Gear Coupling

machine design, Vol.4(2012) No.3, ISSN 1821-1259 pp. 167-170

*Correspondence Author’s Address: JS Co “EZTM”, Electrostal, Krasnaya 19, 144000, Russia, [email protected]

Research paper

GEAR COUPLINGS AND SPINDLES WITH EQUAL IN STRENGTH TEETH

Sergey LAGUTIN1, * - Boris UTKIN1 - Alexey KLOCHKOV1 JS Co “EZTM”, Electrostal, Russia

Received (17.08.2012); Revised (02.09.2012); Accepted (18.09.2012) Abstract: To improve the load carrying capacity of gear couplings the cage and hub teeth at their bases have to be equal in bending strength. It can be achieved by two methods: (i) tangential modification of the basic rack with the use of special gear-cutting tool and (ii) addendum modification with the hub teeth cutting by standard worm hobs and the case teeth processing by gear-cutting shapers due proposed method of their outer cone grinding. To improve the teeth wear resistance it is also proposed to perform a longitudinal line of the hub teeth on curves of so named "natural modification", which tooth takes in the wear process. Improvement of the gear couplings geometry enhances its load carrying capacity by 25…40%. Further increase in load capacity and wear resistance can be achieved by induction-hardening the tooth surfaces. All of the proposed processing methods and calculating algorithms are verified by EZTM manufacturing practice Key words: gear couplings, tangential and addendum modification. 1. INTRODUCTION Gear couplings are used to connect shafts and compensate offsets between them. They consist of two shaft hubs with external teeth, which are connected by a cage (usually of two pieces) containing internal teeth (Fig. 1).

Fig.1. Gear coupling Their high torque capacity combines with low inertia of the drive system. Therefore they are widely used in engineering for high speed applications especially when the connecting shafts work with the distortion angle that are up to 1.5° [1]. Gear spindles are gear couplings with intermediate shaft and are used for large offsets of the connecting shafts, for example, to transmit rotation from gearbox to the working stand of rolling mill [2].

EZTM JSC (The Electrostal Heavy Engineering Works) is one of the main Russian producers of gear couplings and spindles for heavy industry. The normalized gear couplings series includes 19 sizes. Gear couplings sizes 1-8 are designed to transmit torques from 1 to 63 kNm. They are manufactured as commercial products in a specialized section. Technical specifications for their manufacture are regulated by Russian GOST R 50895-96, which replaced the preceding GOST 5006-83 and GOST 5006-55. EZTM JSC was actively involved in developing of all these standards. The large gear couplings sizes 9-19 with a load capacity up to 1250kNm, as well gear spindles are manufactured under individual orders. They are used mainly in the drives of rolling mills and other machines within the nomenclature of the company. The reliability of connecting devices significantly affects the reliability of the machine as a whole. In this regard, design and research department EZTM pay constant attention to improving their design. A number of original technical solutions are protected by inventor's certificates [3]. The research work was carried out in collaboration with the IMASH of RAS and other research institutions. A fundamental contribution to the methods of design and analysis of gear coupling devices was made by Prof. E.L. Airapetov and his co-workers [1, 2]. When designing the gear connections such geometrical parameters, materials and methods of hardening are laid, so that at the given external loading conditions - torque, speed and distortion angles to ensure reliability of their work on the criteria of the failure of teeth and the contact destruction of their active surfaces. However, providing these conditions does not rule out a gradual wear and a failure of gear connections, when their teeth reach a critical thickness. Research work to increase the service life of gear connections are constantly going on.

Sergey Lagutin, Boris Utkin, Alexey Klochkov: Gear Couplings and Spindles With Equal in Strength Teeth; Machine Design, Vol.4(2012) No.3, ISSN 1821-1259; pp. 167-170

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2. CONVENTIAL DESIGN OF GEARING Gear coupling can be regarded as involute spur gear with internal teeth and the gear ratio u = 1. Tooth number z and module m are equal for both elements. The traditional coupling main dimensions are shown in Fig. 2.

Fig.2. Basic parameters of gear coupling.

External teeth of the hub are cut by a worm hob with the standard parameters of the basic rack: pressure angle α=20°, an addendum ha1=m, a dedendum hf1=1.25m. The cage teeth are performed with a short addendum ha2 = 0.8 m. On the one hand, it prevents the damage of interference between cage teeth in machine meshing with a gear-cutting shaper. On the other hand, an increased radial clearance equal to Cr ≈ 0.45 m is required in the engagement to compensate for misalignment of the connection parts in the assembly. Pitch diameter of both parts is equal d = m z. The hub is centering in the cage on the tops of the teeth. In this case nominal values of the hub outside diameter and cage root diameter are equal to each other.

da1= df2= m (z+2) (1)

Nominal values of the pitch thickness of the hub and the cage teeth were taken equal to:

S1= S2= πm/2 (2)

To compensate the misalignment of the shaft ends and the pitch errors it is necessary to provide the side backlash between the teeth, that is measured on common normal to the involute profile. According to EZTM norms, in the couplings with barrel-shaped teeth it is set to Cn = 0.12 m and is provided mandatory thinning of cage teeth on the value δn2 = 0.08 m, and the hub teeth on δn1 = 0.04 m. 3. TOOTH LONGITUDINAL MODIFICATION To prevent the damage of edge contact on the face of the hub its external teeth should be performed with a longitudinal modification or barrel-shaped. A conventional shape of longitudinal modification of the teeth is shown in Fig. 3. The outer surface of the hub teeth is performed as the sphere of radius Ra=da1/2. Side profile

of hub teeth in a section tangential to the pitch cylinder is performed on a curve of constant curvature, which is close to the arc of a circle with a radius R.

Fig.3. Hub with barrel-shaped teeth.

Such a modification ensures that the hub teeth are cut with a variable shift of the base rack along the tooth length due to the longitudinal feed of worm hob in a curve of radius Rc related with R by

Rc = R tan α, (3)

The value of Rc has to take in account the pitch diameter, module, crown width and the designed angle of axes distortion. According to the norms EZTM for the gear couplings it was appointed to the range Rc = (1.7…1.8) d, and for gear spindles Rc = 0.5 d. When operating a gear coupling with the axes distortion angle equal to ωа the center of the bearing contact during one revolution moves along the length of the tooth from one side to another and back again, moving away from the middle on the value of xa = R sinωa The shift of the contact causes a significant increase in bending stresses at the teeth base, so reduction of xa by decreasing R is beneficial to the work of the coupling. On the other hand, the decrease in R leads to an increase in contact pressure between the teeth. So optimization of the radius R is a multi criteria problem. Theoretical and experimental study of load distribution between teeth and along each of them showed that the maximum load occurs at a distance xa from the middle plane, and in the middle of the tooth it is minimal. Therefore, in the process of wear of the teeth their side surface changes the original form and has acquired the so-called "natural modification". This profile (Fig. 4) is symmetrical convex curve of variable curvature. In the middle the curvature radius is minimal and in the normal section must be equal to the curvature radius of the face involute profile in the pole of meshing R0 = m z sinα.


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Fig.4. Tooth normal profile of “natural” modification.

As the profile approaches the end faces the curvature radius should increase and reach a maximum at a distance xa from the hub middle. Several options for the equations of curves that satisfy this condition have been proposed. In particular in [2] it was described by the equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛+−

ω= 5

6

3

42515

16tan

aaa

a

xx

xx

xxy , (4)

that provides a zero curvature at the points of application of maximum load at a given distortion angle ωa. More detail on the teeth longitudinal modification considered in [4]. 4. TOOTH TANGENTIAL MODIFICATION The main criterion for determining the load carrying capacity of gear coupling is a bending strength of the teeth, which in turn depends on the bending stresses in the dangerous section at the base of the tooth. In a traditional coupling design (Fig. 2) the hub tooth thickness Sf1 in this section is essentially smaller than the thickness of the cage tooth Sf2. Accordingly, the bending strength of the hub teeth is less than the cage teeth. . The maximum bending stress at the base of the hub tooth σFmax is calculated by the empirical formula [2]:

σFmax= 6 kc kb P/ Sl12, (5)

where P is a peripheral force, kc and kb are factors taking into account the stress concentration and location of load application. It follows that under otherwise things being equal the coupling load capacity, i.e. the value of the permissible transmitted torque is proportional to Sl1

2. So due to equalizing the strength of hub and cage teeth the coupling load capacity can be significantly improved. In the 90-th the complex of theoretical and experimental works on creation of couplings with equal strength teeth was held at the EZTM. The effect of equal bending strength has been achieved by the tangential modification of the basic rack parameters (Fig. 5). When saving all the diametrical sizes of gears the hub tooth pitch thickness S1 was calculated from the condition that Sl1 = Sf2 and depending on the teeth number was increased by the value ∆S = (0.22…0.25) m. The cage teeth pitch thickness S2 was reduced by the same value. Thus, the thickness of Sl1 was increased by 10 - 12%. This decision was protected by RF patent № 1598563 [3]. It formed the basis of the GOST R 50895-96, and when combined with a number of other decisions allowed to increase load carrying capacity in comparison with couplings produced earlier about half as much.

Fig.5. Tooth tangential modification

With manufacturing application the tangential modification required the development and production of special cutting tools: hobs with thinned teeth for cutting the outer hub teeth and broaches with thick teeth for internal cage tooth. For the first eight sizes of serially produced couplings with small modules (m = 2.5…4), the decision was economically feasible because the cost of a tool scheduled replacement quickly paid off. 5. TOOTH ADDENDUM MODIFICATION Large couplings with modules m = 6…14 are produced individually. In this case, the hub teeth should be cut by standard worm hobs with the tooth pitch thickness S0 = 0.5 π m and the tooth addendum ha0 ≥ 1.25m. The desired thickening of the hub teeth may be achieved with addendum modification, i.e. the displacement of the tool at a distance xm from the machining hub axis. The main proportions of the teeth in the middle section of the modified couplings are shown in Figure 6.

Fig.6. Tooth addendum modification


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The cage tooth depth is retained the same as previously: h2 = ha2 + ha1 = 1.8 m. The radial clearance near the hub teeth bottom is reduced to a value of Cr = 0.3 m. It is sufficient under the condition the simultaneous barrel-shaped modification and allows to reduce the hub tooth addendum to a value ha1= 0.85 m and full tooth depth to h1 = h2+ Cr = 2.1 m. The estimated pitch thicknesses of teeth are defined with accepting the minimum side backlash Ct = Cn/cosα as:

S1 = m (0.5π +2x tan α), S2 = π m – S1– Ct (6)

The measuring thickness chords Sy1 and Sy2 are set on a circle of diameter dy = m (z+2x) and are calculated by conventional for involute gearing methods. The same methods determine the thickness Sl1of the hub tooth in a dangerous section of the diameter da2 and the thickness Sf2 of the cage tooth on the root diameter df2. The cage internal teeth are cut with standard gear-cutting shaper. However to improve the gear shaping accuracy and productivity the shaper is grinded on the outer cone so that the final position it processed the bottom and the both sides of the internal tooth simultaneously. The shaper parameters, such as: the teeth number of z0, addendum factor x0, base diameter db0 and outer diameter da0 should be related to the parameters of a processing cage by equation:

α−α−

−−

⋅α⋅

−=−

sin2]inv)[inv(acos

tan2 02

000 m

Cddddzzxx n

af

bb , (7)

Hence, the diameter da0 can be defined for a given factor x, as well as the value of x is found for the selected da0. When choosing a factor x it is necessary to consider also the following technological restrictions. (i) After rounding the outer diameter the shaper tooth height should be at least 2 modules. (ii) The shaper of the same diameter da0 should be used for cages of the same module with different teeth numbers. (iii) The radius of the fillet between the inner circle and involute profile of the cage tooth shall not exceed 0.1 m. During the revising of the coupling standard series, when necessary, the tooth module was also increased. Comparison of previous and modified couplings is presented in Table 1. In this table T is the permissible transmitted torque, kNm. As it is shown it was increased for modified couplings by 25...40%.

Table 1. Technical specifications of couplings sizes 9-19.

Previous design Modified couplings №

m z T m z x T 9 6 36 35 6 36 0.425 50 10 6 56 50 6 56 0.483 71 11 8 48 71 8 48 0.425 100 12 8 54 100 8 54 0.463 140 13 10 48 150 10 48 0.450 200 14 10 54 200 10 54 0.500 250 15 10 58 250 12 48 0.400 350 16 12 56 375 12 56 0.442 500 17 12 64 560 12 64 0.483 710 18 12 72 750 14 60 0.650 1000 19 12 80 1000 14 68 0.700 1250

6. TEETH HEAT TREATMENT For the couplings sizes 1-10 the high frequency current (HFC) hardening is performed by ring inducers at the teeth both of hubs and cages to hardness of 42…51 HRC. For the couplings sizes 11-19 as well as for gear spindles the HFC hardening is performed at the hub outer teeth by module profile inducers. The cage internal teeth of these connections are subjected to bulk hardening up to the hardness of 260…290 HB. At present, the research works are completed on induction hardening of the cage teeth surfaces for connections with a pitch diameter above 400 mm. The technology of HFC hardening is developed. Three module inducers with modules 12, 14 are designed and manufactured. Hardening of cages prototypes is held with measuring the tooth hardness and the cage geometrical parameters before and after hardening. The results are positive. In the near future HFC hardening of cage teeth will be implemented in several sizes of connections, which will increase their load carrying capacity by next 20...25%. 7. CONCLUSION 1. To ensure equal strength of hub and cage thickness of the teeth at their bases should be equalized. In the mass-produced couplings with small modules, this effect is achieved by tangential modification of the basic rack, provided manufacturing of special tools. 2. For individually produced large couplings and spindles a similar effect is achieved by addendum modification of the teeth. In this case, the hub teeth cut by standard worm hobs and cage teeth by gear cutting shapers. 3. The technique of re-grinding of the shaper outer cone is developed, that provides simultaneous processing of the bottom and both sides of the cage internal teeth. 4. The wear resistance of gear couplings is increased by longitudinal modifying the hub tooth, close to the "natural modification" that the teeth get in the process of wear. 5. Improvement of the gear coupling geometry enhances its load carrying capacity by 25...40%. 6. Further increase in load capacity and wear resistance can be achieved by HFC hardening of the cage tooth surfaces to the hardness of 45...50 HRC.

REFERENCES 1. Airapetov E.L., Mirzajanov D.B. (1991) Gear Joint

Couplings. "Nauka. 248 p. (in Russian). 2. Airapetov E.L. et al (2000). Improvement of Gear

Couplings and Spindles EZTM Design. // “Tyazheloje Mashinostrojenie”. No 12, pp. 10 -12 (in Russian).

3. USSR Author's Certificates and RF Patents: № 1037713 (1981); № 1037714 (1981); № 1410611 (1986); № 1423834 (1986); № 1598563 (1990); № 1672781 (1991) Gear Coupling, Int. Cl.: F 16D 3/18.

4. Lagutin S., Utkin B., Klochkov A. (2012). Upgrading of the Geometry of Gear Couplings, Proceedings of 7-th International Symposium, ISBN 978-86-7892-399-9, Kuzmanovich S. (Ed.), pp. 27-30, Balatonfured.

Gear Coupling

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