Yes, there are Modbus RTU - Modbus ASCII converters, for example:

https://www.rtautomation.com/product/460mrsa/?srsltid=AfmBOopNevY-loRwxD2n27bu8ut9NI3LDk2oEWqu_9KXxLRD7B5xkaG7

But, the CM5 also includes Modbus TCP, perhaps a more cost effective method might be to use one of Automation Direct's Modbus TCP - Modbus RTU/ASCII gateways, for example:

https://www.automationdirect.com/adc/shopping/catalog/communications/protocol_gateways/modbus_gateways/eki-1221-ce

Also, I assume you are using a PLC for the machine control. Your PLC may have a COM module that includes Modbus ASCII, a few examples:

Click Plus PLC - C2-DCM

BRX PLC - BX-SERIO

Hi Kevin, I agree with your proposal. I have a serial connection from my HMI to my axis control via RS-232 using the Modbus ASCII protocol, and an RS-232 K-Sequence connection from my HMI to my DL06 PLC. Honestly, I was looking for the same thing: a serial connection with a DB9 RS-232 connector from my HMI to my NextMove ESB-2. However, now that you mention it, I don't necessarily need to use that specific type of connection and protocol from my HMI to my gateway, right? But I would still like to keep the RS-232 with the DB9 connector for my axis control.

So, I would be connecting an Ethernet cable from my HMI to my gateway using TCP, and then using the gateway's serial connection to my axis control via Modbus ASCII

I see you have a DL06! A lot more possibilities. The DL06 has a serial port that can act as a Modbus RTU master. The DL06 also has D0-DCM that can act as a Modbus RTU master. The DL06 also has H0-ECOM100 that can act as a Modbus TCP master. But, right, you still need to convert to Modbus ASCII for your axis controller. The DL06 and the CM5 do not support Modbus ASCII. I assume you do not want to change the PLC to a PLC that supports Modbus ASCII. Also, to free up a serial port on the HMI, the HMI can also connect to the DL06 thru the H0-ECOM100 via an Ethernet cable. Interesting that you are "going thru" the HMI to control the axis controller, rather than controlling the axis controller directly from the PLC.

I am going to keep the HMI-PLC communication exactly as it currently is, using K-Sequence and RS-232. The only communication I am interested in changing to use the gateway is the one between the HMI and the NEXTMOVE ESB-2. And for that, I will follow your recommendation to use TCP between the HMI and the Gateway, and Modbus ASCII between the Gateway and the NEXTMOVE ESB-2.