Gear Noise and Vibration Episode 1 Part 7 pps

Practical limitations of the "double-divide" high speed system arise from three sources: a Since the system will operate over very large frequency ranges from roughly 0.01 rpm to 6000 rp

frequency divider

frequency divider

phase comparator

phase error which is T.E

Fig 7.6 Block diagram of high speed T.E tester.

Typically, with a gear ratio of 19:31 and the standard 18,000 (x 4) line encoders and 12 bit digital recording, the resolution would be to about 0.1 second of arc and more than adequate for automobile work The detailed design of the electronics requires some care to get the high accuracy necessary for the final phase comparison

This approach, unlike that in section 7.1 (the original pulse frequency multiplying system) is not affected by torsional vibrations at the input so it can be used under industrial conditions in situ on machinery such

as printing machines The encoders can be mounted quite large distances apart (50 m) on printing rolls to investigate dot synchronisation problems and the results show clearly when the gears start coming out of contact

Although intended originally for on site work at moderate speeds of the order of 200 rpm there seems to be no practical limit to operating speeds other than the requirement that for the simplest and most robust system the vibration should not be so severe that there is reversal of rotation This is a requirement for most of the systems

Practical limitations of the "double-divide" high speed system arise from three sources:

(a) Since the system will operate over very large frequency ranges from roughly 0.01 rpm to 6000 rpm, the operator needs to dial tooth numbers, roughly to zero the trace on the screen and to set a low-pass filter according to the conditions so the system is not completely automatic and "idiot proof." This makes it suitable for development or consultancy work but less suitable for production monitoring using unskilled personnel when speeds and tooth numbers change frequently

T E Measurement 101

If on the other hand a test rig is set up to test a particular drive, the settings remain constant and the only requirement is for the operator to centralise the trace on the monitor This can alternatively be done by computer control

(b) Unusual tooth numbers with large numbers of teeth give too coarse a frequency resolution to pick out harmonics of tooth frequency If, for example, a 68 tooth pinion is meshing with a 313 tooth wheel then the carrier wave which contains the phase information is at a frequency of 72,0007(68 x 313) or 3.3 times tooth frequency Setting a very high performance filter (8-th order elliptic) to 2 x tooth frequency cuts out the unwanted "carrier" frequency but means that only the 1/tooth and 2/tooth components of error can be measured This is rarely a limitation It can be avoided by using multiplying circuits [7] as in the original system but measurement is then influenced by vibration Results can also be obtained by using an approximate ratio, see section 7.10

(c) Encoder dynamics The encoders are driven via light but torsionally stiff couplings, but it is not possible to get the torsional resonant frequency much above 1500 Hz so the useful operating range is limited

to about 1200 Hz even with the most careful design of the coupling

To achieve this performance there must be an accessible free end on each shaft The alternative is using encoders mounted directly on the drive shafts but this gives only a limited improvement in frequency range

(d) Non-synchronous drives Occasionally it is not possible to mount an encoder directly on a gearshaft so a friction or belt drive is used This tends to limit the rig dynamics severely and also the drive is no longer

an exact ratio The drive ratio can usually be approximated with sufficient accuracy using tooth numbers of less than 100

An alternative variant possible for on-line high speed work is a blend

of the high speed and velocity approaches Each encoder string is processed separately and is simply taken to a demodulator The two resulting vibrations can then either be logged separately or the input can be scaled by the velocity ratio and subtracted from the output to give the T.E This method appears simple but costs increase as it requires two expensive filters (demodulators) and two accurate flip-flops rather than one and there is an additional scaling involved with possible errors due to small differences of two large quantities

There are different approaches to demodulating the pulse string from

an encoder One used by Tuma [5] involves the analytic extraction of the phase of the pulse string and the steady increase of the phase corresponds to the rotational speed while the variations correspond to the torsional vibration

At each transition from +n/2 to - n/2 the analysis needs to add the value TL

This method is difficult to implement in real time so is more suitable for research where time scales do not need to be short

The corresponding analog approach uses a phase locked loop to generate a reference pulse string at the average rotation speed The phase locked loop behaves as a seismic system with a second order characteristic and will give good vibration information above the natural frequency of the loop while ignoring speed variations or vibrations well below the natural frequency of the loop Fig 7.7 shows a block diagram for one loop but two are needed for T.E determination The divider can be set to any number that allows the output not to exceed full scale but setting the dividers on the two channels to numbers which approximate to the gear drive ratio simplifies subsequent subtraction

input from

encoder

2nd order filter and damped integrator

high precision

flip flop t

0

6th order filter

output

Fig 7.7 Block diagram for phase-locked loop for one encoder channel.

T E Measurement 103

The natural frequency of the loop can be set very low so that the output still records the once per revolution conponents of torsional vibration but it is more customary to set the loop frequency at about a third of tooth frequency The output then gives the tooth frequency and harmonics which are relevant for noise investigations while ignoring eccentricities which are not of interest for noise

7.5 Tangential accelerometers

One alternative analog method of measuring T.E is by the use of tangentially mounted accelerometers to measure the torsional accelerations of each of the shafts as sketched in Fig 7.8 Two matched accelerometers are used and their outputs are summed into the single charge amplifier so that any lateral vibrations are self cancelling The torsional accelerations of the two gears are scaled, proportional to the diameters, to give tangential movements at the pitch radii and subtracted to leave the T.E En route, the levels of the torsional vibration in the system are obtained

Previous attempts using this approach had achieved limited success but detailed checks against encoder measurement of torsional vibration at Cambridge established that:

clamp

bolt

accelerometer

clamp bolt

accelerometer Fig 7.8 Torsional accelerometer arrangement

(a) Information at I/rev was not reliable and should be discarded.

In operation the low cut frequency on the charge amplifiers was set to attenuate the I/rev part of the signal but to pass tooth frequency

(b) There was good agreement between accelerometers and encoders

in the middle frequency range

(c) The accelerometers appeared to give reliable information at high frequencies (>1 kHz) where the encoders were no longer reliable due to torsional resonances

The advantage of the accelerometer system is the extended frequency range at the upper end and the relative ease of fitting tangential accelerometers with a clamped flange compared with aligning encoders and using delicate high frequency couplings The accelerometers do not need a free shaft end

The flange needs care as the match to the shaft should be good, the flange should be light and the clamping powerful enough to ensure that the accelerometers follow the shaft vibrations faithfully

Corresponding disadvantages are the I/rev spurious results due to gravity interacting with accelerometer axis misalignment and the major problems of supplying electrical power and buffering out the signal on a rotating system as slip rings or telemetry tend to be expensive or temperamental

In practice the accelerometer system is only likely to be used when there is no access to a free end of both shafts or the 1/tooth frequencies are too high for encoders It may, however, be fitted independently for monitoring purposes (as in Chapter 15) and the measurement of T.E is then a bonus Tangential accelerometers inevitably give very low outputs at low frequencies

so if tooth frequencies are down at 5 Hz as may occur with worms and wheels the acceleration for 1 um is only 0.0001 g and is down below the noise level

so this method is not suitable Double integration to angular displacement is also temperamental at low frequencies The usual solution as with much vibration testing is to analog integrate acceleration to velocity, data log velocity then frequency analyse velocity and divide each band by the mean angular frequency to derive the amplitude distribution

7.6 Effects of dynamics

For most noise investigations we wish to know the inherent accuracy

of the gears as mounted Running at full speed with encoders fitted will give

us the torsional relative displacement of the gears but this will be a function

of both the inherent forcing due to T.E and the torsional and lateral vibrations of the internals of the drive as well as effects from the external drive system dynamics

T E Measurement 105

T.E

I.E

1 revolution

T.E

1 revolution

T.E

1 revolution

T.E

1 revolution

I revolution

Fig 7.9 Variation of T.E with speed due to internal dynamics.

Running up and down the speed range as in section 6.4 will give information about the resonances but the main interest for production control

is in determining the quasi-static T.E (to assess gear accuracy) avoiding the complications of the system dynamics

This suggests that the ideal test condition would be to run at 10 rpm and full torque This is usually not possible either because drive motor or (dynamometer) load cannot operate at low speed and full torque or because gearbox teeth or bearings would be destroyed Plain bearings will increase their eccentricity as the speed drops so the alignment of the meshing gears may be affected

A knowledge of the position of the first internal resonance is highly desirable, either from theoretical predictions or by running the drive under torque to find the position of the first resonance The resonance may appear either as a peak or as an anti-resonance because the measured torsional effects due to the mesh may decrease if there is high lateral vibration to absorb the errors Typically the T.E traces would appear as in Fig 7.9, with the underlying eccentricity effects unaltered by the speed changes but once-per-tooth showing a resonance Tooth meshing conditions may not be exactly correct but since the frequency of the lowest resonance is very insensitive to tooth mesh stiffness this does not matter

Once the first resonance is located, results up to about 2/3 of that frequency are effectively quasi-static but the effect on scuffing and on hydrodynamic bearings must be checked unless the drive is designed to run over a wide speed range

7.7 Choice of encoders

The choice of encoders is wide and looking at any manufacturer's catalog is confusing as some 50 different designs may be listed Absolute angular position is not required so it is the incremental type of encoder that is used It is simplest to classify the encoders, rather arbitrarily, in groups as in Table 1 which refers to typical sizes in a range made by Heidenhain [2]

As can be seen from Table 1, high accuracy tends to be associated with large diameter (and correspondingly high cost) The largest encoders are not available with TTL output and correspondingly have lower frequency limits The outputs are 11 uA peak to peak up to 90 kHz, allowing 150 rpm or

1 V p-p up to 180 kHz, allowing 300 rpm

The medium size encoders are available with TTL outputs and so with 18,000 lines can be run up to 3330 rpm, though the speed can be increased by using an encoder with less lines The small encoders have a 300 kHz limit but,

as they have fewer (5000) lines, can operate up to 3600 rpm before encountering the frequency limitation

T £ Measurement 107

Table 1 - Encoder parameters

Dia mm

Mass kg

170

2.8

200

3.3

110

0.7

110

0.8

58

0.25

58

0.25

36.5

0.1

36.5

0.1

Shaft

type

Solid

14 <j>

60 mm

bore

Solid

10<t>

20mm

bore

12 mm

bore

Solid

10<j>

Solid

4<J>

6 mm

bore

Accuracy Sec arc

±1

±1

±5

±5

±13

±13

±18

±18

No of lines typically 36000 36000 18000 18000 5000 5000 3600 3600

Output

11 nA 90kHz

1 V 180kHz TTL

1 MHz TTL

1 MHz TTL 300kHz TTL

300 kHz TTL 300kHz TTL 300kHz

Name ROD 800 RON 886 ROD 260 ROD 225 ERN 420 ROD 420 ROD 1020 ERN 1020

Encoder price is roughly proportional to weight so there is a financial incentive to use the smaller encoders All encoders have axial length less than 50mm

When mounting encoders onto a gearbox, choosing between a through-bore or stub shaft installation can be difficult If there is a through shaft such as a collet operating rod then there is no choice and an encoder with sufficient through bore must be used Otherwise, with a free shaft end, the choice is complex but is dictated by the mechanics of the test setup

The through-bore type is usually completely supported by the gear shaft extension and so the installation is simple with high torsional natural frequencies, typically above 1000 Hz even for the medium-sized encoders Reference to "earth" requires a restraint arm as long as possible with rigid light construction so there are small angular movements of the stator due to any eccentricities The corresponding disadvantages are that the shaft must run true or lateral vibrations will be high and the shaft must be strong enough to take the weight and vibration of the encoder body This is not usually true if

an extension has been bonded or pressed onto an existing (short) gearshaft The overhung mass of the encoder may be large in relation to gear masses and

so may give an extra low frequency resonance

mounting plate gearcase

Fig 7.10 Encoder mounting at shaft ends.

Installation of the stub shaft type of encoder is more difficult as the main body has to be held by bolting onto a mounting plate which is itself supported off the end face of the gearbox as in Fig 7.10 The plate should be mounted sufficiently accurately to ensure that the encoder is aligned to the gearshaft extension within about 25 um and the gearshaft extension should be running true within about 25 um so that the flexible coupling between them does not have to cope with large misalignments The manufacturers can supply suitable couplings (such as the KO3) which are torsionally very rigid to maintain high torsional natural frequencies but are flexible laterally as the encoders must not be subjected to high (10 N) spindle loads either axially or laterally The mounting plates for the encoders must be mounted very rigidly

to the end face of the gearcase since if they vibrate torsionally the information will not be correct

T £ Measurement 109

mounting plate

centre distance

mounting plate

support pillars

support pillar

Fig 7.11 Staggered mounting with low centre distance.

A complication can arise with either through or stub mounting since the centre distance of the gear pair may not accommodate the two encoder radii and one shaft must be extended to allow the encoders (and if necessary their couplings) to be staggered axially as in Fig 7.11 Use of smaller encoders such as the 58 mm diameter encoders helps greatly as the centre distance can then be 60 mm without stagger or about 40 mm with an extended shaft and stagger

The smallest practical size is 36.5 mm diameter and without stagger the centre distance is 37 mm or with maximum stagger the centre distance can

be about 22 mm Unfortunately this involves having a shaft extension which is long and slender, making it difficult to ensure that it runs true Long shaft extensions make it more likely that gearbox dynamics will be altered if the encoder is shaft mounted or that the flexible coupling has to accommodate large eccentricities