Differential gear ratio changes

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bimster
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Differential gear ratio changes

Post by bimster » Thu Jul 09, 2009 7:24 pm

Changing the differential gear ratio can be a great performance modification. What follows is a summary for anyone who may be interested.

It’s normally done to increase acceleration. A differential swap takes advantage of the gear ratio in the rear differential to change the wheel torque in a given transmission gear. A higher ratio differential increases the wheel torque. A lower ratio differential reduces the wheel torque.

For example: replacing a 3.07 differential ratio with a 3.46 differential ratio increases the wheel torque by 3.46/3.07 or about 12.7%. That's about a 25 ft-lb increase in wheel troque for a typical 3.0 liter BMW engine...without any engine modifications. Believe me you'll definitely feel that much torque! Non-M BMWs come with a standard differential gear ratio that permits reasonable operation at very high speeds. Those of us who never drive at very high speeds (e.g., on the Autobahn) don’t care much about that end of the performance envelope. What we do care about is the performance available to accelerate through a curve, when merging into faster traffic, when climbing a hill, and so forth.

The differential ratio change is an ideal modification for improving performance in these daily driving situations (or at the track) because it increases wheel torque by the same percentage throughout the entire engine speed range. Mechanically, it provides the same performance improvement as increasing engine displacement by the same percentage, e.g. with the 12.7% torque increase from the example above, a 3.0 liter engine with a 3.46 differential accelerates like a 3.38 liter engine with a 3.07 differential!

Another benefit of larger ratio changes (I drive with a 3.64 ratio that added 18.5% wheel torque) is that they make it quite easy to start off in second gear without slipping the clutch. I can start in 2nd and still comfortably out-accelerate most cars on the road from a stop. I now use 1st gear only for those much rarer situations when I need to get going as fast as possible such as in AutoX events or merging into a tight spot in cross traffic, or when starting off on a steep uphill grade. So, even though the speed ranges of the transmission gears are now shorter, I find that I do less shifting, which certainly helps in commuting traffic.

And, I still get approximately the same fuel economy as before even though my rpms run 500 higher at 70mph and the greater sportiness of the car encourages more spirited driving. When cruising at lower speeds I’m still selecting a gear such that the engine runs between 1500 and 2000 rpm.

In the USA, where 90% of the BMWs (even Z4s) have automatic transmissions, finding a suitable salvaged higher ratio differential like a 3.46, 3.64 or 3.73 is quite easy. Prices generally range from $300 - $500 plus $200 labor for the swap, so swapping a whole salvaged differential is the most common approach. It may be harder to find a higher ratio differential in other countries, such as the U.K., where automatic transmission models are rarer. So, in that case, it may be necessary to order one from the factory or to have a properly trained technician change the gears themselves.
Last edited by bimster on Thu Jul 09, 2009 8:39 pm, edited 1 time in total.

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Re: Differential gear ratio changes

Post by T2FFN » Thu Jul 09, 2009 8:25 pm

Excellent write up. I think this stemmed from a topic I posted a few days ago about the 3.0 feeling slow.

So if I understand, you swap the rear differential from an auto into the manual. Does the diff have to come from a certain auto, ie, 3.0 or are all diffs interchangeable? Now, how do you know what the rating is? 3.46 etc?

Again, excellent write up. I want this modification! :driving:

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Re: Differential gear ratio changes

Post by mattp64 » Thu Jul 09, 2009 9:06 pm

What's the impact on higher speeds. e.g. how many rpm is 100mph in 6th? Plus do you have to change gear more, as the revs move through the ratio more quickly?

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Re: Differential gear ratio changes

Post by bimster » Thu Jul 09, 2009 9:09 pm

T2FFN wrote:So if I understand, you swap the rear differential from an auto into the manual. Does the diff have to come from a certain auto, ie, 3.0 or are all diffs interchangeable? Now, how do you know what the rating is? 3.46 etc?
That's what I did. Someone with an automatic can also change their ratio but they would need to actually change the gears to something like a 4.10 ratio. Diffs are generally interchangeable within a series. My 3.64 diff. came from an automatic 2.5i, but I could just as well have used a 3.46 from a 330 automatic. M diffs are completely different and not interchangeable with non-Ms.

The gear ratio is normally on a plate on the differential housing.

The best source for checking the available options for your car would probably be your mechanic or a local dealer.

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Re: Differential gear ratio changes

Post by bimster » Thu Jul 09, 2009 9:24 pm

mattp64 wrote:What's the impact on higher speeds. e.g. how many rpm is 100mph in 6th? Plus do you have to change gear more, as the revs move through the ratio more quickly?
The rpm in 6th would typically be about what you have in 5th with the stock ratio. At very high speeds you can hit the engine redline and top speed limiter at the same speed. It depends on the specific ratios selected.

The real answer to your second question is that it depends on your driving style. As I wrote before, I believe I shift less, but I will on occasion do things like go from 0-50 WOT in 2nd and upshift directly to 6th.

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Re: Differential gear ratio changes

Post by akash_sky1 » Thu Jul 09, 2009 9:55 pm

Nice write up, although I did know about diff swaps to ^ acceleration I hadn't heard of anyone doing it in their own Zed, more like a muscle car such as camaro, 'stang etc. I do envy how serious tuning is done so much more often in USA than over here.

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Re: Differential gear ratio changes

Post by akash_sky1 » Thu Jul 09, 2009 9:57 pm

Nice write up, although I did know about diff swaps to ^ acceleration I hadn't heard of anyone doing it in their own Zed, more like a muscle car such as camaro, 'stang etc. I do envy how serious tuning is done so much more often in USA than over here.

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Re: Differential gear ratio changes

Post by T2FFN » Thu Jul 09, 2009 10:03 pm

Wonder how the insurance would take it, or is it not required to tell them as you're replacing standard for standard...
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Re: Differential gear ratio changes

Post by T2FFN » Thu Jul 09, 2009 10:04 pm

akash_sky1 wrote:Nice write up, although I did know about diff swaps to ^ acceleration I hadn't heard of anyone doing it in their own Zed, more like a muscle car such as camaro, 'stang etc. I do envy how serious tuning is done so much more often in USA than over here.
I think the thing with the UK is, its just so expensive! If you look at the price of the american cars and parts compared to here, add in the cost of fuel to run a tuned car getting low mpg... its just easier over there. I used to buy parts in the US and have them shipped here for my TT, and it was still cheaper than buying them here!
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Re: Differential gear ratio changes

Post by epbrown » Fri Jul 10, 2009 1:10 am

T2FFN wrote:Wonder how the insurance would take it, or is it not required to tell them as you're replacing standard for standard...
Over here, I don't think you'd say anything. I notified my insurance when I went with CSLs because if the car was stolen I'd want to be reimbursed. I've said nothing to them about my aerokit sideskirts or 3.91 diff.
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Re: Differential gear ratio changes

Post by bimster » Fri Jul 10, 2009 4:53 am

T2FFN wrote:Wonder how the insurance would take it, or is it not required to tell them as you're replacing standard for standard...
Every insurance company is probably a bit different, but I know that mine seems mostly concerned with engine performance modifications, track usage, and expensive custom appearance stuff that they might be asked to cover. They recently sent a limitation notice capping their liability for custom modifications to $1000 if no additional coverage was purchased. I seriously doubt you'd have anything to be concerned about on a differential swap unless you were to do some boy-racer thing like getting the differential polished and chrome plated. That would attract their adjuster's attention if there was a claim. Otherwise, it's all stock hardware. :wink:

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Re: Differential gear ratio changes

Post by T2FFN » Fri Jul 10, 2009 12:34 pm

Ok, so now its down to deciding which diff you think you could live with... higher (3.64/3.07) or (3.46/3/07). You want to notice the difference, but not make the car less enjoyable to drive with the change in engine speed
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Re: Differential gear ratio changes

Post by cj10jeeper » Fri Jul 10, 2009 3:12 pm

Before you rush out and spend remember it's a highly skilled job to rebuild a diff using a new Ring and Pinion. It requires several different settings from preload on pinion bearings to throw and backlash. all set up with crush washers and or shims and using inch pound torque wrenches, dial gauges, etc. Get it wrong and the diff will whine and or clunk and have a short life.

I've actually rebuilt several myself for Jeeps (As I break the teeth off them in competition/hard use) and it's no task for the faint hearted. Translate that into lots of money and a limited number of specilaist that can do it properly.

Without even looking and off the top of my head, I'd expect £500-£750 for OEM R&P gears and say £200 for assorted bearings, seals and oils. Add to that say £500 labour for the rebuild.

Not for one moment putting anyone off just pointing out that it's more than chucking 2 cogs in.

Swapping the whole unit over in the UK may be more sensible if you can find a suitable ratio.
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Re: Differential gear ratio changes

Post by Incompatible » Fri Jul 10, 2009 4:15 pm

cj10jeeper wrote:Before you rush out and spend remember it's a highly skilled job to rebuild a diff using a new Ring and Pinion. It requires several different settings from preload on pinion bearings to throw and backlash. all set up with crush washers and or shims and using inch pound torque wrenches, dial gauges, etc. Get it wrong and the diff will whine and or clunk and have a short life.

I've actually rebuilt several myself for Jeeps (As I break the teeth off them in competition/hard use) and it's no task for the faint hearted. Translate that into lots of money and a limited number of specilaist that can do it properly.

Without even looking and off the top of my head, I'd expect £500-£750 for OEM R&P gears and say £200 for assorted bearings, seals and oils. Add to that say £500 labour for the rebuild.

Not for one moment putting anyone off just pointing out that it's more than chucking 2 cogs in.

Swapping the whole unit over in the UK may be more sensible if you can find a suitable ratio.
X2. If you're going to spend the time and money to do this, it would be wise to consider installing a limited slip at the same time. The lsd allows you to better put the power down on the road. If you can find a good diff to swap out, then it's more of a toss up between cost and performance.
It would be nice if the non M cars could use the lsd from the M's, it can be done but requires changeing over the entire rear suspension which is usually cost prohibitive. An aftermarket setup such as offered by Quaife or Diffs on Line (IIRC) would be an option.
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Re: Differential gear ratio changes

Post by cj10jeeper » Fri Jul 10, 2009 4:25 pm

Agree with that:
Quaife do a nice helical gear Z4 diff, but omit the price:
http://www.quaife.co.uk/BMW-Z8-ATB-differential
Of course the R&P is still needed, but it save doubling up on the labour to fit it later.
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