Near the end of Adon Olam, there is the phrase "Tzur Chevli B'eit Tzarah". What exactly is the meaning of this phrase, and specifically the term "Tzur Chevli"? I have seen it translated rather literally as "Rock of my pain in my time of distress" (Artscroll), which does not seem particularly intelligible, at least to me. I have also seen it more or less glossed over like "The Rock on whom I rely" (Koren), which, while it makes sense in context, kind of ignores the meaning of the words. (I'm only picking on Artscroll and Koren since I happen to have both siddurim with translation at home). It is entirely possible that I am over-thinking this, and it means something like "He is a Rock for me when I am in pain, or am in a time of distress"; however, it seems like the term "Tzur Chevli" means something more specific. Any thoughts?
A possible interpretation can be gleaned from the posuk in Yechezkel 27:8 where the term rope is used metaphorically to signify the ones steering the ship. And in Shmuel II 8:2 ropes are used metaphorically to signify control over life and death.
Thus in keeping with the theme of the piyut that Hashem is “Master of the world”, we praise Hashem by confidently stating that he is “the Rock of my rope(s) in the time of distress” - meaning that Hashem is complete control of my distress. That any suffering which I experience is not due to happenstance (in which case the suffering could be uncontrollably nasty), but comes from Hashem who carefully measures the amount of suffering that I need and that He knows I can bear, and which is being brought upon me intentionally as an atonement, or in order to arouse me to repent, or for some other reason.
The Kehot Annotated Siddur translates it as "the strength of my lot in times of distress".
The "my lot" would be like Devarim 32:9:
יַעֲקֹב, חֶבֶל נַחֲלָתוֹ
Jacob the lot of His inheritance
The Siddur Shay Lamorah quotes Iyun Tefilah that it means that He is my Rock and Refuge (מעוז) to save me from the pains which grab me at a time of trouble.
וצור חבלי - והוא לי צור ומעוז להושיעני מן החבלים אשר יאחזוני בעת צרה
I have looked into this a little in the past, so I can't recall particular sources, but the gist of it is as follows:
Some wish to translate it as in "חבל נחלתו" and many other instances in which it is used to mean "my lot" or "my portion in life". This would parallel the other phrase "מנת כוסי" in the next line. "צור חבלי" would then mean "the Rock who is my lot in life", i.e. who is what my life is about. However, this would not satisfy any grammarians, who know that if this was the intention, the chet would have a patach under it: "חַבלי". But none of the siddurim have such a vocalization. I have seen one or two old siddurim which have a patach, probably just to be able to translate this way but without any manuscript evidence.
As we have it with a segol under the chet, the word usually means pain as in "חבלי מות" or "חבלי שאול" or "חבלי לידה", which from context probably means a time of unbearable pain. In this case, "צור חבלי" would mean "Rock of my pain", i.e. my Rock who helps me when I'm in pain, and the following "בעת צרה" is a parallelism and emphasizing of "חבלי" (with the additional benefit of playing on the words צור/צרה).
An additional possible source for the latter interpretation, I think, is Psalm 18, in which the first few verses express this sentiment of God being always there for you during hard times. Verse 3 refers to God as "צורי" as does the author of Adon Olam in this line, and verses 5 and 6 use the phrases "חבלי מות" and "חבלי שאול" to express painful times. It is possible the author here is alluding to this psalm or using it as a basis for this line of his poem.
צור חבלי בעת צרה is an idiomatic expression. "צור חבלי" means literally "my rope's rock". It is referring to an anchor. So the plain translation (meaning according to peshat) is "My anchor in times of trouble."
There are many ways to give it allegorical meaning as well as according to the Kabbalistic interpretations. But all these other meanings must relate to the plain meaning (the peshat).
I noticed that the root form of חֶבלִי is חבל meaning "rope". However, I also did a Google translate on the full word חֶבלִי and it displayed the synonym נָחוּת which has one translation as "disadvantaged". This makes sense, in this context, as the word "chaval" is often said to someone when a tragedy or danger is mentioned. See also this site which gives a further translation and another angle on the word origin of חבל. It slightly concurs with the other one.
So, a somewhat literal translation to the phrase would be "He is the rock of my disadvantage in (my) time of distress."
A metaphoric translation (mine) would be to imagine a rope that is tightened. In a sense, the paytan (poet) is saying, He is the source of my salvation when the "rope" of distress is tightened around me.
Supplement: I'm humbled by the answer that follows mine. This explanation of the "rope" is excellent.