MEL734 Instrumentation and Automatic Control Systemsweb.iitd.ac.in/~jpkhatait/MEL734/force/slides.pdf · MEL734 Instrumentation and Automatic Control Systems ... Balancing the unknown

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MEL734 Instrumentation and Automatic Control Systems

Force Measurement

J I T E N D R A P R A S A D K H A T A I T

D E P A R T M E N T O F M E C H A N I C A L E N G I N E E R I N G

I I T D E L H I

Force – a vector quantity◦ an action that will cause an acceleration or

◦ a certain reaction of a body.

The methods that can be employed to determine the magnitude of these forces

INTRODUCTION

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1. Balancing the unknown force against a standard mass, either directly or through a system of levers

2. Measuring the acceleration of a known mass to which the unknown force is applied

3. Balancing it to a magnetic force generated by the interaction of a current-carrying coil and a magnet

4. Distributing the force on a specific area to generate pressure, and then measuring the pressure

5. Converting the applied force into the deformation of an elastic element

BASIC METHODS OF FORCE MEASUREMENT

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◦ Analytical balance

◦ Pendulum scale

◦ Platform scale


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◦ Analytical balance

◦ Requires careful design and

operation to realize its

maximum performance


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◦ Pendulum scale

◦ A deflection-type instrument

◦ Unknown force is converted to a torque

◦ Then balanced by the torque of a fixed standard mass arranged as a pendulum

Design – specially shaped sectors and steel tapes


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◦ Platform scale

◦ Utilizes a system of levers to allow measurement of large forces in terms of much smaller standard weights

◦ Proper combination of pan weights and adjustment of the poise-weight lever arm

◦ If a/b=c/d, the reading of the scale is independent of the location of Fi on the platform


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Method 2:

Measuring the acceleration of a known mass to which the unknown force is appliedo Limited application

o The force determined is the resultant force on the mass

o Several unknown forces are acting


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Method 3:

Balancing it to a magnetic force generated by the interaction of a current-carrying coil and a magnet


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Method 3:



Parallelogram flexure system

that guides the motion produced

by an applied force

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Method 3:



• A flexure-pivot lever

system

• All motions are

constrained with

flexure bearings

• Nearly frictionless

performance

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Method 4:

Distributing the force on a specific area to generate pressure, and then measuring the pressure


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Method 5:

Converting the applied force into the deformation of an elastic element


• Widely used for both static

and dynamic loads

• Essentially a spring-mass

system with damping

• Differ mainly in the

geometric form of “spring”

employed

• Displacement sensed may

be gross motion or strain

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Method 5:

Converting the applied force into the deformation of an elastic element


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For measuring compressive forces

Load-sensing member is short enough to prevent column buckling

Foil-type metal gages are bonded on all four sides

Gages 1 and 3 sense the direct stress due to Fi

Gages 2 and 4 sense the transverse stress due to Poisson’s ratio

Provides primary temperature compensation

Insensitive to bending stresses

BONDED-STRAIN-GAGE TRANSDUCERS

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Strain-gage beam transducers

Increased sensitivity

Provide more strain per unit applied force, but at the expense of reduced stiffness and thus natural frequency

Cantilever-beam gage arrangement provides four times the sensitivity of a single gage, temperature compensation, and insensitivity to x and y components of force if identical gages and perfect symmetry are assumed


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Recent techniques

Reduce cost, simplify manufacture, and improve performance of weighing scales

“Folded cantilever” elastic element produces equal tensile and compressive stresses


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Shear-web force transducer

Transducers using shear loading◦ Very compact

◦ Little sensitivity to off-axis forces and moments

◦ Good symmetry for tension/compression

◦ Long fatigue life

◦ Simple overload protection

◦ High stiffness


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LVDT load cells◦ Range: 10g – 10kg

◦ Elastic element: Helical flexures◦ Machined from one solid piece

DIFFERENTIAL-TRANSFORMER TRANSDUCERS

LVDT force transducer

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For dynamic force measurement only

Very high stiffness and natural frequency (10kHz - 300kHz)

Range: ◦ 1kN tension to 5kN compression, permanently preloaded

◦ 4kN tension to 16kN compression, with external preloading nuts

PIEZOELECTRIC TRANSDUCERS

T = top; P = piezoelectric disks;

GP = guide pin; S = preloading screw;

N = preloading nut; B = base

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Modelled as a spring (piezoelectric elements) sandwiched between two end masses


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Piezoelectric impedance head◦ A dual sensor which combines a

separate load cell and an accelerometer into a single, compact package


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In many applications, the force or moment to be measured◦ Unknown in magnitude

◦ Unknown and/or variable direction

Examples◦ Measuring forces on wind-tunnel models

◦ Dynamometers for measuring cutting forces in machine tools

◦ Thrust stands for determining forces of rocket engines

Elastic force transducers of either the bonded-strain-gage or gross-deflection variety are employed

Flexures are used◦ For isolating and measuring different force components

RESOLUTION OF VECTOR FORCES AND MOMENTS INTO RECTANGULAR COMPONENTS

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Six-component thrust stand used in testing rocket engines


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Load cells 1, 2 and 3◦ Mounted at the corners of an equilateral triangle

Load cells 4, 5 and 6◦ Mounted in the sides of a concentric, smaller

equilateral triangle

Force and moments of unknown magnitude and unknown direction

◦ 𝐹𝑥, 𝐹𝑦 𝑎𝑛𝑑 𝐹𝑧

◦ 𝑀𝑥, 𝑀𝑦 𝑎𝑛𝑑 𝑀𝑧


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Forces are transmitted from the mounting plate to the rigid foundation through the six load cells and their associated flexures

Measured load-cell forces◦ 𝐹1 , 𝐹2, … , 𝐹6◦ Stand dimensions: 𝑑1, 𝑑2

CALCULATION OF FORCES AND MOMENTS

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Relationship between unknown forces/moments and the measured load-cell forces

𝐹𝑥𝐹𝑦𝐹𝑧𝑀𝑥

𝑀𝑦

𝑀𝑧

= 𝐵

𝐹1𝐹2𝐹3𝐹4𝐹5𝐹6


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◦ 𝐹𝑥 = 𝐹1 + 𝐹2 + 𝐹3

◦ 𝐹𝑦 = −𝐹4 +1

2(𝐹5 + 𝐹6)

◦ 𝐹𝑧 =3

2(𝐹5 − 𝐹6)

◦ 𝑀𝑥 = ⋯

◦ 𝑀𝑦 = ⋯

◦ 𝑀𝑧 = …


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6-DOF Force sensing module


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Relationship between unknown forces/moments and the measured load-cell forces

◦

𝐹𝑥𝐹𝑦𝐹𝑧𝑀𝑥

𝑀𝑦

𝑀𝑧

= 𝐵

𝐹1𝐹2𝐹3𝐹4𝐹5𝐹6


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Combination of bonded strain gages, Wheatstone-bridge circuits, and flexible elements of various geometries

◦ versatile tool in the development of multicomponent-force pickups of small size and high natural frequencies

A beam with three separate bridge circuits of gages arranged to measure the three rectangular components of an applied force


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Robotic manufacturing and assembly operations

◦ Force sensing at the end of the robot’s arm

◦ A six-axis sensor, connected between the robot arm and end-of-arm tooling

Dynamometer – another word used for force transducer


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Torque measurement can be accomplished

◦ Cradling, reaction force F and arm length L are measured

◦ Torque measured directly in terms of the angular twist or strain of the shaft

TORQUE MEASUREMENT ON ROTATING SHAFTS

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The cradling concept is the basis of most shaft power dynamometers

Utilized mainly for measurements of steady power and torque, by using scales or load cells to measure F

Error resulting from friction in the bearings, static unbalance of the cradled member, windage torque, etc.


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Strain-gage torque table

The cradle-bearing arrangement is replaced by a flexure pivot with strain gages

Reduced frictional effects

Dynamic torque measurements


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Strain-gage torque table

Crossing point of the flexure plates defines the effective axis of rotation of the flexure pivot

Cross-spring flexure pivot◦ Relatively very stiff in all directions

other than the rotational one desired

Strain-gage bridge arrangement is such as to reduce the effect of all forces other than those related to the torque being measured


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Null-balance torquemeterusing feedback principles to measure small torques

Test object is mounted on a hydrostatic air-bearing table

Any torque on the test object tends to cause rotation of the air-bearing table

Rotation is immediately sensed by a differential-transformer displacement pickup …


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Output from this pickup is converted to direct current and amplified to provide the coil current to a torque motor, which applied opposing torque to keep displacement at zero.

The amount of current required to maintain zero displacement is a measure of torque.


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Use of elastic deflection of the transmitting member for torque measurement

◦ Accomplished by measuring either the gross motion or a unit strain

Difficulty is to read the deflection while the shaft is rotating

Strain-gage torque sensors – widely used


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Strain-gage torque measurement

Temperature-compensated and insensitive to bending or axial stresses

The gages must be precisely at 45o with the shaft axis◦ Gages 1 and 3 must be diametrically opposite, as must gages 2 and 4


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Various torque sensor designs


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Shaft torque sensor details


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Shaft torque sensor used in chassis dynamometer


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Documents

MEL734 Instrumentation and Automatic Control Systemsweb.iitd.ac.in/~jpkhatait/MEL734/force/slides.pdf · MEL734 Instrumentation and Automatic Control Systems ... Balancing the unknown