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 Post subject: Bump Forces
PostPosted: June 25, 2016, 12:14 pm 
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I’m designing some shock mounts so I thought I would make a formal write up for my continuing education credits. This design is just for routine daily bumps, not curb hits. I started this study to see if I could predict tire deformation characteristics for those suspension analysis programs by equating the response of tires to bumps to that of ships hitting cylindrical docking fenders. They’re very similar for tire aspect ratios of 30 and above. Thank you for your patience.


Bump Forces

The objective is to calculate the force on the coil-over mount and related chassis structure that results from hitting a bump of a given height and length at a given velocity. Suspension motion from this bump will be under full control of the coil-over and not hit bump stops.

The force on the mount will be the reaction from the bump to the shock absorber and the spring as transmitted by the tire. The maximum reactive force from the shock absorber will be determined from the maximum velocity of the shock absorber in traversing the bump. The spring force will be determined from the spring deflection at the bump.

Basis: Ground movement transmitted to a vehicle by an inflated tire approximates the motion (force vs. time/distance) transmitted by a ship through a pneumatic cylindrical ship fender to a dock. For small deflections (deflection to diameter ratios less than 5%) the wheel motion transmitted by the tire can be represented by a sine curve, starting with zero initial vertical velocity, accelerating to a maximum velocity at mid height of the vertical travel, then decelerating to zero velocity at the maximum deflection of the shock and wheel. The slope of the sine curve at any point defines the velocity of the shock absorber at that point. The corresponding force reaction from the shock absorber can then be found from the shock dyno curve. The corresponding force from the spring can be found from its deflection curve (spring rate).

The force will be calculated for a design running bump as opposed to a catastrophic bump. The design running bump will represent a road bump that flexes the suspension to its maximum deflection at the highest likely velocity. A catastrophic bump will be anything more extreme and will not be considered here. The design running bump will be represented by a straight linear ramp since that shape will impart the maximum energy to the wheel for any given horizontal and vertical bump dimensions.

The system considers that the tire, shock and spring system absorb all energy with no kinetic energy transfer to the vehicle chassis, that is, the vehicle does not move vertically while traversing the bump. This is conservative for force calculations. In addition, the shock stiffness by design is just sufficient to fully absorb the full bump with no excess stiffness, while still being sufficiently stiff to avoid hitting bump stops.

The total force on the coil-over mount will be the shock force plus the spring deflection force at that deflection plus the static weight at the shock. Appropriate factors should be included for loading rate (impact).

In addition, there will be inertial forces on unsprung components caused by the acceleration of the wheel and attached components.


Example:
Vehicle travel velocity = 60 mph = 88 fps
Height of bump = 3” = 0.25 ft
Length of bump = 50 ft
Wheel time on bump = T = D/V = 50 ft / 88 fps = 0.57 sec
Spring rate at wheel = 150 lb per in

Wheel vertical velocity = shock velocity = dD/dT = (slope of curve at mid height) = 0.69 fps (see chart)
= 8.30 ips
= 210 mm/s

Corresponding shock force = 475 lb (see chart)

Spring force at mid height = 150 lb per in x 1.5 in = 225 lb

Total force on coil-over mount and related chassis structure
= 475 lb from shock + 225 lb from spring + static load = 700 lb + static load


Condition at top of bump, zero shock force:
Total force on coil-over mount and related chassis structure = spring reaction only = 150 lb per in x 3 in = 450 lb + static load


Inertial forces on unsprung components
A = dV/dT = 0.69 fps/(0.57/2) = 2.38 fps/s
2.38 fps/s / 32.2 fps/s = 0.07 g’s.


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 Post subject: Re: Bump Forces
PostPosted: June 25, 2016, 4:29 pm 
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Spring rate of the tire is a big part of the total. How was the value of 150 lb/in arrived at?

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 Post subject: Re: Bump Forces
PostPosted: June 25, 2016, 9:25 pm 
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The 150 lb per inch is the spring rate and was chosen just to give an example. The tire "deformation" is considered in the curve shape for a similar ship fender (I'm currently proving their similarities). The curve I chose was the most severe possible and in reality, the tire will deflect slightly differently, but no less, than the S curve I show. I'm after peak velocity here which takes place early in the curve. Beyond that, I shouldn't show anything since it is beyond the force I am after. Does that make sense?


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 Post subject: Re: Bump Forces
PostPosted: June 25, 2016, 9:41 pm 
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Not trying to blow holes in this but I think it's pretty complicated to calculate to any sort of accuracy. Shock valving, tire size, tire construction, aspect ratio, air pressure, and of course pot hole contour; my hat's off to you if you can come up with an equation that gets close to real world results. Even if the number is exactly correct, what happens when the driver increases air pressure or stiffen the shocks? Even if the math is accurate it still means doubling or tripling the final number as a safety factor, ending up using the tube sizes that Locosters use now, typically 1" x 0.063".

Back when I was designing my car I gave up after realized that I couldn't define the above terms well enough to trust the answer. For that reason I went generous on the A-arm tubes because even if my math was right, I couldn't swear that I wouldn't someday hit a pothole that was larger than designed for, so erred on the high side of what other Locosters use.

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 Post subject: Re: Bump Forces
PostPosted: June 26, 2016, 10:08 am 
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KB58
And that is exactly why I try to do it. Because it can't be done.
I get bored easily and need something to keep me busy. Humor me.
And who says it can't be done?


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 Post subject: Re: Bump Forces
PostPosted: June 26, 2016, 11:12 am 
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Bobber wrote:
...And who says it can't be done?

Not me - I said it would be hard, and after you're done, the accuracy will still be an unknown, but let us know where the research leads.

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Kimini book: Designing mid-engine cars using FWD drivetrains, http://www.kimini.com/book_info/


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 Post subject: Re: Bump Forces
PostPosted: June 30, 2016, 12:55 am 
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Location: Mountain View, CA
Bobber wrote:
Length of bump = 50 ft


To me that's a small hill, not a bump.

I'm interested in what forces might be imparted to suspension and chassis in a worst-case but realistic situation, like the far side of a pothole (let's say it's 1 1/2" deep), which could be approximated as vertical.

Care to take a crack at that?

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 Post subject: Re: Bump Forces
PostPosted: June 30, 2016, 2:17 pm 
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I hit a curb awhile back, avoiding a big rig. Probably around 4", and nearly head on. The front tire took some of the shock, the spring some more, but the car lifted up as well. So it seems like you have forces transferring all along the way, and only the weight of the car resisting them. What the maximum force was, I couldn't really say, but the suspension wasn't damaged so it couldn't have been that bad.


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 Post subject: Re: Bump Forces
PostPosted: July 5, 2016, 1:58 pm 
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Right, hitting a curb is an even better severe but realistic load case.

I'm surprised your car survived it w/o damage.

How fast were you going?

How tall is the tire sidewall?

Are the wishbone inner mounts rod ends or compliant bushings? The latter would reduce the forces a lot.

How much of a jolt did you get?

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 Post subject: Re: Bump Forces
PostPosted: July 5, 2016, 8:28 pm 
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Joined: April 23, 2006, 8:26 pm
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Tire pressure, sidewall height, and shock valving all play a big part in the transmitted forces.

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 Post subject: Re: Bump Forces
PostPosted: July 6, 2016, 3:26 pm 
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NoahKatz wrote:
Right, hitting a curb is an even better severe but realistic load case.

I'm surprised your car survived it w/o damage.

How fast were you going?

How tall is the tire sidewall?

Are the wishbone inner mounts rod ends or compliant bushings? The latter would reduce the forces a lot.

How much of a jolt did you get?


I was going about 35-40. It was a big jolt, but I've been jolted worse on bad back roads. I'm running 70-series tires, so lots of give there, and the wishbone mounts are Spitfire Metalastiks, so even better.

The suspension was undamaged but the floor took a hit. Luckily 16 gauge steel with extra cross tubes (Aussie mod) in the seating area. Scraped it up pretty good, though.


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 Post subject: Re: Bump Forces
PostPosted: July 13, 2016, 10:54 am 
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Bobber wrote:
KB58
And that is exactly why I try to do it. Because it can't be done.
I get bored easily and need something to keep me busy. Humor me.
And who says it can't be done?


Ummm, you just did. :D

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 Post subject: Re: Bump Forces
PostPosted: July 13, 2016, 12:07 pm 
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Trochu wrote:
Bobber wrote:
KB58
And that is exactly why I try to do it. Because it can't be done.
I get bored easily and need something to keep me busy. Humor me.
And who says it can't be done?


Ummm, you just did. :D


The actual post:
KB58 wrote:
Bobber wrote:
...And who says it can't be done?

Not me - I said it would be hard, and after you're done, the accuracy will still be an unknown, but let us know where the research leads.

_________________
Midlana book: Build this mid-engine Locost!, http://www.midlana.com/
Kimini book: Designing mid-engine cars using FWD drivetrains, http://www.kimini.com/book_info/


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