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Effect of rotational speed on the performance of unreinforced and glass fiber reinforced Nylon 6 spur gears
Materials & Design Materials and Design 28 (2007) 765–772 www.elsevier.com/locate/matdes
Effect of rotational speed on the performance of unreinforced and glass fiber reinforced Nylon 6 spur gears S. Senthilvelan, R. Gnanamoorthy
*
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India Received 13 June 2005; accepted 2 December 2005 Available online 31 January 2006
Abstract Polymer gears used in power and motion transmission work under different loads and speeds. Mechanical properties of the polymers are severely influenced by the loading rate compared with the metals. The gear rotational speed decides the loading frequency of the polymer gear tooth, which influences the temperature generated and thereby the strength of the material. Performance of polymer base gears at different gear rotational speeds is reported in this paper. Injection molded unreinforced Nylon 6 and 20% short glass fiber reinforced Nylon 6 spur gears were tested at various speeds and torque levels in a power absorption type gear test rig. Gear rotational speed affects the performance of gears made of both the materials at high running speeds and high test torques and not in low speeds and torque levels. On-line measurement of test gear surface temperature and failure analysis was done to understand the failure mechanisms. At all the investigated gear speeds, glass fiber reinforced Nylon 6 gears shows superior performance over unreinforced Nylon 6 gears due its superior mechanical strength and resistance to thermal deformation. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Polymer matrix composite; Gears; Speed; Thermal; Fatigue; Wear
1. Introduction Polymer and polymer composite gears find increasing application because of the low material and manufacturing costs, part weight and quiet performance compared with the metal gears. However polymeric materials suffer from poor mechanical strength and thermal resistance compared with metals. Reinforced polymers offer high mechanical strength and thermal resistance and are suitable for structural/load bearing applications. Short fiber reinforced polymers permit fabrication of complex shaped products economically using injection-molding process. Many research works have been performed on the issues related to the performance of polymer and polymer composite gears [1–9]. In those articles influence of reinforcement on the fatigue performance and wear resistance of polymer gears is well discussed. Since many polymer based gear *
Corresponding author. Tel.: +91 44 2257 4691; fax: +91 44 2257 0509. E-mail address: [email protected] (R. Gnanamoorthy).
0261-3069/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2005.12.002
designs are derived from metal gear design procedure, polymer based gears demand special considerations for the heat build-up and associated effects that occur in service [10]. The temperature rise during service in gears was measured in various ways [11–13]. Faatz and Ehrenstein [11] measured the tooth temperature of acetal gears using thermal camera and correlated with Hachman and Strickle model. Yousef et al. [12] developed a technique to study the running temperature of thermoplastic gears and presented preliminary test results on acetal and polycarbonate gears. Liu et al. [13] suggested analytical techniques to predict the flank temperature of thermoplastic spur gears and measured the flank temperature using a infrared pyrometer. Performance of polymer gears at elevated temperature conditions was investigated by few researchers [14–16]. Tsukamoto et al. [14] conducted the performance test at elevated temperature environment on machined Nylon gear to estimate the service life. Tests on acetal spur gears at various temperatures were conducted and the need for
766
S. Senthilvelan, R. Gnanamoorthy / Materials and Design 28 (2007) 765–772
temperature correction factor in the design is discussed [15]. Hooke et al. [16] measured the surface temperature of acetal gears during testing and correlated with gear wear. A methodology was proposed to predict the gear temperature. Machine elements like gears experience both gear tooth fatigue and contact loading during service. Gear tooth fatigue loading causes hysteresis heating of the tooth. The heat generation in conventional fatigue loading is studied by many investigators [17–22]. Rittel [17] investigated the heat generation during cyclic compressive loading on polycarbonate and polymethylmethacrylate specimens. Both the materials are heated up during cyclic loading and the amount of heat generation depends upon the frequency and amplitude of loading. The failure mode of both the material is influenced by the temperature rise and distribution. An increase in temperature during fatigue testing was observed in glass fiber reinforced polyester resin tensile fatigue specimens loaded at different frequencies [19]. Temperature, frequency and loading type were found to affect the fatigue performance of different polymers [20]. Chen et al. [23] identified pitch line velocity as one of the factors, which affect the fatigue strength of Nylon gears. No work has been performed to understand the influence of gear rotational speed on surface temperature of gear and gear performance. This paper discusses the effect of gear rotational speed on the performance of injection molded Nylon 6 and glass fiber reinforced Nylon 6 spur gears. Test gears were run at different rotational speeds and the performance is discussed. Failure mechanisms at different rotational speeds are investigated using optical microscope.
precision wire cut electric discharge machine considering the shrinkage. The gear data and location of the injection-molding gate in gear are shown in Fig. 1. Detail computer aided simulation studies of gear molding were conducted for finding out the best gate location and are described elsewhere [25]. Molded gears were dried at 313 K for 30 min to remove the moisture content. Test polymer base spur gears were mated against the hobbed standard stainless steel spur gear (AISI SS316). 3. Gear test rig and testing procedure 3.1. Test rig details Fig. 2 shows the schematic of the in-house developed gear test rig used for conducting performance tests. In this test rig, the test gear is driven using a DC motor and can be run at any speed up to 1500 rpm. Test gear mates with an identical standard gear, which is connected to the DC generator. The required test torque is introduced by loading the rheostat connected to the generator. Various features of developed test rig are discussed elsewhere [26]. Severe wear of the gear tooth is one of the gear failure modes, which leads to a gradual increase in sound and vibration of the unit. In the gear test rig, the vibration level of the bearing block, gear tooth surface temperature and sound level of the system are monitored. When any one of monitoring sensor indicated an abnormal value, the tests were terminated and the gears were inspected. Speed sensors and digital counter are suitably placed to monitor the speed and number of cycles run, respectively. Detail methodology followed for test gears condition monitoring is discussed elsewhere [27].
2. Gear materials and processing 3.2. Gear test procedure Commercially available Nylon 6 and 20% glass fiber reinforced Nylon 6 granules were used for injection molding the test gears used in the current investigations. The mechanical and thermal properties of the test materials are shown in Table 1 [24]. The strength, modulus and thermal conductivity of glass fiber reinforced material are superior compared to that of unreinforced material. The granules were preheated at 353 K for 4 h prior to injection molding to remove the moisture content. Test gears were made using an injection molding machine (Macfield) at the molding pressure of 125 MPa and melt temperature of 513 K. Gear profile in the molding die was cut using a
Gear tests were conducted at different torque levels, 0.8, 1.5, 2, 2.5 and 3 Nm. The corresponding gear tooth bending stresses computed using Lewis equation [28] are 8, 15, 20, 25 and 30 MPa, respectively. Tests were conducted at four gear rotational speeds, 600, 800, 1000 and 1200 rpm under unlubricated dry conditions. Rotational speed of the test gear is gradually increased to the test speed and maintained constant throughout the test. Tests were continuously run until the gear failure is observed or until 5 millions of cycles run whichever is earlier. At least three specimens were tested at each torque level. All the gear
Table 1 Properties of Nylon 6 and 20% glass fiber reinforced Nylon 6 material [24]
Flexural strength (MPa) Flexural modulus (MPa) Elongation at yield (%) Deflection temperature at 1.82 MPa (°C) Thermal conductivity (W/m K)
Unreinforced Nylon 6
20% Glass fiber reinforced Nylon 6
ASTM Standard
110 2965 18.5 71 0.3
193 6206 6.57 243 0.42
D790 D790 D638 D648 C177
S. Senthilvelan, R. Gnanamoorthy / Materials and Design 28 (2007) 765–772
767
Fig. 1. Test gear details and gate locations.
Fig. 2. Schematic of the power absorption gear test rig.
tests were conducted at the laboratory conditions (room temperature: 302 ± 5 K and humidity: 64 ± 5%). Tested gears were observed using an optical microscope to understand the failure mechanisms.
Contact ratio ¼ 4. Results and discussion
1 Number of teeth Speed in rps ð2Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2a1 r2b1 þ r2a2 r2b2 ða sin aÞ
Contact period of a tooth ¼
Pb ð3Þ
4.1. Gear tooth rate of loading The mechanical properties of polymer and polymer composites are sensitive to strain rate and temperature [10,17–22]. When the rotational speed of test gear is increased, the rate of loading on each gear tooth during service also increases [29]. Rotational speed of the gear can be correlated with the loading rate of single tooth considering the load sharing. The rate of loading or the strain rate of a gear tooth is expressed as [29,30]. Rate of loading or strain rate ¼
Torque acting on the tooth 1 Contact period Contact ratio
where
ð1Þ
where ra1 and rb1 are radius of addendum and base circle of driver, ra2 and rb2 are radius of addendum and base circle of driven, a is the center distance of gear pair, a is the pressure angle and Pb is the base pitch. The computed theoretical contact ratio for the gear pair under investigation is 1.514. When the gears transmit 0.8 Nm torque at different rotational speeds 600, 800, 1000 and 1200 rpm, the rate of loading of a single tooth is 89.8, 117.8, 149.7, and 179.7 Nm/s, respectively. Similarly for the entire test conditions loading rate of single gear tooth is computed and plotted in Fig. 3. Increase in the gear rotational speed increases the frequency of loading of a single gear tooth. This significant rise in the rate of loading on a single tooth will lead to hysteresis heating of the gear tooth and is discussed in the following section.
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Tooth Loading Rate (Nm/s)
800 700
600 rpm
800 rpm
600
1000 rpm
1200 rpm
500 400 300 200 100 0 0
0.5
1
1.5
2
2.5
3
3.5
Applied Torque (Nm) Fig. 3. Effect of applied torque and gear rotational speed on the tooth loading rate.
4.2. Hysteresis heating
Fig. 5. Gear tooth surface temperature of glass fiber reinforced Nylon 6 gears tested at different speeds at 8 MPa gear tooth bending stress.
In the case of metallic gears tooth deflections are negligible and hence the effect of material hysteresis due to the frequency variation is negligible [28]. The polymer gear tooth deforms severely because of the low gear tooth stiffness (about 100 times less than that of metal). Repeated gear tooth loading and subsequent deformation of gear tooth contributes to hysteresis heating [31–33]. The heat generated in gears is due to friction between the mating gear teeth and hysteresis effects. The equilibrium of generated and dissipated heat in the gear drive determines the net temperature of the test gear [32]. The surface temperature of test gear, which is the net equilibrium between heat generation and heat dissipation, is measured in the current investigations. This on-line measurement of gear tooth surface temperature during testing shows an initial increase in temperature, which stabilizes after a certain period (Figs. 4 and 5). The heat generated due to friction as well as hysteresis loss increases with increase in gear rotational speed. The gear tooth surface temperatures measured during testing of unreinforced Nylon 6 gears at 0.8 Nm torque shows a rise in temperature with the increase in gear rotational speed (Fig. 4). The behavior of glass fiber reinforced Nylon
gears also shows similar trend but the rise in surface temperature due to the increase in gear rotational speed is comparatively less than that at unreinforced gears (Fig. 5). Addition of glass fiber increases the gear tooth stiffness [24] and hence less gear tooth deflection occurs for the same loading condition. Hence the heat generation due to material hysteresis losses is less. In addition due to superior thermal conductivity of the glass fiber reinforced material [24] better heat dissipation occurs. Both the unreinforced and reinforced gears show only a marginal rise in surface temperature due to the increase in gear rotational speed. No sudden rise in temperature due to the increase in gear rotational speed is observed, which indicates that no change in the failure mode can be expected due to the change in speed. Figs. 6 and 7 show the measured surface temperature of unreinforced and glass fiber reinforced Nylon gears tested at various stress levels at 1200 rpm. At a particular stress level, glass fiber reinforced Nylon 6 gears shows less surface temperature than unreinforced Nylon 6 gears. For both the test gears the net surface temperature of gears increases
Fig. 4. Gear tooth surface temperature of unreinforced Nylon 6 gears tested at different speeds at 8 MPa gear tooth bending stress.
Fig. 6. Variation of the gear tooth surface temperature of unreinforced Nylon 6 gear tested at 1200 rpm at different stress levels.
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increases the surface temperature of gear. On-line measurement shows also a sudden rise in temperature after some time at certain loading condition, which clearly indicates that magnitude of stress severely influence the mode of failure. Correlation of surface temperature of gear on failure mode and gear performance is discussed in the following section. 4.3. Gear performance and damage mechanisms
Fig. 7. Variation of the gear tooth surface temperature of glass fiber reinforced Nylon 6 gear tested at 1200 rpm at different stress levels.
with increase in stress levels. At 25 and 30 MPa tooth bending stress tests, there was a continuous rise in the temperature until gear failure was noticed. Whereas at 8, 15 and 20 MPa test bending stress levels, after 0.1 million of life cycles, no rise in surface temperature observed. The increase in gear tooth bending stress level considerably
Gear rotational speed influences the net surface temperature of both the unreinforced and glass fiber reinforced Nylon gears. But no significant difference in the failure mode was observed due to the variation of speed at a particular stress level in the tests conducted. However, the failure mode is severely influenced by the magnitude of stress experienced by the gear tooth. The optical photographs of the failed unreinforced Nylon gears tested at different gear speeds and stress levels are shown in Fig. 8 (a–f). Gear tooth root cracking and tooth wear were observed in gears tested at all rotational speeds and at low gear tooth bending stress, 8 MPa (Fig. 8a and b). However beyond the applied bending stress of 8 MPa, a significant plastic
Fig. 8. (a–f) Failure morphology of unreinforced Nylon 6 gears tested.
S. Senthilvelan, R. Gnanamoorthy / Materials and Design 28 (2007) 765–772
deformation was observed (Fig. 8c–f). Significant temperature rise at high stress levels and poor thermal conductivity of the unreinforced material leads to severe temperature induced plastic deformation. In the case of glass fiber reinforced Nylon 6 gears, the increased resistance to thermal deformation causes gear tooth deformation only above bending stress of 20 MPa (Fig. 9(a–f)). Gear tooth wear and root cracking similar to unreinforced gear was observed in gears tested at 8 MPa and 15 MPa stress levels at all rotational speeds (Fig. 9a–d). At high stress levels (above 15 MPa tooth bending stress) visible plastic deformation of the tooth was observed (Fig. 9e and f). Figs. 10 and 11 show the gear tooth-bending stress plotted against the number cycles run for the unreinforced and glass fiber reinforced gears, respectively. Test results indicate a significant performance difference at different speeds, which is normally not observed in metallic gears. In both the unreinforced and glass fiber reinforced gears, only at higher stress conditions, influence of speed on gear performance is observed. This behaviour is well coincident with the trend indicated by the loading rate at various speeds (Fig. 3). Loading rate significantly influences unreinforced
35 Tooth bending stress (MPa)
770
600 rpm 1000 rpm
30
800 rpm 1200 rpm
25 20 15 10 5
Unreinforced Nylon 6 gear
0 1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
Number of cycles (N)
Fig. 10. Influence of gear rotational speed on the fatigue behavior of unreinforced Nylon 6 gear.
and glass fiber reinforced Nylon gear performance only at high loads. Fig. 10 shows the performance of unreinforced Nylon gears at different speeds, 600, 800, 1000 and 1200 rpm. At low stress levels (8 MPa), no influence of gear rotational speed on gear performance is observed. No thermal or thermal associated failures were observed and only tooth
Fig. 9. (a–f) Failure morphology of glass fiber reinforced Nylon 6 gears tested.
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Acknowledgments
35 Tooth bending stress (MPa)
771
30
600 rpm
800 rpm
1000 rpm
1200 rpm
25 20
Authors acknowledge the financial support provided by the Robotics and Manufacturing Division, Department of Science and Technology, India.
15
References
10 5
Glass fiber reinforced Nylon 6 gear
0 1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
Number of cycles (N)
Fig. 11. Influence of gear rotational speed on the fatigue behavior of glass fiber reinforced Nylon 6 gear.
wear and non propagating tooth cracks were observed at all the investigated gear speeds under low stress conditions (Fig. 8a and b). At high stress conditions (above 8 MPa), thermal associated failures such as tooth deformation and tooth folding were observed (Fig. 8c–f). At high test stress conditions (beyond 8 MPa) high loading rate and heat generation reduces gear tooth strength and hence with increase in gear rotational speed, the gear life reduces. Fig. 11 shows the gear tooth bending stress vs number of cycles run for glass fiber reinforced Nylon 6 gears. Glass reinforced gear doesn’t show a significant performance variation due to the gear rotational speed both at 8 and 15 MPa stress levels. Due to the improved mechanical property and resistance to thermal deformation of glassreinforced gears, no thermal damages were observed even at 15 MPa stress level. Beyond 15 MPa stress levels reinforced gear also shows thermal failures (Fig. 9e–f). Due to the superior mechanical strength than unreinforced material, only beyond 15 MPa stress level, glass fiber reinforced Nylon 6 gear shows significant influence of loading rate on gear performance. At a particular stress level and gear rotational speed, the glass reinforced Nylon 6 gear shows improved fatigue life than unreinforced Nylon 6 gears. 5. Conclusions The performance of injection molded Nylon 6 and glass fiber reinforced Nylon 6 gears was investigated at various gear rotational speeds and applied stress levels. Gear rotational speed influences the performance of both unreinforced and glass reinforced Nylon 6 at high stress levels. At low stress levels, gear tooth root cracking and gear wear were the dominant failure modes and no influence of speed on gear life is observed. At high stress levels, the local temperature rise leads to weakening of gear material and reduces the performance. Increasing the rotational speed considerably increases the loading frequency, and increases the surface temperature of gears, which leads to the reduction of gear life. The applied stress level influences the failure mechanism of the polymer composite gears.
[1] Crippa G, Davoli P. Comparative fatigue resistance of fiber reinforced nylon 6 gears. J Mech Des 1995;117:193–8. [2] Kurokawa M, Uchiyama Y, Nagai S. Performance of plastic gear made of carbon fiber reinforced poly-ether–ether-ketone. Trib Int 1999;32:491–7. [3] Kurokawa M, Uchiyama Y, Nagai S. Performance of plastic gear made of carbon fiber reinforced poly-ether-ether-ketone: Part 2. Trib Int 2000;33:715–21. [4] Kurokawa M, Uchiyama Y, Nagai S. Tribological properties and gear performance of polyoxymethylene composites. J Trib 2000;122:809–14. [5] Kurokawa M, Uchiyama Y, Iwai T, Nagai S. Performance of plastic gear made of carbon fiber reinforced polyamide 12. Wear 2003;254:468–73. [6] Walton D, Croppe A, Weale DJ, Klein Meuleman P. The efficiency and friction of plastic cylindrical gears: Part 1- Influence of materials. Proc IMechE Pt J J Eng Trib 2002;216:75–92. [7] Walton D, Croppe AB, Weale DJ, Klein Meuleman P. The efficiency and friction of plastic cylindrical gears: Part 2 - Influence of tooth geometry. Proc IMechE Pt J J Eng Trib 2002;216:93–103. [8] Wright NA, Kukureka SN. Wear testing and measurement techniques for polymer composite gear. Wear 2001;250:1567–78. [9] Akkurt S. On the effect of surface roughness on wear of acetal–metal gear pairs. Wear 1995;184:107–9. [10] Dominick VR, Donald VR, Marlene GR. Plastics Design Handbook. Kluwer Academic Publishers; 2000. [11] Faatz P, Ehrenstein GW. Temperature calculations of plastic gears. in: Proceedings of SPE annual technical conference; 2000. pp. 1540–4. [12] Yousef SS, Burns DJ, Mckinlay W. Techniques for assessing the running temperature and fatigue strength of thermoplastic gears. Mech Mach Theor 1973;8:175–85. [13] Liu R, Burns DJ, Yelle H. Flank temperature profile for thermoplastic spur gears. in: Proceedings of 7th world congress theory of machines and mechanisms; 1987 pp.1285–8. [14] Tsukamoto N, Maruyama H, Taki T, Nishida N. A study on strength design methods for plastic gears (Estimation of operating life of plastic gears in elevated temperature environment). JSME Int J 1991;34:121–6. [15] Bosshart HJ, Burns DJ, Pick RJ, Yelle H. Influence of ambient temperature on the performance of thermoplastic gears. in: Proceedings of international symposium on gearing and power transport; pp. 467–71. [16] Hooke C, Mao J, Walton D, Breeds AR, Kukureka SN. Measurement and prediction of the surface temperature in polymer gears and its relationship to gear wear. J Trib 1993;115:119–24. [17] Rittel D. An investigation of the heat generated during cyclic loading of two glassy polymers Part 1: Experimental. Mech Mater 2000;32:131–47. [18] Rittel D, Rabin Y. An investigation of the heat generated during cyclic loading of two glassy polymers Part II: Thermal Analysis. Mech Mater 2000;32:149–59. [19] Keller T, Tirelli T, Zhou A. Tensile fatigue performance of pultruded glass fiber reinforced polymer profiles. Compos Struct 2005;68:235–45. [20] Hartwig G, Knaak S. Fatigue behaviour of polymers. Cryogenics 1991;31:231–3. [21] Ochola RO, Marcus K, Nurick GN, Franz T. Mechanical behaviour of glass and carbon fiber reinforced composites at varying strain rates. Compos Struct 2004;63:455–67.
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[22] Goldberg RK, Roberts GD, Gilat A. Incorporation of mean stress effects into the micro mechanical analysis of the high strain rate response of polymer matrix composites. Composites B 2003;34:151–65. [23] Chen JH, Juarbe FM, Hanley MA. Factors affecting fatigue strength of nylon gears. J Mech Des 1981;103:543–8. [24] Product Data Sheet of ST 622 and ST 622GFL Grade of SRF Limited India; 2002. [25] Senthilvelan S, Gnanamoorthy R. Design and manufacturing of short fiber reinforced thermoplastic composite gears. in: Proceedings of 3rd ISAMPE national conference on composites; 2004, pp. 176–181. [26] Senthilvelan S, Gnanamoorthy R. Wear characteristics of injection molded unfilled and glass filled nylon 6 spur gears. J Eng Trib Proc IMechE Part J 2004;218(6):495–502. [27] Senthilvelan S, Gnanamoorthy R. Condition monitoring and failure analysis of composite gear. in: Proceedings 11th national conference of machines mechanics; 2003; pp. 278–282.
[28] Maitra GM. Handbook of Gear Design. New Delhi: Tata McGrawHill; 1994. [29] Tsukamoto N, Yano T, Sakai H. Noise and transmission efficiency under deformation of tooth form of nylon gear. Bull of JSME 1982;25:1465–74. [30] Tsukamoto N. Investigation about the strength of plastic gears (3 rd Report; strength of the nylon gear meshing with the steel gear which was cut by semi topping hob). Bull JSME 1981;24, pp. 2184–93. [31] Koffi D, Gauvin R, Yelle H. Heat generation in thermoplastic spur gears. J Mechan Trans Automat Des 1985;107:31–7. [32] Deng G, Nakanishi T, Kato M. Surface temperature calculation and its application to surface fatigue strength evaluation. J Mechan Des 2002;124:805–12. [33] Gauvin R, Girard P, Yelle H. An improved method to establish the heat transfer coefficient on gear tooth surface. in: Proceedings of sixth world congress on theory of machines and mechanisms; 1983 pp. 864– 7.
Effect of rotational speed on the performance of unreinforced and glass fiber reinforced Nylon 6 spur gears S. Senthilvelan, R. Gnanamoorthy
*
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India Received 13 June 2005; accepted 2 December 2005 Available online 31 January 2006
Abstract Polymer gears used in power and motion transmission work under different loads and speeds. Mechanical properties of the polymers are severely influenced by the loading rate compared with the metals. The gear rotational speed decides the loading frequency of the polymer gear tooth, which influences the temperature generated and thereby the strength of the material. Performance of polymer base gears at different gear rotational speeds is reported in this paper. Injection molded unreinforced Nylon 6 and 20% short glass fiber reinforced Nylon 6 spur gears were tested at various speeds and torque levels in a power absorption type gear test rig. Gear rotational speed affects the performance of gears made of both the materials at high running speeds and high test torques and not in low speeds and torque levels. On-line measurement of test gear surface temperature and failure analysis was done to understand the failure mechanisms. At all the investigated gear speeds, glass fiber reinforced Nylon 6 gears shows superior performance over unreinforced Nylon 6 gears due its superior mechanical strength and resistance to thermal deformation. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Polymer matrix composite; Gears; Speed; Thermal; Fatigue; Wear
1. Introduction Polymer and polymer composite gears find increasing application because of the low material and manufacturing costs, part weight and quiet performance compared with the metal gears. However polymeric materials suffer from poor mechanical strength and thermal resistance compared with metals. Reinforced polymers offer high mechanical strength and thermal resistance and are suitable for structural/load bearing applications. Short fiber reinforced polymers permit fabrication of complex shaped products economically using injection-molding process. Many research works have been performed on the issues related to the performance of polymer and polymer composite gears [1–9]. In those articles influence of reinforcement on the fatigue performance and wear resistance of polymer gears is well discussed. Since many polymer based gear *
Corresponding author. Tel.: +91 44 2257 4691; fax: +91 44 2257 0509. E-mail address: [email protected] (R. Gnanamoorthy).
0261-3069/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2005.12.002
designs are derived from metal gear design procedure, polymer based gears demand special considerations for the heat build-up and associated effects that occur in service [10]. The temperature rise during service in gears was measured in various ways [11–13]. Faatz and Ehrenstein [11] measured the tooth temperature of acetal gears using thermal camera and correlated with Hachman and Strickle model. Yousef et al. [12] developed a technique to study the running temperature of thermoplastic gears and presented preliminary test results on acetal and polycarbonate gears. Liu et al. [13] suggested analytical techniques to predict the flank temperature of thermoplastic spur gears and measured the flank temperature using a infrared pyrometer. Performance of polymer gears at elevated temperature conditions was investigated by few researchers [14–16]. Tsukamoto et al. [14] conducted the performance test at elevated temperature environment on machined Nylon gear to estimate the service life. Tests on acetal spur gears at various temperatures were conducted and the need for
766
S. Senthilvelan, R. Gnanamoorthy / Materials and Design 28 (2007) 765–772
temperature correction factor in the design is discussed [15]. Hooke et al. [16] measured the surface temperature of acetal gears during testing and correlated with gear wear. A methodology was proposed to predict the gear temperature. Machine elements like gears experience both gear tooth fatigue and contact loading during service. Gear tooth fatigue loading causes hysteresis heating of the tooth. The heat generation in conventional fatigue loading is studied by many investigators [17–22]. Rittel [17] investigated the heat generation during cyclic compressive loading on polycarbonate and polymethylmethacrylate specimens. Both the materials are heated up during cyclic loading and the amount of heat generation depends upon the frequency and amplitude of loading. The failure mode of both the material is influenced by the temperature rise and distribution. An increase in temperature during fatigue testing was observed in glass fiber reinforced polyester resin tensile fatigue specimens loaded at different frequencies [19]. Temperature, frequency and loading type were found to affect the fatigue performance of different polymers [20]. Chen et al. [23] identified pitch line velocity as one of the factors, which affect the fatigue strength of Nylon gears. No work has been performed to understand the influence of gear rotational speed on surface temperature of gear and gear performance. This paper discusses the effect of gear rotational speed on the performance of injection molded Nylon 6 and glass fiber reinforced Nylon 6 spur gears. Test gears were run at different rotational speeds and the performance is discussed. Failure mechanisms at different rotational speeds are investigated using optical microscope.
precision wire cut electric discharge machine considering the shrinkage. The gear data and location of the injection-molding gate in gear are shown in Fig. 1. Detail computer aided simulation studies of gear molding were conducted for finding out the best gate location and are described elsewhere [25]. Molded gears were dried at 313 K for 30 min to remove the moisture content. Test polymer base spur gears were mated against the hobbed standard stainless steel spur gear (AISI SS316). 3. Gear test rig and testing procedure 3.1. Test rig details Fig. 2 shows the schematic of the in-house developed gear test rig used for conducting performance tests. In this test rig, the test gear is driven using a DC motor and can be run at any speed up to 1500 rpm. Test gear mates with an identical standard gear, which is connected to the DC generator. The required test torque is introduced by loading the rheostat connected to the generator. Various features of developed test rig are discussed elsewhere [26]. Severe wear of the gear tooth is one of the gear failure modes, which leads to a gradual increase in sound and vibration of the unit. In the gear test rig, the vibration level of the bearing block, gear tooth surface temperature and sound level of the system are monitored. When any one of monitoring sensor indicated an abnormal value, the tests were terminated and the gears were inspected. Speed sensors and digital counter are suitably placed to monitor the speed and number of cycles run, respectively. Detail methodology followed for test gears condition monitoring is discussed elsewhere [27].
2. Gear materials and processing 3.2. Gear test procedure Commercially available Nylon 6 and 20% glass fiber reinforced Nylon 6 granules were used for injection molding the test gears used in the current investigations. The mechanical and thermal properties of the test materials are shown in Table 1 [24]. The strength, modulus and thermal conductivity of glass fiber reinforced material are superior compared to that of unreinforced material. The granules were preheated at 353 K for 4 h prior to injection molding to remove the moisture content. Test gears were made using an injection molding machine (Macfield) at the molding pressure of 125 MPa and melt temperature of 513 K. Gear profile in the molding die was cut using a
Gear tests were conducted at different torque levels, 0.8, 1.5, 2, 2.5 and 3 Nm. The corresponding gear tooth bending stresses computed using Lewis equation [28] are 8, 15, 20, 25 and 30 MPa, respectively. Tests were conducted at four gear rotational speeds, 600, 800, 1000 and 1200 rpm under unlubricated dry conditions. Rotational speed of the test gear is gradually increased to the test speed and maintained constant throughout the test. Tests were continuously run until the gear failure is observed or until 5 millions of cycles run whichever is earlier. At least three specimens were tested at each torque level. All the gear
Table 1 Properties of Nylon 6 and 20% glass fiber reinforced Nylon 6 material [24]
Flexural strength (MPa) Flexural modulus (MPa) Elongation at yield (%) Deflection temperature at 1.82 MPa (°C) Thermal conductivity (W/m K)
Unreinforced Nylon 6
20% Glass fiber reinforced Nylon 6
ASTM Standard
110 2965 18.5 71 0.3
193 6206 6.57 243 0.42
D790 D790 D638 D648 C177
S. Senthilvelan, R. Gnanamoorthy / Materials and Design 28 (2007) 765–772
767
Fig. 1. Test gear details and gate locations.
Fig. 2. Schematic of the power absorption gear test rig.
tests were conducted at the laboratory conditions (room temperature: 302 ± 5 K and humidity: 64 ± 5%). Tested gears were observed using an optical microscope to understand the failure mechanisms.
Contact ratio ¼ 4. Results and discussion
1 Number of teeth Speed in rps ð2Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2a1 r2b1 þ r2a2 r2b2 ða sin aÞ
Contact period of a tooth ¼
Pb ð3Þ
4.1. Gear tooth rate of loading The mechanical properties of polymer and polymer composites are sensitive to strain rate and temperature [10,17–22]. When the rotational speed of test gear is increased, the rate of loading on each gear tooth during service also increases [29]. Rotational speed of the gear can be correlated with the loading rate of single tooth considering the load sharing. The rate of loading or the strain rate of a gear tooth is expressed as [29,30]. Rate of loading or strain rate ¼
Torque acting on the tooth 1 Contact period Contact ratio
where
ð1Þ
where ra1 and rb1 are radius of addendum and base circle of driver, ra2 and rb2 are radius of addendum and base circle of driven, a is the center distance of gear pair, a is the pressure angle and Pb is the base pitch. The computed theoretical contact ratio for the gear pair under investigation is 1.514. When the gears transmit 0.8 Nm torque at different rotational speeds 600, 800, 1000 and 1200 rpm, the rate of loading of a single tooth is 89.8, 117.8, 149.7, and 179.7 Nm/s, respectively. Similarly for the entire test conditions loading rate of single gear tooth is computed and plotted in Fig. 3. Increase in the gear rotational speed increases the frequency of loading of a single gear tooth. This significant rise in the rate of loading on a single tooth will lead to hysteresis heating of the gear tooth and is discussed in the following section.
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Tooth Loading Rate (Nm/s)
800 700
600 rpm
800 rpm
600
1000 rpm
1200 rpm
500 400 300 200 100 0 0
0.5
1
1.5
2
2.5
3
3.5
Applied Torque (Nm) Fig. 3. Effect of applied torque and gear rotational speed on the tooth loading rate.
4.2. Hysteresis heating
Fig. 5. Gear tooth surface temperature of glass fiber reinforced Nylon 6 gears tested at different speeds at 8 MPa gear tooth bending stress.
In the case of metallic gears tooth deflections are negligible and hence the effect of material hysteresis due to the frequency variation is negligible [28]. The polymer gear tooth deforms severely because of the low gear tooth stiffness (about 100 times less than that of metal). Repeated gear tooth loading and subsequent deformation of gear tooth contributes to hysteresis heating [31–33]. The heat generated in gears is due to friction between the mating gear teeth and hysteresis effects. The equilibrium of generated and dissipated heat in the gear drive determines the net temperature of the test gear [32]. The surface temperature of test gear, which is the net equilibrium between heat generation and heat dissipation, is measured in the current investigations. This on-line measurement of gear tooth surface temperature during testing shows an initial increase in temperature, which stabilizes after a certain period (Figs. 4 and 5). The heat generated due to friction as well as hysteresis loss increases with increase in gear rotational speed. The gear tooth surface temperatures measured during testing of unreinforced Nylon 6 gears at 0.8 Nm torque shows a rise in temperature with the increase in gear rotational speed (Fig. 4). The behavior of glass fiber reinforced Nylon
gears also shows similar trend but the rise in surface temperature due to the increase in gear rotational speed is comparatively less than that at unreinforced gears (Fig. 5). Addition of glass fiber increases the gear tooth stiffness [24] and hence less gear tooth deflection occurs for the same loading condition. Hence the heat generation due to material hysteresis losses is less. In addition due to superior thermal conductivity of the glass fiber reinforced material [24] better heat dissipation occurs. Both the unreinforced and reinforced gears show only a marginal rise in surface temperature due to the increase in gear rotational speed. No sudden rise in temperature due to the increase in gear rotational speed is observed, which indicates that no change in the failure mode can be expected due to the change in speed. Figs. 6 and 7 show the measured surface temperature of unreinforced and glass fiber reinforced Nylon gears tested at various stress levels at 1200 rpm. At a particular stress level, glass fiber reinforced Nylon 6 gears shows less surface temperature than unreinforced Nylon 6 gears. For both the test gears the net surface temperature of gears increases
Fig. 4. Gear tooth surface temperature of unreinforced Nylon 6 gears tested at different speeds at 8 MPa gear tooth bending stress.
Fig. 6. Variation of the gear tooth surface temperature of unreinforced Nylon 6 gear tested at 1200 rpm at different stress levels.
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increases the surface temperature of gear. On-line measurement shows also a sudden rise in temperature after some time at certain loading condition, which clearly indicates that magnitude of stress severely influence the mode of failure. Correlation of surface temperature of gear on failure mode and gear performance is discussed in the following section. 4.3. Gear performance and damage mechanisms
Fig. 7. Variation of the gear tooth surface temperature of glass fiber reinforced Nylon 6 gear tested at 1200 rpm at different stress levels.
with increase in stress levels. At 25 and 30 MPa tooth bending stress tests, there was a continuous rise in the temperature until gear failure was noticed. Whereas at 8, 15 and 20 MPa test bending stress levels, after 0.1 million of life cycles, no rise in surface temperature observed. The increase in gear tooth bending stress level considerably
Gear rotational speed influences the net surface temperature of both the unreinforced and glass fiber reinforced Nylon gears. But no significant difference in the failure mode was observed due to the variation of speed at a particular stress level in the tests conducted. However, the failure mode is severely influenced by the magnitude of stress experienced by the gear tooth. The optical photographs of the failed unreinforced Nylon gears tested at different gear speeds and stress levels are shown in Fig. 8 (a–f). Gear tooth root cracking and tooth wear were observed in gears tested at all rotational speeds and at low gear tooth bending stress, 8 MPa (Fig. 8a and b). However beyond the applied bending stress of 8 MPa, a significant plastic
Fig. 8. (a–f) Failure morphology of unreinforced Nylon 6 gears tested.
S. Senthilvelan, R. Gnanamoorthy / Materials and Design 28 (2007) 765–772
deformation was observed (Fig. 8c–f). Significant temperature rise at high stress levels and poor thermal conductivity of the unreinforced material leads to severe temperature induced plastic deformation. In the case of glass fiber reinforced Nylon 6 gears, the increased resistance to thermal deformation causes gear tooth deformation only above bending stress of 20 MPa (Fig. 9(a–f)). Gear tooth wear and root cracking similar to unreinforced gear was observed in gears tested at 8 MPa and 15 MPa stress levels at all rotational speeds (Fig. 9a–d). At high stress levels (above 15 MPa tooth bending stress) visible plastic deformation of the tooth was observed (Fig. 9e and f). Figs. 10 and 11 show the gear tooth-bending stress plotted against the number cycles run for the unreinforced and glass fiber reinforced gears, respectively. Test results indicate a significant performance difference at different speeds, which is normally not observed in metallic gears. In both the unreinforced and glass fiber reinforced gears, only at higher stress conditions, influence of speed on gear performance is observed. This behaviour is well coincident with the trend indicated by the loading rate at various speeds (Fig. 3). Loading rate significantly influences unreinforced
35 Tooth bending stress (MPa)
770
600 rpm 1000 rpm
30
800 rpm 1200 rpm
25 20 15 10 5
Unreinforced Nylon 6 gear
0 1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
Number of cycles (N)
Fig. 10. Influence of gear rotational speed on the fatigue behavior of unreinforced Nylon 6 gear.
and glass fiber reinforced Nylon gear performance only at high loads. Fig. 10 shows the performance of unreinforced Nylon gears at different speeds, 600, 800, 1000 and 1200 rpm. At low stress levels (8 MPa), no influence of gear rotational speed on gear performance is observed. No thermal or thermal associated failures were observed and only tooth
Fig. 9. (a–f) Failure morphology of glass fiber reinforced Nylon 6 gears tested.
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Acknowledgments
35 Tooth bending stress (MPa)
771
30
600 rpm
800 rpm
1000 rpm
1200 rpm
25 20
Authors acknowledge the financial support provided by the Robotics and Manufacturing Division, Department of Science and Technology, India.
15
References
10 5
Glass fiber reinforced Nylon 6 gear
0 1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
Number of cycles (N)
Fig. 11. Influence of gear rotational speed on the fatigue behavior of glass fiber reinforced Nylon 6 gear.
wear and non propagating tooth cracks were observed at all the investigated gear speeds under low stress conditions (Fig. 8a and b). At high stress conditions (above 8 MPa), thermal associated failures such as tooth deformation and tooth folding were observed (Fig. 8c–f). At high test stress conditions (beyond 8 MPa) high loading rate and heat generation reduces gear tooth strength and hence with increase in gear rotational speed, the gear life reduces. Fig. 11 shows the gear tooth bending stress vs number of cycles run for glass fiber reinforced Nylon 6 gears. Glass reinforced gear doesn’t show a significant performance variation due to the gear rotational speed both at 8 and 15 MPa stress levels. Due to the improved mechanical property and resistance to thermal deformation of glassreinforced gears, no thermal damages were observed even at 15 MPa stress level. Beyond 15 MPa stress levels reinforced gear also shows thermal failures (Fig. 9e–f). Due to the superior mechanical strength than unreinforced material, only beyond 15 MPa stress level, glass fiber reinforced Nylon 6 gear shows significant influence of loading rate on gear performance. At a particular stress level and gear rotational speed, the glass reinforced Nylon 6 gear shows improved fatigue life than unreinforced Nylon 6 gears. 5. Conclusions The performance of injection molded Nylon 6 and glass fiber reinforced Nylon 6 gears was investigated at various gear rotational speeds and applied stress levels. Gear rotational speed influences the performance of both unreinforced and glass reinforced Nylon 6 at high stress levels. At low stress levels, gear tooth root cracking and gear wear were the dominant failure modes and no influence of speed on gear life is observed. At high stress levels, the local temperature rise leads to weakening of gear material and reduces the performance. Increasing the rotational speed considerably increases the loading frequency, and increases the surface temperature of gears, which leads to the reduction of gear life. The applied stress level influences the failure mechanism of the polymer composite gears.
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