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 High Speed Weighing System Analysis 
via Mathematical Modelling 
 
 
A thesis presented in partial fulfilment of  
the requirements for a degree of 
 
 
Masters of Engineering 
Mechatronics 
 
 
at 
 
 
Massey University, 
Albany, Auckland, 
New Zealand 
 
 
Rami Elbeltagi 
2011 
 
 Page | I  
 
Abstract 
In-process electronic high speed weighing systems play an important role in the highly 
automated, continuously evolving industrial world of today.  They are an essential component 
in sorting, grading and quality control within a diverse range of industries, including; 
robotics, automotive and food. Load cells are considered to be the definitive force sensor for 
industrial weighing systems. Load cell output is in the form of an oscillatory response in 
which the measurand contributes to the response characteristics. Current methods require the 
oscillatory response to settle in order to achieve an accurate measurement. This is time 
consuming and speed limiting.  
The focus of this paper is to find alternative weighing analysis methods for a system which 
utilises two load cells, placed either side of a carrier travelling on a chain conveyor, running 
at speeds of 10 items a second. It is necessary to determine the value of the measurand in the 
fastest time possible to speed up the process and increase throughput. This has been 
approached by mathematically modelling the system to allow accurate prediction of the 
weights passing the load cells before the settling time of the oscillatory response. Models of 
harmonic motion have been considered for the motion of a load cell.  
An experimental system was built and weighing data collected for different speeds and loads. 
Spectral analysis of the weighing data was analysed to determine dominant frequencies and 
estimate system parameters.  
This thesis describes the work done on load cell modelling and improving an in-process 
electronic weighing system by successfully predicting the weight during the transient period 
of the oscillatory response. The assumptions and results of both simulations and experimental 
data are presented. 
  
 Page | II  
 
Acknowledgments 
I would like to thank everyone who has helped and supported me through this project. I 
would firstly like to thank my family; Osama Elbeltagi, Hala Elattar and Moemen Elbeltagi, 
who have provided me with encouragement and loving support. They made sure I believed I 
could achieve whatever I put my mind to. 
My deep and sincere gratitude to my mentor, Dr. Alona Ben-Tal, B.Sc., M.Sc., Ph.D., 
College of Sciences, Institute of Information & Mathematical Sciences, Massey University. 
Her encouragement, personal guidance and understanding have provided a good basis for the 
thesis. Her wide knowledge and logical way of thinking have been of great value to me. 
I am deeply grateful to my supervisor, Dr. Johan Potgieter, B.Sc., M.Sc., Ph.D., College of 
Sciences, Institute of Technology & Engineering, Massey University, for his detailed and 
constructive comments, and for his excellent advice during the preparation of this thesis. 
I would like to express my warm and earnest thanks to Marcus Davies, R&D Mechanical 
Development Manager, Compac Sorting Equipment, who introduced me to the potential of 
this project and has guided me during the first steps. His ideals and concepts have had a 
remarkable influence on my entire career as a Mechanical R&D Design Engineer. 
During this work I have collaborated with many colleagues, David Williamson, Oliver Grant, 
Nathan Vissers, Frazer Noble and James Scholz, to whom I have great regard, and would like 
to extend my heartfelt thanks. They allowed me to discuss problems and gave me untiring 
help during my difficult moments. 
The financial support of Compac Sorting Equipment as well as providing me with a chance to 
do further study is gratefully acknowledged. 
I am much thankful for the liberality of Dick and Mary Earle for providing me with a 
munificent scholarship. Their interest in this project has been immense and their input has 
been very beneficial. 
  
 Page | III  
 
Table of Contents 
 
Chapter 1: Introduction ...................................................................................................... 1 
1.1 Objectives ................................................................................................................ 2 
1.2 Literature Review .................................................................................................... 3 
1.2.1  Frequency Compensation ................................................................................ 3 
1.2.2  Model Parameters ............................................................................................ 6 
1.2.3  Artificial Neural Networks .............................................................................. 9 
1.2.4  Literature review Discussion ......................................................................... 12 
1.3  Project Approach ................................................................................................... 14 
Chapter 2: The Weighing System .................................................................................... 15 
 Chapter 3:      Modelling ................... .................................................................................. 20 
3.1 Mathematical Model of the system ....................................................................... 20 
3.2 “Averaging” Method ............................................................................................. 23 
3.3 “Frequency” Methods ............................................................................................ 24 
3.4 “Damping” Method ............................................................................................... 28 
Chapter 4: Simulation and Analysis................................................................................. 32 
Chapter 5: Weighing System Testing & Analysis ........................................................... 40 
5.1 Setup ...................................................................................................................... 40 
5.2 Sampling Restrictions ............................................................................................ 45 
5.3 Averaging Method ................................................................................................. 46 
5.4 Damping Method ................................................................................................... 49 
5.5 Frequency Method ................................................................................................. 57 
5.6 Disturbances .......................................................................................................... 60 
5.6.1  Carrier Interference ....................................................................................... 60 
5.6.2  Item’s physical shape (stability) .................................................................... 63 
5.6.3  External noise/vibration ................................................................................ 66 
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5.6.4  External Disturbance – human interference .................................................. 67 
5.7 Spectral Analysis ................................................................................................... 70 
Chapter 6: Results & Discussion ..................................................................................... 74 
Chapter 7: Conclusion & Future Recommendations ....................................................... 79 
References ............................................................................................................................ 82 
Appendices ........................................................................................................................... 84 
Appendix A Load Cell Datasheet .................................................................................. 84 
Appendix B Carrier Weights ......................................................................................... 86 
Appendix C Sample output weighing data file .............................................................. 88 
Appendix D Sampling Restrictions ............................................................................... 89 
Appendix E Peak Detection Algorithm ......................................................................... 90 
Appendix F Damping Method ....................................................................................... 92 
Appendix G Simulation UI ............................................................................................ 95 
Appendix H Frequency depending on speed ............................................................... 101 
Appendix I  Weigh graphs at various speeds ............................................................... 105 
 
 Page | V  
 
List of Figures 
Figure 1: Compac Carrier ........................................................................................................ 15 
Figure 2: Carrier Components in Solidworks .......................................................................... 15 
Figure 3: Apples on a Vishay Load Cell .................................................................................. 16 
Figure 4: Typical Weigh Graph ............................................................................................... 16 
Figure 5: The Weighing Machine ............................................................................................ 17 
Figure 6: Carrier in floating position ....................................................................................... 19 
Figure 7: Mass Spring Damper (MSD) System ....................................................................... 21 
Figure 8: Offset on a Weigh Graph.......................................................................................... 22 
Figure 9: Limit of an oscillating Weigh Graph ........................................................................ 23 
Figure 10: Two Successive Peaks ............................................................................................ 25 
Figure 11: Three Successive Peaks .......................................................................................... 29 
Figure 12: User Interface ......................................................................................................... 32 
Figure 13: Comparing Weigh Graphs with different Damping coefficients ........................... 33 
Figure 14: Comparing Weigh Graphs with Different Spring Constants.................................. 34 
Figure 15: Averaging Method Error in 250ms ........................................................................ 36 
Figure 16: Averaging Method error on Larger Scale ............................................................... 37 
Figure 17: 100g vs 300g Weights Over a Load Cell ............................................................... 37 
Figure 18: Frequency Method error ......................................................................................... 38 
Figure 19: Averaging Method error ......................................................................................... 38 
Figure 20: Damping Method error ........................................................................................... 38 
Figure 21: Frequency Method Trend Line for error Percentages ............................................ 39 
Figure 22: Averaging Method Trend Line for error Percentages ............................................ 39 
Figure 23: Damping Method Trend Line for error Percentages .............................................. 39 
Figure 24: Centred Weigh Bridge Section ............................................................................... 40 
Figure 25: Transition plates onto the Weighing System .......................................................... 41 
Figure 26: Transition plate height ............................................................................................ 41 
Figure 27: Weighing plate height ............................................................................................ 42 
Figure 28: Weigh Bar jig in place ............................................................................................ 43 
Figure 29: Position of Adjustment Bolts ................................................................................. 44 
Figure 30: Graph with disturbance in the final 35% ................................................................ 49 
Figure 31: Weigh Graph of a 200g weight on first load cell ................................................... 50 
Figure 32: Weigh Graph of a 200g weight on second load cell............................................... 50 
 Page | VI  
 
Figure 33: Weigh Graph of a 283g weight running at 400cpm on first load cell .................... 51 
Figure 34: Weigh Graph of a 283g weight running at 400cpm on second load cell ............... 52 
Figure 35: Actual vs Predicted for 189.5g at 300cpm ............................................................. 55 
Figure 36: Actual vs Predicted for 189.5g at 600cpm ............................................................. 55 
Figure 37: Actual vs Predicted for 264g at 300cpm ................................................................ 56 
Figure 38: Actual vs Predicted for 264g at 600cpm ................................................................ 57 
Figure 39: Weigh graph of 122g on third load cell .................................................................. 58 
Figure 40: Weigh graph of 122g placed on fourth load cell .................................................... 58 
Figure 41: Carriers on z-plate .................................................................................................. 60 
Figure 42: Carrier interference on the z-plate .......................................................................... 61 
Figure 43: Load Cell output and their summation ................................................................... 63 
Figure 44: Carriers with Foam ................................................................................................. 64 
Figure 45: Apple on Carriers with Foam ................................................................................. 64 
Figure 46: Disturbance due to excitation ................................................................................. 67 
Figure 47: Disturbance due to human interference .................................................................. 68 
Figure 48: Weigh Graph from removing a 200g Weight off a Load Cell ............................... 69 
Figure 49: Peaks of interest from the 200g removed weight ................................................... 69 
Figure 50: Weigh Graphs of 379g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 3 
(Lane 2, LC 1) .......................................................................................................................... 71 
Figure 51: Weigh Graphs of 379g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 4 
(Lane 2, LC 2) .......................................................................................................................... 71 
Figure 52: Weigh Graphs of 164g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 3 
(Lane 2, LC 3) ........................................................................................................................ 105 
Figure 53: Weigh Graphs of 164g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 4 
(Lane 2, LC 4) ........................................................................................................................ 105 
Figure 54: Weigh Graphs of 528g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 3 
(Lane 2, LC 1) ........................................................................................................................ 106 
Figure 55: Weigh Graphs of 528g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 4 
(Lane 2, LC 2) ........................................................................................................................ 106 
Figure 56: Weigh Graphs of 711g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 3 
(Lane 2, LC 1) ........................................................................................................................ 107 
Figure 57: Weigh Graphs of 711g at 300cpm, 400cpm, 500cpm and 600cpm on Load Cell 4 
(Lane 2, LC 4) ........................................................................................................................ 107 
 
 Page | VII  
 
List of Tables 
Table 1: Weigh results of 10 samples of weights between 0g and 250g ................................... 4 
Table 2: Results on two noise-free simulated signals ................................................................ 7 
Table 3: Simulated testing and training data errors ................................................................. 11 
Table 4: Experimental results of the applied masses ............................................................... 11 
Table 5: Carrier Component Weights ...................................................................................... 19 
Table 6: Results of 57, 145, 197, 242, 272 and 378g during a 250ms period ......................... 34 
Table 7: Results of 57, 145, 197, 242, 272 and 378g while running at 600cpm ..................... 35 
Table 8: Samples due to Speed and Readings ......................................................................... 45 
Table 9: Missed Samples ......................................................................................................... 46 
Table 10:  Results while running at 300cpm ........................................................................... 46 
Table 11: Results while running at 600cpm ............................................................................ 47 
Table 12: Reliability test of a 166g weight on a Carrier .......................................................... 47 
Table 13: Accuracy of empty Carriers ..................................................................................... 48 
Table 14: 200g load cell data ................................................................................................... 51 
Table 15: 283g load cell data ................................................................................................... 52 
Table 16: Weight prediction while being run at 300cpm ........................................................ 53 
Table 17: Weight prediction while being run at 600cpm ........................................................ 54 
Table 18: Frequency comparisons ........................................................................................... 59 
Table 19: 166g Weight on Carriers without Missing Carriers ................................................. 62 
Table 20: 166g Weight on Carriers with Missing Carriers ...................................................... 62 
Table 21: Results of Foam Vs No Foam on Carriers ............................................................... 65 
Table 22: Frequency (Hz) Depending on Speed and Weight .................................................. 72