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MECHANICAL MEASUREMENTS

Prof. Dr. Ing. Andrei Szuder Tel.

40.2.1.4112604 Fax. 40.2.1.4112687 www.labsmn.pub.

ro szuder_at_labsmn.pub.ro

FORCE TORQUE MEASUREMENT

Force vs. Mass measurements

- Balance systems compare weight of the known

etalon with the force applied to the measuring

arm

F

Fe

- If the measured force, F is the weight of a

stationary object, then we balance the mass of

the object with the mass of the etalon.

Force MeasurementBy An ElasticElement

- Elastic elements are often employed for force

measurements via stress/strain Hookes law

Where K is the deflection constant and y is the

deflection at some characteristic point. Table

13.1 in the textbook lists some characteristic

cases

(No Transcript)

Important note Do not confuse the deflection

constant K with the Bridge Constant, also

labeled by K!

Torque Measurements

- Most often, torque sensors are used in measuring

the power of rotary machines, hence their other

name, dynamometers. In this use, we measure

dissipated energy by applying brake load to the

shaft of a rotary engine, and measuring the

angular velocity and torque.

where T is torque, F is force at displacement R

from the axis of rotation and ? is an angular

velocity (rad/s)

Dynamometer types

- The main challenges in dynamomemeter design and

use are controlled energy dissipation and signal

transmission from the rotary member to the

stationary equipment (using some kind of

brushes). Today wireless transmission systems are

often used. - Based on the medium which dissipates energy

(heat), dynamometers are classified as mecanical,

hydraulic, electrical and transmission. - Transmission dynamometers are passive elements

inserted into the system - they do not dissipate

energy.

Torque Measurement By Different Strain

Gauge Configurations

Dynamic response Second Order Systems

- Given the spring stiffness k, the damping

coefficient c and the mass m, the spring/mass

system with the damping element will follow

c

k

y

m

Fapplied

2nd Ord. System Response To A Step Function

If the system is excitedby a step function

The general solution can be expressed as

where

is the undamped natural frequency (in radians)

is the damped natural frequency (in radians)

is the critical damping ratio,

is the critical damping coefficient,

is the static displacement as time goes to

infinity and

is the response phase lag

The displacement due to an impulse signal will

depend essentially on two parameters the

critical damping ratio, ?, and the undamped

natural frequency, ?n.

Underdamped systems will swing above the

equilibrium few times before they settle at the

final level, while overdamped systems approach

the steady state from one side only!

2nd Ord. System Response To A Harmonic Excitation

If the system is excitedby a harmonic function

it will pass through a transient stage and settle

into a stationary oscillation, with a certain

amplification ratio, yd /ys, and a phase lag, ? .

where

is the excitation cyclic frequency (rev/s) and

is the system undamped natural cyclic frequency.

Notice that undamped system excited at natural

frequency will reach infinite amplification

ratio, i.e. it will come into resonance with the

excitation force. In practice, we try to limit

the useful frequency range to 20-40 of the

natural frequency, and have the damping ratio of

around 70.

Torque measurement

- Torque is measured by either sensing the actual

shaft deflection caused by a twisting force, or

by detecting the effects of this deflection.

Torque measurement

- To measure torque, strain gage elements usually

are mounted in pairs on the shaft, one gauge

measuring the increase in length (in the

direction in which the surface is under tension),

the other measuring the decrease in length in the

other direction

Torque measurement

Torque measurement

Torque measurement

Torque measurement

Torque measurement

Torque measurement

- The excitation voltage for the strain gage is

inductively coupled, and the strain gage output

is converted to a modulated pulse frequency - Maximum speed of such an arrangement is 15,000

pm.

Load cells

Load cells

- Load cells became are the method of choice for

industrial weighing applications

Load cells

- Strain-gage load cells convert the load acting on

them into electrical signals. The gauges

themselves are bonded onto a beam or structural

applied. In most cases, four strain gages are

used to obtain maximum sensitivity and

temperature compensation. Two of the gauges are

usually in tension, and two in compression, and

are wired with compensation adjustments - Piezoresistive Similar in operation to strain

gages, piezoresistive sensors generate a high

level output signal, making them ideal for simple

weighing systems because they can be connected

directly to a readout meter.

Load cells

- Inductive and reluctance Both of these devices

respond to the weight-proportional displacement

of a ferromagnetic core. One changes the

inductance of a solenoid coil due to the movement

of its iron core the other changes the

reluctance of a very small air gap. - Magnetostrictive The operation of this sensor is

based on the change in permeability of

ferromagnetic materials under applied stress. It

is built from a stack of laminations forming a

load-bearing column around a set of primary and

secondary transformer windings. When a load is

applied, the stresses cause distortions in the

flux pattern, generating an output signal

proportional to the applied load. This is a

rugged sensor and continues to be used for force

and weight measurement in rolling mills and strip

mills.

Load cells

- New Sensor Developments
- Fiber optic load cells are gaining attention

because of their immunity to electromagnetic and

radio frequency interference (EMI/RFI),

suitability for use at elevated temperatures, and

intrinsically safe nature. Work continues on the

development of optical load sensors. - Two techniques are showing promise
- measuring the micro-bending loss effect of

single-mode optical fiber - measuring forces using the Fiber Bragg Grating

(FBG) effect.

Load cells