Okay so here's what I would do.
Fire up Console, click on "Clear Display."
Now, repeat the steps you mentioned in your post (i.e. connect your Voyager, do your backup, etc.)
And, then, read all the error messages your Console posts.
That is why you will find your answer.
It could be something as simple as you need to properly erase the Voyager, first. And, then run Disk Utility Repair on your newly erased Voyager...
Or, it could be something as complicated as electronic USB-related errors.
Your Console App (located in /Applications/Utilities) will tell you all of that.
Post back, please, and let us know what it said!
That is what I get when I connect the S3 to the back of the iMac with the USB 3.0 that the S3 came with.
"11/8/14 22:02:54.000 kernel[0]: USBMSC Identifier (non-unique): 0123456789ABCDEF0124 0x1e91 0xb0b2 0x100, 3
11/8/14 22:02:57.000 kernel[0]: [0xffffff803f6e2000](0)/(5) Device not responding
11/8/14 22:02:57.000 kernel[0]: IOUSBMassStorageClass: not registry member at registerService()
11/8/14 22:03:18.000 kernel[0]: USBMSC Identifier (non-unique): 0123456789ABCDEF0124 0x1e91 0xb0b2 0x100, 3
11/8/14 22:03:32.000 kernel[0]: USBMSC Identifier (non-unique): 0123456789ABCDEF0124 0x1e91 0xb0b2 0x100, 3
11/8/14 22:03:45.000 kernel[0]: USBMSC Identifier (non-unique): 0123456789ABCDEF0124 0x1e91 0xb0b2 0x100, 3
11/8/14 22:03:47.000 kernel[0]: [0xffffff803fa2f400](2)/(5) Device not responding
11/8/14 22:03:52.000 kernel[0]: USBMSC Identifier (non-unique): 0123456789ABCDEF0124 0x1e91 0xb0b2 0x100, 3
11/8/14 22:03:54.000 kernel[0]: [0xffffff803f722200](1)/(5) Device not responding
11/8/14 22:04:01.000 kernel[0]: USBMSC Identifier (non-unique): 0123456789ABCDEF0124 0x1e91 0xb0b2 0x100, 3
11/8/14 22:04:03.000 kernel[0]: USBF: 17075.593 The IOUSBFamily is having trouble enumerating a USB device that has been plugged in. It will keep retrying. (Port 5 of Hub at 0x15000000)
11/8/14 22:04:05.000 kernel[0]: USBF: 17077.771 The IOUSBFamily was not able to enumerate a device."
Here is what I got when I connected the S3 with the USB 3.0 to a USB 2.0 hub after formatting the disk and assign it to Time Machine and after I hit "Back up now" I got the "Backup Failed" massage.
"11/8/14 22:06:27.000 kernel[0]: hfs: unmount initiated on TimeMachine on device disk1s2
11/8/14 22:06:27.000 kernel[0]: hfs: unmount initiated on TimeMachine on device disk1s3
11/8/14 22:06:36.000 kernel[0]: hfs: Initializing the journal (joffset 0x74e000 sz 0x1800000)...
11/8/14 22:06:36.000 kernel[0]: hfs: mounted Untitled on device disk1s2
11/8/14 22:06:36.725 mds[53]: (Normal) Volume: volume:0x7f98db081000 ********** Bootstrapped Creating a default store:3 SpotLoc:/Volumes/Untitled/.Spotlight-V100 SpotVerLoc:/Volumes/Untitled/.Spotlight-V100/Store-V1 occlude:0 /Volumes/Untitled
11/8/14 22:06:37.071 fseventsd[64]: could not open <</Volumes/Untitled/.fseventsd/fseventsd-uuid>> (No such file or directory)
11/8/14 22:06:37.071 fseventsd[64]: log dir: /Volumes/Untitled/.fseventsd getting new uuid: 0FC2DF36-73C6-4AEA-91C7-92E4C9A70FFC
11/8/14 22:06:37.310 mds[53]: (Normal) Volume: volume:0x7f98d907b000 ********** Bootstrapped Creating a default store:0 SpotLoc

null) SpotVerLoc

null) occlude:0 /private/var/tmp/MPMDRMZY
11/8/14 22:06:45.447 com.apple.prefs.backup.remoteservice[1879]: assertion failed: 13F34: liblaunch.dylib + 25164 [A40A0C7B-3216-39B4-8AE0-B5D3BAF1DA8A]: 0x25
11/8/14 22:06:45.454 com.apple.prefs.backup.remoteservice[1879]: assertion failed: 13F34: liblaunch.dylib + 25164 [A40A0C7B-3216-39B4-8AE0-B5D3BAF1DA8A]: 0x25
11/8/14 22:06:45.669 com.apple.prefs.backup.remoteservice[1879]: Bogus event received by listener connection:
<error: 0x7fff79bd1b50> { count = 1, contents =
"XPCErrorDescription" => <string: 0x7fff79bd1e60> { length = 18, contents = "Connection invalid" }
}
11/8/14 22:06:48.101 WindowServer[86]: window 10f is already attached to window 10d
11/8/14 22:06:52.244 WindowServer[86]: window 112 is already attached to window 10f
11/8/14 22:06:53.693 UserEventAgent[166]: com.apple.TMHelperAgent.SetupOffer enabled
11/8/14 22:06:54.140 WindowServer[86]: _CGXGetWindowOrderingGroup: Operation on a window 0x10f requiring rights 0x5 by caller System Preferences
11/8/14 22:06:54.236 WindowServer[86]: _CGXGetWindowOrderingGroup: Invalid window 0x112
11/8/14 22:06:56.222 WindowServer[86]: window 10f is already attached to window 10d
11/8/14 22:06:57.926 UserEventAgent[166]: com.apple.TMHelperAgent.SetupOffer disabled
11/8/14 22:06:57.945 UserEventAgent[11]: com.apple.backupd-auto launchd job enabled
11/8/14 22:06:58.437 WindowServer[86]: _CGXGetWindowOrderingGroup: Operation on a window 0x10f requiring rights 0x5 by caller System Preferences
11/8/14 22:07:00.589 UserEventAgent[11]: com.apple.backupd-auto launchd job disabled
11/8/14 22:07:02.124 UserEventAgent[11]: com.apple.backupd-auto launchd job enabled
11/8/14 22:07:12.004 com.apple.backupd[1882]: Starting manual backup
11/8/14 22:07:12.062 com.apple.backupd[1882]: Backing up to /dev/disk1s2: /Volumes/Untitled/Backups.backupdb
11/8/14 22:07:12.063 com.apple.backupd[1882]: Ownership is disabled on the backup destination volume. Enabling.
11/8/14 22:07:12.810 com.apple.backupd[1882]: Forcing deep traversal on source: "Macintosh SSD" (device: /dev/disk0s2 mount: '/' fsUUID: 963E58DB-DF2E-394F-B975-5575A4A94858 eventDBUUID: 0D248293-C691-4419-90C5-FE50FC3AE1E5)
11/8/14 22:07:13.901 com.apple.backupd[1882]: Total content size: 262.36 GB excluded items size: 8.27 GB for volume Macintosh SSD
11/8/14 22:07:13.901 com.apple.backupd[1882]: Found 832021 files (254.09 GB) needing backup
11/8/14 22:07:13.902 com.apple.backupd[1882]: 275.56 GB required (including padding), 250.34 GB available
11/8/14 22:07:14.504 com.apple.backupd[1882]: Backup failed with error 7: Not enough available disk space on the target volume."