Q:

Were Mongol or Chinese cavalry charges among the largest in history?

In 1683 at the Battle of Vienna, 20,000 Polish, German and Austrian cavalry charged the Ottoman lines in what Wikipedia says is the largest cavalry charge in history. Other references are more cautious: this page  and one of the Wiki references say “largest known” while 10 Heroic Cavalry Charges says “one of the largest”.
There may be some European / American bias, though. Looking at the list of Notable Charges, almost all those listed are European or from the American Civil War. No mention of the Mongols or any of the armies of Chinese dynasties such as the Sui or the Ming. Of course, the American civil war was comparatively recent so figures are more likely to be available and reliable.
Nonetheless, considering the size of some of the armies that these eastern powers had, these omissions seem to be rather glaring. In Richard A. Gabriel’s Genghis Khan's Greatest General: Subotai the Valiant the author, referring to the Mongols, states that 

The army was almost entirely composed of cavalry, with 40 percent
  heavy cavalry, and the remaining 60 percent designated light cavalry.
  There were no organic Mongol infantry units...

Gabriel also says that

The charge of the heavy cavalry was always the main player in the
  endgame of a Mongol attack.

As Genghis Khan could field an army of up to 100,000 Mongols (see also the Battle of Yehuling) it seems likely that some of the cavalry charges could easily have exceeded 20,000. Then there is the army of Fu Jian in 383 AD which apparently included 270,000 cavalry, and that of Yang Liang in 586 AD numbering “300,000, mostly composed of archer cavalry.” for the invasion of Korea.
There is, of course, a problem knowing the real numbers in many cases. For example, numbers for the Battle of Mohi in 1241 vary considerably.
I’ve been unable to find much information on the size of cavalry charges for either Chinese or Mongol armies and whether or not any of them surpassed in numbers the one at the Battle of Vienna in 1683.
Are there any primary sources on the size of cavalry charges for the Mongol or Chinese armies which are considered reliable by modern historians?
If not, have modern historians been able to make any estimates based on what evidence is available? Do we have any idea what proportion of the cavalry any of these armies might have committed to a single cavalry charge? 

I would accept an answer for either the Chinese or the Mongols. Although I'm not asking about other armies (including Arab, Persian etc. might make the question too broad), I would be interested in reliable primary sources / estimates made which match or surpass the Vienna 1683 cavalry charge. 

A:

While both Mongolian and Chinese mounted armies could easily outnumber those of the American or European at any point in history, it should be noted that the Mongols or Chinese hosts didn't really rely on cavalry shock charges as the Europeans or Americans did. Chinese and Mongolian cavalry were as you mentioned horse archers and wouldn't be used for the same purpose as European shock cavalry. The Polish Winged Hussars used by John Sobieski in the Battle of Vienna were much heavier and meant to cause fear in the enemy lines as well as to route enemy troops. In comparison, the Mongol and Chinese horse archers were meant to be lighter equipped and used for harassment or hit and run tactics to defeat their often unmounted or more heavily mounted foes. 
In summary, yes the Chinese and Mongols definitely had much larger hosts of mounted units, but the Europeans win in crazy all out charges towards the enemies front lines 

A:

I suggested in the comments above, earlier, that the Hindustan peninsula might have some appropriate examples. A cursory look at the Moghul, Maratha and Bengali armies, etc, did show that the cavalry forces put into field were of the order of tens of thousands of cavalrymen (Second Panipat, Tukaroi), I did not find an immediate example of a combined charge. 

The Battle of Kars, 1745
However, I found a possible contender during the Ottoman-Persian conflict of 1743-1746. In 1745, Nader Shah was conducting forward defense of his borders, and met the Ottomans at the Battle of Kars, 1745. In this, Nader Shah is reputed to have won the day by organising a flank attack with 40,000 of his finest cavalry at the right moment. 
I will describe the specifics of this account below, along with some sources. 
Vatatzes' Account
From Michael Axworthy's 'The Sword of Persia' (location 5070):

The armies closed and engaged, but the cavalry of both sides held back.
  The infantry struggle went on for some time, each side attacking and
  counter-attacking; both commanders sending new reinforcements into the
  battle. One account says that, contrary to his usual practice, Nader
  in this campaign against the Ottomans had generally commanded the army
  from his throne within the camp, receiving word of developments and
  issuing commands to his troops by messengers. But by the early
  afternoon on this day his messengers were still telling him the fight
  was undecided, and he resolved to intervene personally. Nader put
  on his armour, mounted up and led a reserve of 40,000 Abdali cavalry in
  a furious attack against the Ottoman flank. Even then the fighting was
  still fierce, and two of Nader's horses were killed under him, but his
  presence encouraged the Persians to new efforts. Ottoman resistance
  finally began to crumble, and 15,000 irregular troops from the
  provinces of Asia Minor fled. The main Ottoman body retreated in
  confusion to the safety of the entrenchments around their camp. Nader
  followed them up, but withdrew with his men to his own encampments at
  sunset.

An accompanying footnote clarifies this is primarily based on the account of Basile Vatatzes, a Greek traveller and merchant in Persia. Axworthy describes Vatatzes' 'additional detail' on the course of the battle as:

Vatatzes, whose account (pp. 282-3) gives colour to what was
  previously known of this battle, is the source that says the cavalry
  of both sides were initially kept back. He says the Persian cavalry
  were superior and the Ottoman cavalry feared to attack them (one of
  the sources presented by Sha'bani also says the Ottomans did not have
  the will for a cavalry fight - Sha'bani 1977, pp. 34-7). By contrast,
  Ottoman sources suggest that their troops came close to beating the
  Persians (Cambridge History of Iran, Vol. 7, p. 309).

I should note that I did not access Vatatzes' account myself.
Quality of Vatatzes' Account
A separate article by Axworthy, 'Basile Vatatzes and His History of NĀDER ŠĀH' describes Vatatzes's work and its merits:

is patchy, often inaccurate, and his judgement is often suspect. ... Frequently, he reports the mood and general drift of events better than the details.

Nevertheless, the examples brought in the paper do not specify any numeric errors (although chronological errors are brought up), and Axworthy specifically says that Vatatzes' military descriptions are particularly useful on the count of their accuracy (e.g., on Persian titles) and thoroughness (e.g., on drilling the troops). 
Astarabadi's Account
An alternative source is Mirza Mehdi Khan Astarabadi whose history of Nader Shah has been accessible in French since 1770 as Histoire de Nader Chah. This book contains the following description of the battle of Kars, much simpler and almost no (useful detail):

Le dix, dans l'après-midi, Mohammed Pacha s'avança avec cent mille hommes de cava lerie, & quarante mille d'infanterie, & campa au pied d'une montagne à deux parasanges de l'armée impériale, où, ayant dressé ses tentes, il commença de fortifier les endroits foibles, & de préparer ses canons & ses mortiers.
L'onzième, les deux armées étant rangees en ordre de bataille, le feu du combat com mença, à flamber, & ses étincelles atteignirent les étoiles. Après plusieurs successifs engagemens, l'armée Ottomane fut mise en déroute par l'interposuion de la' Providence.
La perte sut très-grande du côté des Turcs, leur genéral se retira dans ses retranchemens, & la nuit devenant obscure, les troupes conquérantes retournèrent à leur camp.

An approximate (though good enough in my opinion) (Google) translation reads:

On the tenth, in the afternoon, Mohammed Pasha advanced with a hundred thousand cavalry men, & forty thousand infantry, & encamped at the foot of a mountain with two parasanges of the imperial army, where, having erected his tents, he began to fortify the weak places, and to prepare his guns and his mortars.
The eleventh, the two armies being placed in order of battle, the fire of battle began to flame, and its sparks reached the stars. After several successive engagements, the Ottoman army was routed by the interposition of Providence.
The loss was very great on the side of the Turks, their general withdrew into his retrenchments, and at night becoming dark, the conquering troops returned to their camp.

Quality of Astarabadi's Account
The quality and level of detail is clearly without the colour that Vatatzes provided for Axworthy's account. Nevertheless, the quality of this writer is also in doubt (again by Axworthy, from "The Sword of Persia"):

The Jones translation contains many errors, particularly with dates and names, but is an accessible version for those who cannot read Persian... Mirza Mahdi was Nader's official historian, and understandably avoided including anything critical of Nader in his work. There are also indications that by the time the work was finished (about a decade after Nader's death), Mirza Mahdi needed to avoid offending some of the leading personalities of the Qajar tribe.

Nader Shah's Cavalry
I suppose to conclude, I should sum up what I noted on the Persian cavalry to support the argument that they could have done this (though, indeed, there are many cavalry units which could have done such a charge but did not).
Specifically, in another article on the Persian Army of Nader, Axworthy notes the particular quality of the Afghan (Abdali / Durrani) cavalry:

...his Afghan cavalry were probably the finest shock cavalry in the region.

Though the above article was illuminating in a general sense, and I'd probably recommend a read of it if the above topic sounds interesting, it doesn't bear much more discussion except to note that Nader Shah had plenty of troops armed and armoured exactly to fit the heavy shock trooper role as expected from a cavalry charge, and the troops most suitable are the ones that Vatatzes has placed into the role at Kars.
This is, regrettably, slightly circular as Axworthy's main source on the army is Vatatzes, of course, so this caveat should be borne in mind. 
The numbers do, however, bear up for the general proportions of the army, with Axworthy quoting Jonas Hanway for 1744 (excluding some other larger tribes):

There were 13,000 guard cavalry, 20,000 cavalry from Nader’s own
  Afshar tribe, 50,000 Afghan cavalry, 12,000 jazayerchis and 40,000
  ordinary musketeers. There were also 18,000 Turkmen, Uzbeks, and
  Baluchis, who served as light troops.

It should be noted that Nader Shah's son was conducting a separate campaign at the same time, winning a simultaneous battle near Mosul which completely destroyed the Turkish capacity for defense. Therefore, a good proportion of troops may have been with the son, making this charge unlikely, though Astarabadi implies that these were not troops from the main army (p 100):

Sur cet avis fa Majesté envoya le prince Nasralla Mirza pour s'opposer à ceux qui s'approchoient des frontières de Perse, & lui donna
  les légions victorieuses qui avoient été employées sur les confins de Karmanchah, du Loristan, & du Kiurdestan.

Same Google Translate option:

On this advice the Majesty sent Prince Nasralla Mirza to oppose those who approached the frontiers of Persia, and gave him the victorious legions which had been employed on the borders of Karmanchah, Loristan, & Kiurdestan.

Overall, on the balance of probabilities, I think that this here is a larger cavalry charge than at Vienna 1683, even if it does not stretch to the exact 40,000 as quoted by Axworthy, following from Vatatzes. Nevertheless, I think that if the numbers were ridiculous or the action improbable, Axworthy would have noted this much as he criticised Vatatzes for other reasons. Therefore, I would suggest that the largest cavalry charge we know of took place during the Battle of Kars. 

A:

Question:
  Were Mongol or Chinese cavalry charges among the largest in history?

The Mongol's effectiveness in battle was not based on "riding over" their opponents;  nor was it based on having superior numbers.   It was based upon being the only side which both possessed the super weapon of the day,  the Mongol Bow, and enough talented archer/horsemen who could wield it.
As such the Mongols were less likely to involve themselves in an early cavalry charge and were much more likely to use the mobility of their horses to keep them just out of range of enemy archers while their own mounted archers attrited their opponents.
Take the battle of Mohi for example in 1241.   European Cavalry vastly outnumbered the Mongols.  European forces numbered 80,000 Primarily light cavalry and the Mongols numbered roughly 30,000 Primarily horse mounted archers.   The Hungarian cavalry was among the best in Europe at the time.  The Mongol's victory was still lopsided 10,000 European casualties,  Mongols suffered a few Hundred.
This lopsided victory is credited with Mongol tactics which took advantage of the superior range of it's horse mounted archers, and not because the Mongols fought like traditional European Cavalry and road over their opponents.
The largest Mongol / Chinese battle was the Battle of Yehuling  which was a series of 4 battles 2 sieges and 2 segments fought in terrain chosen by the Chinese to negate the Mongol cavalry advantage (mountains).  Huge Cavalry charges weren't present in any of these battles.

Battle of Wusha Fortress - was fought by the Chinese behind the Great Wall attempting to stop the Mongol invasion before it began.
Battle of Yehuling and Huan'erzui - were fought in mountainous regions chosen by the Chinese because they thought to make it harder for the Mongol cavalry to traverse up and down the mountains.   It did, but it also made it harder for the Chinese to mass their superior number of troops.
Battle of Huihe Fortress -  Another siege.   The cavalry charge which decided the battle was personally led by Genghis Khan but only involved 3,000 mongols.  

