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Transmission efficiency of polyamide nanocomposite spur gears
Materials and Design 39 (2012) 338–343
Contents lists available at SciVerse ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Technical Report
Transmission efficiency of polyamide nanocomposite spur gears S. Kirupasankar, C. Gurunathan, R. Gnanamoorthy ⇑ Indian Institute of Information Technology, Design and Manufacturing (IIITD&M) Kancheepuram, Melakottaiyur, Chennai 600 048, India
a r t i c l e
i n f o
Article history: Received 25 December 2011 Accepted 22 February 2012 Available online 8 March 2012
a b s t r a c t Gears made of polymer and its composites find increasing application due to their superior properties. This paper reports the transmission efficiency of pristine polyamide 6 (PA6) and clay incorporated polyamide nanocomposite (PNC) spur gears. Numerical studies were conducted to predict the frictional and hysteresis power loss. A power absorption type gear test rig, developed in-house, was used to determine the power loss during transmission. The effect of applied torque on the transmission efficiency of PA6 and PNC spur gears are reported. Addition of nanoclay particles improves the stiffness and suppresses the viscoelastic nature of polyamide 6. The increase in gear tooth temperature due to hysteresis and friction, significantly affects the tooth shape, and thereby, the gear performance. The enhancement in mechanical properties of polyamide nanocomposite gears results in higher power transmission efficiency compared to pristine polyamide gear. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Gears are used to transmit motion and/or power. In recent years, polymers are replacing metallic materials in light-duty applications such as measuring instruments, medical instruments, computer peripherals, office printing machines, and automatic teller machines, due to light weight, corrosion resistance, easy manufacturability, and able to run under dry condition. Many experimental and theoretical studies were conducted on the performance of metallic gears [1–7]. However, there are only a few literatures available on the performance of polymeric gears [8–15]. For metallic gears, the gear module is the most influential parameter on gear mesh mechanical efficiency for the high-speed and high-torque operating conditions, followed by gear tooth surface roughness and viscosity of lubricant [1]. Sliding friction between the gear teeth is recognized as one of the main sources of power loss in geared transmission as well as a potential source of vibration and noise. Diab et al. [2] have studied the friction in gear for a wide range of sliding/rolling conditions using elastohydrodynamic lubrication (EHL) simulator and proposed new traction law. Xu et al. [3] proposed a computational model for the prediction of friction-related mechanical efficiency losses of parallel-axis gear pairs. The model incorporates a gear load distribution model, a friction model, and a mechanical efficiency formulation to predict the instantaneous mechanical efficiency of a gear pair under typical operating, surface, and lubrication conditions. It is reported that the proposed model is more accurate with 0.1% deviation with the experimental results. Xu and Kahraman [4] have also proposed similar model for hypoid gear pairs. The effect of addendum and contact ratio on gear ⇑ Corresponding author. Tel.: +91 44 2747 6302; fax: +91 44 2747 6304. E-mail address: [email protected] (R. Gnanamoorthy). 0261-3069/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2012.02.045
strength and basic performance parameters were explained elsewhere [5]. The performance of metallic gears depends on the frictional loss between the contacting pair of gears as the tooth deflection is negligible due to high elastic modulus [6,7]. Walton et al. [8,9] have experimentally studied and reported the influence of gear materials and tooth geometry on the efficiency and friction of plastic cylindrical gears. For some materials the gear efficiency is significantly affected by the load and for others speed. Use of grease as a lubricant in polymer gear significantly increases the efficiency and eliminates the load and speed dependences. Efficiency of polymer gears deteriorates with the increasing running time but reducing the tooth size enhances the efficiency. The polymer gear generates more heat due to its low elastic modulus (100 times lesser than that of steel) and viscoelastic nature [10]. The poor thermal conductivity of polymer causes the generated heat to accumulate within the gear. The increase in tooth temperature degrades the polymer and deteriorates the performance of the gear pair [11]. Mathematical models were developed and reported [12,13] to quantify the amount of heat generated due to friction and hysteresis loss in polymer gears during meshing. The rotational speed of the spur gear affects the performance of unreinforced and glass fiber reinforced spur gears [14]. Initial application of grease significantly reduces the tooth wear in carbon fiber reinforced poly-ether-etherketone gear [15,16] and carbon fiber reinforced polyamide 12 gear [17]. A new design method based on the relation between the wear rate and its surface temperature was developed for acetal gear [18]. Researchers have attempted to reduce the gear tooth surface temperature by increasing the tooth width in single tooth contact region [10]. Providing a hole on the gear tooth reduces the surface temperature and it is further reduced by steel pin inserts [19]. Providing a hole in gear tooth reduces the tooth stiffness and leads to large tooth deflection. Heat dissipation through the hole is
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effectively achieved only through the proper selection of size of the hole and location [20]. Significant reduction in surface temperature and wear is achieved by drilling multiple radial and axial cooling holes [21]. The performance of a gear pair depends upon the material, geometry, speed, loading condition and friction [8]. Power transmission efficiency of the polymeric gears can be improved by reinforcing the matrix by short fibers [14]. Presence of strong fiber on the molding surface deteriorates the surface roughness. Moreover, the orientation of the fibers governs the gear stiffness, and it is difficult to keep the orientation in the effective direction throughout the gear tooth geometry. Thus, only a fraction of short fiber content is effectively used to enhance the stiffness of polymer tooth. Polymer nanocomposite (PNC) materials are new emerging materials which uses the nano-sized particle or platelets as reinforcement. The nano-size particle has large specific surface areas and has good interfacial adhesion with compatible polymer. The molecular level interaction between the nano-size reinforcement and polymer significantly improves the many of their mechanical properties, especially stiffness and strength [22]. Nano-size reinforcement increases the crystallinity of the polymer and reduces the polymeric chain mobility. Nano-size reinforcement also increases the glass transition temperature and barrier properties of the polymer. This paper describes the load sharing in PA6 and PNC gears estimated using numerical analysis. Experimental studies are carried out to understand the effect of torque on the performance. The frictional and hysteresis power loss are discussed. 2. Numerical studies To ensure smooth and continuous operation, gears are made with contact ratio greater than one. During meshing, adjacent tooth comes in contact at the beginning of approach action and at the end of recess action. Since more than one tooth is in contact, there exist a load sharing between the adjacent tooth and a single tooth carries the load for a portion of meshing cycle. The tooth deflection in metallic gear is very small due to high stiffness and, hence, there is no significant difference in load sharing compared to that of ideal gear pair. For polymer gear, the tooth deflection is significantly large due to low stiffness and, hence, there exist a significant difference in load sharing compared to that of ideal gear pair. To understand the effect of polymeric gear tooth deflection in load sharing, a Finite Element Analysis (FEA) is carried out using commercial software package ANSYSÒ. The FE model consists of three teeth in each gear to capture the effect of adjacent teeth in tooth deflection. Since the face width of the gear is very large compared to the tooth contact width, triangular shaped plane strain elements is used to mesh the tooth geometry [23]. The contact condition of gear teeth is sensitive to the geometry of the contacting surfaces and, hence, a fine mesh is used near the contact region. Detailed pictures of the finite element mesh of the gears are shown in Fig. 1. Linear elastic deformation behavior is assumed for all materials and the analysis is done by rotating the steel gear and keeping the polymer gear as stationary one. The FE Analysis of meshed gear pair is carried out at a various roll angles (angle of rotation of the pinion gear) with a fine step size to determine the angle of access and angle of recess during meshing of steel gear with pristine PA6 and PNC gears. 3. Gear materials and gear testing Polymer nanocomposites (PNC) are prepared from the commercial polyamide 6 (PA6) granules and organically modified layered silicate hectorite clay by melt intercalation technique. Material processing details and characterization of PNC are reported elsewhere [24]. Uniformly dispersed nano-size hectorite
Fig. 1. Details of the Finite Element mesh: (a) an overview of the complete model; (b) magnified view near the contact.
clay makes strong bond with the PA6 and thereby enhance the strength and stiffness. The properties of pristine polyamide and polyamide nanocomposites used in the present study are listed in Table 1. Dynamic mechanical analysis (DMA) is carried out to characterize the temperature dependency and viscoelastic nature of PA6 and PNC materials. Three-point bending specimens made from pristine PA6 and PNC were tested using a DMA analyzer (NETZCH) as per ASTM D 5023 standard. The nano-size clay arrest the mobility of the polymer chain and increases storage modulus and temperature resistance compared to PA6 [24]. Fig. 2 shows the schematic diagram of the gear test rig, developed in-house, to study the performance of polymeric gears. The test gear has standard involute tooth profile with 2 mm module, 20° pressure angle and 17 teeth. The PA6 and PNC gears are made by injection molding process at a pressure of 125 MPa and at a temperature of 513 K. A stainless steel (SS316) gear with similar nomenclature is made by hobbing process and used as a driver gear. The driver gear is attached to the speed controllable DC motor and its speed and load are maintained constant throughout the test. Power drawn via driven test gear is dissipated through the DC generator and loading rheostat. Non-contact type infrared temperature sensors are used to monitor the surface temperature of the gears and are recorded using a computerized data acquisition system. The test gears are run at a speed of 1200 rpm at different torque levels (1.5, 2.0 and 2.5 N m) up to failure or ten million cycles (107 cycles) whichever is earlier. High precision torque sensors are connected to driver and driven gear shafts and the torque values are continuously recorded using computerized data acquisition system. The shafts are free from support bearings and the transmission efficiency is computed from the following relation:
Transmission efficiency ðgÞ ¼
Driven gear torque Driver gear torque
ð1Þ
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Table 1 Properties of pristine polyamide 6 and polyamide 6 nanocomposites [24]. Material
Tensile modulus (MPa) (ASTM D638)
Rockwell hardness (R Scale) (ASTM D785)
PA6 PA6 + 3% clay PA6 + 5% clay
550 ± 10% 815 ± 9%
97.5 ± 1.5 100.2 ± 2.7
950 ± 9%
105.3 ± 2.9
Generator
Torque Coupling transducer
Test gear
Coupling
Driver gear (Stainless Steel)
Torque transducer
Fig. 4. Contact ratio for the steel pinion meshing with gears made of different materials at various torque levels.
Driver motor
Fig. 2. Schematic diagram of the polymer spur gear performance test rig.
4. Results and discussion 4.1. Gear tooth deflection Load sharing of a gear tooth may be defined as the total load shared by a single gear tooth. Fig. 3 shows the load sharing in steel, PA6 and PNC gears meshed against steel gear estimated using numerical analysis. The load sharing in steel gear pair slightly differs from that of ideal gear pair due to the deflection of gear tooth. This causes a difference in load sharing between ideal gear pair and PA6 and PNC gears meshed against steel gear. Similar gear pair material results in symmetrical load sharing curve, whereas, dissimilar gear pair material result in unsymmetrical skewed curve. PA6 and PNC gear load sharing data is skewed and indicates the load sharing is approximately 1/3 in the first part and 2/3 in the last part. Gear tooth stiffness significantly affects the load sharing curve shape. Higher the gear tooth stiffness lowers the deviation from ideal curve and vice versa. The study also indicates that the increase in contact path resulting in preliminary contact earlier in the meshing cycle and a prolonged contact at the end, which reduces the period of the single tooth contact. A similar trend was reported by other researchers [23,25].
Fig. 4 shows the contact ratio for each gear pair at different torque levels. PA6 gear has very low stiffness and, hence, severe tooth bending and results in very high contact ratio. PNC gears have high stiffness and, hence, they exhibits lower contact ratio compared to PA6 gear. The contact ratio in each gear pair increases with the increases in torque and this is due to the increases in tooth bending. Higher the contact ratio, larger the duration of tooth contact and more susceptible to higher frictional heat generation and wear failure. 4.2. Transmission efficiency The transmission efficiency of polymer gear indicates the power loss in the gear pair. The power loss in polymer gear consists of two components namely the frictional losses due to relative sliding and hysteresis losses due to viscoelastic nature and tooth bending. Power loss in polymer gear pair results in heat generation. The net heat generated, Eg, in polymer gears can be expressed as [13]:
Eg ¼ Egf þ Egh
ð2Þ
where Egf represents the heat generation due to friction between mating gears, and Egh represents the heat generation from hysteresis effect. The frictional heat generation is given as [13]:
Egf ¼ lW 0
Wi 1 V s Ds W n cos hf
ð3Þ
where l is the coefficient of friction at contact point, W0 is the transmitted load per unit face width, W i =W n is the load sharing factor, hf is the operating pressure angle, Vs is the sliding speed, and Ds is the displacement of the contact point measured along the line of action. The hysteresis heat generation is given by following expression [13]:
Egh ¼
Fig. 3. Load sharing between the steel pinion and gears made of various materials for the applied torque of 1.5 N m estimated using FEA.
tgd r20 t p V s Ds 1 þ tg 2 d 4 E cos hf
ð4Þ
where E is storage modulus of material, ðtgdÞ is the material dissipation factor, r0 is the stress amplitude based on a unit face width and t is the tooth thickness at pitch circle. The frictional power loss is evaluated for PA6 and PNC gears using the Eq. (3), and the results obtained from FEA. To account the sliding velocity and direction of sliding, the instantaneous coefficient of friction is used to evaluate the frictional power loss [26]. During approach action, the sliding velocity reaches zero at the pitch point from its maximum value and the rolling velocity reaches its maximum value at pitch point from its minimum value [6]. During recess action, the rolling velocity reduces and the
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sliding velocity increases. Rolling friction coefficient is much smaller than the sliding coefficient of friction and, hence, the frictional loss due to sliding is significant compared to rolling. Fig. 5 shows the predicted frictional power loss in PA6 and PNC gears running against steel gear for various average coefficients of friction ranging from 0.1 to 0.6 for the rotational speed of 1200 rpm and the torque level of 1.5 N m. The low elastic modulus of PA6 gear increases the contact area, severe tooth bending and extended contact path. These result in increased frictional power loss. The increase in coefficient of friction increases the frictional power losses. Fig. 6 shows the predicted frictional power loss per cycle in PA6 and PNC gears for different coefficient of friction. The frictional power loss is low in PNC gears compared to PA6 gears at all coefficient of friction values assumed. This is due to the better load sharing of the PNC spur gear tooth, lower contact path and reduced sliding coefficient of friction compared to PA6 gears [26]. Polymeric materials exhibit viscoelastic characteristics. The repeated bending of gear tooth leads to hysteresis heat generation. The power loss due to hysteresis mainly depends on the material dissipation factor, also called as loss tangent, and load [13]. The dynamic mechanical analysis (DMA) of the PA6 and PNC materials reveals that the PNC has higher storage modulus and higher temperature resistance compared to PA6 [24]. The hysteresis power loss of the PA6 and PNC gears running at the speed of 1200 rpm and 1.5 N m calculated for various roll angles (angle of
341
Fig. 6. Frictional power loss per cycle in PA6 and PNC spur gears meshed with steel gear at 1200 rpm and torque of 1.5 N m.
rotation of the pinion gear) is shown in Fig. 7. The pristine PA6 gear exhibits the higher hysteresis power loss compared to PNC gear. This is due to the high loss tangent of PA6 material attributed by the unrestricted movement of molecular chains. Whereas, in PNC materials, the molecular chain movement is restricted by the nano-size clay which reduces the loss tangent and thereby the hysteresis power loss. The hysteresis power loss in a single gear tooth per cycle is estimated from Fig. 7 and is shown in Fig. 8. The hysteresis heat generation in PNC gear is low compared to PA6 gear. The PA6 + 5% clay gear exhibits the lowest hysteresis power loss and frictional power loss compared to PA6 and PA6 + 3% clay gears. Thus, PA6 + 5% clay gears have high transmission efficiency and good performance.
4.3. Gear performance Fig. 9 shows the temperature rise in the test gear tooth with increasing number of cycles. Under similar working condition, the tooth temperature of PNC gear is less than the PA6 gear. The mechanical properties of polymeric materials strongly depend upon the temperature, and, hence, the rise in temperature of the gear tooth degrades the mechanical properties of polymer gear and results in deterioration in gear performance. Fig. 10 shows the effect of increasing temperature in the gear efficiency with increasing number of meshing cycles. The PNC material exhibits improved storage modulus than the pristine PA6 material [24], it retains the mechanical properties at higher temperature. The
Fig. 5. Frictional power loss in (a) Steel – PA6, (b) Steel – PA6 + 3% Clay, and (c) Steel – PA6 + 5% Clay gears running at 1200 rpm and torque of 1.5 N m.
Fig. 7. Hysteresis power loss in PA6 and PNC spur gears meshed with steel gear running at 1200 rpm and torque of 1.5 N m.
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Fig. 8. Hysteresis power losses in PA6 and PNC spur gear tooth per cycle meshed with steel gear running at 1200 rpm and torque of 1.5 N m.
enhanced mechanical properties of PNC gear reduces the frictional heat generation, hysteresis heat generation and retain the mechanical properties at elevated temperatures and result in better performance than PA6 gear. Fig. 11 shows the efficiency of PA6 and PNC spur gears measured during the tests conducted at a speed of 1200 rpm and 2 N m torque. PNC gears show higher efficiency compared with PA6 gears due to improved mechanical and tribological properties. Efficiency of polymer gear pair mainly depends upon the frictional losses and hysteresis losses due to relative sliding and tooth bending respectively. The frictional loss depends on the coefficient of friction. The PNC materials exhibit lower coefficient of friction than the pristine PA6 due to improved elastic modulus, high crystalline nature and high hardness [24]. The low elastic modulus of pristine PA6 increases the area of contact and tooth deflection. The coefficient of friction depends upon the apparent area of contact. The dependency of area of contact on coefficient of friction in PNC materials is lower than the PA6 materials [26]. Coefficient of friction, area of contact and length of contact are low in the PNC gear, and hence, the frictional losses in the PNC gears are less compared to the pristine PA6 gears. Addition of nano-clay reinforcement increases the storage modulus and reduces the damping coefficient of PNC compared to PA6 [24]. Reduced viscoelastic nature and improved storage modulus reduce the hysteresis heat generation in PNC gear. The reduction in heat generation implies better the performance. Hence, nano-size reinforcement in the polymer matrix improves the efficiency of the gear pair. The PA6 + 5% clay gear
Fig. 10. Efficiency and test gear tooth temperature rise during the performance tests carried out at a speed of 1200 rpm and torque 2 N m with increasing meshing cycles of (a) pristine PA6, (b) PA6 + 3% clay, and (c) PA6 + 5% clay spur gears.
exhibited higher efficiency compared to PA6 and PA6 + 3% clay gear (Fig. 11). 4.4. Effect of torque on performance of the PA6 and PNC spur gear
Fig. 9. Temperature rise measured in the test gears during the test conducted at a torque level of 1 N m and rotational speed of 600 rpm.
Fig. 12 shows the efficiency of pristine PA6 and PNC gears tested at 1200 rpm and at different torque levels. PNC gear exhibit higher efficiency than the pristine PA6 gears at all tested torque levels. Also PNC gear efficiency shows a less dependency on applied load, whereas pristine PA6 gears shows a drop in efficiency with increase in load. Sliding coefficient of friction of PNC materials is less
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efficiency of the polyamide 6 and polyamide nanocomposite gears. The nano-clay reinforcement reduces the dependency of gear efficiency on applied torque. The increase in weight percentage of nano-clay is beneficial for the efficiency of the gear. The difference in gear efficiency of polymer nanocomposite gears with different weight percentage of nano-clay is more significant at higher torque level compared to lower torque levels. The addition of nano-clay reduces the ductility of the polymer but increases the gear efficiency. Further research could be made to find most appropriate weight percentage of nano-clay in polymer matrix and different nano-size particles to get further enhancements in gear efficiency. References
Fig. 11. Transmission efficiency of PA6 and PNC spur gears mating against SS gear running at 1200 rpm and torque of 1.5 N m.
Fig. 12. Effect of applied torque on the efficiency of PA6 and PNC spur gears.
dependent on load compared to the pristine PA6 materials [26]. Weak transfer film formation during sliding due to increased hardness and improved modulus of PNC materials at all levels of loads attributes to better performance of PNC gears. The lower deflection of PNC tooth and lower damping factor of PNC material causes a reduced hysteresis heating compared to the pristine PA6 gears. Hence, PNC gear efficiency shows less dependency on load and performs better than the pristine PA6 gears. 5. Conclusions The performance of injection molded polyamide 6 and polymer nanaocomposite gears were investigated at various torque levels using a power absorption type gear test rig. The enhanced mechanical and thermal properties of nanocomposite gears due to the addition of nano-clay reduce frictional losses and hysteresis losses in gear during meshing. Applied torque has detrimental effect on the
[1] Petry-Johnson TT, Kahraman A, Anderson NE, Chase DR. An experimental investigation of spur gear efficiency. ASME J Mech Des 2008;130:062601–62610. [2] Diab Y, Ville F, Velex P. Prediction of power losses due to tooth friction in gears. Tribol Trans 2006;49:260–70. [3] Xu H, Kahraman A, Anderson NE, Maddock DG. Prediction of mechanical efficiency of parallel-axis gear pairs. Trans ASME 2007;129:58–68. [4] Xu H, Kahraman A. Prediction of friction-related power losses of hypoid gear pairs. Proc Inst Mech E Part K: J Multi-body Dynam 2007;221:387–400. [5] Li Shunting. Effect of addendum on contact strength, bending strength and basic parameters of a spur gears. Mech Mach Theory 2008;43:1557–84. [6] Maithra GM. Handbook of gear design. 2nd ed. Tata McGraw Hill; 2001. [7] Stolarski TA. Tribology in machine design. Butterworth Heinemann; 2000. [8] Walton D, Cropper A, Weale DJ, Klein MP. The efficiency and friction of plastic cylindrical gears. Part 1 – influence of materials. Proc Inst Mech E, Part J – J Eng Tribol 2002;216:75–92. [9] Walton D, Cropper A, Weale DJ, Klein MP. The efficiency and friction of plastic cylindrical gears. Part 2 – influence of tooth geometry. Proc Inst Mech E, Part J – J Eng Tribol 2002;216:93–103. [10] Huseyin I. Performance improvement method for Nylon 6 spur gears. Tribol Int 2009;42:503–10. [11] Senthilvelan S, Gnanamoorthy R. Efficiency of injection-moulded polymer composite spur gear. Proc Inst Mech E, Part J – J Eng Tribol 2009;223:925–8. [12] Takanashi S, Shoji A. On the equilibrium temperature in the teeth of operating plastic gears. Bull Yamagata Univ 1984;18:11–25. [13] Koffi D, Gauvin R, Yelle H. Heat generation in thermoplastic spur gears. J Mech, Transm, Autom Des 1985;107:31–7. [14] Senthilvelan S, Gnanamoorthy R. Effect of rotational speed on the performance of unreinforced and glass fiber reinforced Nylon 6 spur gears. Mater Des 2007;28:765–72. [15] Kurokawa M, Uchiyama Y, Nagai S. Performance of plastic gear made of carbon fiber reinforced poly-ether-ether-ketone. Tribol Int 1999;32:491–7. [16] Kurokawa M, Uchiyama Y, Nagai S. Performance of plastic gear made of carbon fiber reinforced poly-ether-ether-ketone. Part 2. Tribol Int 2000;33:715–21. [17] Kurokawa M, Uchiyama Y, Iwai T, Nagai S. Performance of plastic gear made of carbon fiber reinforced polyamide 12. Wear 2003;254:468. [18] Mao K. A new approach for polymer composite gear design. Wear 2007;262:432–41. [19] Kim CH. Durability improvement method for plastic spur gears. Tribol Int 2006;39:1454–61. [20] Gurunathan C. Performance improvements approaches for polymer gears. M.Tech. thesis. Indian Institute of Technology Madras, India; 2007. [21] Duzcukoglu H. Study on development of polyamide gears for improvement of load-carrying capacity. Tribol Int 2009;42:1146–53. [22] Srinath G, Gnanamoorthy R. Effect of nanoclay reinforcement on tensile and tribo behaviour of Nylon 6. J Mater Sci 2005;40:2897–901. [23] Walton D, Tessema AA, Hooke CJ, Shippen JM. Load sharing in metallic and non-metallic gears. Proc Inst Mech E 1994;208:81–7. [24] Srinath G. Tribo behaviour of polyamid 6 – layered silicate nanocomposites. PhD thesis. Indian Institute of Technology Madras, India; 2007. [25] Yelle H, Burns DJ. Calculation of contact ratios for plastic/plastic or plastic/steel spur gear pairs. Trans ASME, J Mech Des 1981;103:528–42. [26] Kirupasankar S, Gnanamoorthy R, Velmurugan R. Effect of apparent area, load and filler content on sliding friction characteristics of polymer nanocomposites. Proc Inst Mech E, Part J – J Eng Tribol 2009;224:133–8.
Contents lists available at SciVerse ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Technical Report
Transmission efficiency of polyamide nanocomposite spur gears S. Kirupasankar, C. Gurunathan, R. Gnanamoorthy ⇑ Indian Institute of Information Technology, Design and Manufacturing (IIITD&M) Kancheepuram, Melakottaiyur, Chennai 600 048, India
a r t i c l e
i n f o
Article history: Received 25 December 2011 Accepted 22 February 2012 Available online 8 March 2012
a b s t r a c t Gears made of polymer and its composites find increasing application due to their superior properties. This paper reports the transmission efficiency of pristine polyamide 6 (PA6) and clay incorporated polyamide nanocomposite (PNC) spur gears. Numerical studies were conducted to predict the frictional and hysteresis power loss. A power absorption type gear test rig, developed in-house, was used to determine the power loss during transmission. The effect of applied torque on the transmission efficiency of PA6 and PNC spur gears are reported. Addition of nanoclay particles improves the stiffness and suppresses the viscoelastic nature of polyamide 6. The increase in gear tooth temperature due to hysteresis and friction, significantly affects the tooth shape, and thereby, the gear performance. The enhancement in mechanical properties of polyamide nanocomposite gears results in higher power transmission efficiency compared to pristine polyamide gear. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Gears are used to transmit motion and/or power. In recent years, polymers are replacing metallic materials in light-duty applications such as measuring instruments, medical instruments, computer peripherals, office printing machines, and automatic teller machines, due to light weight, corrosion resistance, easy manufacturability, and able to run under dry condition. Many experimental and theoretical studies were conducted on the performance of metallic gears [1–7]. However, there are only a few literatures available on the performance of polymeric gears [8–15]. For metallic gears, the gear module is the most influential parameter on gear mesh mechanical efficiency for the high-speed and high-torque operating conditions, followed by gear tooth surface roughness and viscosity of lubricant [1]. Sliding friction between the gear teeth is recognized as one of the main sources of power loss in geared transmission as well as a potential source of vibration and noise. Diab et al. [2] have studied the friction in gear for a wide range of sliding/rolling conditions using elastohydrodynamic lubrication (EHL) simulator and proposed new traction law. Xu et al. [3] proposed a computational model for the prediction of friction-related mechanical efficiency losses of parallel-axis gear pairs. The model incorporates a gear load distribution model, a friction model, and a mechanical efficiency formulation to predict the instantaneous mechanical efficiency of a gear pair under typical operating, surface, and lubrication conditions. It is reported that the proposed model is more accurate with 0.1% deviation with the experimental results. Xu and Kahraman [4] have also proposed similar model for hypoid gear pairs. The effect of addendum and contact ratio on gear ⇑ Corresponding author. Tel.: +91 44 2747 6302; fax: +91 44 2747 6304. E-mail address: [email protected] (R. Gnanamoorthy). 0261-3069/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2012.02.045
strength and basic performance parameters were explained elsewhere [5]. The performance of metallic gears depends on the frictional loss between the contacting pair of gears as the tooth deflection is negligible due to high elastic modulus [6,7]. Walton et al. [8,9] have experimentally studied and reported the influence of gear materials and tooth geometry on the efficiency and friction of plastic cylindrical gears. For some materials the gear efficiency is significantly affected by the load and for others speed. Use of grease as a lubricant in polymer gear significantly increases the efficiency and eliminates the load and speed dependences. Efficiency of polymer gears deteriorates with the increasing running time but reducing the tooth size enhances the efficiency. The polymer gear generates more heat due to its low elastic modulus (100 times lesser than that of steel) and viscoelastic nature [10]. The poor thermal conductivity of polymer causes the generated heat to accumulate within the gear. The increase in tooth temperature degrades the polymer and deteriorates the performance of the gear pair [11]. Mathematical models were developed and reported [12,13] to quantify the amount of heat generated due to friction and hysteresis loss in polymer gears during meshing. The rotational speed of the spur gear affects the performance of unreinforced and glass fiber reinforced spur gears [14]. Initial application of grease significantly reduces the tooth wear in carbon fiber reinforced poly-ether-etherketone gear [15,16] and carbon fiber reinforced polyamide 12 gear [17]. A new design method based on the relation between the wear rate and its surface temperature was developed for acetal gear [18]. Researchers have attempted to reduce the gear tooth surface temperature by increasing the tooth width in single tooth contact region [10]. Providing a hole on the gear tooth reduces the surface temperature and it is further reduced by steel pin inserts [19]. Providing a hole in gear tooth reduces the tooth stiffness and leads to large tooth deflection. Heat dissipation through the hole is
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effectively achieved only through the proper selection of size of the hole and location [20]. Significant reduction in surface temperature and wear is achieved by drilling multiple radial and axial cooling holes [21]. The performance of a gear pair depends upon the material, geometry, speed, loading condition and friction [8]. Power transmission efficiency of the polymeric gears can be improved by reinforcing the matrix by short fibers [14]. Presence of strong fiber on the molding surface deteriorates the surface roughness. Moreover, the orientation of the fibers governs the gear stiffness, and it is difficult to keep the orientation in the effective direction throughout the gear tooth geometry. Thus, only a fraction of short fiber content is effectively used to enhance the stiffness of polymer tooth. Polymer nanocomposite (PNC) materials are new emerging materials which uses the nano-sized particle or platelets as reinforcement. The nano-size particle has large specific surface areas and has good interfacial adhesion with compatible polymer. The molecular level interaction between the nano-size reinforcement and polymer significantly improves the many of their mechanical properties, especially stiffness and strength [22]. Nano-size reinforcement increases the crystallinity of the polymer and reduces the polymeric chain mobility. Nano-size reinforcement also increases the glass transition temperature and barrier properties of the polymer. This paper describes the load sharing in PA6 and PNC gears estimated using numerical analysis. Experimental studies are carried out to understand the effect of torque on the performance. The frictional and hysteresis power loss are discussed. 2. Numerical studies To ensure smooth and continuous operation, gears are made with contact ratio greater than one. During meshing, adjacent tooth comes in contact at the beginning of approach action and at the end of recess action. Since more than one tooth is in contact, there exist a load sharing between the adjacent tooth and a single tooth carries the load for a portion of meshing cycle. The tooth deflection in metallic gear is very small due to high stiffness and, hence, there is no significant difference in load sharing compared to that of ideal gear pair. For polymer gear, the tooth deflection is significantly large due to low stiffness and, hence, there exist a significant difference in load sharing compared to that of ideal gear pair. To understand the effect of polymeric gear tooth deflection in load sharing, a Finite Element Analysis (FEA) is carried out using commercial software package ANSYSÒ. The FE model consists of three teeth in each gear to capture the effect of adjacent teeth in tooth deflection. Since the face width of the gear is very large compared to the tooth contact width, triangular shaped plane strain elements is used to mesh the tooth geometry [23]. The contact condition of gear teeth is sensitive to the geometry of the contacting surfaces and, hence, a fine mesh is used near the contact region. Detailed pictures of the finite element mesh of the gears are shown in Fig. 1. Linear elastic deformation behavior is assumed for all materials and the analysis is done by rotating the steel gear and keeping the polymer gear as stationary one. The FE Analysis of meshed gear pair is carried out at a various roll angles (angle of rotation of the pinion gear) with a fine step size to determine the angle of access and angle of recess during meshing of steel gear with pristine PA6 and PNC gears. 3. Gear materials and gear testing Polymer nanocomposites (PNC) are prepared from the commercial polyamide 6 (PA6) granules and organically modified layered silicate hectorite clay by melt intercalation technique. Material processing details and characterization of PNC are reported elsewhere [24]. Uniformly dispersed nano-size hectorite
Fig. 1. Details of the Finite Element mesh: (a) an overview of the complete model; (b) magnified view near the contact.
clay makes strong bond with the PA6 and thereby enhance the strength and stiffness. The properties of pristine polyamide and polyamide nanocomposites used in the present study are listed in Table 1. Dynamic mechanical analysis (DMA) is carried out to characterize the temperature dependency and viscoelastic nature of PA6 and PNC materials. Three-point bending specimens made from pristine PA6 and PNC were tested using a DMA analyzer (NETZCH) as per ASTM D 5023 standard. The nano-size clay arrest the mobility of the polymer chain and increases storage modulus and temperature resistance compared to PA6 [24]. Fig. 2 shows the schematic diagram of the gear test rig, developed in-house, to study the performance of polymeric gears. The test gear has standard involute tooth profile with 2 mm module, 20° pressure angle and 17 teeth. The PA6 and PNC gears are made by injection molding process at a pressure of 125 MPa and at a temperature of 513 K. A stainless steel (SS316) gear with similar nomenclature is made by hobbing process and used as a driver gear. The driver gear is attached to the speed controllable DC motor and its speed and load are maintained constant throughout the test. Power drawn via driven test gear is dissipated through the DC generator and loading rheostat. Non-contact type infrared temperature sensors are used to monitor the surface temperature of the gears and are recorded using a computerized data acquisition system. The test gears are run at a speed of 1200 rpm at different torque levels (1.5, 2.0 and 2.5 N m) up to failure or ten million cycles (107 cycles) whichever is earlier. High precision torque sensors are connected to driver and driven gear shafts and the torque values are continuously recorded using computerized data acquisition system. The shafts are free from support bearings and the transmission efficiency is computed from the following relation:
Transmission efficiency ðgÞ ¼
Driven gear torque Driver gear torque
ð1Þ
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Table 1 Properties of pristine polyamide 6 and polyamide 6 nanocomposites [24]. Material
Tensile modulus (MPa) (ASTM D638)
Rockwell hardness (R Scale) (ASTM D785)
PA6 PA6 + 3% clay PA6 + 5% clay
550 ± 10% 815 ± 9%
97.5 ± 1.5 100.2 ± 2.7
950 ± 9%
105.3 ± 2.9
Generator
Torque Coupling transducer
Test gear
Coupling
Driver gear (Stainless Steel)
Torque transducer
Fig. 4. Contact ratio for the steel pinion meshing with gears made of different materials at various torque levels.
Driver motor
Fig. 2. Schematic diagram of the polymer spur gear performance test rig.
4. Results and discussion 4.1. Gear tooth deflection Load sharing of a gear tooth may be defined as the total load shared by a single gear tooth. Fig. 3 shows the load sharing in steel, PA6 and PNC gears meshed against steel gear estimated using numerical analysis. The load sharing in steel gear pair slightly differs from that of ideal gear pair due to the deflection of gear tooth. This causes a difference in load sharing between ideal gear pair and PA6 and PNC gears meshed against steel gear. Similar gear pair material results in symmetrical load sharing curve, whereas, dissimilar gear pair material result in unsymmetrical skewed curve. PA6 and PNC gear load sharing data is skewed and indicates the load sharing is approximately 1/3 in the first part and 2/3 in the last part. Gear tooth stiffness significantly affects the load sharing curve shape. Higher the gear tooth stiffness lowers the deviation from ideal curve and vice versa. The study also indicates that the increase in contact path resulting in preliminary contact earlier in the meshing cycle and a prolonged contact at the end, which reduces the period of the single tooth contact. A similar trend was reported by other researchers [23,25].
Fig. 4 shows the contact ratio for each gear pair at different torque levels. PA6 gear has very low stiffness and, hence, severe tooth bending and results in very high contact ratio. PNC gears have high stiffness and, hence, they exhibits lower contact ratio compared to PA6 gear. The contact ratio in each gear pair increases with the increases in torque and this is due to the increases in tooth bending. Higher the contact ratio, larger the duration of tooth contact and more susceptible to higher frictional heat generation and wear failure. 4.2. Transmission efficiency The transmission efficiency of polymer gear indicates the power loss in the gear pair. The power loss in polymer gear consists of two components namely the frictional losses due to relative sliding and hysteresis losses due to viscoelastic nature and tooth bending. Power loss in polymer gear pair results in heat generation. The net heat generated, Eg, in polymer gears can be expressed as [13]:
Eg ¼ Egf þ Egh
ð2Þ
where Egf represents the heat generation due to friction between mating gears, and Egh represents the heat generation from hysteresis effect. The frictional heat generation is given as [13]:
Egf ¼ lW 0
Wi 1 V s Ds W n cos hf
ð3Þ
where l is the coefficient of friction at contact point, W0 is the transmitted load per unit face width, W i =W n is the load sharing factor, hf is the operating pressure angle, Vs is the sliding speed, and Ds is the displacement of the contact point measured along the line of action. The hysteresis heat generation is given by following expression [13]:
Egh ¼
Fig. 3. Load sharing between the steel pinion and gears made of various materials for the applied torque of 1.5 N m estimated using FEA.
tgd r20 t p V s Ds 1 þ tg 2 d 4 E cos hf
ð4Þ
where E is storage modulus of material, ðtgdÞ is the material dissipation factor, r0 is the stress amplitude based on a unit face width and t is the tooth thickness at pitch circle. The frictional power loss is evaluated for PA6 and PNC gears using the Eq. (3), and the results obtained from FEA. To account the sliding velocity and direction of sliding, the instantaneous coefficient of friction is used to evaluate the frictional power loss [26]. During approach action, the sliding velocity reaches zero at the pitch point from its maximum value and the rolling velocity reaches its maximum value at pitch point from its minimum value [6]. During recess action, the rolling velocity reduces and the
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sliding velocity increases. Rolling friction coefficient is much smaller than the sliding coefficient of friction and, hence, the frictional loss due to sliding is significant compared to rolling. Fig. 5 shows the predicted frictional power loss in PA6 and PNC gears running against steel gear for various average coefficients of friction ranging from 0.1 to 0.6 for the rotational speed of 1200 rpm and the torque level of 1.5 N m. The low elastic modulus of PA6 gear increases the contact area, severe tooth bending and extended contact path. These result in increased frictional power loss. The increase in coefficient of friction increases the frictional power losses. Fig. 6 shows the predicted frictional power loss per cycle in PA6 and PNC gears for different coefficient of friction. The frictional power loss is low in PNC gears compared to PA6 gears at all coefficient of friction values assumed. This is due to the better load sharing of the PNC spur gear tooth, lower contact path and reduced sliding coefficient of friction compared to PA6 gears [26]. Polymeric materials exhibit viscoelastic characteristics. The repeated bending of gear tooth leads to hysteresis heat generation. The power loss due to hysteresis mainly depends on the material dissipation factor, also called as loss tangent, and load [13]. The dynamic mechanical analysis (DMA) of the PA6 and PNC materials reveals that the PNC has higher storage modulus and higher temperature resistance compared to PA6 [24]. The hysteresis power loss of the PA6 and PNC gears running at the speed of 1200 rpm and 1.5 N m calculated for various roll angles (angle of
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Fig. 6. Frictional power loss per cycle in PA6 and PNC spur gears meshed with steel gear at 1200 rpm and torque of 1.5 N m.
rotation of the pinion gear) is shown in Fig. 7. The pristine PA6 gear exhibits the higher hysteresis power loss compared to PNC gear. This is due to the high loss tangent of PA6 material attributed by the unrestricted movement of molecular chains. Whereas, in PNC materials, the molecular chain movement is restricted by the nano-size clay which reduces the loss tangent and thereby the hysteresis power loss. The hysteresis power loss in a single gear tooth per cycle is estimated from Fig. 7 and is shown in Fig. 8. The hysteresis heat generation in PNC gear is low compared to PA6 gear. The PA6 + 5% clay gear exhibits the lowest hysteresis power loss and frictional power loss compared to PA6 and PA6 + 3% clay gears. Thus, PA6 + 5% clay gears have high transmission efficiency and good performance.
4.3. Gear performance Fig. 9 shows the temperature rise in the test gear tooth with increasing number of cycles. Under similar working condition, the tooth temperature of PNC gear is less than the PA6 gear. The mechanical properties of polymeric materials strongly depend upon the temperature, and, hence, the rise in temperature of the gear tooth degrades the mechanical properties of polymer gear and results in deterioration in gear performance. Fig. 10 shows the effect of increasing temperature in the gear efficiency with increasing number of meshing cycles. The PNC material exhibits improved storage modulus than the pristine PA6 material [24], it retains the mechanical properties at higher temperature. The
Fig. 5. Frictional power loss in (a) Steel – PA6, (b) Steel – PA6 + 3% Clay, and (c) Steel – PA6 + 5% Clay gears running at 1200 rpm and torque of 1.5 N m.
Fig. 7. Hysteresis power loss in PA6 and PNC spur gears meshed with steel gear running at 1200 rpm and torque of 1.5 N m.
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Fig. 8. Hysteresis power losses in PA6 and PNC spur gear tooth per cycle meshed with steel gear running at 1200 rpm and torque of 1.5 N m.
enhanced mechanical properties of PNC gear reduces the frictional heat generation, hysteresis heat generation and retain the mechanical properties at elevated temperatures and result in better performance than PA6 gear. Fig. 11 shows the efficiency of PA6 and PNC spur gears measured during the tests conducted at a speed of 1200 rpm and 2 N m torque. PNC gears show higher efficiency compared with PA6 gears due to improved mechanical and tribological properties. Efficiency of polymer gear pair mainly depends upon the frictional losses and hysteresis losses due to relative sliding and tooth bending respectively. The frictional loss depends on the coefficient of friction. The PNC materials exhibit lower coefficient of friction than the pristine PA6 due to improved elastic modulus, high crystalline nature and high hardness [24]. The low elastic modulus of pristine PA6 increases the area of contact and tooth deflection. The coefficient of friction depends upon the apparent area of contact. The dependency of area of contact on coefficient of friction in PNC materials is lower than the PA6 materials [26]. Coefficient of friction, area of contact and length of contact are low in the PNC gear, and hence, the frictional losses in the PNC gears are less compared to the pristine PA6 gears. Addition of nano-clay reinforcement increases the storage modulus and reduces the damping coefficient of PNC compared to PA6 [24]. Reduced viscoelastic nature and improved storage modulus reduce the hysteresis heat generation in PNC gear. The reduction in heat generation implies better the performance. Hence, nano-size reinforcement in the polymer matrix improves the efficiency of the gear pair. The PA6 + 5% clay gear
Fig. 10. Efficiency and test gear tooth temperature rise during the performance tests carried out at a speed of 1200 rpm and torque 2 N m with increasing meshing cycles of (a) pristine PA6, (b) PA6 + 3% clay, and (c) PA6 + 5% clay spur gears.
exhibited higher efficiency compared to PA6 and PA6 + 3% clay gear (Fig. 11). 4.4. Effect of torque on performance of the PA6 and PNC spur gear
Fig. 9. Temperature rise measured in the test gears during the test conducted at a torque level of 1 N m and rotational speed of 600 rpm.
Fig. 12 shows the efficiency of pristine PA6 and PNC gears tested at 1200 rpm and at different torque levels. PNC gear exhibit higher efficiency than the pristine PA6 gears at all tested torque levels. Also PNC gear efficiency shows a less dependency on applied load, whereas pristine PA6 gears shows a drop in efficiency with increase in load. Sliding coefficient of friction of PNC materials is less
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efficiency of the polyamide 6 and polyamide nanocomposite gears. The nano-clay reinforcement reduces the dependency of gear efficiency on applied torque. The increase in weight percentage of nano-clay is beneficial for the efficiency of the gear. The difference in gear efficiency of polymer nanocomposite gears with different weight percentage of nano-clay is more significant at higher torque level compared to lower torque levels. The addition of nano-clay reduces the ductility of the polymer but increases the gear efficiency. Further research could be made to find most appropriate weight percentage of nano-clay in polymer matrix and different nano-size particles to get further enhancements in gear efficiency. References
Fig. 11. Transmission efficiency of PA6 and PNC spur gears mating against SS gear running at 1200 rpm and torque of 1.5 N m.
Fig. 12. Effect of applied torque on the efficiency of PA6 and PNC spur gears.
dependent on load compared to the pristine PA6 materials [26]. Weak transfer film formation during sliding due to increased hardness and improved modulus of PNC materials at all levels of loads attributes to better performance of PNC gears. The lower deflection of PNC tooth and lower damping factor of PNC material causes a reduced hysteresis heating compared to the pristine PA6 gears. Hence, PNC gear efficiency shows less dependency on load and performs better than the pristine PA6 gears. 5. Conclusions The performance of injection molded polyamide 6 and polymer nanaocomposite gears were investigated at various torque levels using a power absorption type gear test rig. The enhanced mechanical and thermal properties of nanocomposite gears due to the addition of nano-clay reduce frictional losses and hysteresis losses in gear during meshing. Applied torque has detrimental effect on the
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