Impact force calculation due to a rotating object in Overspeed Trip Valve Design

[SurajS]

TL;DR

I want to estimate impact force generated due to collision between rotating body and stationary object. Bolt assembly is in balanced condition with the spring force and centrifugal force. As the speed of the shaft increases , centrifugal force on bolt assembly dominates the spring force which results in outward motion of bolt and thereby colliding with horizontal lever which thereby shuts off the fuel. Can you please guide me how to estimate impact force here.

Bolt comes out by distance d=1.58 mm when speed of rotation of shaft reaches its trip value (w_trip). m is mass of trip weight (Bolt assembly)
One of the approach which I had considered is work energy theorem.
Initial energy = 0.5m*(w_trip*(r+d))^2
Final Energy= 0.5m*(w_trip*r)^2 (Assuming bolt will come back at a distance r (original position) just after impact, and speed will be remain same just after collision)
Workdone = friction force at knife edge (intermediate lever) * knife edge thickness at interface
I want to estimate mass (Bolt assembly(Highlighted))required to produce this work done or in other words, impact should be able to trip the system.
Is this a correct approach?
Can I get to know impact force coming at impact?
Please help.

 

[jrmichler]

I see that your diagram is from: https://marinersgalaxy.com/what-is-overspeed-trip-its-types-and-how-it-works/.
Impact forces are very difficult to calculate because they are dependent on the contact stiffness, mass of each part, and stiffness of each part. A general rule is that if the bolt head moves far enough to hit the trigger, it will eventually hammer the trigger far enough to trip the cutoff. Eventually could be one or two revolutions, or several dozen revolutions.

If the spring constant holding the bolt is low enough, the bolt will have two stable positions. It will be fully retracted up to the trip speed, then jump to the fully extended position at overspeed. With a stiffer spring, the bolt will gradually extend until it is lightly tapping the trigger, then eventually move the trigger far enough to trip the fuel cutoff.

 

[SurajS]

Thanks.
Still if I want to calculate the force generated considering stiff spring, what is formal way to do so..Can ansys help me solve the problem?
Is there any analytical way with simplified assumptions? I want to decide spring and trip mass (Bolt).

 

[jrmichler]

Start with a free body diagram of the bolt. You have a force because it is spinning and the center of gravity is not at the center of rotation, and another force from the spring. One force is larger at low speed, the other force is larger at high speed. Calculate the forces vs speed for the bolt retracted and extended. Do that for a high stiffness spring with minimal preload, and a low stiffness spring with a larger preload. Both of those springs should have the same force with the bolt retracted.

Keep at it until you fully understand the relationship between bolt location (retracted vs extended) and bolt mass, bolt center of gravity location, speed, spring stiffness, and spring preload. Then, and only then, look at the rest of the mechanism. You need to fully understand the bolt and spring by itself before looking at impact. And you do not need simulation software to do this. You are better off using a pencil, paper, and a hand calculator.

 

[JBA]

If it is available to you, my preference would be to use MSExel to allow you to quickly make changes each of the input values and see the effect(s) of each change on the mechanism.

 

[SurajS]

I have understood the motion of bolt as Bolt will always in equilibrium throughout the motion till impact.:
In the running condition, say rpm of 3000 rpm bolt will be in its retracted condition. F_centrifugal= F_spring.
As the speed increases, bolt moves out gradually but still in equilibrium. As speed approaches trip speed (say 3465 rpm) it will be in its maximum extended condition where it hits the trip lever. I also have seen the video of oeperation.


Having understood above aspects, if I try by the aforementioned energy approach, can i estimate mass of the bolt and spring stiffness of spring and also the force of impact.
My ultimate aim is to design the trip system.

 

[SurajS]

I have understood the motion of bolt as Bolt will always in equilibrium throughout the motion till impact.:
In the running condition, say rpm of 3000 rpm bolt will be in its retracted condition. F_centrifugal= F_spring.
As the speed increases, bolt moves out gradually but still in equilibrium. As speed approaches trip speed (say 3465 rpm) it will be in its maximum extended condition where it hits the trip lever. I also have seen the video of oeperation.


Having understood above aspects, if I try by the aforementioned energy approach, can i estimate mass of the bolt and spring stiffness of spring and also the force of impact.
My ultimate aim is to design the trip system.

I wrongly uploaded the video link from youtube. The right link is as given below.

 

[JBA]

In viewing the last example video, it appears that device does not depend upon any impact function. It simply extends the spinning actuator until it reaches an extension that moves the latch a sufficient distance to release the plunger. As a result, no impact analysis is required, the design is simply based upon balancing the centripetal force vs the spring force to get the required plunger extension at the desired rpm.

 

[SurajS]

In viewing the last example video, it appears that device does not depend upon any impact function. It simply extends the spinning actuator until it reaches an extension that moves the latch a sufficient distance to release the plunger. As a result, no impact analysis is required, the design is simply based upon balancing the centripetal force vs the spring force to get the required plunger extension at the desired rpm.

Since the mechanism is activated by interaction between the bodies, which is collision, we have to consider the impact based on stiffness and type of collision which will be inelastic.

 

[JBA]

One difference between your design and the one above is the the one above has a slightly more than 180° contact cam that appears to possibly have a slightly elliptical profile (similar to the valve lift cams in an auto engine) that would minimize the lever acceleration of the point initial contact as opposed to your narrow striker that would have a more abrupt initial lift acceleration.

 

[SurajS]

One difference between your design and the one above is the the one above has a slightly more than 180° contact cam that appears to possibly have a slightly elliptical profile (similar to the valve lift cams in an auto engine) that would minimize the lever acceleration of the point initial contact as opposed to your narrow striker that would have a more abrupt initial lift acceleration.

Yes but how to quantify impact force is still a big question for me!

 

[JBA]

If this were two rigidly mounted striking items it would be easy; but because the lever deflects and that represents the same as striking a relatively soft material it is more difficult. In order to determine the minimum impact calculate the spring force at the point of contact with the lever in its rest (cocked) position and you will be able to determine the maximum travel of the lever at that force based upon the contact force/the spring rate.

Beyond that the calculation it gets more complicated because the rotating inertia of the lever at the above contact force vs its rotating inertia will then determine levers initial vertical acceleration at the point of impact and this then can be used to determine the travel of the lever vs to the resisting spring force. In the end this is what you really need to determine if your device will release the lever. (i.e In actuality, the lever will rotate/travel a bit further due to its inertia once in motion.) The only reason to worry about that actual contact force at the point of impact is if you are concerned about whether your your components materials are strong enough to prevent excessive wearing damage after repeated actuations.