# Negative Temperatures in Thermal Study Using Simulation

**1-GEPWUE**Aug 5, 2010 2:30 PM

Hello, I am a mechanical engineering student currently taking a finite element analysis course. Part of the class curriculum is a major group project that will count for 40% of our total grade. My group and i have chosen to perform FEA on a front disc brake from last year’s formula SAE car. With the guidance of our instructor we have decided to use circular symmetry and to only perform the analysis on a small segment of the disc. The disc segment is only a fraction larger than the size of the brake pad, it’s arc length and radius is related to its angle of 36 degrees, leading to 10 equal segments total.

We have chosen to ignore a few features that the floating rotor contains in order to simplify the process. Meaning that we are ignoring the parts of the rotor where it is mounted to the hub via rivets. We have also decided that we will apply a time varying thermal load (Heat Flux) to the disc segment in order to simulate the heat generated due to the friction between the brake pad and the disc. The time variance is selected in order to recreate the spinning of that segment under application of the brakes. I would like to state that this disc brake is more like a motorcycle disc brake than that of an automobile.

My group and I are attempting to focus on a worst case scenario of braking: when all the kinetic energy of motion is converted to thermal energy without any skidding or slipping of the tires. The vehicle will initially be moving at 80 mph and then come to a complete stop by braking with absolutely no slipping of the tires (idealization). Because the tires cannot exceed a maximum acceleration of 1.5g’s we have taken this as the value of linear decelerating while the vehicle is under motion. Using kinematic equations we have derived the total stopping distance (142.516 ft) and the total stopping time of 2.42925 seconds. Using rigid body dynamics it was possible to calculate the angular velocity of the disc’s center along with the angular acceleration.

If the disc segment were to be outlined on the complete disc it would be seen that under normal operating conditions the segment would spin and be subjected to loading. The loading would be applied to portions of its total area because the far right edge of the segment must reach the far right edge of the brake pad before the entire disc segment is momentarily under a load. Right after the entire disc is loaded the same will occur as the far left edge of the disc segment moves towards the far right edge of the brake pad. Instead of applying not only a time varying load but also a position varying load we have decided to take an average and just say that the time it takes for the far right edge of the disc segment to reach the far right edge of the brake pad is the total time that the disc will be loaded on an double sided imprint of the brake pad.

Through a long and tedious process using angular motion equations and spread sheets we were able to determine the approximate time at which the disc segment’s far right edge was at the brake pad’s far left edge (position1), and when it was at the brake pad’s far right edge (position2) traveling 36 degrees. This allowed us to model the loading (heat flux) of the disc segment as a function of time. In other words, our load scenario will follow the segment of rotor as it travels from the brake pads (modeled by the heat flux) out to into the ambient air (modeled by convection). Now, in order to get the full scope of the temperature changes, from 80-0 mph, we will be repeating the load scenario several times as a transient study. We believe that this is a good replication of the segment as it undergoes rotation; to the pads (flux) and out (conv.), to the pads and out, and so forth. We have assumed that convection is only being applied while the disc is not loaded because of little to no airflow passing past the segment as the rotor is being firmly sandwiched between the brake pads. This lead to modeling convection as a time dependent function that remains at a constant value when it is applied (no loading). We chose to keep the convection constant because we had no way of obtaining an accurate Reynolds Number. The only published Reynolds Number that we found was for an average half-ton truck, while the rotors were exposed to turbulent airflow (the number was a lower bound, any number > 2.4E5). There was no published laminar flow number, so we chose a lower number than 2.4E5 to describe a laminar flow. The airflow around a truck’s brakes would differ from an open-wheel 430 lbs race car. Unfortunately, we have no access to full size wind tunnels, so we made due with the truck’s Re.

To analyze this scenario, we utilized a transient thermal study within SolidWorks Simulation. We applied the material (1020 steel) properties and set the total time to 2.429 seconds, using time intervals of .001 seconds. This yields 2429 steps that need to be calculated. We chose a nanosecond as the time interval in order to accurately capture every time the rotor passed (loaded) by the heat flux, which accounts for only 36 degrees of a full rotation. Based on spreadsheet calculations, a time interval smaller than a nanosecond would just create even more steps, and a time interval larger than a nanosecond would leave omit loadings. We say omit because we want to be able to use every solution (CAD model with gradient colors) of every interval in our class presentation (CDR). After, we applied an initial temperature of 90 degrees Fahrenheit (usual ambient air temperature at the annual competition location), we applied the aforementioned time-varying heat flux. Referring to the book Brake Design and Safety by Rudolf Limpert, we decided to assume linearly decreasing heat flux with the intent that this method was accurate enough to present a real world scenario, while keeping it simple enough to perform quick calculations. An average heat flux was found using a formula in Limpert’s book. The heat flux would start at 2 times the average (at the onset of braking at 80 mph), and linearly drop down to zero (0 mph) over the total time of 2.429 sec. The slope of the line was found, which resulted in a flux load at its given load time. The time and the load multiplier (flux @ t / average flux) were entered into the time-variance table. The same was done to enter the time-variance for convection, except the convection load was applied during the intervals when the flux load wasn’t being applied. We used the default mesh size, and set mesh controls on areas with sharp edges. We ran the study, and the Solver dialogue box stopped on step 9 on several occasions, and on different computers. Despite the hiccup, a solution is found. The problem is that the solution is completely erroneous. We are seeing minimum temperatures of ~85 K! That’s almost -200 degrees Celcius.

We tried varying different minor changes, that did not change the load scenario, to no avail. We’ve sat for hours scouring forums, free technical reports, and websites and have not found anything that fixes the issue.