GB2061532A

GB2061532A - Determining Moment of Inertia

Info

Publication number: GB2061532A
Application number: GB7936088A
Authority: GB
Original assignee: Ferranti PLC
Current assignee: Ferranti International PLC
Priority date: 1979-10-17
Filing date: 1979-10-17
Publication date: 1981-05-13
Also published as: GB2061532B

Abstract

Apparatus for determining the moment of inertia of a body includes a turntable 10 mounted on a shaft 11 for rotation about a vertical axis 12. Two ligaments 15, 16 are attached to the shaft and are wound around it in opposite directions. The free end of each ligament is attached by way of a spring 17, 18 to an anchor point 19, 20 so that each ligament is always maintained in tension. Means comprising a vane 21 and transducer 22 are provided for measuring the period of oscillation of the turntable when displaced from a datum position, and calculating means 23 may also be provided for determining the moment of inertia from this period. <IMAGE>

Description

SPECIFICATION Apparatus for Determining the Moment of Inertia of a Body This invention relates to apparatus for determining the moments of inertia of a body.

It is known to determine the moment of inertia of a body by placing the body on a turntable and allowing the body and turntable to oscillate about an axis of rotation against a restoring torque. The body is positioned on the turntable so that the axis of rotation coincides with the axis of the body about which its moment of inertia is to be determined. The actual calculation is based on the period of oscillation of the turntable and body, as compared with that of the turntable alone.The moment of inertia of the turntable alone is easy to calculate because of its regular shape, and the moment of inertia 1B of the body may be determined from the expression IB=IT[(T2/T1) 1 ] where IT is the moment of inertia of the turntable alone, T1 is the period of oscillation of the table alone, and T2 is the period of oscillation of the table and the body together.

Several forms of apparatus have been devised to make use of this simple calculation, all comprising some form of spring-biased turntable.

The spring bias may be provided by a coil-spring around a shaft on which the turntable is mounted.

Alternatively, a torsion bar may be provided, located along the axis of the shaft. Other forms of apparatus use a form of crossed-spring suspension which provides both support and restoring torque to the turntable. These forms of apparatus all have the disadvantage that it is difficult to change the spring torque to cater for different ranges of moment of inertia. In the case of the crossed-spring suspension this also has a limited range of rotational movement.

It is an object of the invention to provide apparatus for determining the moment of inertia of a body, which does not suffer from the disadvantages set out above.

According to the present invention there is provided apparatus for determining the moment of inertia of a body, which includes a turntable mounted on a shaft for rotation about a vertical axis, a pair of ligaments each secured at one end to the shaft and extending around the shaft in opposite directions so as to be in contact with the shaft over an angle greater than the angle of rotation of the turntable from a datum position, a pair of spring members each connecting the free end of a separate ligament to an anchor point such that the ligaments are always maintained in tension, and means for determining the period of oscillation of the turntable when displaced from the datum position.

Preferably the turntable is supported in some form of air bearing.

The means for determining the period of oscillation may include electronic timing means actuated by a sensor co-operating with the turntable. Means may also be provided for calculating directly the moment of inertia of a body mounted on the turntable.

An embodiment of the invention will now be described with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of one form of the apparatus; Figure 2 is a view of the apparatus showing the shaft and the restoring means; and Figure 3 is a block diagram of the processor of Figure 1.

Referring now to Figure 1 , this shows a turntable 10 carried on a shaft 11 for rotation about a vertical axis 12, and supported in an air bearing 1 3. Air under pressure is admitted to the bearing as shown by the arrow 14. Two ligaments 1 5 and 1 6 are attached at one end to the shaft 11 and their other ends are attached, by way of tension springs 1 7 and 18, to anchor points 1 9 and 20. The arrangement of the ligaments will be more fully described with reference to Figure 2.

The shaft 11 carries a vane 21 which co-operates with a transducer 22, conveniently of photoelectric form. The output of the transducer is connected to a processor 23 having an associated display 24.

Figure 2 illustrates the attachment of the ligaments 15 and 1 6. The shaft 11 is shown in section, and one end of each ligament is attached to the shaft at a point 25. The two ligaments extend tengentially to the shaft 11 at a point diametrically opposite to point 25, and are connected via their respective springs 1 7 and 1 8 to the two anchor points. The ligaments have been shown spaced from the shaft for clarity, in practice they would of course be on the surface of the shaft. The two ligaments arranged as shown are in fact equivalent to a single ligament attached to the shaft at the point 25.

The transducer 22 and vane 21 may take a number of forms. Conveniently the transducer comprises a light-emitting device and a lightsensitive device between which the vane may pass. If the vane is very narrow, effectively a pointer, then the light path is interrupted twice in each complete cycle of oscillation of the turntable. If, however, the vane normally obstructs the light path, then the path is completed once per cycle of oscillation. Either arrangement may be used.

The object whose moment of inertia is to be measured may be mounted on the turntable in any desired position, and may be secured by jigs if necessary. The apparatus will function to measure the moment of inertia of the body about that axis of the body which coincides with the axis of rotation 12 of the turntable. Thus, as shown in Figure 1 , the axis need not pass through the body at all, but may be offset from it.

As will be seen from the equation given earlier the measurement is essentially comparative, and it is necessary to know the moment of inertia of the unloaded turntable, This has to be calculated from the dimensions and geometry of the turntable. Equally, if any jigs are used on the turntable to hold a body in place, it is first necessary to determine the moment of inertia of the turntable and jigs alone.

The apparatus is used as follows:- Having first determined the moment of inertia of the trntable plus any necessary jigs, the body whose moment of inertia is to be determined is secured to the turntable in the desired position and attitude relative to the axis of rotation 1 2. The turntable is then displaced angularly from its normal rest or datum position, and then released and allowed to oscillate. A convenient displacement angle would be, say 400. The processor 23 measures the period of oscillation of the turntable plus its load, and from the period determines the moment of inertia, using the equation given above. The result of the calculation, that is the required moment of inertia, is displayed on the display 24.

If the range of operation of the apparatus is to be changed it is only necessary to detach the springs 1 7 and 1 8 from their anchor points and ligaments, and replace them by other springs having the required characteristics.

Figure 3 is a block diagram of the processor 23.

Referring now to Figure 3, the transducer 22 and vane 21 of Figure 1 form a switch SW which controls a clock CK. The clock output, in the form of a train of pulses passes through a frequency divider FD to a decade counter DC. The output of the counter may be connected via gates G to the calculator logic.

A second clock is also provided to control the sequence of operation of the processor. This is the sequence clock SC, which applies a sequence of clock pulses to the sequence decoder SD. This decoder controls the gates G, and also controls the sequence of operation of the calculator logic.

The calculator logic controls a digital display in the normal manner.

The number of stages in the decade counter DC will depend upon the timing accuracy required for the period of oscillation of the table. A clock pulse train having a frequency of 1 KHz applied to a four-stage decade counter will enable the period to be determined to an accuracy of one thousandth of a second.

The sequence decoder SD is arranged to perform the required sequence of operation of the calculator logic required to perform the calculation already described. Some of these operations represent the input of data to the calculator logic whilst others represent instructions to the logic to perform a particular calculation. It is possible to couple the outputs of the gates G, representing digital data, and the sequence decoder SD, through a suitable interface to a standard logic package of the type used in hand-held calculators, so that each successive output represents the pressing of a button on the keyboard of the calculator. The sequence of operations of the sequence decoder thus represents a simple program.

As stated earlier, it is necessary to determine the moment of inertia of the table, and this must be set into the sequence decoder for use in future calculations. If jigs are used to hold a body in position on the table, then the process has to be followed through twice, firstly to determine the moment of inertial of the jigs, and secondly to determine the moment of inertia of the body plus the jigs. The moment of inertia of the body is the difference between these two values. The following description will, for simplicity, assume that no jigs are used and hence only a single calculation is necessary.

Assuming that the counters and decoders have been reset, the empty table is displaced and allowed to oscillate as already described. The vane and transducer start and stop the clock CK on successive oscillations, and the decade counter is operated so as to store the duration of one cycle of oscillation. Four successive steps of the sequence decoder control the gates G and apply successively to the calculator logic the four digits of the period of oscillation, namely the seconds, the decimal point and the tenths, hundredths and thousandths of a second. The sequence decoder then applies to the calculator logic a signal equivalent to the operation of the "M=" or "input memory" key of the calculator, and the measured time period T1 is stored in the memory of the calculator logic. Unless the table or the springs are changed, this time period will remain constant.

The body is then placed on the table, the decade vounter DC is cleared, and the new period of oscillation (T2) is measured. This applied to the calculator logic in the same way as the previous period by the next series of steps of the control sequence. The next three steps represent the operations "divide", "memory recall" and "equals" so as to divide T2 by T,. The quotient is then squared by the two operations "multiply" and "equals", and the digit "1" is subtracted by the steps "minus", "one' and "equals". The final steps needed to obtain the moment of inertia 12 in imperial units is to multiply the result of the preceding calculations by the known value of the moment of inertia IT of the table above. This will probably be stored in a further memory. Hence the successive operations represent "multiply" the digits representing ITT and "equals". The resulting digits give the required moment of inertia.

If the result is required in metric units, then the imperial to metric conversion factor may also be stored and used as a final factor in the calculation.

In simple terms the above sequence may be represented by the folowing instruction table: Input 4 digits of T, store in memory (M=) Input 4 digits ofT2 divide by T, (-:; MR;) square (x;=) subtract 1 1;) multiply (x) insert digits of IT (from second memory) equals (=) The operation to be performed by the calculator logic are basic functions and hence a simple calculator chip with two accessible memories is all that is required.

The sequence decoder may take any of a number of forms. It may, for example, comprise a series of decade counters to which the sequence clock output are applied, arranged so that each output represents a separate instruction, and so that the end of a cycle of one counter allows the clock input to be applied to the next. Facilities are provided to enable the sequence to stop when the moment of inertia in imperial units has been obtained, or to continue the sequence until the metric equivalent has been calculated. A reset switch may be provided to clear the counters ready for a new measurement and provision may be made to stop the sequence automatically after the measurement of the period T,. Other facilities may be provided as required, though it should be remembered that the basic function of the processor described is to solve the equation given earlier.

In order to improve the accuracy and balance of the apparatus described with reference to Figures 1 and 2, a second pair of ligaments and springs may be attached to the shaft 11. The ligaments will conveniently be attached to the shaft at a point diametrically opposite to point 25 and the ligaments and springs will extend parallel to those shown in Figure 2. Other arrangements of two or more springs and ligaments may be used, so long as the shaft and turntable are able to rotate through a limited angle in either direction from a datum position.

Claims

1. Apparatus for determining the moment of inertia of a body, which includes a turntable mounted on a shaft for rotation about a vertical axis, a pair of ligaments each secured at one end to the shaft and extending around the shaft in opposite directions so as to be in contact with the shaft over an angle greater than the angle of rotation of the turntable from a datum position, a pair of spring members each connecting the freeend of a separate ligament to an anchor point such that the ligaments are always maintained in tension, and means for determining the period of oscillation of the turntable when displaced from the datum position.

2. Apparatus as claimed in Claim 1 in which the turntable is supported in air bearing.

3. Apparatus as claimed in either of Claims 1 or 2 in which the springs are detachable from the ligaments and from the anchor points.

4. Apparatus as claimed in any one of Claims 1 to 3 in which the means for determining the period of oscillation included electronic timing means actuated by a sensor co-operating with the turntable.

5. Apparatus as claimed in Claim 4 in which the sensor comprises a movable vane rotating with the turntable and a stationary transducer.

6. Apparatus as claimed in Claim 5 in which the transducer includes a light source and a lightresponsive device arranged such that the light path between them may be interrupted by the vane.

7. Apparatus as claimed in any one of the preceding claims which includes calculating means responsive to the electronic timing means to calculate the moment of inertia.

8. Apparatus as claimed in Claim 7 in which the calculating means includes calculating logic and means for generating a sequence of instructions for the calculating logic.

9. Apparatus as claimed in either of Claims 7 or 8 which includes display means operable to display the result of the calculation.

10. Apparatus for determining the moment of inertia of a body, substantially as herein described with reference to the accompanying drawings.