Impact Force, Cantelever Beam, Elastic
Impact Force, Cantelever Beam, Elastic
(OP)
Background Informatiom:
I have a problem that requires the input of impact force data into an FEA for structural design. I have a machine with two front wheels and one rear caster. The wheels and caster are suspected to have implications on strength requiresments of the machine frame; therefore, to minimize the total cost of frame, wheels, and caster I am investigating the effect of different wheel and caster designs on frame strength requirement. In other words, I can pay for a more expensive caster or wheel if it allows me to design a sufficiently less expensive frame. In this problem, I will only be dealing with the rear caster.
The machine CG (center of gravity) is between the front wheels and rear caster, and rather high so that ramp angles shift the machine weight between front wheels and rear caster.
The impact force of concern is the result of driving the machine off a three inch tall curb or ledge. To simulate this scenario, I placed the placed the front wheels of the machine on a lift table and I held the rear of the machine with a quick release trigger so that the rear caster had three inches below it and the "ground". Now what I refer to as the "ground" is actually a load cell that will measure force versus time. I also have an accelerometer mounted to the top of the caster mounting plate, so there is a load cell at the bottom of the caster and an accelerometer at the tope of the caster so elasticity of caster tread will cause some differences and/or lag between force and acceleration measurements.
The rear caster is attached to the machine via a stiff (not rigid) beam. The wheels are directly attached to the machine frame.
Test Conditions:
The machine began level with the ground and the rear of the machine was suddenly dropped three inches (rotational motion about the front wheel axis). A small DOE was run so that there was two different caster tread hardnesses tested and two different weights applied to the caster. The caster loading was measured at the end of each test run because the weight distribution had changed (ramp angle) and because the weights in the machine were launched slightly out of position (this represents real-world application, although not ideal for testing).
The low weight tested was 60 lb and the high weight tested was 90 lb.
The hard caster tread was Shore D 95 (phenolic material), and the soft caster tread was Shore D 15 (neoprene material).
Data:
Impact forces (load cell measurements) for both casters was approximately 700 lb for the low caster loading condition and approx 1050 lb for the high caster loading condition.
The data shows that the impact force measured is linearly correlated to the weight placed over the caster (at the end of the test, with the machine 3" out of level) with an r^2 value of 82.1%. Therefore, the wheel hardness had close to zero effect on measured impact force.
The soft tread caster had g-loads (acceleration) of 15 g's for both high and low caster loading conditions.
The hard tread caster had g-loads of 55 g's for both high and low caster loading conditions.
The data shows that tread hardness has a significant effect on measured acceleration during impact.
Problem Statement:
The force measured at impact is the same for the soft and hard caster tread, but the acceleration values are different by a factor of ~3.7. I do not know if I should use the measured g-loads (acceleration divided by gravity) or if I should use the force loads. I do not believe that the tread hardness has no effect on machine frame stress during impact, but my superior engineer (almost boss) does believe that the tread hardness should not effect impact forces the frame must support.
Questions:
1) What force should I use in my FEA in order to calculate stresses in the cantelevered beam that the caster mounts to?
2) Can anyone explain why the measured force is not effected by tread hardness?
3) My superior engineer said that the resonant frequency of the frame (i.e. system) that attaches the caster and wheels to the machine must have some resosnant frequency that forbids/prevents the tread hardness to eefect the impact force...which he knows because he used to do isolation designs for computer parts.
4) Is there a way for me to upload JPEG files of my Free Body Diagram, test results, etc. onto this forum?
Thanks in advance for your help!
Justin
I have a problem that requires the input of impact force data into an FEA for structural design. I have a machine with two front wheels and one rear caster. The wheels and caster are suspected to have implications on strength requiresments of the machine frame; therefore, to minimize the total cost of frame, wheels, and caster I am investigating the effect of different wheel and caster designs on frame strength requirement. In other words, I can pay for a more expensive caster or wheel if it allows me to design a sufficiently less expensive frame. In this problem, I will only be dealing with the rear caster.
The machine CG (center of gravity) is between the front wheels and rear caster, and rather high so that ramp angles shift the machine weight between front wheels and rear caster.
The impact force of concern is the result of driving the machine off a three inch tall curb or ledge. To simulate this scenario, I placed the placed the front wheels of the machine on a lift table and I held the rear of the machine with a quick release trigger so that the rear caster had three inches below it and the "ground". Now what I refer to as the "ground" is actually a load cell that will measure force versus time. I also have an accelerometer mounted to the top of the caster mounting plate, so there is a load cell at the bottom of the caster and an accelerometer at the tope of the caster so elasticity of caster tread will cause some differences and/or lag between force and acceleration measurements.
The rear caster is attached to the machine via a stiff (not rigid) beam. The wheels are directly attached to the machine frame.
Test Conditions:
The machine began level with the ground and the rear of the machine was suddenly dropped three inches (rotational motion about the front wheel axis). A small DOE was run so that there was two different caster tread hardnesses tested and two different weights applied to the caster. The caster loading was measured at the end of each test run because the weight distribution had changed (ramp angle) and because the weights in the machine were launched slightly out of position (this represents real-world application, although not ideal for testing).
The low weight tested was 60 lb and the high weight tested was 90 lb.
The hard caster tread was Shore D 95 (phenolic material), and the soft caster tread was Shore D 15 (neoprene material).
Data:
Impact forces (load cell measurements) for both casters was approximately 700 lb for the low caster loading condition and approx 1050 lb for the high caster loading condition.
The data shows that the impact force measured is linearly correlated to the weight placed over the caster (at the end of the test, with the machine 3" out of level) with an r^2 value of 82.1%. Therefore, the wheel hardness had close to zero effect on measured impact force.
The soft tread caster had g-loads (acceleration) of 15 g's for both high and low caster loading conditions.
The hard tread caster had g-loads of 55 g's for both high and low caster loading conditions.
The data shows that tread hardness has a significant effect on measured acceleration during impact.
Problem Statement:
The force measured at impact is the same for the soft and hard caster tread, but the acceleration values are different by a factor of ~3.7. I do not know if I should use the measured g-loads (acceleration divided by gravity) or if I should use the force loads. I do not believe that the tread hardness has no effect on machine frame stress during impact, but my superior engineer (almost boss) does believe that the tread hardness should not effect impact forces the frame must support.
Questions:
1) What force should I use in my FEA in order to calculate stresses in the cantelevered beam that the caster mounts to?
2) Can anyone explain why the measured force is not effected by tread hardness?
3) My superior engineer said that the resonant frequency of the frame (i.e. system) that attaches the caster and wheels to the machine must have some resosnant frequency that forbids/prevents the tread hardness to eefect the impact force...which he knows because he used to do isolation designs for computer parts.
4) Is there a way for me to upload JPEG files of my Free Body Diagram, test results, etc. onto this forum?
Thanks in advance for your help!
Justin





RE: Impact Force, Cantelever Beam, Elastic
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RE: Impact Force, Cantelever Beam, Elastic
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RE: Impact Force, Cantelever Beam, Elastic
I would build a simple 2 dof spring mass system and see if I can understand the time histories with that.
If you carefully optimise everything for a 3" drop, what will happen in the case of a 4" drop?
Cheers
Greg Locock
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RE: Impact Force, Cantelever Beam, Elastic
maybe you can investigate the resonance suggestion by slightly changing the test conditions ... 2.5" drop, 3.5" drop. highly corelated results (linear?) would suggest against resonance.
Quando Omni Flunkus Moritati
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
Ted
RE: Impact Force, Cantelever Beam, Elastic
i think the acceleration exists during the impact, when the cart is still pivoting about the front wheels. you know how much energy the cart has before the contact. the ground opposes this energy with a contact force (through the resilent tire), and this causes the cart to decelerate.
Quando Omni Flunkus Moritati
RE: Impact Force, Cantelever Beam, Elastic
There are no differences in mass. The two different casters each weigh within 0.01 lb of each other, purely by coincidence. The machine weights were not different between casters; however, the low caster load required a machine weight of ~12 lb less than the high caster load.
I can't technically say that the caster is mounted via a suspension system, but I can say that the caster is attached to the frame by a short piece of sheet steel so some flexibility exists. I cannot see the steel deflect or bend when I put my body weight on it (175 lb).
I do not understand how to do this time history analysis you speak of. Can you explain, or direct me to a textbook, or give me a technical name I can research? I'll attach data plots for acceleration and force in separate replies.
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
RE: Impact Force, Cantelever Beam, Elastic
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RE: Impact Force, Cantelever Beam, Elastic
Quando Omni Flunkus Moritati
RE: Impact Force, Cantelever Beam, Elastic
Also, the acceleration plots correlate with the notion that a squishier wheel would result in prolonging the impact, which is borne out by the duration of the force curves. The prolonged impact is where the peak accelerations wind up being different.
TTFN

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RE: Impact Force, Cantelever Beam, Elastic
The force is measured at the bottom of the caster wheel. The caster is colliding with the force gage.
The acceleration is measured on top of the steel plate to which the caster is mounted, directly over the caster swivel bearing axis.
The force is measured with a strain type force gage and not calculated.
The acceleration is measured with an accelerometer, probably the type that measure the resulting vibration of a crystal.
RE: Impact Force, Cantelever Beam, Elastic
Phase shift at beginning of data: The accelerometer outpust data slightly before the force gage, and I do not believe the time shift is reasonable. The point of impact is the point where the force is measured (well, there is a two inch thick aluminum plate between the caster and force gage). The accelerometer is at the opposite end of the caster, which is about 4 inches away. I brought this up to my test engineer and he is so far convinced the data is correct and my theory is incorrect.
Phase shift between peak acceleration and peak force: I think it is reasonable for peak force to occur after peak acceleration because peak force should exist when all material are fully compressed and at that moment the acceleration should be instantaneously at zero...then the force should reduce and acceleration should be in the opposite direction as it was just before the force peaked. I suspect peak acceleration should exist at the instant of impact, and peak force should exist moments later when the parts are all fully compressed given their respective spring rates (stiffness, or elasticity).
RE: Impact Force, Cantelever Beam, Elastic
If F is the same, and a is 4 times different, then m must be different. We aren't talking about rigid bodies, we are talking about the effective mass that is coupled to the impact, which is what your almost boss was getting at.
I haven't the time tonight to look at your plots, but I will try to in the next day or so. It would help greatly if you could post the corresponding data in csv format.
Cheers
Greg Locock
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RE: Impact Force, Cantelever Beam, Elastic
If you just concentrate on the accelerations, the soft caster is doing a pretty good job of minimizing the impact shock. Note that the hard caster actually bounces a few times; even the second bounce has about a 25-g peak (at ~0.23s), which is still bigger than the first shock from the soft caster, and the soft caster does not appear to have more than possible second bounce at ~0.4s.
TTFN

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RE: Impact Force, Cantelever Beam, Elastic
Since your a and F signals aren't in phase all the blathering about mass I made was irrelevant.
The time constant of the ringing on the force signal is the same for both tests which implies to me that you have an instrumentation issue, since I would expect the ringing frequency to be modified by the tire compliance.
So, overall I don't trust your force measurement. That's a pity as it is far more important than the acceleration for your purposes.
I was going to build a 2dof model, but given the massive change in static load caused by the drop I don't think that is quite as easy as I'd hoped. I haven't worked out the geometry that can cause a weight change from 60 to 200 lb with a 3 inch drop, but it is pretty odd. The water weighs 100lb so if it moved from over the front wheels to over the rear wheel that would do it, but that seems like a curious geometry as well.
Cheers
Greg Locock
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