How to calculate this torque? (steel ball in a spiral tube)

[vxiaoyu18]

I believe I can now identify the position of the dip that a ball will rest in.
I need numbers for these four parameters;

1. Pitch of the helix; = axial advance per turn.
2. The angle of the helix rotational axis, measured from the vertical.
3. Radius of the helix, that the central axis of the tube follows.
4. The internal radius of the tube.

Let me just reimagine the problem for the sake of math.

Gravity coefficient g= 9.8n /kg;
π= 3.14;
Density of 304 steel ρ =7930 kg/m³;
Rolling friction coefficient between steel ball and stainless steel material u₁=0.0015;
Friction coefficient of deep groove ball bearing u₂=0.0015.

Steel ball:
Radius r₁= 0.045m;
The quality of the m₁ = 3.03 kg;
Gravity G₁ = 29.65 N;
Radius of rotation of steel ball in tube is r₂=0.064 m.

Center axis:
radius r₃= 0.005m;
The length of the L₁= 2.8 m;
The quality of the m₂ = 1.74 kg;
Gravity G₂= 17.08 N

Spiral pipe (304 stainless steel) :
Inner diameter d= 0.1 m;
Outside diameter D₁ = 0.108 m;
Wall thickness s = 0.004 m;
Pitch L₁ = 0.25 m;
Number of turns n = 10;
H₁ = 2.5 m;
Diameter of helix D₂=0.118 m;
Outside diameter of spiral tube rotation D₃=0.226 m;
Length of spiral tube L₂= 2.5 m;
Helix length L₃=4.47 m;
Mass m₃=46.30 kg;
Gravity of spiral tube G₃= 453.74 n;
Helix Angle α =34°;
Angle of inclination between spiral tube and horizontal plane β =45°;
Angle of inclination between helix and horizontal plane θ=23.30°;
The inclination height of spiral pipe is H₂= 1.77 m.

 

[vxiaoyu18]

These are all the parameters that I calculated here, so let's see what we can use. For the convenience of calculation, only the initial torque of steel ball to spiral tube can be calculated.

 

[Baluncore]

Let me just reimagine the problem for the sake of math.

Unlike an engineering drawing, a numerical model can be very simple.
1. Pitch of the helix; = axial advance per turn.
2. The angle of the helix rotational axis, measured from the vertical.
3. Radius of the helix, that the central axis of the tube follows.
4. The internal radius of the tube.
When I asked for those four specific numbers, you did a snow job that confuses things.

Parts of your reply, for example...

Helix Angle α =34°;
Angle of inclination between spiral tube and horizontal plane β =45°;
Angle of inclination between helix and horizontal plane θ=23.30°;

seem to make no sense together. You may know what you meant, but you need to be more precise in your description.

The length of the helix is irrelevant to the torque. One turn is sufficient.
The simple spherical ball has a mass m, and fits freely inside the tube.
The ball rolls on the inside surface of the tube. That contact is one tube radius from the tube axis.
The tube axis follows a helical path about the helix axis.

A “helix” is like the thread on a bolt or cylinder. It has a pitch independent of radius.
Mathematically, a “spiral” is a line drawn about a point on a plane. It has a changing radius.

Please don't use the informal term "spiral" when referring to a "helix". Not only are there helical tube pumps, but there are also spiral tube pumps. It is important to avoid confusion.

You seem to use the word “quality” to refer to a “quantity” of mass. Why not just use the word mass?

 

[vxiaoyu18]

Unlike an engineering drawing, a numerical model can be very simple.
...

I'm very sorry, because I don't know English, many sentences are translated by translation software. Some inaccuracies can only be understood as best as possible. These parameters are the parameters of the machine model I am actually calculating at present. I have listed all the parameters I know and can calculate, so that you can choose which ones you need. If you find the data too cluttered, I take the time to re-create a simpler model, illustrated graphically, perhaps more directly.

 

[vxiaoyu18]

1. Pitch of the helix; = axial advance per turn.
2. The angle of the helix rotational axis, measured from the vertical.
3. Radius of the helix, that the central axis of the tube follows.
4. The internal radius of the tube.

1. Pitch of the helix; = axial advance per turn.
L₁ = 0.25 m
2. The angle of the helix rotational axis, measured from the vertical.
β=45°
3. Radius of the helix, that the central axis of the tube follows.
r₄=D₂/2=0.059 m
4. The internal radius of the tube.
r₅=d/2=0.05 m

 

[Baluncore]

Here is a view of your helical tube.
X is to the right. Y is away from viewer. Z is up.
Helix axis passes through origin at angle of 45°.
Yellow line is valley. Yellow circle is where ball will rest in dip.
Magenta circle is a crest. Blue is volume that will hold a liquid.

 

[vxiaoyu18]

Here is a view of your helical tube...

You are very professional! Admire!
Yes, I reserved a little space for the ball to be there. I just want to figure out how to calculate the initial torque of the coil when the ball is in that yellow spot.

 

[JBA]

@vxiaoyu18 For someone having to translate what you receive and then translate your response, you have done an amazing job of communicating on this forum with me. I would never realized that you were not fluent in English had you not revealed that; and some of your variations in terminology are just as present in those fluent in English.

@Baluncore : I do not understand your "path" of the ball because the rolling ball will a always remain in the lowest point of each wrap of the helix of the rotating helix tube; and, as a result, its path will be a straight line parallel to the axis of rotation from its bottom entry to its top exit of the helix.

 

[JBA]

@vxiaoyu18 Go to the below website to see an animation of a ball being lifted in a Screw Conveyor which is a accurate representative of the path of a ball in your device.

https://en.wikipedia.org/wiki/Screw_conveyor

 

[vxiaoyu18]

I couldn't figure out how to calculate the moment arm.

 

[vxiaoyu18]

@vxiaoyu18 Go to the below...
https://en.wikipedia.org/wiki/Screw_conveyor

Thank you. I mainly want to find out how to calculate it. I have searched many places on the Internet, but I haven't been able to find a detailed introduction.

 

[Baluncore]

I do not understand your "path" of the ball because the rolling ball will a always remain in the lowest point of each wrap of the helix of the rotating helix tube; and, as a result, its path will be a straight line parallel to the axis of rotation from its bottom entry to its top exit of the helix.

As the helix rotates the ball will roll in a straight line, parallel with the helix axis.

The yellow line is not the path of the ball. It is the valley down which water would flow with the helix held fixed in the illustrated position. It helps to follow that valley minimum in order to find the crest that sets the local liquid level, and the dip in which a ball would rest.
I wrote the code in BASIC to simulate and measure the capacity of a helical tube pump. The approximate grid position of the ball is a bonus. If the position of the local minimum was needed more accurately I could interpolate between the mesh points.

 

[vxiaoyu18]

As the helix rotates the ball will roll in a straight line, ……

You are a professional, a rare talent in mechanics. After five years of efforts, I have mastered the manufacturing principle of perpetual motion machine, which is a machine that continuously converts the gravity of machine parts into mechanical power output by using a machine. I have mastered several styles, and now it is the initial promotion stage. If there is an opportunity in the future, would you like to work with me to develop this technology? It's enough to change the world's power supply patterns.
My machine can't be used yet because it hasn't been patented. In order to facilitate promotion and display, I need to design another machine with reduced functions. I came across that the spiral tube might be useful, so I had to figure it out and see if I could use it, and when I knew how to calculate the torque of the ball in the spiral tube, I could figure out whether the machine was feasible or not.

 

[Baluncore]

Perpetual motion is not possible in physics, only in the mind.
The rules of PF do not allow perpetual motion to be discussed.

 

[JBA]

This is intended as a philosophical comment only: "And yet the Earth continues to spin and planets to orbit the sun"

 

[vxiaoyu18]

Perpetual motion is not possible in physics, only in the mind.
The rules of PF do not allow perpetual motion to be discussed.

I also know that PF BBS is not allowed to discuss the machine that is considered impossible to achieve. All my machines can be physically calculated. The manufacturing parameters of machine parts are complete and can be manufactured and used. I'm working on a prototype part of this more hidden technology, and when I figure out how to calculate the torque of the steel ball in the spiral tube, I verify that if it works, I may show you the complete machine structure in due course, and ask you to do the physical calculation again, which I believe will be a very interesting thing.

 

[vxiaoyu18]

This is intended as a philosophical comment only: "And yet the Earth continues to spin and planets to orbit the sun"

Light can heat, wind energy using wind, hydraulic, water use is a machine that I use is gravity, strictly speaking, it is only a "gravity" engine, is a force is a force difference, a difference value can cause some changes in the mechanical power, should be able to be used, will not violate any of the existing knowledge of physics.

 

[Baluncore]

The dip is located with a Y value of 0.041113 m. That is the horizontal offset from the axis.
So I think the torque will be; T = y * m * g * Cos( 45° )
T = 0.041113 * 3.03 * 9.8 * 0.7071 = 0.8632 Nm

 

[vxiaoyu18]

Keep trying to find the algorithm for the torque of the steel ball, we now know its trajectory, see where it stays, get closer and closer to the core, find the calculation method for its position, and we can complete the calculation process.

 

[vxiaoyu18]

The dip is located with a Y value of 0.041113 m. That is the horizontal offset from the axis.
So I think the torque will be; T = y * m * g * Cos( 45° )
T = 0.041113 * 3.03 * 9.8 * 0.7071 = 0.8632 Nm

If the torque caused by the ball is so small, then my machine can achieve it completely. Because to write the patent, I need to find a more accurate physical formula algorithm. I'll go to bed first. It's almost three o 'clock in the morning. Thank you.

 

[JBA]

On a minor point since the result for 45° is the same for both,the direction of force parallel to the helix axis is mg*sin (45°), not cos(45°) which in this case is the identical value anyway. The cos() is the radial force on the tube.
On the other hand, while I agree the force along the axis is as calculated, I am not sure that is the force that provides the actual torque on the screw because the angle of the slope due to the helix's pitch is much less.
As an example, looking at the reference animation, freezing it (mentally) and then observing the immediate slope under the ball indicates not all of the force along the helix axis is actually applied to act as a torque on the screw.
Another way of looking at it is if you unwind the helix tube and lift one end to the same elevation as the top of the helix, the angle of its slope = 23.3°, which exactly the same value @vxiaoyu18 calculated for the combined helix pitch angle and 45° helix axis angle, relative to the horizontal in his post #31.
In other words if you want a high torque from a ball drop then you want a combined helix axis and pitch angle as close to vertical as possible, you just won't get many rotations from each ball drop.

 

[vxiaoyu18]

On a minor point since the result for 45° is the same for both……

I can see from the three-dimensional structure of its running state, but can't find the calculation formula for its physical, and I have to find a calculation way to crack its state, or foreign unconvincing, that's what I'm upset, you know, if you don't have enough calculation and the actual machine, few people would agree with this kind of machine, ha ha. The machine is simple to make, but the spiral tube is difficult to calculate.

 

[Baluncore]

On a minor point since the result for 45° is the same for both,the direction of force parallel to the helix axis is mg*sin (45°), not cos(45°) which in this case is the identical value anyway. The cos() is the radial force on the tube.

I measure the tilt of the helix axis as declination from the vertical, which changes the sine to a cosine.

As an example, looking at the reference animation, freezing it (mentally) and then observing the immediate slope under the ball indicates not all of the force along the helix axis is actually applied to act as a torque on the screw.

The slope where the ball sits is zero. The radius of the ball is not important as the weight is a vertical force.
One turn of the helix will advance the ball one pitch parallel to the helix axis. Maybe there should be a two Pi in there?

 

[JBA]

Another way to look at it is to turn the helix axis vertical and observe the resulting tangent rotation force on the screw from the ball's weight. What you see is as the helix pitch reduces so does the slope the ball sitting on and with its tangent force vector becoming progressively smaller relative to its vertical weight force vector to the point that when the helix pitch becomes 0 then there is a 100% of the downforce on the helix but no tangent force to rotate it.

 

[vxiaoyu18]

You just won't get many rotations from each ball drop...

In fact, my machine is to overcome the torque caused by the steel ball, and the smaller the torque, the easier my machine is to build. If the torque of the steel ball on the spiral tube is greater than the power I give it, I can only change the design and try to use the torque of the steel ball as the driving force. No matter which force is large, my machine can be built as long as the driving force and the resistance are not equal.

 

[JBA]

OK, I am writing a bit more at this time but will revise it for a minimum torque requirement.

You have already reduced the torque arm to a minimum by wrapping the tube directly around the shaft.
I believe the best method of determining the torque from the ball weight on the helix is to first determine the torque from the ball wt on the helix vs a given helix pitch angle is with the helix axis vertical.
The shorter the helix pitch, the lower the the torque from the pitch.
The all other factors being equal, the smaller the angle of the helix axis from the horizontal the lower the torque from the ball.
Having offered that, I think you fully understand the issues at hand; but, will be here to assist if needed.

 

[vxiaoyu18]

The shorter the helix pitch, the lower the the torque from the pitch.
The all other factors being equal, the smaller the angle of the helix axis from the horizontal the lower the torque from the ball.

According to the fuzzy calculation and experimental results, the correlation is correct. In my calculation Excel, only the accurate algorithm of steel ball torque is missing.

 

[JBA]

Length of spiral tube L₂= 2.5 m;
Helix length L₃=4.47 m;

I am working on an equation for the torque and noticed that the above dimensions in your Post#31 do not appear to be correct because they indicate that the helix tube length is shorter than the helix length. What am I misreading?
Edit: I used the calculation to determine the tubing length and that resolved the terminology issue I had.

 

[vxiaoyu18]

I am working on an equation for the torque and noticed that the above dimensions in your Post#31 do not appear to be correct because they indicate that the helix tube length is shorter than the ...

I calculate so spiral length: D ₂ for spiral diameter, namely projection diameter, L ₁ for pitch, lap spiral length: L₄=sqrt((πD₂)^2+L₂^2). Spiral tube high for H ₁, spiral length: L₃ = (H₁/L₁)*L₄ = H₁/L₁*sqrt((πD₂)^2+L₂^2) = 4.4697 m

If you think your calculation is correct, you can use your calculation results, which are calculated by using the physical formula, but I can't guarantee that all my calculations are correct.

 

[JBA]

No problem It was strictly a terminology issue.

Below is a formula I have developed based upon my last best theory (i.e. the pitch angle and tangent force determined with the helix axis vertical and then modified by the the helix angle; and, the ball contact radius being from the helix axis to the centerline of the ball). Whether this equation is actually accurate will be for you to determine.

T = M2*g*[sin(asin(H2/L3))*sin(α)]*((D3/2)-s-r)

The torque values are valid for α from 90°to (the point at which the pitch angle is 90° to the horizontal which is now 23.3°) and the helix angle α is measured from horizontal