# Measure a varying force

Bob Higgins
how do I measure a rapidly and cyclically varying vertical force

I have a rotating mass that generates centrifugal and aerodynamic forces. I want to see the variation thru one rotation at steady state. how do I measure the vertical force generated and display it on my computer screen, with a graduated scale?

[Mentor Note -- more details added from a different/duplicate thread (now deleted)]

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Staff Emeritus

russ_watters
Mentor
how do I measure a rapidly and cyclically varying vertical force

I have a rotating mass that generates centrifugal and aerodynamic forces. I want to see the variation thru one rotation at steady state. how do I measure the vertical force generated and display it on my computer screen, with a graduated scale?

[Mentor Note -- more details added from a different/duplicate thread (now deleted)]
What is the approximate frequency of vibration? If it's not too high, just use a spring scale and take a video of the scale readout with your cell phone camera for analysis...

russ_watters
Staff Emeritus
Instead of measuring force directly, measure change in vertical position Y. For example, you could do that by analysis of video images.

Then you can use ##F=ma=m\frac{d^2Y}{dt^2}## to calculate the force from position. Think of the simplification is Y is purely cos(wt).

Mentor
Measuring rapidly varying forces is something that mechanical engineers commonly do. The process starts with some basic physics calculations to determine the approximate speed and force. Yes, you need to know what you are measuring in order to measure it. The measurement then tells if your calculations were correct, and it also tells if you truly understand the system. We also need a diagram showing the system.

Measuring 1 lb varying at 1 Hz is completely different from measuring 1000 lbs varying at 1000 Hz. The equipment is different, the setup is different, even the analysis is different.

Dr.D
Bob Higgins
The apparatus consists of a U-shaped frame with a shaft going between the free ends. On the shaft is a wheel containing wing shapes. Under the U I want to place a load cell of some kind and rig it to my laptop so I can see the variation in net radial load as the wheel rotates at about 30 hertz. The purpose is to study various airfoil shapes. It is a substitute for a wind tunnel. I also need torque and rpm measurement but both should be reasonably steady.

Bob Higgins
What is the approximate frequency of vibration? If it's not too high, just use a spring scale and take a video of the scale readout with your cell phone camera for analysis...

View attachment 289505
The apparatus consists of a U-shaped frame with a shaft going between the free ends. On the shaft is a wheel containing wing shapes. Under the U I want to place a load cell of some kind and rig it to my laptop so I can see the variation in net radial load as the wheel rotates at about 30 hertz. The purpose is to study various airfoil shapes. It is a substitute for a wind tunnel. I also need torque and rpm measurement but both should be reasonably steady.

Mentor
Your description is not enough to give us a clear idea of what you want to do. We need a diagram. Show how you will drive this apparatus, show the orientation of the airfoil(s), show the direction of the force(s) that you want to measure, wheel speed in RPM, approximate dimensions, and anything else that we need to know.

YOU know what you are trying to do, we do not.

Bystander
Bob Higgins
Your description is not enough to give us a clear idea of what you want to do. We need a diagram. Show how you will drive this apparatus, show the orientation of the airfoil(s), show the direction of the force(s) that you want to measure, wheel speed in RPM, approximate dimensions, and anything else that we need to know.

YOU know what you are trying to do, we do not.
Most of the information you request is not necessary to solve the problem. Essentially, there is a load sensor device and the load on it varies in a sinusoidal pattern with a frequency of about 30 hertz. I want to see the load variation as a sinusoidal wave on the screen of my laptop and be able to discern the peak force quantities (upward and downward).

Mentor
Most of the information you request is not necessary to solve the problem.
Please remember who you are having this discussion with, Bob. We are a very experienced group of engineers, so understanding the full setup is important in order for us not to waste lots of time trying to suggest things that will not work as well as the optimum solution. Unless there is some proprietary reason for concealing details, please be more forthcoming. Detailed sketches would be helpful.
Essentially, there is a load sensor device and the load on it varies in a sinusoidal pattern with a frequency of about 30 hertz. I want to see the load variation as a sinusoidal wave on the screen of my laptop and be able to discern the peak force quantities (upward and downward).
Do you have experience working with accelerometers and data aquisition equipment? Which data acq vendor do you use (NI, Omega, others)? Do you prefer USB or Ethernet or GPIB or some other interface between your data acq equipment and your computer? What programming language do you generally use for acquiring and processing this data?

Bystander and jrmichler
Bob Higgins
Please remember who you are having this discussion with, Bob. We are a very experienced group of engineers, so understanding the full setup is important in order for us not to waste lots of time trying to suggest things that will not work as well as the optimum solution. Unless there is some proprietary reason for concealing details, please be more forthcoming. Detailed sketches would be helpful.

Do you have experience working with accelerometers and data aquisition equipment? Which data acq vendor do you use (NI, Omega, others)? Do you prefer USB or Ethernet or GPIB or some other interface between your data acq equipment and your computer? What programming language do you generally use for acquiring and processing this data?
I have no experience with accelerometers and only with strain gauge data acquisition (>50 years ago). I have never bot such equipment personally. My laptop has USB ports or ethernet with an adaptor. I haven't programmed in 30 years (in Basic) and hope it is not necessary. I expect the hardware and wring apparatus already exist for measuring force and transmitting to a computer.
BTW, I am also a very experienced mechanical engineer and can distinguish necessary information from unnecessary. Also, I am working toward a patent.

Mentor
Also, I am working toward a patent.
Ah, well that would explain the proprietary nature. Thanks for the clarification.

I have no experience with accelerometers and only with strain gauge data acquisition (>50 years ago). I have never bot such equipment personally. My laptop has USB ports or ethernet with an adaptor. I haven't programmed in 30 years (in Basic) and hope it is not necessary. I expect the hardware and wring apparatus already exist for measuring force and transmitting to a computer.
Here is a good tutorial on basic vibration sensing. I'll see if I can find a canned system that you can connect to your computer via USB and get data reports out...

Mentor
Since you cannot tell us about the application, we need information on what measurements you want to make:

Force: Minimum, maximum, resolution, bandwidth. Does the force have a static component, or are you measuring only dynamic force?
Acceleration: Peak acceleration, resolution, bandwidth. Does the acceleration have a static component, or are you measuring only dynamic acceleration?
Data acquisition: Peak voltage, resolution, maximum sample rate, maximum number of samples per data file, interface (USB?). Do you need anti alias filtering?

There are systems that do what you want, and some are surprisingly affordable. But we need to know more about your measurement needs.

Bob Higgins
Measuring rapidly varying forces is something that mechanical engineers commonly do. The process starts with some basic physics calculations to determine the approximate speed and force. Yes, you need to know what you are measuring in order to measure it. The measurement then tells if your calculations were correct, and it also tells if you truly understand the system. We also need a diagram showing the system.

Measuring 1 lb varying at 1 Hz is completely different from measuring 1000 lbs varying at 1000 Hz. The equipment is different, the setup is different, even the analysis is different.
Force varies from around -125 N to + 125 N and frequency of about 30 hz . These differ somewhat for different load cases.

Bob Higgins
My preliminary scheme is to support the axle of the wheel at one end by a standard bearing in solid frame structure and the other end going thru a slot in the frame to allow vertical movement and then support it via a pressure type load cell that is connected rigidly to the frame. The four wires from the load cell will be connected a) to ground b) neutral (white) c) positive terminal (red) and d) negative terminal (black). I assume that when the force is up there will be a positive reading on a voltmeter (touching neutral and positive) and when the force is down there will be zero reading if the lead remains on the positive terminal and a positive reading when it is on the negative terminal. Is there something wrong with this arrangement?

Mentor
Your partial description is enough to make some rough guesses. A rotor turning 1800 RPM (30 Hz) will generate a sinusoidal bearing force if it is out of balance AND the entire structure has a natural frequency several times higher than 30 Hz AND nothing is bouncing between clearances.

You mention studying airfoil shapes in conjunction with 30 Hz, or once per revolution. I do not understand how an airfoil on a rotor spinning 1800 RPM will cause a 30 Hz sinusoidal force, but I can easily understand how such an airfoil can cause a force with frequency components over 10 times 30 Hz. If so, you need a load cell with natural frequency at least 1000 Hz as installed in the test fixture. And you need a data acquisition system with sample rate at least 2000 Hz. You may need higher frequency response. Do not expect to get usable results with lower frequency response.

Your description is not sufficient to tell me if you can get usable results without an analog anti alias filter, so assume that you will need anti alias filtering with 1000 Hz corner frequency.

That's the best that I can do right now. With better information, I can make specific recommendations for a load cell and a data acquisition system that does not require a programming language.

Bob Higgins
The apparatus is essentially two radial arms at about 1 foot separation, with an axle thru their centers and keyed to the arms and going thru bearings in a supporting frame at each end. At one end of the arms is an airfoil spanning the arms but at the other end is a symmetrical airfoil (no radial aerodynamic force) of the same mass as the test airfoil and spanning the arms. The former will generate an aerodynamic lift force acting radially and is an unbalanced radial force like an eccentric mass. I want to measure the lift force for several airfoil test pieces.

I now think I can do this by measuring the load at the bearing at one end of the axle and doubling it to get full load from the airfoil.

My on-line research suggests a load cell of the hydraulic type, to be connected between the end of the axle and the frame support. I have no experience with such equipment and am unclear as to how to manage the signal to see what I want which is the amplitude of the sinusoidal force. If the signal is voltage, maybe measuring it as an AC voltage would be enuff, altho I expect it would be the rms value. I could calculate max. value from that.

If you cannot visualize the apparatus, I can try to draw it using sketchup s/w and insert it as an image (later).

Mentor
We really need a sketch. You do not need to use CAD - a simple pencil sketch is good enough. Make the sketch, photograph it or scan it to JPG, then paste it into your post using Attach files > Insert > Full image.

Bob Higgins
The test apparatus, omitting the base, the electric motor drive and belts from motor pulley to shaft pulley that is shown on the left side. It turns the rotor that has the test airfoil at one end (top) and a symmetrical airfoil, having the same weight, at the other end (bottom). The test airfoil generates lift from the tangential velocity and the force is radial, the vertical component generating a force sine wave as the rotor spins. I want to measure the amplitude of this wave.

On the right side of the support the axle goes thru a slot in the support to allow vertical movement. The upper support block is free to move vertically and houses the bearing for the axle and holds the upper threaded protrusion from the load cell underneath. The lower support block is fixed to the vertical support frame. From the load cell, which I assume is hydraulic, there are four wires. My guess is the following.
Bare- ground, White- neutral, Black- negative terminal, Red- positive terminal
I suppose a voltmeter for AC and connected from white to red will indicate an rms value for upward force. Connection from white to black will indicate rms value for downward force. Maybe vice versa.
BTW, I see a mistake in left rotor arm thickness. It should be uniform all along.
The measured value I can double to get total force values for the test airfoil.

Mentor

30 rev/sec (from above)
Diameter = 12 inches
Airfoil length = 12 inches
Airfoil chord = 2 inches
##C_L## = 1.0 (lift coefficient)

Velocity = ##12 inches * \pi * 30 rev/sec / 12 inches/foot = 94 ft/sec##
Dynamic pressure at 94 ft/sec = ##0.5*\rho*V^2## = ##10.3 lb/ft^2##
Lift at ##C_L = 1.0## = ##1.0 * 2*12/144 * 10.3 lb/ft^2 = 1.7 lbs##

Your peak to peak force would be twice that, or 3.4 lbs. You would want to measure lift at ##C_L## ranging from 0.1 to 2.0, or 0.34 lbs peak to peak up to 7 lbs peak to peak. The desired accuracy would be about 10% of the lowest force, or about +/-0.03 lbs.

A major confounding factor is centrifugal force due to unbalance. Centrifugal acceleration is ##\omega^2*r## = ##(30*2*\pi)^2*6 inches## = 213,000 ##in/sec^2## = 550 G's. The maximum allowable unbalance weight is then 0.03 lbs / 550 = 5E-5 lbs, or 0.02 grams. Keep in mind that the airfoil will deflect due to the centrifugal forces, which will bend it outward and increase the unbalance force.

Also, the airfoil is running through air disturbed by the previous pass of the airfoil plus the rod opposite the airfoil.

Bob Higgins
Actual dimension of the test airfoil is 30.5 cm in length. Chord is also 30.5 cm. Radius from hub to center of airfoil is 40.0 cm. Assumed max. coeff. of lift is 1.4 Air density= 1.225 kg/m^3
ang. vel.= 1800*(2*pi)/60= 188.5 rad/sec tang. vel.= 0.4*188.5= 75.4 m/s
lift force = C*A*d*v^2/2= 1.4*(0.305^2)*1.225x75.4^2/2= 453.5 N
My set-up above intends to measure half the load which is 227 N.
The help I need is to zero in on the details of measuring the load. I am unfamiliar with load cells but obtained much info using search engines. However, exactly how to set it up to measure a sinusoidally varying load is unclear, particularly how to deal with the signal from the device.
The effect of the airfoil moving thru disturbed air is something I must find out from experimentation.

Mentor
At 250 ft/sec, there is significant kinetic energy in the rotating parts. This setup needs serious guarding and careful operation. The centrifugal acceleration is 1500 G's. That calls for careful design of the rotating parts, both for strength and deflection. And keep in mind that unbalance forces are exactly in phase with lift force, so it needs to be balanced both statically and at speed.

I suggest a button type load cell. Mount the bearing in a rectangular bearing housing that slides up and down in a slot in the frame. Set the load cell on the frame under the bearing block. Put a spring above the bearing block and preload it enough to hold the bearing block down onto the load cell. Size the load cell accordingly. Be aware that these load cells can typically tolerate an overload of 100% or so, and that anything more than that permanently damages the load cell.

Here are two possibilities:
https://www.sparkfun.com/products/13331?_ga=2.170547744.1853601799.1637959614-791085291.1637959614

The load cell needs to be stiff enough so that the mass of the rotating assembly and the spring constant of the load cell will result in a natural frequency well above 100 Hz. The Omega load cell data sheet gives deflection at full load, from which the spring constant is easily calculated. I know from experience that Omega sells top quality products, I have no experience with Sparkfun. The Sparkfun will probably meet your needs.

These are strain gauge load cells, which need a strain gauge signal conditioner. A good source of information to get started is: https://learn.sparkfun.com/tutorial...10.1853601799.1637959614-791085291.1637959614. You need a signal conditioner with at least 100 Hz bandwidth because the output is 3 dB down at the rated bandwidth. Sparkfun might have something, Omega certainly will. In either case, give them a call and ask for a strain gauge full bridge signal conditioner with at least 100 Hz bandwidth.

Concentrate on getting everything working before dealing with the signal. Also, do your first test runs with a dummy load cell to make sure that the spring holds the bearing block in place. If it hammers, even once, the load cell will be destroyed.

Are you studying a curved airfoil with the chord line on a 40 cm radius? If not, the average angle of attack could be zero, the leading edge could be stalled, and the trailing edge would be at significant negative angle of attack.

Bob Higgins
Thanks Mr. Michler for your input.