Issues with tense

In your first sentence -- If it should fail for any reason other than physical abuse, we will replace the part free of charge – the speaker/ writer is saying that it is not expected that it (a mechanical device here?) will fail, but in case that it does, they will replace the part.

This sentence is very similar to "if it fails for any reason." However "if it should...." indicates that the event is unlikely, at least in the mind of the speaker/ writer. It shows a greater degree of improbability.

This construction is often seen in descriptive literature about products. The manufacturer, or store, is saying that the product is good and that no trouble is expected. They are saying that failure is a remote possibility. Other examples could be:

If the tires should wear out before twenty-five thousand miles, bring them to an authorized dealer for replacement.

If the appliance should fail to start, call the 800 number for further instructions.

If the pizza should need reheating, heat it a slow oven.
________________

Another form of this use of "should" – to mean "in case" – is subject/verb inversion:

Should it fail for any reason.....
_______________

If it has failed...." describes a slightly different situation. The failure would have already occurred. "If it fails/ should fail" refers to a possible situation in the future.
_______
In your other set of sentences: these, too, are close in meaning.

"Anticipating his arrival, she cleaned up her place" shows that because she anticipated his arrival, she cleaned up her place. This use of the present participle in an adverbial phrase indicates that the action happened almost simultaneously with that of the main verb, and indeed, caused the action of the main verb.

Other examples could be:

(a) Seeing that plants need a lot of care, I've decided to buy artificial ones. I don't want to waste time and money trying to keep plants alive.
b) Growing up in a bilingual household, the children speak both languages with native fluency.
(c) Realizing that I wasn't a good dancer, I went to a dance studio for lessons. I'm going to surprise everyone with my dancing skills at the big party next month.

Your sentence with "having" + the past participle -- having anticipated his arrival, she cleaned up her place – also indicates a cause/ effect relationship. However, there is an additional meaning: the anticipation happened before the action of the main verb. Your two sentences are similar, but the first action – "anticipating" in this case – is completely over and could have happened at a time not immediately before the cleaning up.
.
The same is true of sentences (a), (b), and (c) above when converted to (d), (e), and (f) below:

(d) Having seen that plants need a lot of care, I've decided to buy artificial ones. I've lost a lot of time and money trying to keep plants alive in the past, and I don't want to lose more time and money.
(e) Having grown up in a bilingual household, the children speak both languages with native fluency.
(f) Having realized that I wasn't a good dancer, I went to a dance studio for lessons. I was so embarrassed at the big party last month – I couldn't dance a step and decided then and there to sign up for dancing lessons.


Rachel

Thank you Rachel for your explanation.
Let me ask you a follow up question.

Sometimes the perfect tense appears in a situation anticipated in the future. For example:

I will send you a notice when the part has become available.

But in a similar context, the present tense can be used such as:

I will send you a notice when the part becomes available.

A friend of mine who is a native speaker said that the present tense is more common, and that the perfect tense tends to appear in a more formal and carefully written text. Do you have anything to add to this?

"...when the part becomes available" and "....when the part has become available" are almost identical. I agree with your friend about the greater frequency with the present form and the greater formality with the past form.

"When the part becomes available" implies AS SOON AS the part becomes available. "When the part HAS become available" implies after the part becomes available.

I know that Marilyn has some thoughts on this. See her posting (upcoming) below.

Rachel

Here's a more technical explanation. The distinction between

...when the part becomes available and

...when the part has become available

...is very subtle. It's a difference in aspect. Let's call the action of "becoming available" the "event." If the present simple "becomes," is used, the focus is on the moment of "becoming available."

In contrast, if the present perfect "has become" is used, the focus is on the time immediately following the event of "becoming available"--the "aftermath" of the (completed) event.

Sometimes the perfect, not the simple present, is necessary to show completion of an action. "Have a chance to + verb" is a stative verb phrase, as in

When I have a chance to look over the contract, I will be glad to do so

The present perfect, in contrast, shows completion:

I'll give you my answer when I've had a chance to look over the contract

The answer, in other words, will come after the speaker not only has the chance to look over the contract but after s/he acts on that chance and completes the action of looking over the contract.

In short, when the present simple is used in a when-clause about the future, it indicates the beginning but not necessarily the end of the event. On the other hand, when the present perfect is used in a when-clause about the future, it implies the beginning and also the end of the event, and focuses on the aftermath, not the beginning or the duration, of the event.

Marilyn Martin