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1.FUNCTIONS AND STRUCTURES OF SCALE 1

1.1 BASIC STRUCTURE AND WEIGHING PRINCIPLE 1

1.2 SYSTEM CONFIGURATION OF ELECTRICAL AND ELECTRONIC SCALES 2

1.3 FUNCTIONS AND SYSTEM CONFIGURATIONS OF THE SCALES FOR INDUSTRIAL USE 3

1.3.1 Functional Characteristics and Classification 3

1.3.2 Control Purpose 4

1.3.3 System Configurations 4

2.1.1 Classification of Levers 7

2.1 STATICS OF LEVERS 7

2.STATICS OF SCALES 7

2.1.2 Single Levers 8

2.1.3 Compound Lever Systems 10

2.2 ROBERVAL-TYPE SCALE 12

2.3 PLATFORM SCALE 13

2.4 DOUBLE-BEAM-TYPE LOADCELL SCALE 15

3.2.1 Undamped Case 19

3.2 FREE RESPONSE 19

3.1 DYNAMIC MODEL 19

3.DYNAMICS OF SCALES 19

3.2.2 Damped Case with Viscous Damping 21

3.2.3 Damped Case with Coulomb Damping 22

3.2.4 Measurement of the Static Equilibrium Position of Balance 23

3.3 FORCED RESPONSE 25

3.3.1 Step Response 25

3.3.2 Settling Time of Scales 26

3.3.3 Ramp Response 28

3.3.4 Response of a Hopper Scale 28

3.3.5 Frequency Response 31

3.3.6 Response of Scales with Levers to the Base Excitation 34

3.3.7 Response Calculation Method Using Transfer Function 37

3.3.8 Response of Conveyor Belt Scales 38

3.3.9 Response of Control Systems 42

3.3.10 Response of a Weigh Feeder 44

4.1 DIGITAL SIGNAL AND DIGITAL SYSTEM 47

4.1.1 Representation of Digital Signal 47

4.SIGNAL PROCESSING IN WEIGHING 47

4.1.2 Block Diagram Representation and Transfer Function 49

4.2 DIGITAL FILTERS 50

4.2.1 FIR Filter 50

4.2.2 IIR Filter 51

4.2.3 Frequency Response 52

4.3 DIGITAL FILTER DESIGN METHODS 52

4.3.1 Impulse-invariant Method 52

4.3.2 Bilinear z-transformation Method 53

4.4 DIGITAL SIGNAL PROCESSING OF WEIGH SIGNAL 54

4.4.1 Simulated Weigh Signal 54

4.4.2 Low-pass Filter Application 55

4.4.3 Notched Filter Application 56

5.ANALYTICAL CONSIDERATIONS ONWEIGHING SYSTEMS 59

5.1 EFFECT OF THE BASE VIBRATION ON THE SCALES COMPOUND WITH LEVERS 59

5.1.1 Equation of Motion 59

5.1.2 Vibrationproof Condition for Weighbeam 60

5.1.3 Physical Meaning of J-balance 62

5.1.4 Experimental Verification of the Vibrationproof Condition 63

5.2 VIBRATIONAL CHARACTERISTICS OF DOUBLE-BEAM-TYPE LOADCELL SCALE 64

5.2.1 Natural Modes 64

5.2.2 Frequency Response 66

5.3 COMPENSATION FOR BASE VIBRATIONS IN A DOUBLE-BEAM-TYPE LOADCELL SCALE 69

5.3.1 Concept of the Compensation 69

5.3.2 Equations of Motion 70

5.3.3 Block Diagram Representation of the System 72

5.3.4 Feasibility Test of the Theory 74

5.4 PHENOMENA IN PROBABILITY AND STATISTICS FOUND IN AN ASSOCIATIVE WEIGHER 76

5.4.1 Associative(Selective Combination)Weigher Model 76

5.4.2 Mathematical Description of the Combinatorial Problem 77

5.4.3 Mathematical Description of the Combination Process 78

5.4.4 Computer Simulation Results and Considerations 79

APPENDIXES 82

A.1 Table of Laplace transform 82

A.2 Properties of Laplas transforms 83

REFERENCES 84