tech-spring report 20a: use of strain gauges to measure

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L:\PROJECTS\810CollectiveResearchProg\90420 No 20A

Tech-Spring Report 20A: Use of Strain Gauges to Measure Dynamic Stresses in Springs

1. Introduction The measurement of static and dynamic stresses in components using strain gauges is common practise. With springs it is considerably more difficult because of the size of the wire and the curved surface that the gauge has to be glued to. This report looks at a method of simplifying the process and the results achieved. 2. Equipment required. Three pieces of equipment are required to undertake basic strain gauge testing:

1. Strain gauges and adhesives. 2. Amplifier. 3. Monitoring equipment. 4. Method of loading the spring to simulate the application.

2.1 The strain gauges required for the majority of spring testing need to be very small to

enable the to be glued onto wire diameters down to 3mm. For smaller wires grid sizes of 0.2 x 0.2mm are available, but become more costly and difficult to use such that their application needs to be contracted to a specialist at a cost of 3-400 Euros. For the spring used in the test program a 2 x 2mm gauge was used. Three other gauges are required to form a balanced whetstone bridge. Although precision resistances can be used to form the bridge, it was been found that gauges proved a simpler and mere stable solution. Foil gauges are generally supplied in two resistances, 120 and 350Ω. Semiconductor gauges are also available for higher outputs and have substantially higher resistance. To connect the gauge to the test equipment they are supplied with either short leads to enable connection via a solder pad or with flying leads already connected. The connecting wires need to be small so they can be wound around the spring back to the static end without inhibiting or being damage by spring movement.

2.2 The signals from the strain gauges are very small and require amplifying to usable levels for the monitoring equipment. By adjusting the amount of amplification the output can be a direct measure of the measured stress. This is useful when absolute values are required rather than measurements of proportional increases. The amplifier must be designed for use with strain gauges and be able to supply a very stable bridge voltage. The type of test, static or dynamic also dictates the type of amplifier system used. For static tests, stability is of major importance and hence large amounts of filtering may be used. AC energised bridge amplifiers also give good zero stability at the expense of speed so are used for static or slow test speeds. DC

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amplifiers are used for the faster applications.

2.3 The monitoring equipment required will depend on the type of tests being undertaken. For static test a simple digital readout will be sufficient, but for dynamic tests a digital storage scope is ideal. PC based units, which offer spectrum analysis, range and peak capture will enhance the system performance.

2.4 To cycle the spring a load tester can be used for static applications, but for dynamic testing then a fatigue machine, electromagnetic shaker, or better still the actual mechanism can be used.

Overall the amount of equipment is modest, but care is required when setting up for dynamic measurements. Much of the available equipment is for static work and will introduce measurement errors when used above semi static conditions. This is because the bandwidth of the amplifier system is low to promote stability and causes an ever-increasing loss of signal as the test speed increases. The bandwidth is often expressed as -3dB at a particular frequency (eg –3dB at 500Hz). Where:

Input

OutputdB 10log20

This means the output signal amplitude at 500hz is ~71% of the 0Hz level. As an approximate guide a bandwidth of 15 times the test speed will give 1% accuracy and 40 times will give 0.1% (ie if you wish to test at 5000rpm– 83.33 Hz with 1% accuracy then the system bandwidth needs to be about 1250Hz). It should be noted that the bandwidth of an amplifier will reduce as the gain is increased. The above assumes that the spring loading is sinusoidal and if a system that has much faster rise times is being tested then the amplifier system will require a faster bandwidth based on the rise times of the cam. 3. Type and alignment of gauges. The shape of a spring with its three dimensional surface complicates the fixing of strain gauges. A strain gauge will only measure strain in the direction of the grid and hence must be aligned with the stress direction of interest. Any deviation from the correct axis will cause errors in the magnitude of the measured stress. A way round this is to use a strain rosette that will be made up of 2 or 3 gauges arranged at 45 or 90 degrees to each other. This system enables the magnitude and direction of the maximum stress to be found. The disadvantage of the rosette system is that the gauges are larger and you need to double or treble the monitoring equipment. The simple solution is to use a single gauge, which is glued to the wire at approximately 45deg to the wire axis. The 45 deg is to enable the gauge to maximise its sensitivity to the torsional strain, which is of primary interest in compression springs. For torsion springs the gauge would be aligned with wire axis to maximise the bending strain sensitivity.

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The gauge can then be used as a proportional measurement system, where the strain/stress/voltage/ vs. deflection/load characteristics can be measured statically on a load tester. The measured loads or lengths can be used to calculate the stress using classical theory;

3

8

d

kDPStress

or

nD

kdGStress

2

Where: P = Applied load d = Wire diameter D = Mean coil diameter k = Stress correction factor Δ = Deflection N = Number of active turns From the load testing a relationship between load and output voltage is known;

pConstvoltP Constvolt

thus:

3

8

d

kDConstvoltStress

p

or

nD

kdGConstvoltStress

2

4. Bonding of gauges to springs. Strain gauges work by stretching or compressing with the specimen under test, causing the gauge resistance to change in proportion to the applied strain. It is thus imperative that the gauge is firmly bonded to the test specimen. Two basic families of glues are used for gluing gauges; two pack epoxy adhesives, and cyanoacrylate (superglue) adhesives. It has been found that epoxy superglues, which hold within 90 seconds, are fine for most applications. For very arduous conditions then proprietary glue supplied by the gauge supplier may be a better choice. For a good bond it is essential that all grease, paint or scale is removed from the surface of the wire. The surface should be roughened with a fine grade emery cloth and the thoroughly degreased.

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Protective coating Gauge at ~45deg Wires from second gauge

Wires to amplifier Solder terminal pad Wires from gauge

Fig 1 Close up of strain gauge layout on so spring If the gauges used have short leads then a solder terminal will need to be glued adjacent to the gauge to enable soldering together of the gauge wires and the wires to the amplifier. Once the gauge and signal wires are soldered into place it should be checked to ensure the electrical resistance matches the gauge specification and isolation from the spring is present. A thin coating of epoxy or silicon should then be applied to form a protective barrier. The wires can then be wound around the spring wires in a gentle spiral back to the static end on the spring. A small amount of glue can be used to fix the wires at intervals if required.

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5. Equipment used in test program A schematic of the equipment used can be seen in below fig 2

Fig 2 Schematic of test equipment used The spring gauge was connected to three additional gauges to form the four-arm bridge. The three gauges were glue to a piece of steel to help with temperature stability. The bridge was connected to a strain gauge amplifier that exhibits a unity gain bandwidth in excess of 400kHz. A limited amount of filtering was used to remove the inevitable high frequency noise. The gain was set to an arbitrary 3000 which equates to ~69dB which theoretically gave a bandwidth of 700hz which at 70 hz gives an error of approximately 1%. The output was fed to a pc based oscilloscope and spectrum analyser to enable the strain outputs to be visually seen and stored. The oscilloscope had an analogue bandwidth of 250kHz and 12bit resolution. A variable speed IST single station fatigue machine was used to cycle the spring and set to a 3mm stroke. The machine has a maximum test speed up to 70Hz.

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6. Test spring The spring used was chosen to have a low natural frequency and have a reasonable wire diameter. The design is show below:

The gauge was glued to the spring at approximately 0.6 of an active turn from the end coil tip. This position was selected because many fatigue failures occur at this position.

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7. Test Proceedures and results. Test 1: Natural frequency measurement. The spring has a theoretical natural frequency of 82.9Hz. A test to confirm this requires the test spring to be fitted into a special fixture that enables the spring to be compressed and then quickly released by 0.5mm so that the spring ‘rings’ at its natural frequency. The resulting output is subject to a FFT spectrum analysed to measure the frequency.

Fig 3 Natural frequency test FFT output It can be seen that the FFT result indicates 82Hz, which correlates well with theory. Test 2 : Resonant frequency identification and effect. For this work the spring was fitted into the fatigue machine. From the above test It would

be expected that resonant sub harmonics to occur at frequencies of; 2

n,

3

n,

4

n etc where

n is the natural frequency. Thus it was expected to see resonance effects occurring at 41,

27, 20, 16, and 10Hz. The machine was slowly sped up until definite resonance effects could be seen. These are produced when the waveform produced by the cycling of the spring come into phase with the natural frequency waveform. These combine additively to produce the waveforms shown below.

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Fig 4 10Hz test Scope output

Fig 5 10Hz test FFT output

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10




11




12




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It can be seen from the above scope screens that with the odd sub-harmonics (3

n,

5

n,

etc) the peaks add and for the even sub-harmonics, one peak adds and the second peak subtracts. It can also be seen clearly that the pk-pk stresses at the sub-harmonic frequencies are much higher that the theory predicts (seen next section) for the general dynamic stress (Note the Volts/Div setting on the scope screen when comparing plots and do not simply assume larger wave means higher stress). However, if the theoretical stress ratio is plotted using ω/2.ωn then the formula predicts the sub harmonic stress with reasonable precision up to the third harmonic after which it seems that damping becomes dominant.

Sub - Harmonic stress vs speed - end located gauge

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1

ω/ωn

Str

es

s r

ati

o

Theoretical pk-pk stress

Theoretical 2xWn pk - pk stress

Measured Sub-Harmonic stress

Fig 14 Measured vs theoretical Dynamic/Static stress ratios at sub-harmonics

Test 3: Effect of cycling speed on stress. The previous test clearly showed the potential stress raising effects of running a spring at a sub-harmonic frequency. The underlying effect on stress amplitudes of increasing running speed away from a sub-harmonic was investigated by measuring stress the stress range at various speeds up to 70Hz.

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82n Run 1 Run 2 Run 3 Average

(Hz n

Dynamic

pk-pk

Dynamic

pk-pk

Dynamic

pk-pk Static

PkDynamicPk

4 0.0489 855 840 835 1.000

10 0.1220 886 850 838 1.017

15 0.1829 898 875 858 1.040

20 0.2439 940 902 880 1.076

30 0.3659 1056 1015 1060 1.238

40 0.4878 1290 1224 1240 1.484

50 0.6098 1810 1735 1690 2.068

60 0.7317 3100 2940 2650 3.433

70 0.8537 4310 4620 3940 5.086

Fig 15 Measured pk-pk Dynamic vs Static stress ratios.

Gross (Appendix 1) developed a theoretical calculation for the stress increase with speed;

)(n

n

Stat

Dyn

Sin

n

(Hz) Static

Dynamic

0 0 1

0.2 16.4 1.07

0.4 32.8 1.32

0.6 49.2 1.98

0.8 65.6 4.28

0.85 69.7 5.88

1.0 82 ∞

Fig 16 Theoretical pk-pk dynamic vs Static stress ratios

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82n Run 1 Run 2 Run 3 Average

(Hz n

Dynamic

Mean

Dynamic

Mean

Dynamic

Mean Static

nDynamicMea

4 0.0489 507 577 543 1.000

10 0.1220 527 590 560 1.031

15 0.1829 533 603 577 1.053

20 0.2439 546 614 587 1.074

30 0.3659 553 622 600 1.091

40 0.4878 530 589 530 1.014

50 0.6098 553 613 609 1.091

60 0.7317 480 528 507 0.931

70 0.8537 536 531 548 0.993

Fig 17 Measured Mean Dynamic vs Static stress ratios.

This formula ignores any effects of damping that a spring may be subject to. However it is generally found that damping effects are small when running at moderate speeds and Fig 18 shows that theory and practise agree closely until ω/ωn exceed 0.8.

Dynamically induced stress vs speed - end located gauge

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

ω/ωn

Str

es

s r

ati

o Theoretical pk-pk stress

Measured pk-pk stress

Measured mean stress

Sub-Harmonic stress

Fig 18 Measured vs theoretical Dynamic/Static stress ratios

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The above also shows the peaks that are produced when running at a sub-harmonic.

Test 4: Centre vs end gauge location

Comparing Fig 18 and Fig 19 it can be seen that the gauge at the centre of the spring gives considerably different results compared to the end gauge. It can be seen that the pk-pk stress only shows any sort of significant rise in stress at the highest (70Hz) test speed. The mean stress stays approximately constant.

Dynamically induced stress vs speed - centre located gauge

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

W/Wn

Dyn/S

tatic

Theoretical pk-pk stress

Measured pk-pk stress

Measured mean stress

Sub-Harmonic stress

Fig 19 Measured vs theoretical Dynamic/Static stress ratios – centre guage

The centre gauge also indicates that the sub-harmonics do not have such a detrimental affect on this section of the spring.

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Fig 20 40Hz test Scope output – centre gauge vs end gauge

Fig 21 40Hz test FFT output – centre gauge vs end gauge Comparing the scope outputs it can be seen that the waveforms are of considerably different shape and magnitude (note the centre gauge is set to 0.2v/division and the end gauge to 1V/division). The FFT screens show that the as well as the fundamental test frequency of ~40Hz both tests had a second significant frequency. For the centre gauge this was 162Hz, which equates to twice the natural frequency. For the end gauge the frequency peak occurs at the expected natural frequency of 82 Hz. The 162Hz peak on the centre gauge is due to the 80Hz surge wave passing the gauge twice for each cycle as it moves along the spring and then back again. This motion of the surge wave also seems to inhibit the dramatic build up of stress that occurs as the speed increases and at the sub-harmonics. 8. Discussion The equipment used was modest and the cost of the amplifier, power supply, gauges and pc scope (not including laptop) was less than a €500. The gauges are typically €5-10 each. Labour costs need to be added to this for the packaging, assembly and wiring etc. Care needs to be taken to ensure the equipment is suitable for the test speeds to be

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encountered. Electrical noise is often a problem and limited filtering combined with good analogue electronic layout will be required. The above work has all been undertaken using small deflections and an essentially pure sine wave excitation. For real world applications then the mode of loading must model the application very closely otherwise the test results will be misleading. The use fast rising waveforms produced by automotive cams will induce more extreme deflection at the various sub-harmonics but not alter the frequencies. With higher rise times damping may start to become more dominant at lower frequencies, but will not change the sub-harmonic frequencies. When deflecting a spring axially it should be noted that rotational and lateral deflections will be induced. These two additional modes will each have their own natural frequencies and hence their sub-harmonics will be seen when a speed sweep of the spring is made. If the natural frequency for one of these other modes is particularly low then the axial dynamic performance could be compromised even though the theoretical axial performance suggests otherwise. Also be aware that the Gross formula does not account for these other resonance modes. A high-speed video camera running at 1000 frames/sec was also used to look at the spring when running at 21, 27, 41, and 68Hz. The first three speeds showed the surge wave passing up and down the spring with increasing magnitude. At the 41Hz test the torsional movement of the centre coils could be clearly seen showing that deflecting the spring axially induces movements in other axis. The test at 68 Hz, which is not an axial sub-harmonic, reinforced this further, as the spring was clearly seen to be deflecting significantly in the lateral direction. See Tech Spring Report 20B, which shows that 68Hz is the lateral resonant frequency for this spring.

Conclusion 1. The equipment required to undertake meaningful dynamic strain gauge testing is

modest.

2. Using the static to dynamic stress ratio system alleviates the need for multiple gauges/rosettes and precise gauge location.

3. The measured and calculated theoretical natural frequencies correlated closely.

4. The results from the centre and end mounted gauges were dramatically different indicating that the first active coil is subject to a significantly higher dynamic stress than the centre. This may explain why most fatigue failures occur within the first active coil.

5. The formula produced by Gross predicts the dynamic increase in stress accurately up to a ω/ωn ratio of 0.8.

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6. The Gross formula does not attempt to predict the peak stresses that occur at the sub-harmonics.

7. Using ω/2.ωn in Gross’s formulae give a reasonable estimate of the pk-pk stresses induced up to and including the third sub-harmonic.

8. The mean stress does not appear to be subject to a dynamic effect.

9. High speed camera work was valuable in showing the coil movements at resonance.

10. Deflecting the spring axially at a resonant frequency of the lateral mode induced significant oscillation.

11. Deflecting the spring axially at a resonant frequency of the torsional mode induced significant oscillation.

Appendix 1

1. Calculation and design of Metal Springs by:Siegfried Gross Published: Chapman & Hall, 1966

2. Tech Spring Report 20B: Non Axial Resonances in Compression Springs by: Mike Bayliss Published: IST 2009

tech-spring report 20a: use of strain gauges to measure

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