Strength of plastic helical wheels meshed with various types of worms

Makoto Nomura, Takao Koide, Akio Ueda, Yusuke Ishida, Atsutaka Tamura

(1.Tottori University, 4-101 Minami, Koyama-cho, Tottori680-8552, Japan;

2.Amtec INC., BayTower 2510 1-2-1 Minato-ku Benten,Osaka552-0007, Japan)

Strength of plastic helical wheels meshed with various types of worms

Makoto Nomura1, Takao Koide1, Akio Ueda2, Yusuke Ishida1, Atsutaka Tamura1

(1.Tottori University, 4-101 Minami, Koyama-cho, Tottori680-8552, Japan;

2.Amtec INC., BayTower 2510 1-2-1 Minato-ku Benten,Osaka552-0007, Japan)

Abstract:This study investigates the strength of plastic helical wheels meshed with enveloping and cylindrical worms whose tooth profiles mesh in line contact with helical wheels. Running fatigue tests of plastic helical wheels together with a conventional cylindrical involute worm, a line contact enveloping worm, and a line contact cylindrical worm were conducted. The tooth bearings, tooth temperatures, and fatigue lives of plastic helical wheels meshed with the different worms were examined at various center distances. Main results obtained are as follows : The lives of both line and point contact wheels depended upon backlash, but the lives of line contact wheels are more sensitive to backlash than those of point contact wheels. At the backlash that maximizes the wheel life, the line contact wheels last longer than point contact wheels at smaller applied torques, but the influence of worm type on wheel life reduced at higher applied torque.

Key words:plastic gear; worm wheel; helical wheel; temperature; fatigue life

Plastic worm gears are usually constructed with helical wheels, which are more easily fabricated by injection molding than worm wheels. However, because helical wheels establish point contact with conventional involute worms, their strengths tend to be lower than those of worm wheels, which are meshed in line contact with involute worms. In this study, running fatigue tests of plastic helical wheels together with a conventional cylindrical involute worm (CIW), a line contact enveloping worm (LCEW), and a line contact cylindrical worm (LCCW?) were conducted using a power-absorbing-type worm gear test machine. Based on these results, the effects of worm tooth forms on the strength of the plastic helical wheels were determined.

1Experimental method and apparatus

1.1　Test gears

The test wheels were plastic helical wheels composed of standard grade polyacetal homopolymer (POM-H; POLYPENCO?ACETAL). The helical wheels were hobbed from rod stock. No annealing was performed after hobbing. The worms were a conventional CIW, a LCEW, and a LCCW?. The designs of the LCEW and LCCW?tooth profiles, that establish line contact with helical wheels, were based on the profile of the mating helical wheel. The dimensions and materials of the worms and wheels used in this experiment are summarized in Table 1. Figures 1 and 2 illustrate the shapes of the tested wheels and worms, respectively. The tooth bearing renderings of worm gears were calculated by the simulation software “involute Σ (Worm and Helical Gear)” of Amtec INC. The results are shown in Fig.3.The helical wheels meshed with the LCEW and LCCW established line contacts, and those meshed with CIW established point contacts.

1.2　Experimental apparatus

The plastic worm gears were tested by a power-absorbing-type worm gear test machine. The worm gear test machine is shown in Fig.4.The worm shaft was driven by an electric motor, and a powder brake was used as the power absorber.

1.3　Experimental conditions

Running tests of the worm gears were conducted under grease lubrication conditions at wheel shaft torquesTwh= 14 and 20 N·m and worm rotational speedsnw=600 r/min. These conditions were determined on the basis of the practical use condition. The grease was Daphne grease PG (Idemitsu Kosan Co., Ltd) . The atmospheric temperature was controlled at (23±2) ℃. The tooth temperatures of the plastic helical wheels during operation were measured using an infrared thermo sensor. The fatigue life of the wheel was defined as the number of load cycles at failure.

Table 1　Dimensions of test gears

Fig.1　Shapes of helical wheel/mm

Fig.2　Shapes of worms/mm(a)—CIW; (b)—LCEW; (c)—LCCW?

Fig.3　Tooth bearing rendering(a)—CIW; (b)—LCEW; (c)—LCCW?

Fig.4　Worm gear test machine

2Experimental results and discussion

2.1　Failure mode

The failure mode of helical wheels meshed with various worms under grease lubrication conditions was tooth breakage. Representative photographs of failed teeth are shown in Fig.5.

2.2　Tooth bearings

Fig.5　Failure modes of helical wheels meshed with different worms(a)—CIW; (b)—LCEW; (c)—LCCW?

Fig.6 shows the tooth bearings of helical wheels meshed with the CIW, LCEW, and LCCW?at various circumferential backlashesjt. The tooth bearings were obtained using the red lead primer at various center distances. The number of point contact wheel teeth that simultaneously meshed with the CIW is essentially independent of backlash. By contrast, the number of line contact wheel teeth that simultaneously meshed with the LCEW and LCCW?increases with decreasing backlash.

Fig.6　Tooth bearings(a)—CIW; (b)—LCEW; (c)—LCCW?

2.3　Tooth temperature

Fig.7　Tooth surface temperature of wheels(a)—CIW; (b)—LCEW; (c)—LCCW?

Fig.8　Power transmission efficiencies of worm gears(ηw=600 r/min)(a)—Twh=14 N·m； (b)—Twh=20 N·m

Fig.7 shows how the maximum tooth temperatureθmof the helical wheels meshed with various worms depends on the number of load cyclesNwhat applied torques ofTwh=14 and 20 N·m and rotational speednw=600 r/min. The tooth temperature increase as the number of load cycles increase, up to tooth breakage. For all worm types, the tooth surface temperatures at steady state are independent of the circumferential backlashjtof the wheel and were increasing functions ofTw. The temperature increase is more sensitive to applied torque when the helical wheels were meshed with the LCEW and LCCW?than when meshed with the CIW.

Fig.9　Lives of wheels (nw=600 r/min)

2.4　Power transmission efficiencies

Fig.8 shows how the steady-state power transmission efficiencyηof helical wheels meshed with various worms depended on the number of load cyclesNwh. The applied torques wereTwh=14 and 20 N·m, and the rotational speednwwas 600 r/min. For all worm types, the power transmission efficiencies at steady state are independent of the circumferential backlashjtof the wheel and increase with increasingTw. Regardless of worm type and backlash, the steady-state power transmission efficiencies (ηs) of the helical wheels were approximately 60 and 65% atTwh=14 and 20 N·m, respectively.

2.5　Wheel lives

Fig.9 shows the lives (numbers of load cycles until tooth breakage) of helical wheels meshed with various worms underTwh=14 and 20 N·m, withnw=600 r/min. The lives of helical wheels meshed with various worms depended on backlash. In addition, the lives of helical wheels meshed with the LCEW and LCCW?are more sensitive to backlash than wheels meshed with the CIW. As shown in Fig.9, the optimum backlash that maximized the fatigue life of helical wheels meshed with any worm type isjt=0.05 mm. AtTwh= 14 N·m, the life for the optimum backlash is longer for wheels engaged with the LCEW and LCCW?than for wheels engaged with the CIW. The life of the helical wheel meshed with LCCW?is shorter than that with LCEW, but is considered more insensitive with the shaft angle error. So, we think that the LCCW?with which the life of helical wheel is longer than that with CIW exhibits best properties in the practical use. AtTwh=20 N·m, the fatigue life is dramatically reduced for all worm types, because the tooth root bending stress and the tooth temperature of plastic helical wheels atTwh=20 N·m are higher than those atTwh=14 N·m. The effect of worm type on fatigue life considered to become smaller with an increase of applied torques, because the deformation of the tooth surface becomes lager with an increase of applied toruques.

3Conclusions

The main results of this investigation are summarized below.

(1) The number of teeth that simultaneously meshed with the line contact wheels and worms increase as the backlash decrease.By contrast, the number of teeth meshing with point contact wheels is independent of backlash.

(2) The teeth surface temperatures of helical wheels during operation are independent of backlash and also of worm type at smaller applied torques. At higher torques, the teeth temperature depend on worm type.

(3) The lives of both line and point contact wheels depended upon backlash, but the lives of line contact wheels are more sensitive to backlash than those of point contact wheels. At the backlash that maximizes the wheel life, the line contact wheels last longer than point contact wheels at smaller applied torques, but the influence of worm type on wheel life reduced at higher applied torque.

References

[1] Ishida Y, Koide T, Ueda A,etal. Strength of plastic helical wheels meshed at line contact with worms // Proc of Mechanical Engineering Congress 2013 Japan (MECJ-13). Okayama, Japan: JSME, 2013: S112023 (on CD-ROM).

[2]Amtec INC. Gear Design Program Vol. 15 . Osaka, Japan: Amtec INC, 2012: 106-109.

[3]Koide T, Takahashi M, Takahashi H,etal. Heat generation, power transmission efficiency, and life of plastic worm and helical wheels meshed with steel worm //Proc of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2011). Washington DC, USA: ASME DETC2011-47557, 2011: 507-513.

中圖分類號：TH 140.1

文獻標識碼：A

文章編號：1671-6620(2015)03-0232-04

doi:10.14186/j.cnki.1671-6620.2015.03.015