@MichielW
Assuming that you're using an edit form with the data source set to Table1, the form will update the machine_ID field to whatever you define for the 'update' property of the form card that corresponds to the machine_ID field.
Therefore, you would unlock the machine_ID card and add your dropdown control there. You would set the items property of the drop down to Table2, and the Value to Machine_Name.
Assuming that you name the drop down control cboMachine, you would set the update property of the form to cboMachine.Selected.Machine_ID.
To make sure that the existing dropdown record loads correctly, you would set the default property of your drop down control to the following:
LookUp(Table2, Machine_ID=ThisItem.MachineID)