Differential Gear

In close cooperation with International Space Education Institute a new Differential Gear was developed for NASA Human Exploration Rover Challenge. It has been stated to design a new differential gear for pedal driven moon rover within the participation on actual challenge. This blog post is basically a description of the Best Report Award, to which this design report was applied and I would like to highlight some most significant moments of development process, as well as other interesting things in rover construction generally.

Process

Process of constructing any parts includes next steps: draft design with different variants, rough calculations, 3D modeling, stress analysis, control and production. It is the so-called product life cycle and this happens in aerospace industry as well. I would like to start with description of our one of the main part in the vehicle – Differential Gear. That gear already was changed in the past and that what was constructed is 3rd generation. We decide to change the cups which hold the shafts and both fastened to the middle ring. They should be produced very fast, be light and stress stable. Molding technology was considered to use. Anytime we were guided by the principle “KISS – Keep It Simple, Stupid”. Constructing process was began from choosing of appropriate material. The following four materials has been taken as assumed with next stress at brake values:

  • FORTRON 1140L4 – PPS-GF40, 195 MPa
  • TROGAMID T5000 nc (nf) – PANDT/INDT – Evonik Industries AG, 90 MPa
  • Makrolon 2405 – PC – Bayer MaterialScience, 65 MPa
  • SCHULAMID 66 GF 30 H – PA66-GF30 – A. Schulman GmbH, 185/120 MPa

After the rough calculations of the forces in the Differential Gear (fig. 1, 2) it was clear that axial force in the shafts is one of the main factors of stability. When the torque on the gear is 100Nm (double as critical was taken into account, real torque is 50Nm), the axial force pulled tooth wheels apart is equal 550N. That was the first factor affected on the gear.

Another factor is bending moment. Due the intensive rotating of the pedals on the race from the both drivers and with the critical torque 100Nm, we get that the chains from the both Rohloff Gears act on the Differential Gear as resulted force equal 1062N (fig. 3) and pull it up. After that a model with required parameters was designed in CAD and analyzed with FEM for the stress (fig. 4). Maximal stress von Mises was 15,5 MPa. So that was not so critical for us.

Figure 4. Cup shear analysis

The results were nice and we decide to choose Schulamid 66 GF 30 H for our differential cup. Other materials were either too strong or too weak. The molding process was fully simulated at our computer, we got the perfect results, and to be exact we came to nothing more than two molding parts, core and cavity, without any secondary devices for injection. Injection time, including cooling step, for whole operation was about two seconds (fig. 5).

Figure 5. Injection simulation

After that  a core and a cavity for milling it at the molding factory were designed (fig.6). Also was the variant to produce this cup with radial ribs (fig. 7) for specified stability, but it was not necessary, because that material we chose was reinforced with glass fiber for 30% and heat stabilized. That’s why its mechanical properties were enough, to do it without radial ribs.

All the model files were sent to the molding company 1st Mould GmbH, who kindly sponsored the production of these parts. One of our students was there to monitor the process and went through all steps taking a part in production. That was her practical work. They chose how many injection nozzles should be for proper liquid material distributing, have simulated injection and milling process once again (fig. 8), to be sure. Than the core and the cavity were milled and as result those cups were molded (fig. 9).

After the parts were ready the time has come to assemble the Differential Gear. As we expect the parts were a bit smaller, because of shrinkage in time of cooling process. Press fits were no more “press fits”, and some another places lost their sizes. But anyway we have got it assembled :)

In process of discussing and prototyping one following idea was born, to make in future a straight differential gear (fig. 10). In this construction it is not necessary to observe the point of intersection the lines from conic bevel gears and pinions (pitch apex), what we actually have now. But of course that new design has advantages as well as disadvantages. Maybe it will be designed and manufactured it in nearest future.

 

Figure 10. New prototype of differential gear

Technical challenge

In that part of our report we will describe the technical challenges we faced developing or improving the vehicle. Most of technical challenges were concerned with Differential Gear designing.

The molding technology allows us to design the differential cup any design we want. That’s why we tried to design that cups as thinner and the same time as closer to the bevel and pinion gears as possible (fig. 11). Space reducing and minimalism are preferred. Reading a lot of technical literature we got to know a lot about molding, such as recommended radiuses, thickness of the walls and preferred values of the sizes.

Figure 11. Cup design

So we met the first problem, where to place the set screw fixes bevel tooth wheel on the outlet shaft again axial displacement. We found a solution to fix it with retaining ring in at the end of the shaft.

The problem was then to insert that ring between the shaft and tooth wheel. In the DIN standard there was no appropriate size for such ring. It was either too thick or too big to insert it inside. But, we didn’t watch inch rings. And exactly there were required size and thickness. Therefore we took Truarc retaining ring with fitting sizes (fig. 12, 13).

It allowed us do not process the tooth wheels especially for DIN retaining rings. It means we reduced one turning operation, what in my honest opinion was already not bad.

Next was the difficult to maintain the pitch apex of bevel gear. It means that tooth wheels in conic differential gear must be located only in one definite position (fig. 14). The mistake of previous construction was neglecting that requirement. As consequence the tooth wheel contact spot places were injured with scratches. That is not admissible. How we maintain that requirement we will explain in Construction part of report.

Changing cup construction and minimizing all the parts, we minimize the sealing ring against oil leaking (fig. 15). Everything was good; we took standard sealing ring from CAD database, inserted it and forgot. After that that was problematic to find in internet the shop in Germany and order it. Almost all companies deliver up to 500 rings at once. But, for our test series we need only 10 pieces. That was our headache to buy it. In the end anyway we bought it.

Middle ring in the Differential Gear also undergo a change. Reducing amount of the screws, we vary the holes with thread and set pins around the middle ring, to find a compromise (fig. 16). Sometimes it was difficult to find a periodicity of those holes, and in the same time we must pay attention that the cups should be symmetric from both sides, because it’s not efficient to design two different cups for molding process.

Figure 16. Middle ring

Another challenge is to maintain good assembling ability of the Differential Gear. Calculation of the linear dimension chain is responsible for it. This is one of most important processes in the engineering work. The dimensional chain consists of partial components (input dimensions) and closed component (resulting dimension). There are also different methods to obtain that resulting dimension, such as full interchangeability, partial interchangeability, fitting method and adjusting with help of fixed compensator. We considered fitting method as most easiest. After the calculation we chose the place of closed component between slide bearing and the cup (fig. 11).

We suspected that after the shrinkage of material in time of cooling (molding process) all cup dimensions will be changed. To assemble the Differential Gear we are forced to machine all the cups for 0.5 mm of excess material.

Construction

In this part of our report we will explain step by step the design features and changes we did in construction, and will explain why we did it this or another way, and of course with comparing pictures from previous construction.

Main mistake in previous design were the outlet axles, which were fixed only in one (!) place. It allowed moving them freely in axial direction, and therefore were already described tooth surface injures. The outlet axles were wobbling in the air like outrigger, without required precision. To avoid it we extended the tooth wheel shafts until the anchor in the middle and supplied it with IGUS slide bearings. Thereby we obtained precision of shafts positioning, such as coaxiality and excluded the radial whipping of the shafts and in the same time distributed the surface of the one slide bearing in two bearing supports (compare fig. 17 and 18).

After the race 2012 we found out that the whole Differential Gear was in oil, it was leaking from everywhere. The problem was the place of flat attachment of the cup and the middle ring – one of the greatest technical design mistakes. Also we discovered that the screws located around the cup to fasten all together, from one side were unscrewed. The next greatest constricting mistake we’ve ever seen was “Double screw tightening!” Let’s try to explain what it means.

In each cup were 12 interlaced holes, 6 drilled holes with countersink and 6 thread holes. These cups are located symmetrically relatively the middle ring, and were tightened together with screws through the middle ring (fig. 19). Pulling together could keep continue until end of the days, because tightening up from one side, another side with screws gets weaken. Moreover, were no centering rib, and the cups under the forces were moving relatively each other. As result the screws from one side were completely unscrewed after the race and bent above the frame (fig. 21).

Figure 21. Self-unfastening

For that we exceeded the fixed hours of work with sketches (fig. 22, 23) and different designs, and in the end we killed two birds with one stone – screw problem and leaking. On the figure 20 you can see also the centering rib from both sides and sealing groove for the proofing compound.

For the good centering of the molded parts and against excess displacements we provided two groove pins located radially opposite each from other (fig.24).

In the end we did small cosmetic and esthetic work. For example the bearings mounting place was reduced (fig. 17, 18). It is difficult to say why it was so long in the previous construction, and during the time the deep groove was formed in the aluminum under the bearings, what adversely affected on bearings unmount. Overall sizes of the gear were also modified. It gets smaller, compacter and pretty good looking.