chapter 4 experimental investigation of resonance...

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CHAPTER 4

EXPERIMENTAL INVESTIGATION OF RESONANCE

4.1 INTRODUCTION

In this chapter, the experimental set-up and the investigation of

resonance are presented. This investigation is based on experimentation carried

out on hybrid stepper motor subject it to resonance and non-resonance

conditions under various excitation schemes and loading conditions. The

experimental hardware of HSM and detailed experimental study are also dealt

with.

4.2 EXPERIMENTAL SET-UP

The HSM experimental set-up and the motor set-up are shown in

Figures 4.1 & 4.2. They consist of HSM motor model ST601 whose

specification details are given in Table 4.1. HSM model ST1701 set-up is

shown in Figure 4.3. Sensors are used for measurement of torque and position.

UC3717 Integrated Circuit (IC) driver circuit is used for driving the motor for

full step and half step mode. The driver supply range is 10-46V. Data

Acquisition Card (DAC) is used to provide micro step sequence from the digital

platform. HSM is loaded with brake drum and pulley arrangement.

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1. Driver set-up. 2. DAC Interface Card. 3.Digital Oscilloscope.

4. Pulse generator. 5. DC Power supply. 6. Current amplifier.

7. HSM set-up

Figure 4.1 HSM experimental set-up

2 3 4 5 1 6 7

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1. Loading set-up. 2. Torque sensor. 3. HSM ST601 model.

Figure 4.2 Hybrid stepper motor model ST601 set-up

1. ST1701 HSM model. 2. Loading set-up.

3. Power supply. 4. Driver circuit.

Figure 4.3 Hybrid stepper motor model ST1701 set-up

1 2 3

1 2 3 4

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Table 4.1 Hybrid stepper motor specifications

Motor Parameter, units ST601 ST1701 KP39HM2-S07

Voltage (Volts) 12 12 12

Current (Amp) 0.5 6 0.16

Number of Phases 2 2 2

Number of rotor teeth (Nr) 50 50 50

Step angle (Deg) 1.8 1.8 1.8

Number of steps per revolution 200 200 200

Torque (Nm) 0.19 12.5 0.10

Detent Torque(Nm) 0.018 1.10 0.01

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4.2.1 UC 3717- Stepper Motor Drive Circuit

The UC3717 is an improved version used to switch drive the current

in one winding of a bipolar stepper motor as explained in detail UC3717

data sheet. It has been modified to supply higher winding current and gain

improved efficiency. Advantages are full step and half step capability, bipolar

output current up to 1A, wide range of motor supply voltage 10-46V, low

saturation voltage with integrated bootstrap, built -in fast recovery commutating

diodes, selectable current levels in steps and thermal protection with soft

intervention. The block diagram of UC3717 drive circuit as shown in

Appendix 1 includes the components H-bridge output stage, phase polarity

logic, voltage divider coupled with current sensing comparators, two-bit D/A

current level select, monostable generating fixed off-time and thermal

protection.

4.2.2 H-bridge Output Stage

The output stage consists of four Darlington power transistors and

associated recirculating power diodes in a full H-bridge configuration as shown

in Appendix 2. While in switched mode, with a low level phase polarity input,

Q2 is on and Q3 is being switched. At the moment Q3 turns off, winding current

begins to decay through the commutating diode pulling the collector of Q3

above the supply voltage. Meanwhile, Q6 turns on pulling the base of Q2 higher

than its previous value. The net effect lowers the saturation voltage of source

transistor Q2 during recirculation, thus improving efficiency by reducing power

dissipation.

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4.2.3 Phase Polarity Input

Phase polarity input controls the current direction in the motor

winding as shown in Appendix 3.

4.2.4 Current Control

The voltage divider, comparators, monostable generating fixed off-

time and two-bit D/A (Digital/Analog) provide a means to sense winding peak

current, select winding peak current and disable the winding sink transistors. The

switched driver accomplishes current control using an algorithm referred to as

fixed off-time . When the voltage is applied across the motor winding, current

increases exponentially.

Appendix 4 presents the relationship between the two-bit D/A input

signal and selectable current level.

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4.3 TESTS CARRIED OUT FOR INVESTIGATION OF

RESONANCE

Following tests are carried out on HSM for investigation of resonance.

No-load test

Various phase excitation mode

Load test

with various constant loads

Measurements made

Voltage

Current

Position

Velocity

Excitation techniques used

Full step

Half step

Micro step

Driver used

Bipolar

4.4 ANALYSIS OF PHASE CURRENT WAVESHAPES

HSM behaviour is assessed for various speed ranges based on the

current built up in the windings. The behavior is presented as follows,

At low speeds, the winding current has sufficient time to reach its

steady value before having to change polarity.

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At high speeds, the winding current does not have enough time to

reach its steady value, before changing its polarity.

These speed ranges will be used to analyse the stepper motor

currents for both the cases with different loaded and unloaded conditions. The

current wave shape which varies at different speeds is very important for control.

The low speed current waveform is shown in Figure 4.4(a) and is similar to

square wave. Signal analysis of square wave is difficult than smooth oscillating

sine wave. Medium speed current waveform is shown in Figure 4.4(b) and is

close to a sine wave. Sine wave has many known properties for easier analysis of

electric circuits compared to other shapes. The high speed current waveform is a

distorted wave as shown in Figure 4.4(c). Generally the resonance can be easily

identified if the phase current wave shape is normally sinusoidal and the micro

step excitation exhibits sinusoidal current wave shape.

Figure 4.4 Experimental phase current waveforms of HSM with full step excitation under no-load condition

(a) Low speed (b) Medium speed (c) High speed

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4.5 TORQUE Vs SPEED CHARACTERISTICS OF HSM

Torque Vs speed experiment is conducted to investigate the resonant

frequency with different excitation schemes. Two HSM models (ST1701) and

(ST601) are chosen for this purpose. For HSM model ST1701 Figures 4.5 and

4.6 show simulation and experimental results. Resonance frequencies are noted

as sudden dip in the torque Vs speed curve with various excitation schemes. It is

also observed that frequent dips are noted for full step than half and micro step

excitation. Results are tabulated in Table 4.2.

Similarly for HSM model ST601 Figures 4.9 and 4.10 show the

simulation and experimental results. Resonant frequencies identified for various

excitation schemes are tabulated in Table 4.3.

Figure 4.5 Torque Vs speed curve simulation results with various excitation

schemes (Model ST1701)

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Table 4.2 Resonant frequency for various excitations (Model ST1701)

Excitation Type Resonant frequency (Hz)

Simulation result Experimental result

Full step 35 , 70 & 110 35, 70 & 109.5

Half step 40 & 80 40 & 79.8

Micro step 50 50

Figure 4.6 Torque Vs speed curve experimental results with various excitation schemes (Model ST1701)

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Figure 4.7 Torque Vs speed curve simulation results with various excitation schemes (Model ST601)

Figure 4.8 Torque Vs speed curve experimental results with various

excitation schemes (Model ST601)

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Table 4.3 Resonant frequency for various excitations (Model ST601)

Excitation Type Resonant frequency (Hz)

Simulation result Experimental result

Full step 17 , 44 & 85 17, 44 & 84

Half step 49 & 87 49 & 87

Micro step 20 20

4.6 EXPERIMENTAL INVESTIGATION OF PHASE CURRENT

WAVEFORMS

It is observed that during the resonance conditions, actual and

expected speeds (RPM - Revolution Per Minute) do not match. The captured

phase current waveforms with full step, half step and micro step excitation under

various speed and load conditions for model ST601 are shown in Figures (4.9 -

4-16). Actual speed is measured with digital tachometer. Figures 4.9 - 4.12

correspond to full step excitation. Ripples in the current wave shapes under no-

load condition is observed to be more compared to loaded condition as shown in

Figures 4.9 and 4.10 Similarly current

-load and loaded conditions with half

step and micro step excitations are shown in Figures 4.13a, 4.13b, 4.15a and

4.15b.

The current waveform shown in Figure 4.11 at

is noted that under loaded condition resonance is eliminated as in Figure 4.12.

The results are tabulated in Tables 4.4, 4.5 and 4.6 for full step, half step and

micro step excitation respectively.

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Similarly c -load and

loaded condition with half and micro step excitation are shown in Figures 4.14a,

4.14b, 4.16a and 4.16b.

Expected speed = 6.6RPM Actual speed = 6.6RPM

Figure 4.11a Phase current waveform at 22Hz in full step excitation under

no- load condition with a current probe scale of 5A/V


Figure 4.11b Phase current waveform at 22Hz in full step excitation under

loaded condition (TL=0.10Nm) with a current probe scale of 5A/V

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Expected speed =13.2RPM Actual speed = 13.7RPM

Resonance is identified by the ripple during initial rise of

phase current in both directions


no- load condition with a current probe scale of 5A/V




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Table 4.4 Resonance and non-resonance observations with full step

excitation under different loading conditions

Current (A)

Excitation Clock Frequency

( Hz)

Synchronous Speed (RPM)

Actual Speed (RPM)

Difference in speed (RPM)

Load Torque (Nm)

0.32

17

5.1

5.3 +0.2 0

0.32 5.1 0 0.07

0.31 5.1 0 0.18

0.31

22

6.6

6.6 0 0

0.30 6.6 0 0.03

0.30 6.6 0 0.16

0.29

30 8.9

8.9 0 0

0.29 8.9 0 0.04

0.29 8.9 0 0.15

0.28

44 13.2

13.7 +0.5 0

0.26 13.2 0 0.07

0.26 13.2 0 0.11

0.25

56 16.8

16.8 0 0

0.24 16.8 0 0.07

0.23 16.8 0 0.12

0.21

85 25.6

25.7 +0.1 0

0.20 25.6 0 0.07

0.20 25.6 0 0.09

0.15 100 30

30 0 0

0.14 30 0 0.07

0.11 130 39

39 0 0

0.10 39 0 0.07

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Figure 4.13a Phase current waveform at 25Hz in half step excitation under

no-load condition with a current probe scale of 5A/V


Figure 4.13b Phase current waveform at 25Hz in half step excitation under


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Expected speed = 7.3 RPM Actual speed = 7.6 RPM

Figure 4.14a Phase Current waveform at 49Hz in half step excitation under





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Table 4.5 Resonance and non-resonance observations with half step


Current

(A)

Excitation Clock

Frequency

( Hz)

Synchronous

Speed

(RPM)

Actual

Speed

(RPM)

Difference

in Speed

(RPM)

Load

Torque

(Nm)

0.29

25 3.75

3.75 0 0

0.29 3.75 0 0.07

0.28 3.75 0 0.15

0.29

44 6.6

6.6 0 0

0.29 6.6 0 0.07

0.29 6.6 0 0.12

0.27

49 7.3

7.6 +0.3 0

0.27 7.3 0 0.07

0.26 7.3 0 0.09

0.24

87 13

13.5 +0.5 0

0.23 13 0 0.07

0.23 13 0 0.11

0.17 172 25.8

25.8 0 0

0.17 25.8 0 0.08

0.11 400 60

60 0 0

0.09 60 0 0.006

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Expected speed =12.1 RPM Actual speed =12.1RPM

Figure 4.15a Phase current waveform at 10Hz in micro step excitation

under no-load condition with a current probe scale of 5A/V


Figure 4.15b Phase current waveform at 10Hz in micro step excitation

under load condition (TL=0.19Nm) with a current probe scale of 5A/V

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Expected speed =24RPM Actual speed = 24.1RPM


under no- load condition with a current probe scale of 5A/V

Expected speed =24RPM Actual speed = 24 RPM


under load condition (TL=0.19) with a current probe scale of 5A/V

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Table 4.6 Resonance and non-resonance observations with micro step


Current

(A)

Sine wave

Frequency

( Hz)

Synchronous

Speed

(RPM)

Actual

Speed

(RPM)

Difference

in Speed

(RPM)

Load

Toque

(Nm)

0.18

10 12.1

12.1 0 0

0.17 12.1 0 0.03

0.17 12.1 0 0.15

0.13

15 18

18 0 0

0.14 18 0 0.03

0.15 18 0 0.14

0.12

20 24

24.1 +0.1 0

0.14 24 0 0.03

0.15 24 0 0.04

0.12

25 30

30 0 0

0.11 30 0 0.03

0.10 30 0 0.07

0.09

30 36

36 0 0

0.10 36 0 0.03

0.11 36 0 0.04

0.05 45

54 54 0 0

0.10 Stalled - - 0.003

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HSM Motor model ST601 is subjected to different types of phase

excitation schemes with different loading conditions. Points observed from the

tabulated results are given as follows,

Maximum speed that can be achieved under no-load condition is

220Hz for full step,

420Hz for half step and

45Hz for micro step (due to the limitation in the digital hardware

used).

In full step, during resonance condition, difference in speed (RPM) is

high. Loading dampens the resonance. The number of resonant frequencies is

less in half step and micro step when compared to full step excitation.

The phase current waveforms are compared under resonance and non- resonance

conditions. It leads to the following inference.

1. Phase currents contain the resonance information.

2. Information is in the ripples present in the rising, falling transience of

the phase current.

4.7 EFFECT OF RESONANCE DURING HIGH SPEED

In this machine, the electrical time constant (L/R=2ms) is greater than

the mechanical time constant (J/B=1ms). This limits the achievable stepping rate

to 500Hz(R/L) against the maximum possible rate of 1000Hz (B/J).

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Hence, in order to investigate the performance for higher speeds, the

electrical time constant needs to be reduced by inserting resistance in series only

for investigation purpose. A maximum resistance of 66

Maximum achievable speed is even up to 1050Hz (315 RPM) for full step

excitation, 1900Hz (285 RPM) for half step excitation & 80Hz (112 RPM) for

micro step excitation. Maximum resonance leading to instability is observed

around 770Hz to 790Hz with half step excitation. Tables 4.7, 4.8 and 4.9

present the values of resistance added in series, the maximum speeds achieved

and the frequencies at which resonance is noted for micro step, full step and half

step excitation respectively.

It is observed that the speed of the motor can be increased with the

addition of resistance per phase. The voltage applied to the phase is maintained

constant for all the speeds. There is a limitation on adding resistance and

maintaining the phase voltage to the motor as it produces more heat and

damages the permanent magnet properties. This exercise is tried only for

investigation.

Table 4.7 HSM high speed response with micro step excitation

External resistance

added per phase

(ohms)

Maximum speed

achieved

(Hz)

Frequency at

which resonance is

noted (Hz)

0 45 15

66 60 55

144 75 65

210 80 70

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Table 4.8 HSM high speed response with full step excitation

External

resistance added

per phase (ohms)

Maximum speed

achieved

(Hz)

Frequency at

which resonance

is noted (Hz)

0 180 44 & 89

66 380 330

144 540 330

210 620 330

330 750 330 & 660

460 1050 330 ,660 & 970

Table 4.9 HSM high speed response with half step excitation

External resistance

added per phase

(ohms)

Maximum speed

achieved

(Hz)

Frequency at which

resonance is noted

(Hz)

0 380 49 ,89

66 680 330 &660

144 1650 330 ,660

770- 790 (very high)

210 1730 330 &660

330 1830 330 & 660

460 1900 330 ,660 & 970

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Current waveshape with full step excitation under no-load and loaded

-load and

loaded condition. Similarly current waveshape is shown in Figures (4.19 - 4.22)

for half step and micro step excitation.

Expected speed = 45RPM Actual speed = 45RPM






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Expected speed = 99RPM Actual speed = 99.3 RPM



Expected speed = 99RPM Actual speed = 99 RPM


load condition (TL=0.19Nm) with a current probe scale of 5A/V

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The and condition observations during high speed operation

of HSM with full step, half step and micro step excitations under different

loading conditions are tabulated in Tables 4.10, 4.11 and 4.12 respectively.

Table 4.10 Resonance and non-resonance observations during high speed

operation of HSM with full step excitation

Current

(A)

Excitation clock

Frequency

( Hz)

Synchronous

Speed

(RPM)

Actual

Speed

(RPM)

Difference

in Speed

(RPM)

Load

Torque

(Nm)

0.51

160

48

48 0 0

0.55 48 0 0.09

0.42

330

99

99.3 +0.3 0

0.46 99 0 0.07

0.39

660

198

198.1 +0.1 0

0.45 198 0 0.07

0.36

960

288 288 0 0

0.39 288 0 0.003

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Expected speed = 99RPM Actual speed = 99.2RPM





load condition (TL=0.25Nm) with a current probe scale of 5A/V

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no -load condition with a current probe scale of 5A/V


Figure 4.20b Phase Current waveform at 770Hz in half step excitation


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operation of HSM with half step excitation

Current

(A)

Excitation clock

Frequency

( Hz)

Synchronous

Speed

(RPM)

Actual

Speed

(RPM)

Difference

in Speed

(RPM)

Load

Torque

(Nm)

0.49 330

49.5

49.5 0 0

0.51 49.5 0 0.06

0.43 660

99

99.2 +0.2 0

0.47 99 0 0.04

0.37 770

115.6

117.2 +1.6 0

0.41 115.6 0 0.03

0.35 1250

187.7

187.7 0 0

0.39 187.7 0 0.03

0.31 1800

270 270 0 0

0.36 Stalled - - 0.003

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Expected speed =9RPM Actual speed = 9RPM






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79


operation of HSM with micro step excitation mode

Current

(A)

Excitation Sine

wave Frequency

( Hz)

Synchronous

Speed

(RPM)

Actual

Speed

(RPM)

Difference

in Speed

(RPM)

Load

Torque

(Nm)

0.20 30 9

9 0 0

0.23 9 0 0.06

0.29 45 13.5

13.5 0 0

0.33 13.5 0 0.04

0.41 55 16.5

16.6 +0.1 0

0.44 16.5 0 0.03

0.38 80

24 24 0 0

0.43 Stalled - - 0.003

4.8 CONCLUSION

The mathematical model of hybrid stepper motor has been duly

explained. The resonance effect has been studied with different excitation

schemes and loading conditions. Experimental phase current waveform is found

to contain .

chapter 4 experimental investigation of resonance...

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