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LIGHTWEIGHT DESIGN BEVEL GEAR DIFFERENTIAL WITHOUT CAGE Bevel gear differentials are an application in which a technical solution has been used virtually unchanged for many decades. The increasing demands with regard to the weight and installation space of a bevel gear differential are met with the innovative structure of the NT LightDiff by Neumayer Tekfor. As a result, it can make a major contribution to achieving efficiency and CO2 targets. Here the weight advantage of 25 % is achieved through the substitution of the differential cage with a lateral extruded bevel-gear carrier.
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AUTHORS
DR.-ING. FALKO VOGLER is Chief Engineer of the Research and Development Department for Transmission Components at Neumayer Tekfor Holding GmbH in Hausach (Germany).
DIPL.-ING. CHRISTOPH KARL is Product Manager in the Research and Development Department for Transmission Components at Neumayer Tekfor Holding GmbH in Hausach (Germany).
MOTIVATION
Automotive suppliers already provide support during the development of products with the objective of achieving a lightweight design practical from the standpoint of production and efficiency. The following central statement characterises the requirements for a modern compensating gearbox [1], called differential: The axle drive must more efficiently transfer more power with lower weight and smaller installation space. The new differential NT LightDiff by Neumayer Tekfor fulfils these goals and introduces the proven bevel gear differential to the altered challenges of the „hybrid age“. Here the proven method for speed compensation with bevel gears is retained. TECHNICAL SOLUTION
A differential compensates distortion of a vehicle axle by compensating speed differences unconstrainedly between the wheels, for example when driving in curves, and distributing the torque equally to both wheels [2]. Today‘s differentials are usually designed according to the same concept, which is centred around the differential cage [3]. This cage holds all other components of the differential and transfers the torque from the ring gear to the differential pin. With the fundamentally new concept of the lightweight design differential, ❶, presented here, it is possible to reduce the weight by up to 25 %. The basis for this is the bevel-gear carrier, which replaces the differential cage. In this differ-
ential, it assumes the tasks of the differential cage, that means supporting and guiding the bevel gear set and the differential pin, but also transferring the torque. The bevel-gear carrier is formed nearnet-shape with lateral extrusion. It is machined at the bearing points for the bevel gear set and then nitrided. The manufacturing of the bevel gears does not differ from that used for a conventional differential. The distance pieces are manufactured near-net shape through the combination of hot and cold forming and finish-machined at minimal expense. The machining of the ring gear is simplified, as in addition to the toothing, only the inside diameter is a functional surface. In assembly the focus of the pinion gears is adjusted with thrust washers before being joined with the distance piece on the bevel-gear carrier. The subassembly is laid in the ring gear and welded on with an electron beam. Finally, the side bevel gears are mounted. For the results described and shown quantitatively in the following, an actual application with a nominal axle torque of 2200 Nm was assumed. Compared to the reference, a reduction in the bearing spacing by 44.5 mm to 62.5 mm resulted for this application. While the conventional differential weighs 7 kg, the NT LightDiff is just 5.5 kg, which is equivalent to savings of 21.5 %. Furthermore, additional material can be saved and the installation space can be reduced further on with a corresponding design of the gearbox casing due to the reduced bearing spacing so that the mentioned 25 % can be possible. ❷ shows the two differ-
❶ Concept and parts of the lightweight design differential 06I2013
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entials in an installation space comparison. It can easily be recognised here that the bearing point on the short differential side can almost be retained, however the differential is significantly shortened on the long side. In addition to its use as a spur gear differential, as is usually the case with front-wheel drives with a transverse engine, the differential can also be designed as a bevel-gear axle drive. Due to the compact dimensions of the NT LightDiff, it might also be used as a centre differential. STRESS-RELATED DESIGN
Like the conventional differential, the NT LightDiff is subject to loading by the forces resulting from tooth contact. The force components in the direction of the circumference and along the axis of rotation result in a bending load on the thin extrusions of the bevel-gear carrier. This stress is mainly dependent on the following factors: Torque, pitch circle diameter, helix angle of the toothing and bending modulus of the extrusions. ❸ shows the results of a static FE analysis of the lightweight differential. It describes the strain on the assembly during loading with the nominal axis torque. As it can be recognised in ③ with red colour, a concentration of tension results in the area of the transition between the thick and the thin extrusions on the bevel-gear carrier. Geometric and material changes were implemented to optimise the durability of the component. The shape was adapted
❷ Comparison of the more compact NT LightDiff and the reference differential coloured in blue (reduction in the bearing spacing by 44.5 mm to 62.5 mm)
according to bionic findings. As a result, loading decreased without disadvantages for the formability. By using an alternative material, it was possible to increase the flexural fatigue strength by 25 %. Cold forming increases the loading capacity of the material, as the material fibres remain undamaged and strain hardening occurs [4]. The residual compressive stresses introduced by the nitrogen carbide layer required for the plain bearing additionally increase the loading capacity of the component in the surface region [5] in which the greatest bending stress occurs. This enables the full lightweight design potential of the concept to be utilised through the skilful design of the cross-sectional transitions with the choice of a suitable material and manufacturing processes matched to the incurred loads.
❸ Incurred stress at nominal torque, determined in the FE analysis
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The dimensioning of the bevel-gear carrier based on these relationships is a major factor for specifying the overall size of the lightweight design differential. The dimensions of the extrusions correspond to the inside diameters of the bevel gears. This is the starting point for the design of the bevel-gear toothing. Its production using forming processes with a suitable toe and heel connection enables high power densities to be achieved here as well [6]. STATIC COMPONENT BEHAVIOUR
The experimental testing of the static component behaviour visualises the deformations in the entire system and enables a comparison to the findings gained from the simulation results. The pitch circle diameter of the ring gear is 190 mm. At an axis torque of 2200 Nm, the toothing data result in the following forces: : in the circumferential direction Ftan = 23,400 N : in the axial direction Fax = 10,750 N : radially to the axis Frad = 9250 N. The NT LightDiff shown here is mounted by means of modified tapered roller bearings of the 32009 series, like those also used in the conventional differential. The contact angle of the taper roller bearings was adapted to the increased axial loading. ❹ shows the curve of bearing load and load ratio over the axle torque in the vehicle’s acceleration mode. The spreading forces from the bevel gear set act directly on the bearing points in the NT LightDiff, allowing the bearing preload to be considerably
reduced compared to the conventional solution. On the other hand, large spreading forces occur at the rolling bearings at high torques. In loaded condition, the axial force component from tooth meshing results in an one-sided force addition. The symmetrical design and the altered transfer of the axial forces lead to a constant ratio of radial to axial force components on the NT LightDiff, enabling the optimal adjustment of a rolling bearing to the application. The ratio of the bearing loads which occurs with the NT LightDiff proves to be particularly advantageous for the use of angular contact ball bearings, which generate lower bearing friction compared to the tapered roller bearings [5], however have larger dimensions with the same load rating. The installation space and weight reductions result in a change in the system stiffness. To determine this, the system was statically clamped to a gearbox test bench in various positions and the shifting and inclination of the differen-
tial measured in the process. The axial and radial drift and the tilting are measured in the overrun and acceleration modes from a torque of 0 Nm up to the nominal axial torque of 2200 Nm. The axial drift of the NT LightDiff is shown in excerpts in ❺. At 1100 Nm, with 0.312 mm (FEA 0.285 mm) the axial shifting of the differential, which is not critical for tooth meshing, is higher than that of the conventional differential (0.06 mm). The inclination of the toothing of 11´ proved not to be disturbing or conspicuous in the following tests. Comparable values are known from other applications. DYNAMIC COMPONENT BEHAVIOUR
Prior to the dynamic testing of the assembly, the bending fatigue strength of the bevel-gear carrier was determined on a resonance test bench. For this purpose, the bevel-gear carrier with a weldedon ring gear was clamped in at the thick
A
B
A
B
Conventional differential
NT LightDiff
60,000
50,000
Bearing Bearing Bearing Bearing
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A (conv.) B (conv.) A (NT LightDiff) B (NT LightDiff)
Ratio between axial and radial load
1.400 1.200
Load ratio [-]
40,000 Bearing load [N]
extrusions. An axial basic load was applied in the pitch point of the toothing, which was overlaid with a load amplitude. For this purpose, the multi-axle stress state familiar from the FE analysis, which was converted to a single-axle state, was utilised for this purpose. The bending stress of the bevel-gear carrier created per oscillation in this way illustrates the loading of the bevel-gear carrier during one rotation of the differential. The evaluation of this test showed that the component‘s stress-number diagram is almost identical to the stressnumber diagram of the material, and can therefore be utilised as a design criterion. ❻ shows the stress/number diagram (S/N or Wöhler diagram) of the material with the test results. The evaluation of the differential in various driving states with a changing load and the durability is carried out dynamically on a gearbox test bench. The „towing test“ simulates vehicle operation with an emergency wheel. In the
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1.000 0.800 0.600 0.400
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Bearing A (NT LightDiff) Bearing B (NT LightDiff) 400
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1000 1300 1600 1900 2200 2500 Axle torque [Nm]
❹ Curve of the bearing load (left) and load ratio (right) over the axle torque for a comparison of the NT LightDiff and a conventional differential 06I2013
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μ-split test, the behaviour of the differential with suddenly changing ground conditions is tested. The fatigue properties are determined both in the full-load driving tests and with the endurance tests. Depending on the application, additional tests are conducted according to the customer‘s requirements.
Sensor 1
CONCLUSION AND OUTLOOK
Displacement [mm] -0.400
-0.300
-0.200
0 0.000
-0.100
Sensor 2 0.100
0 Nm 250 Nm Sensor 1
500 Nm 750 Nm 1000 Nm 1150 Nm
Sensor 2 Sensor 3 -75
Sensor 3
❺ Displacement and axial drift of the lightweight design differential under static load; measured at the three measuring locations with sensor 1, 2 and 3
Crack 2
The new differential concept, that means the NT LightDiff from Neumayer Tekfor, demonstrates a significant lightweight design advantage compared to conventional differentials. For an application with an axle nominal torque of 2200 Nm it was possible to prove a weight reduction by 21.5 %, operation and durability in extensive tests. Here the weight advantage is achieved through the substitution of the differential cage with an extruded bevel-gear carrier. Both in the FE analyses and in the experimental tests, the axial force occurring in the spur toothing proved to be a decisive characteristic for the component design. After having carried out applications as a spur gear differential, currently examinations are being conducted on the use as a bevel-gear axle drive. In addition, the potential as a centre differential, including with a locking effect, is also being considered.
Oscillation amplitude [N/mm2]
1200 1000 Crack
Fatigue-tested specimen without rupture
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Crack 3
Specimen 100 % load
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Specimen 80 % load
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Specimen 65 % load
0 1.0E+03
Specimen 75 % load S/N curve of 16 MnCr5 1.0E+04
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No. of load cycles [-]
❻ Determination of a component’s stress-number diagram (Wöhler) for the bevel-gear carrier
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1.0E+09
REFERENCES [1] Naunheimer, H.; Bertsche, B.; Lechner, G.: Fahrzeuggetriebe. Berlin/Heidelberg: SpringerVerlag, 2007 [2] Leske, A.; Schäffler, R.: Getriebe. Würzburg: Vogel-Buchverlag, 1994 [3] Kirchner, E.: Leistungsübertragung in Fahrzeuggetrieben. Berlin/Heidelberg: Springer-Verlag, 2007 [4] Doege, E.; Behrens, B.-A.: Handbuch der Umformtechnik. Berlin/Heidelberg: Springer-Verlag, 2008 [5] Niemann, G.; Winter, H.; Höhn, B.-R.: Maschinenelemente. Band 1. Berlin/Heidelberg: Springer-Verlag, 2005 [6] Gutmann, P; Zitz, U.: Leicht und hoch belastbar: Präzisionsgeschmiedete Getriebeteile. In: Umformtechnik 33 (199), No. 4, pp. 16 – 18
