Planet Load-Sharing and Phasing
Abstract
:1. Introduction
2. Load Sharing Model
- Not applicable to gear sets having a small module
- Require strain gauges with high accuracy and sufficient sampling rate
- Increase the probability of measurement error due to the high dependency on the deviations of actual gauge-mounting locations from the desired nominal location
- Since errors in the planets, e.g., spacing, indexing, and run-out errors or eccentricities, could be time-dependent, the results might not be sufficiently accurate.
3. Effective Parameters on Load-Sharing
- Manufacturing errors
- Elastic deformation
- Bearing effects
- Backlash
3.1. Manufacturing Errors
- Time-invariant and assembly-independent errors: such as carrier and planet pinhole position errors and pinhole diameter errors.
- Time-invariant and assembly-dependent errors: these errors, once the planetary gear set is assembled, maintain their value as the gears rotate, but the gear set can have different load-sharing outcomes depending on how each planet gear and planet pin are assembled in the carrier. Planet tooth thickness errors, planet bore diameter errors, planet bearing needle diameter errors, and planet pin diameter errors are some examples of these errors.
- Time-varying and assembly-dependent errors: they have a time-varying effect on the load taken by each planet due to the way they are placed during the assembly of the gear set, since they are both rotation and assembly dependent, such as pitch line run-outs of the sun gear, planets, and the internal gear.
3.2. Position Error
3.3. Run-Out Error
3.4. Influence of Bearing and Backlash
4. Enhance the Load-Sharing
- Flexible ring gears
- Floating sun gear
- Floating planet carrier
- Double helical gear with floating members
- Floating planetary gear
- Flexible pin (flex-pin)
- Higher quality gear members.
- Increased precision of carrier elements that locate planet gears.
- Matching planet gear sets by tooth thickness.
- Improve tooth alignment of compound planets by using matched sets of planets (compound epicyclic only).
- Oil film thickness variation due to changes in oil flow and loads in journal bearings.
- Allowing radial float of one or more elements.
- Elastic deformation of the ring or the sun gear, or both.
- Reducing tooth stiffness.
- Elastic deformation of planet gear shafts.
- Elastic deformation of planet carrier.
- Eccentric planet shafts with load responsive rotation device.
- Load sensitive displacement of journal bearing oil films.
- Load sensitive consumption of planet shaft material when utilized as a journal bearing.
- Improved gear and shaft alignment.
- Reduced shaft run-out.
- Improved bearing quality and alignment (true position of bearing location in carrier).
- Improved assembly (location) of the carrier if the carrier is split axially.
- Improved compliance of components (gears, shafts, bearings, housing).
- Improved dynamics (operating speed versus resonant frequencies).
4.1. Floating Systems
4.2. Flexible Pin
5. Planetary Gear Phasing
5.1. Efficiency Effects
5.2. Experimental Investigations
5.3. Frequency Interplay
5.4. Instability
6. Fault Effects on Planet Phasing
7. Summary and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
List of Symbols
N | Number of planets |
The load on each planet as part of the whole load in the system | |
The load on each planet | |
LSR | Load-sharing ratio |
LSFn(t) | Load sharing factor of the nth planet |
SGLR | Strain gauge load ratio |
Total input torque | |
The meshing torque in the sun due to each of the planet–sun meshes | |
Each peak-to-peak value obtained from the strain gauge in contact with each planet | |
Each peak-to-peak value obtained from the strain gauge in contact with each planet as part of the summation of all the peak-to-peak values | |
Pin bending stresses | |
Pin bending stresses as part of the whole pin bending stress |
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Section | Main Key Points | Author (Year) [References] | |
---|---|---|---|
Load sharing model | Non-torque load | Park et al. (2019) [28]; Qiu et al. (2015) [29]; Guo et al. (2015) [30]; Guo et al. (2014) [31]; Li et al. (2020) [32]; Chung et al. (2020) [89]; | |
Input load effects | Xun and Dai (2021) [35]; Xu et al. (2018) [36]; Sanchez-Espiga et al. (2020) [43]; Iglesias et al. (2015) [52]; Kim et al. (2016) [57]; Singh (2011) [60]; | ||
Lifetime | Kim et al. (2018) [37]; Rasekhi Nejad et al. (2015) [38]; | ||
Load-sharing model | Cunliffe et al. (1974) [15]; Kahraman (1999) [23]; Li et al. (2011) [24]; Suzuki et al. (2011) [25]; Cooley and Parker (2014-Review Paper) [27]; Guo et al. (2015) [30]; Rasekhi Nejad et al. (2015) [38]; Seager (1970) [44]; Leque and Kahraman (2017) [46]; Hu et al. (2018) [47]; Hu et al. (2019) [48]; Ryali and Talbot (2021) [49]; Pedrero et al. (2022) [50]; Singh et al. (2008) [55]; Ge et al. (2021) [56]; Hidaka et al. (1977) [58]; Ligata et al. (2009) [61]; Han et al. (2021) [62]; Lewicki and Ballarini (1997) [80]; AGMA (2006) [86]; | ||
Experiment test | Ligata et al. (2008) [13]; Hidaka and Terauchi (1976) [14]; Hidaka et al. (1979) [16]; Hayashi et al. (1986) [19]; Krantz (1992) [21]; Kahraman (1999) [23]; Suzuki et al. (2011) [25]; Funchun et al. (2011) [26]; Guo et al. (2015) [30]; Götz et al. (2021) [33]; Ryali et al. (2021) [34]; Rasekhi Nejad et al. (2015) [38]; Mo et al. (2016) [45]; Sanchez-Espiga et al. (2022) [51]; Sanchez-Espiga et al. (2021) [53]; Boguski et al. (2012) [54]; Singh et al. (2008) [55]; Ge et al. (2021) [56]; Kim et al. (2016) [57]; Han et al. (2021) [62]; Guo et al. (2020) [79]; Lewicki and Ballarini (1997) [80]; Fox and Jallat (2003) [81]; | ||
FEM | Kahraman and Vijayakar (2001) [8]; Bodas and Kahraman (2004) [9]; Cheon and Parker (2004) [10]; Singh (2005) [11]; Botman (1980) [17]; Li et al. (2020) [32]; Iglesias et al. (2015) [52]; Hidaka et al. (1977) [58]; Ligata et al. (2009) [61]; Han et al. (2021) [62]; Li et al. (2016) [66]; Gill-Jeong and Parker (2004) [72]; Bakh and Parker (2013) [82]; Montestruc (2011) [90]; | ||
Other | Meshing impact: | Hu et al. (2021) [39]; | |
Geometrical configuration: | Singh (2005) [11]; Ligata et al. (2008) [13]; Sanchez-Espiga et al. (2019) [40]; Sanchez-Espiga et al. (2020) [43]; Hu et al. (2018) [47]; Pedrero et al. (2022) [50]; Sanchez-Espiga et al. (2022) [51]; Singh et al. (2008) [55]; Ligata et al. (2009) [61]; Singh (2010) [63]; Liu et al. (2019) [69]; Kahraman et al. (2003) [87]; Montestruc (2011) [90]; | ||
Structural optimization: | Theling et al. (2021) [42]; | ||
Effective parameters on load-sharing | Manufacturing error: | Bodas and Kahraman (2004) [9]; Cheon and Parker (2004) [10]; Xun and Dai (2021) [35]; Sanchez-Espiga et al. (2020) [43]; Leque and Kahraman (2017) [46]; Hu et al. (2018) [47]; Kim et al. (2016) [57]; Li et al. (2016) [66]; Cao and Rao (2021) [71]; James and Harris (2002) [88]; | |
Position Error | Iglesias et al. (2017) [5]; Bodas and Kahraman (2004) [9]; Cheon and Parker (2004) [10]; Singh (2005) [11]; Ligata et al. (2008) [13]; Kahraman (1994) [22]; Kahraman (1999) [23]; Park et al. (2019) [28]; Ryali et al. (2021) [34]; Xun and Dai (2021) [35]; Xu et al. (2018) [36]; Kim et al. (2018) [37]; Sanchez-Espiga et al. (2020) [43]; Sanchez-Espiga et al. (2020) [43]; Leque and Kahraman (2017) [46]; Hu et al. (2018) [47]; Sanchez-Espiga et al. (2021) [53]; Boguski et al. (2012) [54]; Singh et al. (2008) [55]; Kim et al. (2016) [57]; Singh (2011) [60]; Ligata et al. (2009) [61]; Singh (2010) [63]; Gu and Velex (2011) [67]; Liu et al. (2019) [69]; Fox and Jallat (2003) [81]; Chung et al. (2020) [89]; Gu and Velex (2012) [91]; Zhu et al. (2013) [95]; | ||
Run-out Error | Kahraman and Vijayakar (2001) [8]; Bodas and Kahraman (2004) [9]; Cheon and Parker (2004) [10]; Kahraman (1994) [22]; Kahraman (1999) [23]; Leque and Kahraman (2017) [46]; Hu et al. (2018) [47]; Hu et al. (2019) [48]; Gupta et al. (2017) [73]; | ||
Misalignment: | Ma and Botman (1985) [18]; Rasekhi Nejad et al. (2015) [38]; Fan et al. (2020) [64]; Fox and Jallat (2003) [81]; Zhu et al. (2013) [95]; | ||
Crack: | Han et al. (2021) [62]; Li et al. (2019) [65]; Lewicki and Ballarini (1997) [80]; | ||
Eccentricity: | Iglesias et al. (2017) [5]; Hidaka et al. (1979) [16]; Kahraman (1994) [22]; Rasekhi Nejad et al. (2015) [38]; Hu et al. (2021) [39]; Mo et al. (2016) [45]; Leque and Kahraman (2017) [46]; Li et al. (2016) [66]; Gu and Velex (2013) [68]; Liu et al. (2019) [69]; Mo et al. (2019) [70]; Sheng et al. (2015) [75]; | ||
Influence of bearing and backlash | Singh (2007) [12]; Li et al. (2011) [24]; Suzuki et al. (2011) [25]; Funchun et al. (2011) [26]; Guo et al. (2015) [30]; Guo et al. (2014) [31]; Kim et al. (2018) [37]; Mo et al. (2016) [45]; Gill-Jeong and Parker (2004) [72]; Sheng et al. (2015) [75]; Zhang et al. (2016) [76]; Chen et al. (2009) [77]; Zhang et al. (2020) [78]; Guo et al. (2020) [79]; Fox and Jallat (2003) [81]; | ||
Tooth wedging: | Guo and Parker (2010) [7]; Guo et al. (2014) [31]; | ||
Tooth wear | Zhang et al. (2020) [6]; | ||
Enhance the load-sharing | Floating systems | Iglesias et al. (2017) [5]; Kahraman and Vijayakar (2001) [8]; Botman (1980) [17]; August and Kasuba (1986) [20]; Kahraman (1994) [22]; Kahraman (1999) [23]; Ryali et al. (2021) [34]; Xu et al. (2018) [36]; Kim et al. (2018) [37]; Rasekhi Nejad et al. (2015) [38]; Seager (1970) [44]; Mo et al. (2016) [45]; Sanchez-Espiga et al. (2022) [51]; Boguski et al. (2012) [54]; Singh (2010) [63]; Li et al. (2016) [66]; Gu and Velex (2011) [67]; Gu and Velex (2013) [68]; Gill-Jeong and Parker (2004) [72]; Müller (1982) [2]; Chung et al. (2020) [89]; Gu and Velex (2012) [91]; Yoo et al. (2022) [96]. | |
Flexible pin | Cunliffe et al. (1974) [15]; Xu et al. (2018) [36]; Montestruc (2010) [59]; Zhang et al. (2020) [78]; Fox and Jallat (2003) [81]; Montestruc (2011) [90]; Hicks (1967) [92]; Vosátka (2016) [93]; Fox (2007) [94]; Zhu et al. (2013) [95]; Yoo et al. (2022) [96] | ||
Profile modification | Xun and Dai (2021) [35]; Rasekhi Nejad et al. (2015) [38]; Hu et al. (2018) [47]; Ryali and Talbot (2021) [49]; Bakh and Parker (2013) [82]; Iglesias et al. (2015) [83]; | ||
Flexible ring | Kahraman and Vijayakar (2001) [8]; Ma and Botman (1985) [18]; Iglesias et al. (2015) [52]; Ge et al. (2021) [56]; Hidaka et al. (1977) [58]; Fan et al. (2020) [64]; Gu and Velex (2011) [67]; Cao and Rao (2021) [71]; Zhang et al. (2020) [78]; Kahraman et al. (2003) [87]; | ||
Planetary gear phasing | Phasing | Hidaka et al. (1979) [97]; Parker (2000) [98]; Parker and Lin (2004) [99]; Shweiki et al. (2016) [100]; Ambarisha and Parker (2007) [101]; Huang et al. (2022) [102]; Wang and Parker (2022) [103]; Ryali and Talbot (2021) [49]; Sanchez-Espiga et al. (2021) [53]. Ryali et al. (2021) [34]; Sanchez-Espiga et al. (2019) [40]; Sanchez-Espiga et al. (2020) [43]; Bakh and Parker (2013) [82]; Zhu et al. (2013) [95]; | |
Efficiency effects | Mohammadpour et al. (2016) [104]; Fatourehchi et al. (2018) [105]. | ||
Experimental research | Gawande and Shaikh (2014) [106]; Chen et al. (2022) [107]. | ||
Frequency interplay | Ambarisha and Parker (2006) [108]; Guo et al. (2022) [109]. | ||
Instability | Lin and Parker (2002) [110]; Canchi et al. (2008) [111]; Parker and Wu (2012) [112]; Wu and Parker (2008) [113]; Wang and Parker (2021) [114]; Ericson and Parker (2021) [115]. | ||
Fault effects on planet phasing | Fault effects on planet phasing | Feng et al. (2017) [116]; Peng et al. (2019) [117]; Liu et al. (2020) [118]; Sanchez-Espiga et al. (2020) [40]; Luo et al. (2021) [119]; Ha and Youn (2022) [120]; Hu et al. (2022) [121] |
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Molaie, M.; Deylaghian, S.; Iarriccio, G.; Samani, F.S.; Zippo, A.; Pellicano, F. Planet Load-Sharing and Phasing. Machines 2022, 10, 634. https://doi.org/10.3390/machines10080634
Molaie M, Deylaghian S, Iarriccio G, Samani FS, Zippo A, Pellicano F. Planet Load-Sharing and Phasing. Machines. 2022; 10(8):634. https://doi.org/10.3390/machines10080634
Chicago/Turabian StyleMolaie, Moslem, Samira Deylaghian, Giovanni Iarriccio, Farhad S. Samani, Antonio Zippo, and Francesco Pellicano. 2022. "Planet Load-Sharing and Phasing" Machines 10, no. 8: 634. https://doi.org/10.3390/machines10080634