I've been following the production buildup of artillery rounds for Ukraine closely and this is roughly what I've come up with so far. Note that not all production quantities have been released.
USA: Their intent is to ramp up to 40,000 rounds of 155mm production per month by this spring (April / May timeline). Further ramping up of production will take 12 to 18 months.
Germany: It's unclear what Germany will produce moving forward on a continued basis, but Rheinmetall has committed to producing 300,000 rounds of 155mm by this summer (July / August timeline). After that order is filled, it's unclear what the production rate will be for the remainder of 2023 and beyond.
Canada: General Dynamics Ordnance is currently in negotiations with the American military, to produce 12,000 rounds of 155mm ammunition each month, for an undisclosed period of time. General Dynamics Ordnance is the regular producer of artillery shells for the Canadian Armed Forces.
France / Australia: The French and Australians recently signed an agreement to produce 155mm artillery shells for Ukraine. The contract was awarded to French weapons manufacturer Nexter, and no details were provided regarding quantity of ammunition being produced, nor its delivery timeline.
Britain: In fall 2022, BAE Land Systems agreed to ramp up their productions of 155mm artillery rounds for the British Government. The production increase total was not made public , but it's believed that production will increase into the neighbourhood of 10,000-15,000 rounds per month. The timeline for the ramp up has not been disclosed.
Slovakia: Artillery round production in Slovakia was about 19,000 rounds per year prior to the war. In 2022 the Slovaks announced that they would be expanding production to 100,000 rounds per year, which equates to roughly 8300 rounds per month. No timeline was given for the production ramp up. Of important note, Slovak firm ZVS Holding produces 122mm and 152mm artillery rounds, compatible with Ukraine's significant quantity of Soviet / Russian made artillery.
Czech Republic: Prior to the war, the Czechs were producing approximately 1/3 of all artillery made in Europe each year. Czech manufacturer CSG leads the way in production, with pre-war capacity of 100,000 rounds per year, however, they announced that due demand, they would be expanding production to 150,000 rounds year, which equates to 12,500 rounds per month. Like the Slovaks, the Czechs produce both 155mm ammunition and the much needed 152mm and 122mm Russian caliber ammunition.
Ukraine: It's been noted that Ukraine continues to produce its own 152mm and 122mm artillery rounds, but where, and at what rate, is a tightly guarded secret. One can only imagine that production lines are limited in nature on Ukrainian territory, but there are bigger questions about whether or not Ukrainian firms have been able to set up production capacity in neighbouring countries.
Other Parties: There is no doubt that countries such as Sweden and Poland have also increased their production capacity, but by how much and over what time frame, is unknown at this point. Furthermore, Ukraine has received unknown quantities of ammunition from third party sources such as Pakistan, Morocco, Turkey and South Korea (backfilling USA and Canada).
With the numbers you see above, and the small quantities of other production that I'm unaware of (and not including in this post as a result), I suspect that Ukraine's access to artillery ammunition with ramp up into the 90,000-120,000 shell per month range, by the spring, which will allow them to sustain a 3000-4000 round per day pace, moving forward. By the summer, I suspect that number will increase into the 4000-5000 round per day range, and by early 2024 that number should increase, again, into the 6000-7000 round per day range.