Innovative design of a transmission mechanism for variable

Bulletin of the JSME

Journal of Advanced Mechanical Design, Systems, and ManufacturingVol.9, No.3, 2015

Paper No.15-00252© 2015 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2015jamdsm0032]

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Innovative design of a transmission mechanism for variable speed wind turbines

Abstract An innovative transmission mechanism, referred to here as an independently controllable transmission (ICT), for application in variable speed wind turbines is described. This ICT mechanism can transmit rotational output speed that can be independently regulated by a controller and is not affected by the speed of the input shaft. Use of this ICT mechanism would make it possible for a variable speed wind turbine to be unaffected by rotor speed fluctuations and allow the generation of constant frequency electrical output of improved quality. The ICT mechanism is comprised of two planetary gear trains and two transmission-connecting members. The kinematic, static characteristics, and power flow of the ICT mechanism have been analyzed and derived as analytical equations. Demonstration examples and a prototype of the device have been built and tested to examine their kinematic and static characteristics and to verify the validity of the results.

Key words : Variable speed wind turbine, Independently controllable transmission (ICT), Planetary gear train, Transmission-connecting member

1. Introduction

Because wind speed fluctuates constantly over time, so does the speed of the wind turbine generator input shaft. To

facilitate good aerodynamic performance, it is necessary that a wind turbine be able to operate efficiently under conditions of variable wind speed. An ability to continue to perform under such conditions makes energy capture more efficient, and yields a higher power as well as decreasing costs for a variable speed wind turbine. Consequently, variable speed wind turbines become more key roles in wind energy systems (Carlin, et al., 2001; Şahin, 2004; Balat, 2009).

An efficient speed and torque transmission mechanism is a vitally important component in many variable speed wind turbines. A number of different transmission mechanism designs have been proposed and applied in variable speed wind turbines. For example, Mangialardi and Mantriota (1996) proposed a wind power system with a continuously variable transmission (CVT) to improve efficiency. Idan and Lior (2000) presented the theory and design of a hybrid electro-mechanical variable speed wind turbine transmission and discussed a robust control solution for optimal power output. Zhao and Maiβer (2003) proposed an electrically controlled power splitting drive train for variable speed wind turbines. Müller et al. (2006) analyzed grid integration aspects of a new type of variable speed wind turbine that is directly coupled to a synchronous generator with a hydro-dynamically controlled gearbox that does not need a power electronics converter. Lahr and Hong (2009) proposed a cam-based infinitely variable transmission (IVT) with a ratcheting drive for variable speed wind turbines.

In this study, an independently controllable transmission (ICT) mechanism is suggested that provides variable speed and torque transmission (Hwang and Tsay, 2013). The ICT mechanism can produce steady output at a predetermined speed which can be independently controlled and is not affected by the input speed. Using this ICT mechanism in variable speed wind turbines could negate the effect of rotor speed fluctuation and provide a steady input

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Guan-Shyong HWANG* and Chung-Chi LIN** *Department of Computer Science and Information Engineering, Nanhua University

No. 55, Sec 1, Nanhua Rd, Dalin Township, Chiayi 62248, Taiwan

E-mail: [email protected]

**Lithography Engineering Department, RD Process Centre, TSMC

8, Li-Hsin Rd 6, Hsinchu Science Park, Hsinchu 30078, Taiwan

Revised 26 April 2015

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Hwang and Lin, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.9, No.3 (2015)

© 2015 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2015jamdsm0032]

to the drive shaft of the generator to output electricity of constant frequency and good quality. The proposed ICT mechanism is comprised of two planetary gear trains and two transmission-connection members. No additional sliding friction elements such as belts or sliding discs are involved. The kinematic, static characteristics, and power flow of the ICT mechanism are determined and their relative analytical equations derived. Simulations of the mechanism have been made and a prototype of the ICT mechanism has been built and extensively tested to validate both the theory and practical application.

2. Nomenclature

A first planetary gear train B second planetary gear train cmg1D gear mounted on cmsD cmg1E gear mounted on cmsE cmg2D gear in D mounted on the shaft coming from A cmg2E gear in E mounted on the shaft coming from A cmg3D gear in D mounted on the shaft coming from B cmg3E gear in E mounted on the shaft coming from B cmsD shaft of D used to connect to the input power source cmsE shaft of E used to connect to the free-transmission end D first transmission-connecting member E second transmission-connecting member

0i basic speed-ratio of a planetary gear train Ai0 basic speed-ratio of A Bi0 basic speed-ratio of B

nX rotational speed of the shaft indicated by the subscript NX number of teeth on the gear indicated by the subscript paA planet gear carrier of A paB planet gear carrier of B pp1A gear of the compound planet gear set in A pp1B gear of the compound planet gear set in B pp2A gear of the compound planet gear set in A pp2B gear of the compound planet gear set in B ps1A sun gear of A ps1B sun gear of B ps2A second sun gear of A ps2B second sun gear of B pss1A shaft on which ps1A is mounted pss1B shaft on which ps1B is mounted pss2A shaft on which ps2A is mounted pss2B shaft on which ps2B is mounted PX power introduced by the shaft indicated by the subscript TX torque introduced by the shaft indicated by the subscript α kinematic constant for speed-ratio between shafts β kinematic constant for speed-ratio between shafts

3. Configuration of the ICT mechanism A different configuration based on the conceptual scheme and structure of the ICT mechanism reported in an

earlier research (Hwang, et al., 2011), is shown in Fig. 1. The proposed ICT mechanism comprises two planetary gear trains, denoted by A and B, two transmission-connecting members, indicated by D and E, as well as four rotational shafts, denoted by cmsD, cmsE, pss1A, and pss1B. The four rotational shafts can connect to the input power source, the

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free-transmission end, the output power end, and the controller, respectively. In the application suggested here, the input power would be obtained from the rotor of a wind turbine, and the output shaft would transmit power to the generator. A servo motor whose angular velocity is controllable serves as a controller. The free-transmission end can be either a secondary power input source or a secondary power output end handled by the controller. For example, the free-transmission end can connect to a secondary generator in a wind turbine or a motor-generator in a hybrid vehicle to output or input power. The purpose of the proposed ICT mechanism is to regulate the speed of the output power shaft, mediated by the controller, so that this is unaffected by any variation of the input rotational speed.

cmg1

E

cmg1

D

Output Power

cmg2D

Free-Transmission Input Power

Controller

App1

B

A

cmsD

pss1A

pss1B

cmsE

App2

paA

Aps1 Aps2

Bpp1 Bpp2

paB

Bps1 Bps2

D E

Apss2

Bpss2

cmg2E

cmg3E cmg3D

Fig. 1 Configuration of the ICT mechanism.

With the previous concept of the transmission design, the proposed ICT mechanism shown in Fig. 1 can yield its

kinematic requirements. They are described as follows:

paApaB nn (1)

ApssBpss nn 11 (2)

ApssBpss nn 22 (3)

where n denotes the rotational speed of the shaft indicated by its subscript, α and β are the kinematic constants for speed-ratios between the rotational shafts. 3.1 Positive-ratio planetary gear train and transmission-connecting member

As shown in Fig. 1, both the planetary gear trains A and B in the proposed ICT mechanism are positive-ratio types. A positive-ratio planetary gear train includes a sun gear, such as ps1A or ps1B mounted on the rotational shaft pss1A or pss1B, a second sun gear, such as ps2A or ps2B mounted on the rotational shaft pss2A or pss2B, at least one compound planet gear set, such as pp1A, pp2A or pp1B, pp2B meshing with two sun gears, and a planet gear carrier, such as paA or paB. In a positive-ratio planetary gear train, the shafts of the two sun gears rotate in the same direction when the carrier is fixed. This means that the basic speed-ratio, which is denoted by 0i and defined as a ratio of relative velocities between the two sun gear shafts with respect to the carrier, is positive and cannot be equal to 1 (Müller, 1982). According to the definitions, the basic speed-ratios of the planetary gear trains A and B, denoted by Ai0 and

Bi0 , can be expressed as follows:

AppAps

ApsApp

paAApss

paAApssA NN

NNnnnn

i21

21

2

10

(4)

3

2



BppBps

BpsBpp

paBBpss

paBBpssB NN

NNnnnn

i21

21

2

10

(5)

where N is the number of teeth on the gear indicated by the subscript. Each of the transmission-connecting members D and E comprises a gear, such as cmg1D or cmg1E mounted on the

shaft cmsD or cmsE, to mesh with the gears, such as cmg2D, cmg3D or cmg2E, cmg3E, which are mounted on the shafts coming from the two planetary gear trains A and B. The shafts cmsD and cmsE can be used to connect either to the input power source or to the free-transmission end.

3.2 Design formulas for the ICT mechanism

The formulas used for designing the ICT mechanism are derived by similarly using the methods and procedures established earlier (Hwang, et al., 2011) and the results are expressed as follows:

1 if

1 and1, if1

,)1(

00

00

BA

BA

ii

ii (6)

DcmgDcmg NN 32 (7)

EcmgEcmg NN 32 (8)

4. Kinematic, static characteristics, and power flow of the ICT mechanism

The kinematic, static characteristics, and power flow of the proposed ICT mechanism, shown in Fig. 1, are also

derived according to the methods and procedures presented in an earlier research (Hwang, et al., 2011). The results will be summarized in the following sub-sections.

4.1 Relationships of the rotational speed of shafts

The relationships of the rotational speed between shafts in a simple planetary gear train can be determined from the definition of its basic speed-ratio (Müller 1982). Simultaneously applying and solving these relationships as well as the design formulas shown in Eq. (6), it can yield the analytical equations of rotational speed between the shafts of the ICT mechanism. The results are summarized as follows:

BpssApss nn 11

1

(9)

)1(

110

2

120

210Bpss

EcmgA

EcmgcmsD

EcmgDcmgA

EcmgDcmgAcmsE n

NiN

nNNi

NNin

(10)

4.2 Torque distribution of shafts

The analytical relationships of torque distribution in a simple planetary gear train were reported in earlier work (Müller 1982; Pennestri and Freudenstein 1993). Basing on these relationships and the kinematic results shown previously, this study can further derive the torque distribution on shafts of the ICT mechanism. The results are summarized as follows:

BpsscmsDDcmgA

DcmgApss TT

NiN

T 110

21 )1(

(11)

cmsDEcmgDcmgA

EcmgDcmgAcmsE T

NNiNNi

T

210

120

)1( (12)

where T denotes the torque distributed in the shaft indicated by the subscript.

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4.3 Power flow of shafts When neglecting friction losses, the sum of power on the shafts of a transmission mechanism will be zero

according to the principle of conservation of energy (Müller 1982; Pennestri and Freudenstein, 1993). It is expressed as:

0 XP (13)

where P denotes the power introduced by the shaft indicated by the subscript. The input shaft is defined as the one that introduces positive power into the ICT mechanism, and consequently its

torque and rotational speed have the same sense of rotation so carry the same sign. Conversely, an output shaft introduces negative power and the torque and the rotational speed carry opposite signs (Müller 1982; Pennestri and Freudenstein, 1993). The power introduced by the shaft of the ICT mechanism can be expressed as:

XXX nTP (14)

From previous results with respect to rotational speed and torque distribution, this study can derive the power flow introduced to the ICT mechanism as follows:

BpsscmsDDcmgcmsDA

DcmgBpssApss PP

NniNn

P 110

211 )1(

(15)

cmsDDcmgcmsDA

DcmgBpsscmsE P

NniNn

P

1

1)( 10

21

(16)

5. Example demonstration of the ICT mechanism

Two examples of the proposed ICT mechanism are used to demonstrate the design procedures as well as the

kinematic and static results obtained in the previous sections. As shown in Fig. 1, both examples use shafts pps1A, cmsD, pss1B, and cmsE to connect the output and input power, the controller, and free-transmission ends, respectively. Figure 2 shows schematic diagrams of the ICT mechanism including a brief structure and a 3D solid model for the example demonstration. These examples also explain the design methods and procedures and how they can be applied.

5.1 Demonstration example 1

Here, the kinematic constants shown in Eqs. (1) and (2) have been chosen as 2 and 5.1 , respectively. According to Eq. (6), the basic speed-ratios of the planetary gear trains A and B are 3/10 Ai and 5.00 Bi , respectively. From Eqs. (4)-(5) and (7)-(8), the number of teeth on each gear used in this ICT example can be chosen as listed in Table 1.

Table 1 Number of teeth on each gear used in Example 1.

Gear cmg1D cmg2D cmg3D cmg1E cmg2E cmg3E ps1A

Number of teeth 50 80 40 50 60 60 45

Gear ps2A pp1A pp2A ps1B ps2B pp1B pp2B

Number of teeth 30 15 30 40 30 20 30

5

2



Output Power

Free-Transmission

Controller

Input Power

cmg2D

App1 App2

Aps1 Aps2

Bpp1 Bpp2

Bps1 Bps2

cmg2E

cmg3E cmg3D

cmg1D cmg1E

(a)

Output Power

Free-Transmission

Controller

Input Power

(b)

Fig. 2 Schematic diagrams of the ICT mechanism: (a) a brief structure, and (b) a 3D solid model.

Substituting all the kinematic constants and numbers of teeth, the kinematic, static equations, and power flow shown in Eqs. (9)-(12) and (15)-(16) can be rewritten as follows:

ControllerBpssApssOutput nnnn32

32

11 (17)

42512.41.5 1 ControllerInputBpsscmsDcmsEonTransmissiFree n. n.nnnn (18)

ControllerInputOutput TTT 5.14.2 (19)

InputonTransmissiFree TT32

(20)

ControllerInputInput

ControllerOutput PP

nnP

6.1 (21)

InputInput

ControlleronTransmissiFree P

nnP

16.1 (22)

5.2 Demonstration example 2

Here, the kinematic constants shown in Eqs. (1) and (2) have been chosen as 1 . According to Eq. (6), the basic speed-ratios of planetary gear trains A and B are given as 9/2500 BA ii . From Eqs. (4)-(5) and (7)-(8), the number of teeth on each gear used in this ICT example can be chosen as listed in Table 2.

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Table 2 Number of teeth on each gear used in Example 2.

Gear cmg1D cmg2D cmg3D cmg1E cmg2E cmg3E ps1A

Number of teeth 50 50 50 50 50 50 25

Gear ps2A pp1A pp2A ps1B ps2B pp1B pp2B

Number of teeth 15 15 25 25 15 15 25

Substituting all the kinematic constants and numbers of teeth, the kinematic, static equations, and power flow equations shown in Eqs. (9)-(12) and (15)-(16) can be rewritten as follows:

ControllerOutput nn (23)

925

916

ControllerInputonTransmissiFree nnn (24)

ControllerInputOutput TTT 1.5625 (25)

InputonTransmissiFree TT 0.5625 (26)

ControllerInputInput

ControllerOutput PP

nnP

5625.1 (27)

InputInput

ControlleronTransmissiFree P

nnP

15625.1 (28)

6. Experiments with a prototype of the ICT mechanism

Figure 3 is a picture of a prototype of the ICT mechanism with components arranged as shown in Fig. 2 and

Example 1. Working models and experiments such as the rotational speed and the static torque are investigated and the findings would be used to verify the validity of the derived formulas and equations.

Fig. 3 A prototype of the ICT mechanism.

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6.1 Rotational speed experiments Figure 4 is a schematic diagram of the test-bed for kinematic experiments and Fig. 5 is a picture of the actual

test-bed that was built. A plot of the rotational speed of the shafts, including the experimental and theoretical results, is shown in Fig. 6. Except for some small oscillations, it can be seen that the rotational speed of the output power shaft (thin-red-solid line) is coincident with the theoretical value obtained from Eq. (17) (bold-red-solid line). Because the kinematic constant β is 1.5, it can be also observed that the magnitude of the rotational speed of the controller shaft (green-dashed line) is always 1.5 times that of the output power shaft. Although there are larger irregular vibrations which can be attributed to component backlash and a lack of precision in the components of the prototype, the rotational speed of the free-transmission shaft (thin-black-dashed line) is also consistent with the theoretical value obtained from Eq. (18) (bold-black-dashed line). It can be also observed that the controller can regulate the output rotational speed independently, irrespective of the speed variations of the input shaft (blue-dash-dot line). Consequently, a steady-speed command from the controller to the ICT mechanism will result in a steady-speed output to the shaft.

ICT

Servomotor (MITSUBISHI HC-KFS053)

Servomotor (MITSUBISHI HC-KFS23)

Encoder (HEIDENHAIN ROD-454m)

Encoder (HEIDENHAIN ROD-454m)

Counter card (HEIDENHAIN ik-220)

PC

PC

Command Signal Speed

Fig. 4 A schematic diagram of the test-bed for kinematic experiments.

Fig. 5 Test-bed for kinematic experiments.

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2



Fig. 6 Rotational speeds of the ICT prototype shafts.

6.2 Static torque experiments

Figure 7 is a schematic diagram of the test-bed for static-torque experiments, and Fig. 8 shows the actual working model. The experimental torque data of shafts are shown in Table 3. For convenience, the results of Eqs. (19) and (20) have been rearranged in dimensionless parameter form, InputControllerOutput TTT /)5.1( and InputonTransmissiFree TT / , and their corresponding theoretical values are 2.4 and 2/3 respectively. The experimental torque data for the dimensionless parameter forms are also calculated and listed in Table 3. Figure 9 is a plot of the dimensionless experiment values and their least squares approximations. It can be observed that the values of the least squares approximations for

InputControllerOutput /TT.T )51( and InputonTransmissiFree TT / are 2.38 and 0.64 respectively, which is close to the theoretical values and the experimental results verify the validity of the derived equations.

Table 3 Torque values.

Experiment No.

InputT (Nm)

ControllerT (Nm)

OutputT (Nm)

onTransmissiFreeT

(Nm) Input

ControllerOutput

TTT 5.1

Input

onTransmissiFree

TT

1 2.04 2.04 1.72 1.2 2.34 0.59

2 3.51 2.04 4.08 1.55 2.03 0.44

3 4.98 2.04 7.7 2.61 2.16 0.52

4 6.45 2.04 10.99 3.37 2.18 0.52

5 2.04 3.51 0.7 1.91 2.92 0.94

6 3.51 3.51 2.56 2.03 2.23 0.58

7 4.98 3.51 5.56 2.76 2.17 0.55

8 6.45 3.51 9.43 3.91 2.28 0.61

9 2.04 4.98 -1.54 1.8 2.91 0.88

10 3.51 4.98 1.2 2.48 2.47 0.71

11 4.98 4.98 3.16 2.63 2.13 0.53

12 6.45 4.98 6.12 3.32 2.11 0.51

13 2.04 6.45 -3.57 1.86 2.99 0.91

14 3.51 6.45 0.03 2.95 2.76 0.84

15 4.98 6.45 2.22 3.31 2.39 0.66

16 6.45 6.45 3.49 3.17 2.04 0.49

0 20 40 60 80 100 120 140-300

-250

-200

-150

-100

-50

0

50

100

150

Time (second)

Rot

atio

nal s

peed

s (r

pm)

outputtheoretical outputfree-transmissiontheoretical free-transmissioninputcontroller

9

2



Torque Transducer KYOWA TP-5KMCB

torque

Torque Transducer KYOWA TP-5KMCB

torque

Instrumentation Amplifier KYOWA WGI-400A

torque signal torque

Instrumentation Amplifier KYOWA WGI-400A

ICT

Fig. 7 A schematic configuration of the test-bed for static-torque experiments.

Fig. 8 Test-bed for static-torque experiments.

least squares approximation of

0.64

Input

onTransmissiFree

TT

experimental values of

Input

onTransmissiFree

TT

experimental values of

Input

ControllerOutput

TTT 5.1

least squares approximation of

38.25.1

Input

ControllerOutput

TTT

Fig. 9 Dimensionless parameters and least squares approximations.

6.3 Discussion The validity of the design formulas and the derived kinematic and static equations are clearly verified and validated

by the experimental work of the ICT mechanism. By adjusting the kinematic constants, α and β shown in Eqs. (1) and (2), the configuration of the ICT mechanism can be modified according to design requirements. The proposed ICT

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© 2015 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2015jamdsm00 ]32

transmission mechanism is new and has four rotational shafts, while a simple planetary gear train has only three. The differences between kinematic and static behavior of the two types of transmission mechanism are quite clear.

7. Conclusion

This study proposes the ICT mechanism which is a new type of transmission device for use with variable speed

wind turbines. The ICT mechanism can provide steady regulated output speed that can be independently controlled and is not affected by speed variations of the input power shaft. This ICT mechanism is suitable for use in variable speed wind turbines where its kinematic characteristics allow the transmission of steady regulated rotational speed to the shaft of a generator to generate electricity of stable frequency and good quality. Independent regulation of the ICT mechanism by the controller also allows the provision of functions similar to those of an infinitely variable transmission (IVT) or a continuously variable transmission (CVT). Further research into applications of the ICT mechanism is proceeding.

Acknowledgement

The financial support of the Ministry of Science and Technology of Taiwan under grant (MOST 103-3113-E-110

-001) is gratefully acknowledged.

References Balat, M., A review of modern wind turbine technology, Energy Sources, Part A: Recovery, Utilization, and

Environmental Effects, Vol. 31, No. 17 (2009), pp.1561-1572. Carlin, P.W., Laxson, A.S. and Muljadi, E.B., The history and state of the art of variable-speed wind turbine technology,

NREL/TP-500-28607 (2001) Hwang, G.S. and Tsay, D.M., Independently controllable transmission mechanisms, US Patent 8585530 B2 (2013). Hwang, G. S., Tsay, D. M., Liao, W. H., Kuang, J. H. and Chern, T. L., Kinematic analysis of an independently

controllable transmission with a parallel type, International Journal of Automation and Smart Technology, Vol. 1, No. 1 (2011), pp.87-92.

Idan, M. and Lior, D., Continuous variable speed wind turbine: Transmission concept and robust control, Wind Engineering, Vol. 24, No. 3 (2000), pp.151-167.

Lahr, D. and Hong, D., Operation and kinematic analysis of a cam-based infinitely variable transmission, ASME Journal of Mechanical Design, Vol.131, No.8 (2009), DOI: 10.1115/1.3179004, pp.081009-1-081009-7.

Mangialardi, L. and Mantriota, G., Dynamic behavior of wind power systems equipped with automatically regulated continuously variable transmission, Renewable Energy, Vol. 7, No. 2 (1996), pp.185-203.

Müller H., Pöller M., Basteck A., Tilscher M. and Pfister J., Grid compatibility of variable speed wind turbines with directly coupled synchronous generator and hydro-dynamically controlled gearbox, Sixth Int’l Workshop on Large-Scale Integration of Wind Power and Transmission Networks for Offshore Wind Farms, Delft, NL (2006), pp.307-315.

Müller, H.W., Epicyclic Drive Trains - Analysis, Synthesis, and Applications, (1982), Wayne State University Press, Detroit.

Pennestri E. and Freudenstein F., A systematic approach to power-flow and static-force analysis in epicyclic spur-gear trains, ASME Journal of Mechanical Design, Vol.115, No.3 (1993), pp.639-644.

Şahin, A.D., Progress and recent trends in wind energy, Progress in Energy and Combustion Science, Vol. 30, No. 5 (2004), pp.501-543.

Zhao, X. and Maiβer, P., A novel power splitting drive train for variable speed wind power generators, Renewable Energy, Vol. 28, No. 13 (2003), pp.2001-2011.

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Innovative design of a transmission mechanism for variable