Table of Contents

Key Questions for SubsystemLevel Design Phase
Our goal for Phase 3 was to answer the following questions:
 Will we model off of the DS264 or develop a unique design?
 How many rollers will we use and what is the approximate size? Two Rollers  400 mm long with an outer diameter of 320 mm
 Where is the most power being used? During the cutting process but the inertial power is not negligible
 How powerful do the motors need to be? still open
 What material will the rollers be made of? still open
Key Takeaways from Customer Visit
 Pitch settings are determined by the customer and vary from 1.5 to 6.7 mm
 The cuts per run depends on the length of the roller which should be 400 mm
 The largest ingot size is a 220 mm cube
 The rollers do have two separate motors
 The coolant in the bearings has not been changed to date
 Americanmade parts are requested due to patriotism and reliability
 Documentation on how to change the rollers has been provided
 Able to see how the rollers are mounted
 Unable to take current draw readings from the machine at this time
Engineering Considerations
The live document can be found here
Selection Parameters
The following information was used to make consistent engineering considerations through this phase:
The live document can be found here
Assumptions
Overall Assumptions
 Length of roller= 400 mm
 Mass of roller (2 roller system) = 65 kg (½ of DS 264 roller mass)
 Mass of roller (3 roller system) = 16 kg
 Outer diameter of 3 roller = .16 m
 Roller material: steel
Power Consumption Assumptions
Using the model of the DS264, the power that is not used to turn the rollers (inertial torque) is being used in the cutting process. The DS264 was designed to make 4100 cuts at a time.
Torque Assumptions
 Derived calibrated equation is somewhat representative of the torque required. During a meeting with our guide Ed Hanzlik and Professor Wellin, no major objections were raised against it.
 Three roller configuration will probably require 3 motors of the same size for each roller. It is possible the third roller does not require any motor or requires a motor that is weaker than the other two, but this is an unknown with the three roller configuration.
 The assumption is that having a higher total rated horsepower will correlate to having more energy consumption in the long run.
 Scaling original mass of DS264 rollers based on volume ratios.
 Acceleration of wire remains the same at 2 m/s^2 and maximum wire velocity is still 15 m/s for both configurations.
Stability Assumptions
The force from the workpiece on the wire in the direction of the wire is scalable from the MB DS264 and all of the power is going to overcoming this force.
In order to make this assumption, the inertia of the rollers in the MB DS264 must be neglected and the MB DS264 must be fully wound with the max number of wires. It is okay to say inertia is negligible in this situation because it accounts for only about 10% of the power. It is okay to think of the MB DS 264 as fully wound because it must have been designed for this full capacity since we know it runs like this in other applications.
Mechanical Stress/Deflection Assumptions
 The material properties determined by the group will be used for this analysis where possible. Otherwise properties are taken for 1040 steel.
 Length is 400mm (Customer Requirement).
 Elastic Modulus is 200 GPa for 1040 steel (metweb.com).
 Yield Stress is 415 MPa (matweb.com).
 Ultimate Stress is 620 MPa (matweb.com).
 The rollers will be treated as a solid shaft. In actuality there will be a hollowed roller slid over a shaft. In terms of mechanical roller stress this will be the same, but for now critical features such as splines, keyways, and pins are ignored. They will be done next phase.
 There is an additional 20 mm of non work area added to each side. Presumably the wire will not wrapped all the way to the edge of the roller, we will need a small length for mounting. This could be a smaller diameter (as shown in sketch) or the full OD. 20 mm is taken from current roller.
 Wire tension is treated as a distributed load with wire tension assumed to be 25 N for the worst case analysis. Pitch is assumed to be 1.515 mm for the smallest pitch setting.
 Tm = 10.99 Nm for two rollers and 0.78 Nm for three rollers (Group Numbers).
Vibration Assumptions
 Rotating mass unbalance
 Light damping
 1 degree of freedom
 Roller is a simply supported circular beam
 Pseudodensity and solid circular cylinder used to calculate mass
Thermal Effects Assumptions
 The primary mode of heat transfer between the wires and the guide rollers is via conduction.
 The temperature effects of the bearings are unable to be calculated at this time.
The live document can be found here
Analysis
Power Consumption
The inertia of the rollers were found using the equation:
This was converted to a torque by multiplying by the angular/rotational acceleration which is kept at a constant 12 rad/sec^2 throughout all calculations using equation 2 below.
The total power available to use from the original 47 kW motor was calculated using equation 3 below. The motor efficiency (labeled η) was set to a constant 80% based on NEMA standards but can be changed for more accurate results. FS is the factor of safety, which will be determined next phase.
This value was then converted to a torque in Nm by dividing the available power by the PRM of the system. The motor speed needed to be converted to radians/second first. This is present in equation 4 below.
We are assuming that if the torque required to overcome the inertia of the roller is subtracted from the total available torque, the remainder will be put into the cutting process. We make this assumption because the torque required to overcome the inertia is such a small portion of the motor capability. This means that the size of the motor must have been originally selected to overcome the cutting requirements. Taking this into account, the torque used for each individual cut was found through equation 5 below, assuming the DS264 was meant for 4100 cuts.
By multiplying the torque per cut by the new estimated maximum number of cuts (265), the torque required for our new motor is calculated. Adding in the inertial torque of the new rollers and converting back to horsepower, the total required power for a two and three roller system can be found. Taking into account an efficiency of 80% and varying factors of safety, the new size of an over powered motor can be found, as seen in the tables below.
The live document can be found here and the live calculator can be found here
Torque
RPM, Roller Diameter, and Total Horsepower required analysis:
The equation may not be and most likely is not a precise model of the system. Rather it is a calibrated and approximated model. Below, the calibration is shown on the leftmost column where at maximum cuts, the torque required is about 500 Nm, which is the DS264 guide roller motor nominal torque as found on the motor nameplates. Note that the total horsepower multiplies the single motors hp by 2 or 3 depending on roller configuration. If the three roller system requires three motors, it will require a combined horsepower of motors that is greater than the two roller configuration. If it is possible to leave the third roller to spin freely without a motor, than the three roller configuration is more efficient than the two roller configuration. However, removing the third motor might cause larger tension differences in the roller system, which may or may not affect operation and cut quality.For high cuts, 3 motors/rollers is actually less efficient than 2 rollers/motors, if we want to keep the same wire speed of 15 m/s. This is partly due to a higher RPM at smaller rollers and the fact that a frictional force will affect larger rollers less proportionally. However, for a low number of cuts, the three roller system does start to be more efficient comparatively. This could be a reason why the DS 264 has two rollers. Looking at inertia alone, 3 rollers is clearly more efficient if the three roller radius is half of a two roller system.
The live document can be found here
Additional Graphs can be found here and a summary table can be found here
Stability
Will using smaller rollers critically affect the stability of their tangential velocity? How might perturbations affect a smaller roller vs. a bigger roller?
It is important to us that the tangential velocity of the rollers is consistent between rollers because any difference in speed will cause a change in wire tension.
Using the standard dimensions for comparison that the team decided on. These dimensions are not all necessarily accurate, but allow us to make an adequate comparison between the options.
A valid example of a perturbation for our application is hitting a rough spot in the workpiece. How will our system react to a change in force from the workpiece? Using previous calculations we can assume the force from the workpiece on the wire in the direction of the wire is about 55N for when there are 260 loops of wire (our max) and 11N for when there are 58 loops (our min). Let’s analyze the effect of different levels of perturbation in this force for our max and min cases.
Using T=Fd, T=I*alpha;, and a=r*alpha; yields
We see that there is a direct and linear relationship between the change in force from the workpiece and the acceleration. For both the MIN and MAX cases we find that a change in torque from the workpiece results in 4.08 times the tangential acceleration for a 3 roller system when compared to a 2 roller system. This tangential acceleration, if not immediately, sufficiently, and synchronously corrected for by the motors, could cause the wire to stretch too much and yield. This effect applies anywhere on the wire path.
Further analyzing the equations, it is evident where this 4.08x number comes from:
* From T=Fd we get the ratio of the radii * From T=I*alpha; we get the inverse ratio of the inertias * From a=r*alpha; we get the ratio of the radii
For our application this gives (I1/I2)*(r2/r1)^2=(.832/.051)*(.08/.16)^2=4.08
So although decreasing the radius alone increases stability in wire velocity, this causes a decrease in the inertia, which has a dominant negative effect.
Now what if the perturbation comes from a motor? Suppose that one motor supplies a slightly different torque than it is supposed to. The effect this would have breaks down into (I1/I2)*(r2/r1)=(.832/.051)*(.08/.16)=8.15
A perturbation from the motor would result in 8.15 times the effect in our 3 roller system than our 2 roller system.
Conclusion: Our 2 roller system offers better stability than our 3 roller system. Perturbations along the wire path result in 4.08 times the tangential acceleration of the wire with 3 rollers and perturbations from a motor result in 8.15 times the tangential acceleration of the wire with 3 rollers. Better motors and controllers could make this a nonissue.
The live document can be found here
Mechanical Strength
Draw the Shear and Moment diagrams. Moment is the area under the Shear plot
Area under the curve:
Combining these equations yields at the center of the roller.
There are also critical points at the edge of the work area, if there is a decrease in diameter, as this will yield a stress concentration. This will be analyzed next phase as it is not a part of roller sizing. In order to predict factor of safety, the Soderberg Failure Theorem will be used. This is the most conservative failure theory, and will ensure the shaft survives.
When taken from Shigley’s Mechanical Design, Soderberg’s theorem states equation 3 below.
This gives the relation between diameter and design factor.
For the roller loading, torque is not alternating, and moment is fully reversing, so this simplifies to equation 4 below.
For analysis of the work area critical point, the stress concentrations are 1 as there is no diameter change or feature to experience a stress concentration.
In order to determine the endurance limit, equation 5 below was used.
Assuming machined or cold drawn material, the following parameters were used.
For ultimate stress less than 1400 MPa, we can use equation 6 below.
Therefore, the stress in the two different roller diameters are calculated and shown below.
The magnitude of the distributed load is calculated using equation 7 below.
Where theta is the angle between the direction of tension and the y axis. For two rollers this value is zero, and for three rollers this value is 15 degrees.
Plugging (7) into (2) and solving for maximum moments yields the values shown below.
Solving (4) for factor of safety yields the results shown below
The factor of safety is much higher for the 2 roller configuration, however the factor of safety for both roller configurations is so high that either one should be more than adequate for the mechanical stress that the system is experiencing. Even if something was overlooked, either roller should be adequate. It is more likely the system will mechanically fail where it is coupled to the motor.
The live document is part of the mechanical analysis which can be found here
Deflection
Taking the elastic curve for a distributed load from Beer and Johnston:
Using the distributed load and equation 2, deflection can be calculated using equation 3 below.
The result of this analysis are shown below:
The live document is part of the mechanical analysis which can be found here
Critical Speed Analysis
Using Rayleigh’s Method, the critical speed is determined by breaking the shaft up into several lumps and plugging into equation 1 below.
Solving using 8 equal sized lumps yields critical speeds of 470707.6 rpm for the two roller configuration and 117676.9 rpm for the three roller configuration.
The live document is part of the mechanical analysis which can be found here
Vibration
A rotating mass unbalance vibration model can be used to determine impact of unbalance in a rotating part. Assuming the rollers are constrained to 1D motion in the vertical direction, the rotating unbalanced mass will have a net effect of a sinusoidal input force on the system. It is important to see how periodic input forces compare with the natural frequency of the system to avoid detrimental instabilities at resonance.
It was shown that for a 1DOF rotating mass unbalance model that, with light damping, the highest response amplitude (due to the sinusoidal input from the unbalanced mass) occurs when the rotational speed of the roller is equal to the natural frequency of the roller. If the ratio of input frequency to natural frequency is much less than 1, there will be a reduction in response amplitude. If the ratio is much larger than 1, the response amplitude will approach the input amplitude.
From this model we can conclude that is it desirable for the natural frequency of the rollers to be significantly higher than the maximum operating speed of the rollers (i.e. the input frequency due to an unbalanced mass). This will diminish any vibration due to unbalanced mass and support maintaining uniform tension and high cut quality.
After reviewing schematics of the DS 264 and seeing how the rollers are actually mounted, the model was revised from that used in the previous feasibility analysis in phase 2. In the revised model, the spring constant of the system comes from the roller itself, modeled as a simply supported circular beam. This yields the following expression for an estimate of the natural frequency of one roller, which is identical in form to the previous model.
However, R is now the radius of the roller, rather than the radius of some small mounting rod. E is the modulus of elasticity of the roller, L is the length of the roller, and M is the mass of the roller. This can be used to analyze the impact of change the mass and dimensions of the roller on the resulting natural frequency. Natural frequencies for a variety of systems are shown in the table below. Assuming we maintain the maximum speed of the DS264 in our system, 15m/s, the resulting frequency ratios are also calculated.
It is clear that for all systems, the ratio is much less than 1 and reduction in response amplitude should be observed. The 2 roller systems, for both lengths, will exhibit more reduction than the 3 roller systems. However, the reduction in the 3 roller system is already so significant, further reduction that might be seen in a 2 roller system is probably negligible.
The live document can be found here
Thermal Effects
Heat generation rate only analyzing conduction:
Where A is the cross sectional surface area, dT is the change in temperature, k is the conductivity, and d (dr) is equal to thickness. Both the conductivity and change in temperature will be the same in both the two and three roller scenarios
Electrical Architecture
Motor Analysis
The electrical engineers on the team are heavily leaning towards a 3Phase 480 VAC Permanent Magnet Synchronous Motor, similar to the one on the DS264, but the decision is not set in stone.
The live document can be found here
The tabulated version in excel can be found here
The Powerflex series offers reliable closedloop control for any type of motor the team eventually gets.
The PowerFlex Brochure can be found here
Automation Architecture
The 4 hierarchy levels of the automation process are the device, the drives, the controller, and the process control network/ distributed controls system. For more dynamic systems there can be an intranet and internet but our system will not utilize these features. Keeping the system below these levels allows for a very low security risk since the system will be internally contained and does not risk hackers or hot changes to the system.For the first level of our system, the devices, will have 2 3phase synchronous motors used to drive the guide rollers. The reason 3phase synchronous motors are the choice is because they are robust and efficient.
For our applications the margin of error in the position of the motor is not so effective on the system design that the precision of a servo motor would be required. Second, the reason of a DC motor is the constant switching. Have 3phase motors allows for the system to be brushless and which allows for less wear and longer life cycle. Deciding synchronous vs. asynchronous goes into the controls of the system. Having a magnetic field that rotates at the same speed as the rotor is easier to control than one that is at a reduced speed.
Every motor needs a drive (or at least some way of controlling them, the simplest is a drive). For our switching speeds and controlling the speeds of the motors variable frequency drives (VFD)
For these guide rollers there will be variable frequency drives to control the motors directions and speed.
On the third level there will be a programmable logic controller (PLC) to be used for the logic blocks and the inputs and outputs of the system. The PLC will take the inputs and outputs and apply the logic designed for the system. This allows for the interlocks to be applied and the system to be controlled with more precision than the VFDs allow. This also allows for the sensors to be integrated into the system.
The 4th level of the system is the display or the Human Machine Interface which will allow for the operator to make changes and observe the system running. This display will allow for changes for the entire system, not just the guide rollers, so purchasing more than 1 would be unnecessary. The PLC will come with its own software that will be used for the system.This architecture is represented in Figure 2.
Additional information can be found in the live document as needed. More detailed analysis will occur in the upcoming phase.
This isn’t an original document for this project. I created this for a fake system but it can be used as a benchmark or a standard.
The live document can be found here
Engineering Requirements
The live document can be found here
Risk Assessment
The live document can be found here
Bill of Materials (BOM)
The live document can be found here
Plans for next phase
Plans for Next Two Phases
The live document can be found here
Subsystem Roles
The live document can be found here
Individual Contributions
This document was removed due to proprietary information. If you would like to request a copy, please email a team member. Contact information can be found on the home page.
Resources
A live document showing all resources used can be found here
Thank you to Professor Wellin and Professor Humphrey for answering team questions to help us complete this phase
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