P16601: Glass Cutting Machine:Guide Rollers
/public/

Subsystem Design

Table of Contents

Key Questions for Subsystem-Level Design Phase

Our goal for Phase 3 was to answer the following questions:

  1. Will we model off of the DS264 or develop a unique design?
  2. How many rollers will we use and what is the approximate size? Two Rollers - 400 mm long with an outer diameter of 320 mm
  3. Where is the most power being used? During the cutting process but the inertial power is not negligible
  4. How powerful do the motors need to be? still open
  5. What material will the rollers be made of? still open

Key Takeaways from Customer Visit

Engineering Considerations

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Selection Criteria.JPG

The live document can be found here

Selection Parameters

The following information was used to make consistent engineering considerations through this phase:

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Calculation Parameters.JPG

The live document can be found here

Assumptions

Overall Assumptions

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

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

Vibration Assumptions

Thermal Effects Assumptions

The live document can be found here

Analysis

Power Consumption

The inertia of the rollers were found using the equation:

Equation 1

Equation 1

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.

Equation 2

Equation 2

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.

Equation 3

Equation 3

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.

Equation 4

Equation 4

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.

Equation 5

Equation 5

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:

Baseline Equations

Baseline Equations

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 left-most 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.
Results Table

Results Table

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.
Required Horsepower Evaluated with 300 cuts

Required Horsepower Evaluated with 300 cuts

Required Horsepower Evaluated with 30 cuts

Required Horsepower Evaluated with 30 cuts

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.

Graph 1

Graph 1

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

Results Table

Results Table

Tangential Acceleration Due to Pertubations

Tangential Acceleration Due to Pertubations

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 non-issue.

The live document can be found here

Mechanical Strength

Set Up of Guide Roller Loading

Set Up of Guide Roller Loading

Draw the Shear and Moment diagrams. Moment is the area under the Shear plot

Shear and Bending Diagram

Shear and Bending Diagram

Area under the curve:

Equation 1

Equation 1

Combining these equations yields at the center of the roller.

Equation 2

Equation 2

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.

Equation 3

Equation 3

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.

Equation 4

Equation 4

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.

Equation 5

Equation 5

Assuming machined or cold drawn material, the following parameters were used.

Endurance Factors

Endurance Factors

For ultimate stress less than 1400 MPa, we can use equation 6 below.

Equation 6

Equation 6

Therefore, the stress in the two different roller diameters are calculated and shown below.

Roller Stress

Roller Stress

The magnitude of the distributed load is calculated using equation 7 below.

Equation 7

Equation 7

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.

Maximum Moment Results

Maximum Moment Results

Solving (4) for factor of safety yields the results shown below

Factor of Safety Results

Factor of Safety Results

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:

Equation 1

Equation 1

Equation 2

Equation 2

Using the distributed load and equation 2, deflection can be calculated using equation 3 below.

Equation 3

Equation 3

The result of this analysis are shown below:

Deflection of Guide Roller Under Tension and Their Own Weight

Deflection of Guide Roller Under Tension and Their Own Weight

Deflection Magnitude of Guide Roller

Deflection Magnitude of Guide Roller

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.

Equation 1

Equation 1

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.

Equation 1

Equation 1

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.

Results Table

Results Table

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:

Heat Generation Equations

Heat Generation Equations

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

Results Table

Results Table

Electrical Architecture

Motor Analysis

Motor Types

Motor Types

The electrical engineers on the team are heavily leaning towards a 3-Phase 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

Rockwell PowerFlex AC Drives

Rockwell PowerFlex AC Drives

The Powerflex series offers reliable closed-loop control for any type of motor the team eventually gets.

The PowerFlex Brochure can be found here

Automation Architecture

Figure 1: Electrical Architecture from “http://processautomationinsights.com/”

Figure 1: Electrical Architecture from “http://processautomationinsights.com/”

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 3-phase synchronous motors used to drive the guide rollers. The reason 3-phase 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 3-phase 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.

Figure 2: High Level Architecture for the system

Figure 2: High Level Architecture for the system

Additional information can be found in the live document as needed. More detailed analysis will occur in the upcoming phase.

Figure 3: Electrical Drawing Diagram for Motors and an AC drive

Figure 3: Electrical Drawing Diagram for Motors and an AC drive

Figure 4: Logic Diagram for Motors and Switches

Figure 4: Logic Diagram for Motors and Switches

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

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Engineering Requirements.jpg

The live document can be found here

Risk Assessment

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Risk Assessment.jpg

The live document can be found here

Bill of Materials (BOM)

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Bill Of Materials.JPG

The live document can be found here

Plans for next phase

Plans for Next Two Phases

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Project Plan.jpg

The live document can be found here

Subsystem Roles

public/Reviews/MSD1 P3 Subsystems Level Design Documents/Subsystem Roles.JPG

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


Home | Imagine RIT | Final Technical Paper | Final Poster

Problem Definition | Systems Design | Subsystem Design | Preliminary Detailed Design | Detailed Design | Gate Review

Build & Test Prep | Subsystem Build & Test | Integrated System Build & Test | Integrated System Build & Test with Customer Demo | Customer Handoff & Final Project Documentation | MSD2 Gate Review