Positive displacement motor stators with diameter reliefs compensating for rotor tilt

1. A positive displacement motor (PDM) power section, comprising:

a rotor and a stator, the rotor configured to be received within the stator, the rotor having a rotor length such that a first portion of the rotor length has a substantially uniform transverse cross-sectional profile;

the stator having a longitudinal centerline;

the stator further including an internal elastomer liner such that the elastomer liner provides the stator with a stator internal surface, wherein the stator internal surface has lobes formed therein, wherein the lobes define helical pathways in the stator internal surface, wherein the helical pathways define a contour length between a contour inlet end and a contour outlet end, wherein the contour length includes an outlet region starting at the contour outlet end and extending up to 25% of the contour length towards the contour inlet end;

wherein transverse cross-sections of the elastomer liner taken orthogonal to the longitudinal centerline provide alternating lobes and valleys around a circumference of the stator such that 2× a distance between the longitudinal centerline and a zenith point of the lobes defines a minor diameter and 2× a distance between the longitudinal centerline and a nadir point of the valleys defines a major diameter;

wherein the outlet region further includes a first relief length disposed thereon, wherein the first relief length extends between a first relief length inlet towards the contour inlet end and a first relief length outlet towards the contour outlet end;

wherein the first relief length inlet has a first relief length inlet minor diameter and the first relief length outlet has a first relief length outlet minor diameter;

wherein the first relief length outlet minor diameter is larger than the first relief length inlet minor diameter by more than 0.0002 inches per inch of first relief length; and

wherein all of the first relief length opposes the first portion of the rotor length when the rotor is received within the stator.

2. The stator of claim 1 , in which the first relief length inlet minor diameter increases at least in part towards the first relief length outlet minor diameter according to a taper profile.

3. The stator of claim 2 , in which the taper profile is non-linear.

4. The stator of claim 1 , in which the first relief length inlet minor diameter increases at least in part towards the first relief length outlet minor diameter according to a step function.

5. The stator of claim 1 , in which:

(a) the elastomer liner has a tensile stress in a range between about 250 psi and about 1000 psi at 25% elongation;

(b) the elastomer liner further has a tensile stress in a range between about 400 psi and about 1200 psi at 50% elongation; and

(c) the elastomer liner further has a tensile stress in a range between about 500 psi and about 1600 psi at 100% elongation.

6. The stator of claim 1 , in which the elastomer liner has at least one tensile stress value selected from the group consisting of:

(a) a tensile stress in a range between about 250 psi and about 1000 psi at 25% elongation;

(b) a tensile stress in a range between about 400 psi and about 1200 psi at 50% elongation; and

(c) a tensile stress in a range between about 500 psi and about 1600 psi at 100% elongation.

7. The stator of claim 1 , in which:

(i) both the first portion of the rotor length and a second portion of the rotor length have a common and substantially uniform transverse cross-sectional profile; and

(ii) the contour length further includes a second relief length disposed thereon;

wherein the first relief length is located nearer the contour outlet end than the second relief length;

wherein the second relief length extends between a second relief length inlet towards the contour inlet end and a second relief length outlet towards the contour outlet end;

wherein the second relief length inlet has a second relief length inlet minor diameter and the second relief length outlet has a second relief length outlet minor diameter;

wherein the first relief length inlet minor diameter increases towards the first relief length outlet minor diameter according to a first constant taper profile;

wherein the second relief length inlet minor diameter increases towards the second relief length outlet minor diameter according to a second constant taper profile;

wherein the first constant taper profile is more aggressive than the second constant taper profile; and

wherein all of the second relief length opposes the second portion of the rotor length when the rotor is received within the stator.

8. The stator of claim 7 , in which the first and second relief lengths are contiguous.