machine design, Vol.3(2011) No.2, ISSN 1821-1259 pp. 105-108

*Correspondence Author’s Address: Slovak University of Technology, Mechanical Engineering Faculty, Nám. slobody 17 812 31 Bratislava, Slovakia, miroslav.veres@stuba.sk

Preliminary note THEORETICAL AND EXPERIMENTAL RESEARCH OF THE HCR GEAR’S CONTACT

STRENGTH

Miroslav VEREŠ1, * - Miroslav BOŠANSKÝ2 - Milan RACKOV3

1,2 Slovak University of Technology, Mechanical Engineering Faculty, Bratislava, Slovakia 3 University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia

Received (25.02.2011); Revised (12.05.2011); Accepted (27.06.2011) Abstract: The paper deals with the problem of contact strength of involute gearing with extended period of engagement, in the literature also known as the HCR gearing (High Contact Ratio). The research was focused on HCR gearing with profile contact ratio coefficient εa≈2. The HCR gearing is not even today sufficiently researched in terms of fatigue and lifetime. Based on experimental tests, it has been found that in the HCR gearings occur differences in the process of creation of pitting, which has direct impact on the gears lifetime. Majority of standard methods and procedures applies for standard involute gearing only. However, these methods can not be directly applied to HCR gearings without any modifications. It relates primarily to material constants experimentally measured in the past. In the paper authors describe all the basic problems concerning the contact load capacity of HCR gearing and these theoretical ideas are supported by results of their own experimental measurements. Key words: HCR gearing, high contact ratio, pitting, contact load capacity 1. INTRODUCTION For the smooth engagement of the gears it is important that a couple of teeth of together engaging wheels remained engaged until the next couple of teeth comes in the engagement, which means that the next tooth sides must be engaged in before the previous sides terminate the engagement. For qualitative and quantitative assessment of this condition’s fulfillment is used so called profile contact ratio coefficient of involute‘s engagement εα. The value εα for conventional involute gearings with straight teeth is in the range 1 < εα <2. 1.1 HCR Gearing

αw

t

pbt

pbt

gara1 rb1

ra2

rb2

pbt

αwt

αwt

pbt

pbtpbt

r 2w

r1

w

Fig.1. Geometry of the involute HCR gearing With the HCR gearings the contact ratio coefficient of involute‘s engagement is at least equal to 2, implying that in the engagement are always at least two pairs of teeth

(Fig. 1), eventually when εα >2 the third pair of teeth as well. For the gear with HCR gearing with εα >2 it can be expected that it has more favorable conditions for engagement in comparison with the standard involute gears. The gear with εα>2 works also in the three pair engagement, which means that along the engaging line the third pair of teeth comes into contact too. Two-and three-pair engagement means higher overall carrying capacity and lower noisiness of the gear.

Fig.2. Shapes of the total power transmitted curves along the contact line in one pair of HCR teeth (3)

These favorable characteristics of the HCR gearings should also show itself in increase of its resistance to fatigue contact damage - pitting, which is one of the main requirements for the design of the gears used e.g. in automotive transmissions. Creation of fatigue damage to

Miroslav Vereš, Miroslav Bošanský, Milan Rackov: Theoretical and Experimental Research of the HCR Gear’s Contact Strength; Machine Design 2011, Vol.3, No.2, ISSN 1821-1259; pp. 105-108

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the teeth sides by pitting directly depends on the gear load. Workload at the three pair engagement divides between 2, respectively 3 pairs of teeth sides instead of one, respectively 2 pairs of sides (standard gearing), so its value decreases (Fig.3).

Fn

n

[ ]%

ga

n

Fig.3. Course of total transmitted power along the path of

contact line in one pair of the HCR teeth Pitting damage is one of the most common types of damage of the teeth sides in the gears. It is caused by contact fatigue and its typical appearance is creation of the small holes on the surface of the operating part of the side of the tooth. Their creation is caused by the gradual accumulation of defects in the subsurface material layer at multiple touch tensions.

Fig.4. Pitting in the HCR gearing 2. PITTING IN THE HCR GEARING According to current knowledge, creation and character of the pitting in the HCR gearing is different from the standard involute profiles. The main reasons are significantly higher slides, longer engagement and different load distribution between the teeth in gear. The area damaged by pitting is in the case of HCR gearings (Fig.4) localized more under the pitch cylinder, is more solid, the pitting is "more progressive", oval shaped and usually affects larger area than pitting generated in standard involute gears (Fig.5). The shape and location of the pitting in the HCR profiles is clearly shown in the figure 4. Due to the larger specific slides at the beginning and the end of the engagement the profiles are

significantly more prone to the creation of the thermal scuffing, which is clearly shown in the figure 4. Profit from a more favorable load distribution along the engagement is partially eliminated by less favorable course of the values of the reduced radius of curvature along the engagement. Due to the longer contact line is its value in the peripheral areas lower, which of course leads to higher values of the Hertz pressure in contact area. Therefore we cannot expect significantly greater resistance of the HCR gearings to the standard gearings with comparable geometric parameters. ÚDTK SjF STU (Institute of Transport Technology and Design, Faculty of Mechanical Engineering) performed extensive experimental tests of HCR gears, which proved this statement.

Fig.5. Standard gear pitting damage

3. EXPERIMENTAL TESTS OF THE HCR GEARING

Tab.1 Basic parameters of the HCR gears samples

Parameters

Name Symb. Unit PINION GEAR

Centre distance a mm 144

Gear ratio i - 2,428

Module m mm 4

Teeth number z - 21 51

Face-width real b mm 15 15

Face-width active bw mm 14

Helix angle β ° 0

Pressure angle α ° 20

addendum *ah - 1,30 1,29

dedendum *fh - 1,70 1,70

Relative values of the basic profile

radius *ρ - 0,212

Addendum modification coefficient x - 0,400 -0,400

Profile contact ratio αε - 2,003

Miroslav Vereš, Miroslav Bošanský, Milan Rackov: Theoretical and Experimental Research of the HCR Gear’s Contact Strength; Machine Design 2011, Vol.3, No.2, ISSN 1821-1259; pp. 105-108

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The purpose of tests of the HCR gears was to provide the limit of fatigue in contact stress σHlim according to the methodology DIN 51354. For this purpose was used the tester with closed-flow performance. Tested, as well as technological gears have been manufactured according to class 6 of the DIN 3962 standard (Determination of tolerances of frontal gears). Mentioned class also meets the requirements of standards for stress testing according to DIN 3990 T5. Basic parameters of the test gears are evident from Table 1. Test gears (Fig.5) were made from not hardened carbon steel of class 12061. Surface roughness of teeth sides of both gears is Ra=0,8 µm

Fig.6. Model and manufactured test HCR gear in gear-box

For lubrication was chosen the hypoid gear oil PP 90H considering the high pressures in the gears. In addition to its good resistance to high loads, it also prevents thermal scuffing. Due to the lower circumferential speed of gear (v = 3.18 m/s) the wading lubrication was used. The obtained results of experimental measurements are sorted by size of burdensome pinion torque Mk shown in tab. 2. According to the input values from Table 2 was plotted dependence log Hσ - log N and extrapolating to N = 5.107 cycles also found between the fatigue stress at the contact (Fig. 7).

2,60

2,68

2,76

2,84

2,92

3,00

3,08

6,00 6,50 7,00 7,50 8,00 8,50

1200

1000

690

570

470

σH[

]M

PaLo

g

Log N1.106 3.10 6 1.10 7 3.10 7 5.107 1.108 3.10 8

830

Fig.7. Wöhler curve including extrapolated values of σHlim for the number of cycles 7N = 5.10

Tab.2 Input values for plotting the Wöhler curve

According to Figure 7 may be written equation describing the linear part of the Wöhler curve written in the form:

0,1845 4,182= - +y x (1)

Then the limit of fatigue strength of the HCR gearing made from a material 12061.1 in contact is: σHlim = 578,15 MPa and exponent of the corresponding Wöhler curve qH= 5,42. In comparison with the conventional involute gearing it is clear that the exponent of the curve qH is lower in the HCR gearing, since the shape of the tooth is less sensitive to the higher load. 4. CONCLUSION Suitable for strain and working life HCR gear has not been sufficiently researched up-to-date. It has been identified that in HCR gears different process of pitting birth arose while gear processing, having direct impact on gear working life. Majority of standard methods and procedures apply for standard involute gear only. There is no possibility to use mentioned procedures without any further change while applying on HCR gear. It relates primarily to material constant ( limHσ ), experimentally measured in the past.

Rank Mk [Nm] Hσ [MPa] Number of cycles Ni

1s 267,71 1134,82 1 650 000

2s 262,32 1123,34 1 890 000

3s 261,01 1120,53 2 050 000

4s 185,34 944,23 2 240 000

5s 182,30 936,46 2 310 000

6s 189,12 953,82 2 730 000

7s 122,28 766,96 10 370 000

8s 127,11 781,96 11 510 000

Extrapol. - 578,15 50 000 000

Miroslav Vereš, Miroslav Bošanský, Milan Rackov: Theoretical and Experimental Research of the HCR Gear’s Contact Strength; Machine Design 2011, Vol.3, No.2, ISSN 1821-1259; pp. 105-108

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By theoretical analysis and the experimental fatigue tests some differences of pitting damage on the HCR gearings to the standard profiles were confirmed. It was shown that the pitting damage on the gears with a larger coefficient of the duration of involutes engagement is more extensive and initialization fissure is much deeper, as evidenced by metallographic analysis. From this first experience, it is concluded that the HCR gearing has not the expected properties in terms of resistance to pitting damage, i.e. its resistance is according to this limiting state only slightly higher than the resistance of the standard profiles, of course, the usage of this gear is appropriate in terms of noisiness. Even experimental measurements showed that the noise factor of the HCR gearings with coefficient of the duration of involutes engagement εa≈2 is significantly lower than the noise of the gear with a lower value of εα . In the design of the HCR gear one must bear in mind its greater susceptibility to damage by temperature scuffing, which has been confirmed in the experiments and required to use EP (hypoid) oil. ACKNOWLEDGEMENT Contribution has been written as a result of the solution of project’s 1/0189/09 subtask supported by the VEGA grant agency.

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