Greetings! I am in the process of revamping the PLC code for a machine that slices and rewinds rubber-coated fabric rolls. The current code struggles with controlling letoff tension and has various other issues. I have a precise speed feedback signal for the "main pull rolls" (0-400fpm) and know the diameters of both the letoff and rewinder rolls when empty and full. By accurately calculating the processed stock length based on the main pull roll speed, I aim to determine the rewind roll diameter throughout the cycle. For example, with a roll length of 1650 feet, rewind core diameter of 3.5", and rewind full diameter of 28", the formula needs to consider the varying circumference due to fluctuations in stock thickness (0.031"). Although stock thickness can vary, I prefer not to include it in the calculation unless necessary. The accuracy of the final calculation will significantly impact the machine's performance. Once I devise this formula, I intend to apply the same concept to calculate the letoff roll and web rewind roll diameters. These calculations are crucial for enhancing speed and tension control to improve user experience. Currently, operators frequently need to adjust tension, resulting in speed control issues, especially with non-standard letoff cores. Unfortunately, adding a device to measure diameter is not feasible for this machine. Thank you for your assistance in advance. Rest assured, these enhancements will optimize the machine's operations. Warm regards, Paul C.
The calculation formula is based on the area of the material, whether it is rolled up or laying flat on the floor. When flat on the floor, the cross-sectional area is determined by multiplying the length by the thickness of the material. However, when rolled up, the area can be calculated using the formula (PI/4) * (OD^2 - ID^2). To find the outer diameter (OD), you can rearrange the formula L * t = (PI/4) * (OD^2 - ID^2) and solve for OD. If there are variations in material thickness, an alternative method involves adding additional sensors. By using a sensor that signals once per revolution of the unwind or rewind process, you can keep track of the time between signals in your PLC. Multiplying the line speed by this time will give you a length equivalent to the circumference of the outer layer of the material. Dividing this circumference by PI will give you the diameter.
Below are the equations used to calculate the dimensions of a roll of material. These equations were developed by comparing the total volume of material in the roll to that of a cylinder with the same volume. For simplicity, we assume the roll is 1 unit wide. The formulas are as follows: Length = (Diameter^2 - Core Diameter^2) * π / (4 * Thickness) Thickness = (Diameter^2 - Core Diameter^2) * π / (4 * Length) Diameter = √((Length * 4 * Thickness / π) + Core Diameter^2) Please note: This is a simultaneous post. We apologize for any confusion caused.
Given the varying diameter of the roll, I need to clarify where you are sourcing the speed feedback from. Is it coming from the unwinding roll of stock or another piece of machinery pulling material from your equipment? This is crucial for maintaining consistent performance and efficiency.
Thank you for sharing the formula, which is primarily based on area. I realized that the main pull rolls drive, responsible for line speed feedback, controls rollers with a fixed diameter, regardless of the variable diameter letoff and rewinders. To ensure accurate results using the formula, I will gather measurements of finished rolls and calculate the average thicknesses of each type of material we use. Achieving accuracy within a few percentage points will greatly improve the machine's performance. I truly appreciate this platform as I can quickly ask questions and receive reliable answers from experienced individuals. The knowledge shared here has saved me a significant amount of time on research. Thank you for all the help! - Paul C.
After reviewing your post, I wanted to suggest considering the use of an ultrasonic sensor to measure the diameter on this machine. While adding a device for measurement may not be feasible, an ultrasonic sensor like the UC2000-30GM-IU-V1 model could potentially work on rubber materials. This sensor is teachable and provides a 4 to 20 output. For more information on how this sensor could benefit your application, you can refer to the data sheet at http://www.am.pepperl-fuchs.com/pdf/fa/documents/SC02_AnalogCurrentandVoltageOutput-p290-293.pdf.
Hi Paul, What you're looking to achieve is indeed rather challenging, but not impossible. In terms of calculating the rewind roll diameter without calculating for varying stock thickness, it might be necessary to consider it to ensure a more accurate result, given that the thickness could influence the roll diameter over time. Regarding the PLC code, implementing a PID (Proportional Integral Derivative) controller might help significantly with the tension issue, as it could provide continuous adjustment to the system's operation based on error measurements. A load cell could possibly be used to get good feedback for tension control. I would really suggest working with a controls engineer, if possible. Reach out if you have any other questions!
Hi Paul, Your project certainly sounds challenging yet exciting! You've done a good job dissecting the issue so far. When it comes to calculating the diameter as the web rewinds, consider using the principle of conservation of volume. Given the need to account for varying stock thickness, enforcing this principle can provide you the necessary compensation. Simply put, you can keep a running count of the amount of stock material processed and use that to estimate the growing diameter of the rewinding roll. Remember, the volume of cylindrical drum equals the area of the cross-section multiplied by the length (in your case, the length of material processed), and the cross-sectional area can be written in terms of the diameter. Given the initial and final diameters (and hence the volumes) of the roll, you can then estimate the diameter for a given amount of processed material. Just a friendly note: Fine-tuning might be required as real-life conditions may differ somewhat from theoretical assumptions. All the best with your project! Cheers, Michael
Hi Paul, Interesting challenge. If you aim to keep the stock thickness out of the calculation, it'll be crucial to maintain a high level of accuracy in your speed feedback signal, as any error could cause a significant misestimation of the rewinder roll's diameter. And to help with your formula, have you considered the principle of conservation of volume for cylindrical objects? The volume of the roll remains consistent despite its changing diameter and length. Using the basic formula for volume (V = πr²h), you could possibly extract a relationship between the changing diameter and the known length of the fabric. Keep in mind, this is a simplified approach and might work differently in real scenarios. However, any potential error from stock thickness variation can be minimized through real-time adjustments based on the observed tension control performance. I look forward to seeing how your calculations and adjustments will improve the machine's operations. Best of luck!
Hey Paul, Interesting challenge you've got there! I work with CNC machines but can appreciate the complexity the varying stock thickness adds to your calculations. You may want to consider a recursive formula that updates the diameter with each revolution based on the pull roll length processed, core diameter, and length of processed stock. Factor in the material thickness only if it significantly skews results, as you suggested. Converting your main pull roll speed to a displacement per revolution metric might also simplify the calculations. Another factor to consider is your PLC scan time, as slower scan times may not reflect instantaneous tension changes accurately. Good luck, and do keep us posted with your progress!
Hi Paul, it sounds like you're tackling an interesting challenge with the PLC code! I completely understand your concerns about controlling letoff tension and the complexities of varying roll diameters. Since you have a precise speed feedback signal, maybe you could create a dynamic feedback loop that updates the roll diameter calculations in real-time based on the processed stock length. This way, even if the thickness varies slightly, you'll have a more consistent tension and speed control. It might also help to incorporate a predictive model based on historical performance data to fine-tune your calculations. Looking forward to hearing how your implementation goes!
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Answer: - Optimizing unwind and rewind formulas is crucial for achieving better speed and tension control, which ultimately enhances user experience and operational efficiency of the machine.
Answer: - Factors such as the speed feedback signal, roll lengths, core diameter, full diameter, and variations in stock thickness need to be taken into account for accurate calculations.
Answer: - The accuracy of the calculated rewind roll diameter plays a significant role in ensuring precise tension control and speed regulation, thus directly impacting the overall performance of the machine.
Answer: - While variations in stock thickness can impact the accuracy of the calculation, the decision to include it depends on the level of precision required for the specific machine operation.
Answer: - Operators often face difficulties in adjusting tension and speed control when working with non-standard letoff cores, leading to operational issues that can be mitigated through optimized formulas for roll diameter calculations.
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