Formula to calculate piston shaking force

jseng1

jseng1

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Does anyone have the formula for calculating the piston shaking force at TDC with a Norton twin at various RPMs?
 
Morning Jim
Do you mean the force (or forces) the piston sees when it reverses travel at TDC ? i.e. the force it will exert on the conrod? Obviously that force will increase with speed. That is quite apart from the combustion pressures also exerting their force. 'Piston shaking force' seems a bit of a coverall statement that i fear wont find a solution. Phil Irvines book 'Tuning for speed' had some equations in, i will have a look in the copies i have and report back.
 
jseng1 said:
Does anyone have the formula for calculating the piston shaking force at TDC with a Norton twin at various RPMs?
Click to expand...
"shaking force" is a bit nebulous.
Do you mean the vertical force due to piston mass and deceleration or the relatively minor horizontal force due the the fore-and-ft moment of the piston.
Do you want to exclude the conrod from the analysis?
Without knowing why you need it, it's a bit difficult to guess!
 
robs ss said:
"shaking force" is a bit nebulous.
Do you mean the vertical force due to piston mass and deceleration or the relatively minor horizontal force due the the fore-and-ft moment of the piston.
Do you want to exclude the conrod from the analysis?
Without knowing why you need it, it's a bit difficult to guess!
Click to expand...
May be he means , heavy/std pistons vs light ones and /or short/std rods vs longer ones ....
 
Jim, this is what chat GPT was made for:

Calculating the vibration of a piston at top dead center (TDC) in an engine, such as on a 1970 Norton Commando motorcycle, involves understanding some key principles of dynamics and mechanics, particularly in the realm of reciprocating engines. Here’s a basic approach to estimate the vibration:

Step-by-Step Guide to Calculating Piston Vibration

1. Identify Engine Specifications:
- **Type of Engine**: Norton Commando typically uses a 745 cc, twin-cylinder engine.
- **Stroke of the Piston**: The distance the piston travels in one motion, usually found in the engine specifications. Norton Commando engines from 1970 typically have a stroke of about 89 mm.
- **Mass of the Piston Assembly**: Includes the piston, rings, piston pin, and connecting rod. This might need to be estimated or measured directly if not specified.

2. Calculate the Angular Velocity (v):
- RPM (Revolutions Per Minute)**: Given in the problem. Convert this to radians per second for calculations:

V = {RPM} X (2pi/60)


3. Estimate the Reciprocating Forces:
- The primary source of vibration in piston engines is the reciprocating force due to the mass of the piston assembly moving up and down.
- The force ( F ) can be estimated by ( F = M x A), where (M) is the mass of the piston assembly, and (A) is the acceleration of the piston.

4. Calculate the Piston Acceleration at TDC**:
- At TDC, the acceleration is primarily due to the change in direction of the piston rather than the combustion forces (assuming this is the moment just before combustion).
- The acceleration (A) can be estimated using the formula for the acceleration of a piston in a simple harmonic motion (approximation):

A = V^2 x R x cos(theta)

At TDC (\theta = 0 ) degrees, so (cos(0) = 1 ), making ( a = V^2 x R).

5. Calculate the Force of the Reciprocating Mass:
- F = M x V^2 x R, where (M) is the mass, (V) is angular velocity, and (R) is the radius of the crank (half the stroke).

6. **Estimate Vibration**:
- The force calculated gives an idea of the magnitude of the vibrations produced. The actual transmission of these vibrations to the motorcycle frame and the rider depends on various factors, including engine mounts, the rigidity of the frame, and damping mechanisms.
Click to expand...
 
Ideally what I need is a spread sheet embedded with formulas similar to those shown in the post above. The shaking forces I'm concerned with are those caused by the reciprotating weight when the piston reverses direction around TDC. Variables are counterbalance, RPM, the reciprocating weight which includes the complete piston assembly and the upper end of the rod etc. Also the stroke and rod length because rod length changes the intensity of the reversal near TDC. If such a spread sheet exists (and hopefully it does) then different variables could be plugged into the blanks and comparisons could be made. Hoping for such a spreadsheet may be pure fantasy on my part but is seems like high tech racing teams would use one.

The math gets very thick in a hurry and leaves me behind but the link below points in the right direction and there are some good points about overbalancing a single cylinder engine.

https://scholarworks.calstate.edu/downloads/x346d8356
 
Last edited:
In a vertical twin or single cylinder engine the balance factor depends on the upper limit of the usable rev range. A 70% balance factor is smooth at 7000 RPM, an 80% balance factor is smooth at 8000 RPM. It is all in Ripley's 'Believe It Or Not'. It is probably the source of the information in the pdf file from Cal. Tech.
 
maaseyracer said:
Jim, this is what chat GPT was made for:
Click to expand...
You need to be cautious when using such A.I. (Apparent Intelligence) tools as chat GPT because although you may get a comprehensive answer, there is no guarantee that it is correct. Always check the answer if it is something important.
 
hybridracer said:
You need to be cautious when using such A.I. (Apparent Intelligence) tools as chat GPT because although you may get a comprehensive answer, there is no guarantee that it is correct. Always check the answer if it is something important.
Click to expand...

You mean you cannot trust everything you read on the internet?
 

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