# Need some tips in designing a deep ratio helical gear pair

Hi,

For a final drive of a light commercial truck, I have to design a final drive helical gear pair. The expected ratio is 8.2. The centre distance is 134 mm. The input max. torque is 120 Nm. I have sized few combinations.

I have a feeling that this ratio is too deep. Pl. share me your opinions and views on this. I mainly need few check-points while designing such a deep ratio helical gear pair. Thanks.

## Answers and Replies

Baluncore
Science Advisor
2021 Award
What do you mean by the ratio being too "deep".
The final drive usually refers to the differential.
Do you need a 90° angle between the gear shafts?

The pinion is usually hypoid, running on a simple flat faced tooth crown wheel.

Here is a table of ratios that can be used. Avoid common ÷ divisors.
Code:
Hunting Tooth.    Differential Gear Ratios without Common Factors.

Pinion    5      6      7      8      9     10     11     12     13
Crown

20           ÷ 5    ÷ 2   2.857   ÷ 4   2.222   ÷ 10  1.818   ÷ 4   1.538
21          4.200   ÷ 3    ÷ 7   2.625   ÷ 3   2.100  1.909   ÷ 3   1.615
22          4.400   ÷ 2   3.143   ÷ 2   2.444   ÷ 2    ÷ 11   ÷ 2   1.692
23          4.600  3.833  3.286  2.875  2.556  2.300  2.091  1.917  1.769
24          4.800   ÷ 6   3.429   ÷ 8    ÷ 3    ÷ 2   2.182   ÷ 12  1.846
25           ÷ 5   4.167  3.571  3.125  2.778   ÷ 5   2.273  2.083  1.923
26          5.200   ÷ 2   3.714   ÷ 2   2.889   ÷ 2   2.364   ÷ 2    ÷ 13
27          5.400   ÷ 3   3.857  3.375   ÷ 9   2.700  2.455   ÷ 3   2.077
28          5.600   ÷ 2    ÷ 7    ÷ 4   3.111   ÷ 2   2.545   ÷ 4   2.154
29          5.800  4.833  4.143  3.625  3.222  2.900  2.636  2.417  2.231

30           ÷ 5    ÷ 6   4.286   ÷ 2    ÷ 3    ÷ 10  2.727   ÷ 6   2.308
31          6.200  5.167  4.429  3.875  3.444  3.100  2.818  2.583  2.385
32          6.400   ÷ 2   4.571   ÷ 8   3.556   ÷ 2   2.909   ÷ 4   2.462
33          6.600   ÷ 3   4.714  4.125   ÷ 3   3.300   ÷ 11   ÷ 3   2.538
34          6.800   ÷ 2   4.857   ÷ 2   3.778   ÷ 2   3.091   ÷ 2   2.615
35           ÷ 5   5.833   ÷ 7   4.375  3.889   ÷ 5   3.182  2.917  2.692
36          7.200   ÷ 6   5.143   ÷ 4    ÷ 9    ÷ 2   3.273   ÷ 12  2.769
37          7.400  6.167  5.286  4.625  4.111  3.700  3.364  3.083  2.846
38          7.600   ÷ 2   5.429   ÷ 2   4.222   ÷ 2   3.455   ÷ 2   2.923
39          7.800   ÷ 3   5.571  4.875   ÷ 3   3.900  3.545   ÷ 3    ÷ 13

40           ÷ 5    ÷ 2   5.714   ÷ 8   4.444   ÷ 10  3.636   ÷ 4   3.077
41          [B]8.200[/B]  6.833  5.857  5.125  4.556  4.100  3.727  3.417  3.154
42          8.400   ÷ 6    ÷ 7    ÷ 2    ÷ 3    ÷ 2   3.818   ÷ 6   3.231
43          8.600  7.167  6.143  5.375  4.778  4.300  3.909  3.583  3.308
44          8.800   ÷ 2   6.286   ÷ 4   4.889   ÷ 2    ÷ 11   ÷ 4   3.385
45           ÷ 5    ÷ 3   6.429  5.625   ÷ 9    ÷ 5   4.091   ÷ 3   3.462
46          9.200   ÷ 2   6.571   ÷ 2   5.111   ÷ 2   4.182   ÷ 2   3.538
47          9.400  7.833  6.714  5.875  5.222  4.700  4.273  3.917  3.615
48          9.600   ÷ 6   6.857   ÷ 8    ÷ 3    ÷ 2   4.364   ÷ 12  3.692
49          9.800  [B]8.167[/B]   ÷ 7   6.125  5.444  4.900  4.455  4.083  3.769

50           ÷ 5    ÷ 2   7.143   ÷ 2   5.556   ÷ 10  4.545   ÷ 2   3.846
51         10.200   ÷ 3   7.286  6.375   ÷ 3   5.100  4.636   ÷ 3   3.923
52         10.400   ÷ 2   7.429   ÷ 4   5.778   ÷ 2   4.727   ÷ 4    ÷ 13
53         10.600  8.833  7.571  6.625  5.889  5.300  4.818  4.417  4.077
54         10.800   ÷ 6   7.714   ÷ 2    ÷ 9    ÷ 2   4.909   ÷ 6   4.154
55           ÷ 5   9.167  7.857  6.875  6.111   ÷ 5    ÷ 11  4.583  4.231
56         11.200   ÷ 2    ÷ 7    ÷ 8   6.222   ÷ 2   5.091   ÷ 4   4.308
57         11.400   ÷ 3   [B]8.143[/B]  7.125   ÷ 3   5.700  5.182   ÷ 3   4.385
58         11.600   ÷ 2   [B]8.286[/B]   ÷ 2   6.444   ÷ 2   5.273   ÷ 2   4.462
59         11.800  9.833  8.429  7.375  6.556  5.900  5.364  4.917  4.538

60           ÷ 5    ÷ 6   8.571   ÷ 4    ÷ 3    ÷ 10  5.455   ÷ 12  4.615
61         12.200 10.167  8.714  7.625  6.778  6.100  5.545  5.083  4.692
62         12.400   ÷ 2   8.857   ÷ 2   6.889   ÷ 2   5.636   ÷ 2   4.769
63         12.600   ÷ 3    ÷ 7   7.875   ÷ 9   6.300  5.727   ÷ 3   4.846
64         12.800   ÷ 2   9.143   ÷ 8   7.111   ÷ 2   5.818   ÷ 4   4.923
65           ÷ 5  10.833  9.286  [B]8.125[/B]  7.222   ÷ 5   5.909  5.417   ÷ 13
66         13.200   ÷ 6   9.429   ÷ 2    ÷ 3    ÷ 2    ÷ 11   ÷ 6   5.077
67         13.400 11.167  9.571  [B]8.375[/B]  7.444  6.700  6.091  5.583  5.154
68         13.600   ÷ 2   9.714   ÷ 4   7.556   ÷ 2   6.182   ÷ 4   5.231
69         13.800   ÷ 3   9.857  8.625   ÷ 3   6.900  6.273   ÷ 3   5.308

Thank you Baluncore. This is for a final drive inside transaxle with input and output on one plane. Hence it is a helical gear pair.

My fear is if the targeted ratio 8.2 is too high to achieve... If we assume 49 teeth for bull gear and 8 for pinion teeth, do I have to anticipate any specific problems? Thanks again!

Baluncore
Science Advisor
2021 Award
You will have a problem. A basic helical gear is designed using the same fundamental rules as those of a spur gear. The number of teeth on the pinion will be a minimum determined by tooth profile, maybe about 13, which will require the bull gear to have 106 or 107 teeth.

The advantage of the 90° hypoid is the very low number of teeth needed on the pinion while still avoiding tooth interference. I would expect a light truck to have a final drive ratio of about 4.7, maybe slightly lower with a torque converter. You should check your calculation of the 8.2 ratio. You should also check the size and possibility of reducing the road wheel diameter.

If you examine examples of the ratios used by the gear manufacturer in a manual gearbox, you will find the larger gear (on the mainshaft) is driven by the first gear pinion (part of the layshaft/countershaft). The tooth count on the first gear pinion will be very close to what is achievable on your final drive.

Hi Balluncore,
Sorry if I am beating about the bush... What if I use 16t in pinion and 131t in bull gear? Since I have a good centre distance of 134mm, I can have a transverse module of 1.8mm (approx.). If my calculation shows there is no undercut, what do you feel about this combination.
Thanks for your helps in many of my posts. :)

Baluncore
Science Advisor
2021 Award
I feel the individual teeth will be too small to handle the expected torque. The gear will have to be very wide.
You need to examine a manual gearbox 1'st gear pinion from a vehicle with similar performance.

1 person
Yeah, I will do that. I will try to find if a ratio more than 6 is used anywhere else as well. :)