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Help with some results regarding the Restitution Coefficient

Hi,

I'm using the Hertz-Mindlin Contact model to calculate the collision energies in my mixing system. From the theory the damping should decrease logarithmically with increasing Coefficient of restitution. However the results show me the exact opposite effect, normal and tangential collision energy loss do increase with higher CoR. So what is the reason for this, if do not change anything else then the CoR in my system? Thanks

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Stephen Cole

Hi Clemens,

In the current release of EDEM the 'Energy Loss' calculation (in track collisions) uses the following formula:

Energy loss = F * Vel * dt +T1 * ω1 * dt +T2 * ω2 * dt

Where:

F = total contact force (undamped)
TΧ= total torque on particle Χ generated from other models(e.g Rolling friction)
Vel = (vel1Before - vel2Before + vel1After - vel2After) / 2
ωX = (ωXBefore+ ωXAfter) / 2
dt = time step

The undamped force doesn't include restitution in the calculation and so the restitution only comes into play for the Vel calculation. Where higher restitution means higher Vel value and lower restitution means lower value, which is the effect you are seeing.

For definitions of the Damped and Undamped forces this is detailed in the e-learning, lesson 2.1 Hertz-Mindlin

https://learn.altair.com/course/view.php?id=148

This can be misleading as not really what you expect from Energy Loss, we have an alternative API method here:

https://community.altair.com/community/en/edem-api-contact-model-example-energy-loss?id=kb_article&sysparm_article=KB0121821

This alternative method uses the Damped component of the force which as you mention should decrease with increasing Restitution value, so I think the API model is more suited to what you are looking for.

This is not currently implemented in EDEM but targeted for future releases.

Regards

Stephen

Clemenslischka

Thank you Stephen for your reply. I found in the 2022 manual that collision energy loss is calculated based on the damped forces and the overlap. So i'm confused since you said, it's calculated by the undamped contact forces. Has there been a change in the calculation in newer versions?

I understood now (regarding my other post) and confirmed with a test simulation, that negative energy loss is actually energy gain of colliding particles. However if energy loss is calculated correctly, the net energy gain must be the same energy lost by the mixing tool. The reason that i do not use the Power value is that it gives me very fluctuating values (often zero then very high values), since it can only calculate the momentary forces this depends very much on the save interval, in contrast to the integral value of every collision energy transfer.

I came up with another way of calculating the energy transfer: Since the relative velocity before and after collision contact should include every collision losses (friction, damping, coeffcient of resitution) can i calculate the net energy transfer by:

(m_1*m_2 / 2*(m_1 + m_2)) * (vrel)^2 --> basic balance for kinetic energy based on the relative velocity before and after collision. Vrel should include then every information about collision efficiency/losses. Can you please confirm if this is also a valid approach?

Stephen Cole

Thank you Stephen for your reply. I found in the 2022 manual that collision energy loss is calculated based on the damped forces and the overlap. So i'm confused since you said, it's calculated by the undamped contact forces. Has there been a change in the calculation in newer versions?

I understood now (regarding my other post) and confirmed with a test simulation, that negative energy loss is actually energy gain of colliding particles. However if energy loss is calculated correctly, the net energy gain must be the same energy lost by the mixing tool. The reason that i do not use the Power value is that it gives me very fluctuating values (often zero then very high values), since it can only calculate the momentary forces this depends very much on the save interval, in contrast to the integral value of every collision energy transfer.

I came up with another way of calculating the energy transfer: Since the relative velocity before and after collision contact should include every collision losses (friction, damping, coeffcient of resitution) can i calculate the net energy transfer by:

(m_1*m_2 / 2*(m_1 + m_2)) * (vrel)^2 --> basic balance for kinetic energy based on the relative velocity before and after collision. Vrel should include then every information about collision efficiency/losses. Can you please confirm if this is also a valid approach?

Hi Clemens,

There was a change in 2019 (based on a customer request at the time), it looks like the documentation for that hasn't been updated. In EDEM 2019 the energy loss works as shown above and in 2019.1 it was changed to the undamped force. The 2019 version had issues with time-step dependency and accuracy due to the velocity averaging only happening before the time-step.

With the power that is correct that it fluctuates a lot, it is useful for steady state systems where you get a constant power value over time but not so good for dynamic cases .

Regards

Stephen

Clemenslischka

Hi Clemens,

There was a change in 2019 (based on a customer request at the time), it looks like the documentation for that hasn't been updated. In EDEM 2019 the energy loss works as shown above and in 2019.1 it was changed to the undamped force. The 2019 version had issues with time-step dependency and accuracy due to the velocity averaging only happening before the time-step.

With the power that is correct that it fluctuates a lot, it is useful for steady state systems where you get a constant power value over time but not so good for dynamic cases .

Regards

Stephen

Hi Stephen,

can you please give me the equation for energy loss in the API version? At the moment the page were the .dll can be downloaded looks like this (attachment) and i can not find any other documentation for it.

Also, when i integrate the .dll, how can i access the results? Is it simply by exporting the total collision energy data as usual?

Thanks

https://community.altair.com/community/en/edem-api-contact-model-example-energy-loss?id=kb_article&sys_id=c93bf888db26e910cfd5f6a4e29619c4

Unbenannt.jpg

Stephen Cole

Hi Stephen,

can you please give me the equation for energy loss in the API version? At the moment the page were the .dll can be downloaded looks like this (attachment) and i can not find any other documentation for it.

Also, when i integrate the .dll, how can i access the results? Is it simply by exporting the total collision energy data as usual?

Thanks

https://community.altair.com/community/en/edem-api-contact-model-example-energy-loss?id=kb_article&sys_id=c93bf888db26e910cfd5f6a4e29619c4

Hi Clemens,

Strange that you can't see the equations, this maybe the browser you are using or the version. I've taken a screenshot which hopefully you can see below: