the head block) the valve, and with the cam holding its upper part at a certain height, the lower part would now enter the combustion chamber, creating an obstacle for the cylinder, and not allowing for the closure of the air intake.

A short ramp means you decided at certain height of its profile (consider again the FIG 2), and a certain length.
The length means you know, angularly, when the cam is going to hit the valve.
The height implies you know the maximum deformation of the valve.
Both depends of the thermal deformation.
Even dimensioning the ramp with the worst deformation possible (using the maximum operating temperature), the ramp is used even at lower temperatures, and the graph is a general one, with the engine revving at its top speed, but not at its top temperature.
So we don't know exactly at which height the valve will hit the cam, again considering the FIG 2.

So the ramp is required, and has to be a combination of its height and length so to have a certain slope.

Again the valve is closed, standing, while the cam is rotating.
The higher the slope is the stronger hit would be.
It's up to your design to see how much the ramp can be inclined.
A racing cam will have a short and very inclined ramp, using a very tough and expensive material to resist to the impact.

Why are we using the ramp?
Again, the valve is standing. If the cam would enter in contact with the valve in the origin of the graph, it would be required to achieve a certain speed of opening instantly.
That means an infinite acceleration, which means (F=m*a) an infinite force. Not possible.

So the graph must start with it. The ramp can't be horizontal because that would define exactly the height at which the cam and the valve enter in contact, which means a precise deformation. you may even be able to calculate it, but the would require the engine running always at that specific temperature. Not possible again.

Attached images from the pdf linked above.

As you can see the graph is symmetrical around the axle passing at THETA S.
It isn't so in the real world obviously, it's just to simplifying the calculation which will be done until the maximum height of the valve, in THETA S. Then the same argument can be repeated until the closure of the valve at the end of the graph.

NOTE: by height I obviously refer to the distance from the head of the engine and the valve, assuming it's movement is vertical (doesn't really matter), so it should be a "negative" height.

[Matra et Alpine]

^what he said ^
With the additions ...

1. are you to consider the valve opening and the throat dimensions/characteristics ?
2. are you to consider the overlap requirements of the engine ?
3. what piston speeds are you to consider ?

These can have impact on the shape you want the open and close profile to be on the cam.
eg, you may want to open the inlet a little durign overlap to maximise mixture speed and limit the volue dorung the overlpa dn then when the exhaust closes to quickly fully open the inlet to take advantage ot that flow ... OR you may open it fully if having a larger overlap to pull more gasses ? LOTS of very fine tweaks to be played with there.

[LeonOfTheDead]

^what he said ^
With the additions ...

1. are you to consider the valve opening and the throat dimensions/characteristics ?
2. are you to consider the overlap requirements of the engine ?
3. what piston speeds are you to consider ?

These can have impact on the shape you want the open and close profile to be on the cam.
eg, you may want to open the inlet a little durign overlap to maximise mixture speed and limit the volue dorung the overlpa dn then when the exhaust closes to quickly fully open the inlet to take advantage ot that flow ... OR you may open it fully if having a larger overlap to pull more gasses ? LOTS of very fine tweaks to be played with there.

There is no engine to be honest.
The process, which I'm going to write one piece at a time, is made to determinate the cam to achieve the movement you want.
The movement itself is whole different story, it's supposedly already designed and I just have to make it possible with the proper cam.
The cam is symmetric in this case for the sake of the exercise, but it's unreal.
The engine is going to rev at 6.000 rpm, and the cam shaft is connected to the crank shaft with a a 0.5 transmission ration, so the camshaft, and the cam, are rotating at 3.000 rpm.

I'm wondering...were you talking to me or Rasmus?

[Matra et Alpine]

REading the thread now I guess I was talking to everyone
Being symmetric and no other parts to be taken in to accout I can see why everyone steals from last years answesr It's all "Mechanical" effort to get the answer.

[LeonOfTheDead]

REading the thread now I guess I was talking to everyone
Being symmetric and no other parts to be taken in to accout I can see why everyone steals from last years answesr It's all "Mechanical" effort to get the answer.

yeah, the reasoning behind the exercise is even interesting, but the brutal calculation force required to solve the problem is almost pointless, being so tough but even unrealistic at the same time.
Once you understood the theory, I don't see the pro of solving such exercises, apart from ruining my life

[LeonOfTheDead]

So here we are again.

If I didn't already, I consider THETA as the angular position of the cam.
We'll calculate the equations of motion* of the valve, as a function of THETA.

* as "equations of motion" is usually considered the position of a body in function of time. THETA is itself a function of time though.

- The equations of motion Y(THETA) (from now on Y) is symmetric to the angular position (THETA S) of maximum opening of the valve
- maximum opening= H (without considering the height on the ramps)
- opening-closing of the valve takes place in 240° of crank shaft rotation (without considering the ramps)
- height of the two ramps= H1
-maximum speed of impact on the ramps = U (equal to the slope of the ramp)
- engine revving at its top rpm = 6.000 rpm
- graph Y composed by 3 arches:
1: from the origin of the system to THETA 1 it's a fifth order curve
NOTE: THETA 1 is measured from THETA S.
2: from THETA 1 (on the left side of THETA S) to THETA 1 (on the right side of THETA S) it's fourth order curve
3: as 1

See attached image for better explanation.
Now, why 4th and 5th order? Why exactly THETA 1?
Because it is so. It's for the sake of the exercise, and in rality, it would be what the guys designing the fluid dynamics of the combustion chamber told me to realize.

- for the homogeneity of the graph, and therefore of the movement of Y, the third derivative of Y in THETA 1 (both) has to be same coming both from the 4th and 5th degree curves
- same but limited to the second derivative between the ramps and the 5th degree curves

- in THETA 2 (measured from THETA S) the acceleration of the cam (so the second derivative of Y) has to be null, so it's when the valve stop accelerating and begins to decelerate before of reaching the top of the opening.

WHY?
marginally explained before, if the graph has a discontinuity of position (that's to say a jump of from a thetaA to thetaB) it would required an infinite speed to reach those two points instantly.
As you know, speed has to be finite.
That implies first order continuity, and introduces a linear graph of Y(theta).

That means passing from a null speed when the graph is horizontal to a certain value of the speed when the graph presents a slope.
In the points in which the speed passes from zero to a certain value, the acceleration is instantly infinite, which implies and infinite force between the cam and the valve. Not tolerable.
So we got second order continuity.

Considering a motion with the acceleration kept finite and constant, with its value null when the valve is standing, constant and positive when the valve is opening, constant and negative when the valve is closing and then null again.
The speed graph then has a triangular shape,the speed is null when the cam is standing, the the speed increases until the valve reaches the top of the opening, then it decrease until the valve is closed again.
The graph of the position is therefore made by two parabolas.

The problem now is having a discontinuity of acceleration, which implies a discontinuity of the force between cam and valve, which may cause the spring to bounce. If the delta is limited, there shouldn't be problem.

To avoid this possibility, we move from a a parabolic graph to a polynomial one. (EDITED sentence)

Which order for the polynomial arches?
It depends on how many conditions I have to satisfy, which will be the next step.

See images from my notes during classes for the moment.

[LeonOfTheDead]

We'll use a polynomial graph so to satisfy the requests we are given without being bound to follow a regular pattern, as a parabol.
The number of requests we have to satisfy will influence the order of the polynomial graph.
Remember we are considering a graph which is symmetric around the axle in the THETA S, therefore the requests made from the beginning to THETA S are the same of those from THETA S to th end.
In such situation we are usually asked to design a graph, therefore a movement of the valve, so that:

-position, speed and acceleration are all null at the beginning (THETA=0)
-speed and acceleration are null when the opening is maximum (THETA=S)

So we have at least 6 requests, which ask for six parameters, and therefore a fifth order graph to say the least. Then other requests could come, as the exact position when the valve stops accelerating and starts decelerating and so on.

A generic fifth order polynomial describing the position of the valve is like this, with A1 being the first coefficient and so on:

(A5)x^5+(A4)x^4+(A3)x^3+(A2)x^2+(A1)x+A0=0 (=0 as requested)

Speed:
5(A5)x^4+4(A4)x^3+3(A3)x^2+2(A2)x+A1=0

Acceleration:
20(A5)x^3+12(A4)x^2+6(A3)x+A2=0

Imposing the first three requests gives back
A0=A1=A2=0

While imposing theother requests gives us three equations which need to be resolved.
For making the situation a bit easier, the reference system is taken so that the maximum opening of the valve is equal to 1, with the cam rotating of 1 unit.
It's a mathematical trick that would require some more explanation, but it works, I guarantee.

So now the remaining requests become:
- Y(1)=1
- Y'(1)=0
- Y''(1)=0

These requests combined to the former three give us the following system of three equations in three unknowns:

A5+A4+A3=1

5(A5)+4(A4)+3(A3)=0

20(A5)+12(A4)+6(A3)=0


It results Y= 6X^5 - 15X^4 + 10X^3

[Feliks]

We'll use a polynomial graph so to satisfy the requests we are given without being bound to follow a regular pattern, as a parabol.
The number of requests we have to satisfy will influence the order of the polynomial graph.
Remember we are considering a graph which is symmetric around the axle in the THETA S, therefore the requests made from the beginning to THETA S are the same of those from THETA S to th end.
In such situation we are usually asked to design a graph, therefore a movement of the valve, so that:

-position, speed and acceleration are all null at the beginning (THETA=0)
-speed and acceleration are null when the opening is maximum (THETA=S)

So we have at least 6 requests, which ask for six parameters, and therefore a fifth order graph to say the least. Then other requests could come, as the exact position when the valve stops accelerating and starts decelerating and so on.

A generic fifth order polynomial describing the position of the valve is like this, with A1 being the first coefficient and so on:

(A5)x^5+(A4)x^4+(A3)x^3+(A2)x^2+(A1)x+A0=0 (=0 as requested)

Speed:
5(A5)x^4+4(A4)x^3+3(A3)x^2+2(A2)x+A1=0

Acceleration:
20(A5)x^3+12(A4)x^2+6(A3)x+A2=0

Imposing the first three requests gives back
A0=A1=A2=0

While imposing theother requests gives us three equations which need to be resolved.
For making the situation a bit easier, the reference system is taken so that the maximum opening of the valve is equal to 1, with the cam rotating of 1 unit.
It's a mathematical trick that would require some more explanation, but it works, I guarantee.

So now the remaining requests become:
- Y(1)=1
- Y'(1)=0
- Y''(1)=0

These requests combined to the former three give us the following system of three equations in three unknowns:

A5+A4+A3=1

5(A5)+4(A4)+3(A3)=0

20(A5)+12(A4)+6(A3)=0


It results Y= 6X^5 - 15X^4 + 10X^3

Trouble associated with cams, with designing them,, with assortment of materials, with necessity of the existence of valve room, with restrictions of maximum turnovers of the engine, induced me for drawing the brand new structure of the engine up. it is an animated version of this answer


More information on the page :New 4 Stroke Engine

Basic sizes :http://www.new4stroke.com/volume.zip

Regards Andrew

[Feliks]

Weight piston and valve same diameter - 62 mm
Right now without springs. Only retainers.




Regards Andrew

[Feliks]

So that you get rid of the doubt next photographs with accurate data :




Diameter popped 75 mm , diameter piston 76.5 mm

Right now are you shure ?? Any washes.



Weight popped 75 mm 1000 G
weight piston & rod 76.5 mm 850 G
weight popped 62 mm 400 G
weight piston & rod 62 mm 370 G

But the window of the flight of the valve of 75 mm is only 64 mm, what is very similar to the window of the flight piston 62 mm .

That is it results from it that the valve of 75 mm is giving the same flight as the piston 62 mm that is 1000 G to 370 G !!!!!

==~~ 2.5 more weight popped to piston& rod !!

It only looks impossibly. but this way is.





In principle ,for them greater popped/piston diameter, it is this difference in weight will be to the benefit of pistons.

Andrew

[Feliks]

Since when the keg came into existence, for it is her shipping by ships constituted a spot of bother. That is how, they forgot to attach, while swinging the ship rolled from one side to other side, hitting in not around with great energy. There was this great danger for the crew. That is how, they forgot to attach, while swinging the ship rolled from one side to other side, hitting in not around with great energy. I decided to use this energy for the production of the electric current with the help of the oscillatory dynamo. It is a pendulum driving the oscillatory dynamo around so with keg. It will be sufficient to install shipboard or for other swimming raft, and during waving we have the electricity, rather than danger


block of osillating dynamo:




And mutation pendulum dynamo:



Or magnet tooth plate.








So far we exploited the energy arising with the help of the pendulum only for stopping him.


Clik on picture, see animation

Wahad?o Waltenhofena

Regards Andrew

[Feliks]

They want to cultivate the Christmas Eve, going behind the tradition in Poland which is telling us that on this special day one should be reconciled with all people which are surrounding us. My wishes of the vision Merry Christmas and modified return to sources that is poped valves.
I think that with traditionalists an approval will also take place in this special day.

My proposal it is modified poped valve which let for very effective picking up the warmth by chilling with intense stream of oil.
Thanks to widening the leading part of the valve to the maximum dimension which can only to fit in the nest , the surface of the joint of the valve with the head repeatedly was increased.
Thanks to widening the leading part of the valve to the maximum dimension which can only to fit in the nest the surface of the joint of the valve with the head repeatedly was increased. much simpler sailing across the warmth causes it to the well chilled head. a here also omitted Valve Guide which is usually of materials worse being a heat conductor than aluminium stayed. the additional crack of the baulk still became the Valve Guide to head liquidated in this new structure of the valve. The new structure allows to move heat to the head very efficiently. with valve quide omitting, and big relatively with area.
In the new structure it is an important thing, that inside valve on 3 / 4 one's length is feeling empty inside and has the enormous area for the exchange of the warm with chilling oil.
Chilling jst oil passed to the middle of the valve with the help of two tubes from which the very intense stream of cooling oil is flowing out.

I think that at such a construction of the valve, the temperature of the valve should not exceed 500 degrees Celsius, and NOx coming into existence in a combustion chamber can be limited about about 80 %

It will also be possible to increase the efficiency of the engine by increasing the degree of tensing, or else there will be no great temperature in a combustion chamber what the significant reduction of self-ignitions will cause, and will cause more laminar burning.

And the most important case. Since temperature of the new valve on 3 / 4 his lengths she should not be bigger than the temperature of the head, it will be possible to resign entirely from devices for placing valve clearance, since the sum of the expandability of the new valve and the expandability of the head will be approximately similar.

therefore keeping valve clearance of manner will be unnecessary as a result of the same complete expandability of the valve and the head.

Below I am describing two models of the latest version of valves, and the disintegration of the temperature on the length in the traditional valve.









Marry Christmas Andrew

[Feliks]

Good alternate on flywheel ? ( turning the principle away perhaps of theses to be starter ( Large stepper motor))

Linear stepper
Stepper basic





Now I will show and I will explain the rule of operation my new dynastarter :





Next on hard PCB put some coils end electronics.
Every so the "green cylinder" has the magnet, two coils with shuffled teeth for the half of their size of the division, a bit electronics of the type small bridge on mossfets, securities on varistors electronics controlling generate the electricity . Current on each coil about 5 Ampers menage mossfets.
Everything controled of course with microprocessor .






It is put on this hard PCB plate about 150 of such arrangements with coils and the electronics parts





everyone so complet of elements is decreeing with 5 amperes, rally if to do about 150 pieces of these elements and to put them on this PCB tile, we can manage about 750 amperes what should completely be enough for the warming up the engine. Receiving the electric current in the same way for charging a battery is already a banally simple matter.



I think, that such PCB it "Automotive mother board" the same "Automotive mother board" is replacing the alternator and the starter. Flywheel still is always in the engine.




Principe as same , but in disc version linear stepper

Regards Andrew