WO2013004780A1

WO2013004780A1 - Backlash measurement and compensation to increase the accuracy of laser shaft alignment

Info

Publication number: WO2013004780A1
Application number: PCT/EP2012/063132
Authority: WO
Inventors: Karl VIETSCH; Allan Todd
Original assignee: Aktiebolaget Skf
Priority date: 2011-07-05
Filing date: 2012-07-05
Publication date: 2013-01-10
Also published as: EP2729762A1

Abstract

An alignment process for aligning a pair of mating shafts, wherein the alignment process utilizes a first laser sensor (212) attached to a first shaft (112) of a pair of mating shafts and a second laser sensor (222) attached to a second shaft (122) of the pair of mating shafts. The process determines an initially read erroneous radial displacement (324) and a backlash generated laser angular offset (234). The initially read erroneous radial displacement (324) and backlash generated laser angular offset (234) are entered into a geometric formula to determine a true radial displacement (310).

Description

BACKLASH MEASUREMENT AND COMPENSATION TO INCREASE THE ACCURACY OF LASER SHAFT ALIGNMENT

CROSS-REFERENCE TO RELATED APPLICATIONS

This PCT application claims the benefit of co-pending United States Non- Provisional Patent Application Serial No. 61/504,500, filed on July 05, 2011, which is incorporated herein by reference in its entirety.

Technical Field

The present invention relates to an apparatus and method for aligning machine shafts using laser equipment, more specifically a method of aligning a pair of coupled shafts while including considerations for backlash.

Background

Rotating machinery, equipment, or other devices can be provided in many form factors, such as an electrical motor, a combustion motor, a pump, a transmission or other gear box, and the like. Rotating equipment is commonly configured coupling at least two rotating devices together, referred to as a machine train. The configuration can couple two or more like devices together, such as motors, pumps, and the like to provide serial addition of power or parallel functionality, respectively. Alternatively, the configuration can couple two or more dissimilar devices together, such as coupling a motor and a transmission, coupling a motor and a pump, and the like to provide joint functionality. In any configuration, alignment between two adjacent components impacts the efficiency and reliability of the equipment.

Many factors can impact alignment between equipment. Alignment of the equipment dictates that the equipment remains stationary, and thus the alignment process is completed when the equipment is in a non-operational state. Additionally, the alignment process is commonly completed in an ambient environment. Unfortunately, this requirement removes a number of variables, which impact the alignment during operation, where those variables are only present during operation. Examples include thermal effects on each element of the equipment, balance of rotating elements, changes in compressive components such as soft feet, changes due to torsional effects, and the like. The operational environment commonly changes in temperature, which affects the mounting area, the equipment, and the like. In most operational scenarios, the equipment and operating environment increases in temperature, impacting the alignment between adjacent equipment.

Each individual machine arrangement is different resulting from each

arrangements unique characteristics. Even identical sets of machinery can dictate different terms for alignment. Factors of each configuration including location, mounting schematics, and the like affect the alignment.

Laser alignment was introduced in the 1980's. This process utilized one or more diode lasers and detectors (PSD's). The PSD's were able to detect fairly accurately (within ΙΟμιη'β) relative positioning between two adjacent shafts. Information is provided to the service person through a display unit. The system determines what information needs to be conveyed to the service person in order to direct the service person on what is required to optimize alignment between two adjacent components. The display unit can be provided in any of many known form factors, including a computer, preferably comprising a wireless interface. Software converts the detector signals into a set of instructions in an understandable format for the operator or service person. Alignment or registration between two adjacent components is commonly defined in two components:

A) Angular misalignment

B) Parallel or offset misalignment

Parallel registration can be defined in two directions, horizontal and vertical, basically referring to respectively X-axis and Y-axis.

Another component that could be considered is end-to-end registration, ensuring sufficient gap is provided for thermal expansion, vibration, and the like.

The fundamental setup of the laser alignment instrumentation has remained unchanged since its inception in the 1980's, including a diode laser based system with a detector and a portable computer with standard alignment software. As technology has evolved, the technological advances have been integrated into the process. Examples include the introduction of wireless technology changed the method of data transfer from the laser/detector to the portable computer, by removing cables previously connecting therebetween. Although technology has advanced and aided the user in certain areas, the overall fundamentals of the process, including the hardware and respective software have remained unchanged over the years.

There are three common errors made in shaft alignment: soft foot, coupling backlash, and not tightening and loosening moveable machine securing bolts in a proper sequence. Of these common errors, soft foot can be the most problematic, while coupling backlash runs a close second.

Backlash is an angular movement within any mechanical system between mating parts. Coupling backlash is common, and to a point, desirable in many types of couplings. Coupling backlash can cause a variety of issues during an alignment procedure, and can cause loss of efficiency, premature wear, and other issues if not properly accommodated during the alignment process.

When performing a laser alignment measurement it is generally assumed that the two measuring units (laser heads) are at the same rotational angle. This is so that in each case the laser line is perpendicular to the sensor on which it is detected: this means that a radial displacement (i.e. movement relative to the shaft) of one head is directly measured as a linear displacement (i.e. movement relative to a fixed point on the sensor) on the sensor of the other head. This process fails to take backlash into consideration.

What is desired is a shaft alignment procedure that includes a process for compensating for backlash between two coupled shafts.

SUMMARY OF THE INVENTION

The present invention is directed towards an apparatus and respective method for aligning two coupled shafts while includes steps for compensating for backlash between two coupled shafts.

In a first aspect of the present invention, a method of aligning two coupled shafts, the method comprising the steps of: attaching a first laser sensor to a first shaft of a pair of mating shafts; attaching a second laser sensor to a second shaft of the pair of mating shafts; determining an initially read erroneous radial displacement; determining a backlash generated laser angular offset; calculating a true radial displacement by using a formula including the initially read erroneous radial displacement and the backlash generated laser angular offset.

In a second aspect, the true radial displacement is utilized to correct radial displacement between the pair of mating shafts along a distance that is parallel to a first laser radial reference line, wherein the first laser radial reference line is a radial centerline of the laser located from a respective shaft rotational axis.

In another aspect, the first laser sensor transmits a laser emitting line to the second laser sensor, wherein the second laser sensor determines an intersecting location of the laser emitting line thereon.

One advantage of the present invention is the ability to align a pair of coupled shafts, including compensation for backlash between the pair of coupled shafts. The steps enable compensation between the two shafts during the alignment process, thus reducing the overall number of steps for completing the alignment procedure.

Compensating for errors due to backlash provides the following advantages for the design of a laser alignment system:

• Geometries where the laser sensor is not central can be adopted - this may make the mechanical design easier or more compact • Backlash can be estimated by asking the user to rock the shafts back and forth and monitoring the change in centroid - reversing the equations for compensation allows the amount of backlash to be compensated

These and other features, aspects, and advantages of the invention will be further understood and appreciated by those skilled in the art by reference to the following written specification, claims and appended drawings, which follow.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the nature of the present invention, reference should be made to the accompanying drawings in which:

FIG. 1 presents an elevation view of an exemplary pair of coupled rotating shafts presenting an axial offset during an exemplary laser alignment process;

FIG. 2 presents an elevation view of the exemplary pair of coupled rotating shafts presenting an angular offset during the exemplary laser alignment process;

FIG. 3 presents an isometric side view of the exemplary pair of coupled rotating shafts presenting a backlash condition causing a rotational angular offset during the exemplary laser alignment process;

FIG. 4 presents an elevation end view illustrating the exemplary laser alignment process;

FIG. 5 presents an elevation end view illustrating the exemplary laser alignment process and introducing a backlash angular offset;

FIG. 6 presents a graphical representation of a geometric relationship between a first laser line radial reference line and a second laser line radial reference line resulting from the backlash angular offset;

FIG. 7 presents a graphical representation of a complex offset geometric relationship between the first laser line radial reference line and the second laser line radial reference line resulting from the backlash angular offset further comprising an axial offset; and

FIG. 8 presents an enlarged view of a portion of the graphical representation of the complex offset geometric relationship between the first laser line radial reference line and the second laser line radial reference line.

Like reference numerals refer to like parts throughout the several views of the drawings. DETAILED DESCRIPTION

The following detailed description is merely exemplary in nature and is not intended to limit the described embodiments or the application and uses of the described embodiments. As used herein, the word "exemplary" or "illustrative" means "serving as an example, instance, or illustration." Any implementation described herein as

"exemplary" or "illustrative" is not necessarily to be construed as preferred or advantageous over other implementations. All of the implementations described below are exemplary implementations provided to enable persons skilled in the art to make or use the embodiments of the disclosure and are not intended to limit the scope of the disclosure, which is defined by the claims. For purposes of description herein, the terms "upper", "lower", "left", "rear", "right", "front", "vertical", "horizontal", and derivatives thereof shall relate to the invention as oriented in FIG. 1. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, brief summary or the following detailed description. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification, are simply exemplary

embodiments of the inventive concepts defined in the appended claims. Hence, specific dimensions and other physical characteristics relating to the embodiments disclosed herein are not to be considered as limiting, unless the claims expressly state otherwise.

Alignment between a pair of coupled shaft assemblies 110, 120 (FIGS. 1 through 3) is critical to optimize uptime and longevity. Misalignment between adjacent rotating machines can impact the configuration in a variety of ways, including premature failure. The following are examples of the impact of premature failure caused by misaligned machinery:

- Increased frequency of replacing parts, such as bearings, couplings, seals, and the like, which result in additional operational costs including replacement parts and labor;

- Increased logistic costs, including materials procurement, inventory holding costs, materials management costs, and the like;

- Increased frequency of interventions, including man hours, materials, tools, transportation, and the like, and thus adding associated intervention costs to the overall operating budget; and - where applicable, impacts from resultant downtime of the machinery, including reduction in productivity, reduced labor efficiencies (revenue per labor cost), reduced real estate efficiency (revenue per area of real estate), lost revenue, and the like.

Alignment of the rotating machinery is accomplished while the machinery is in a non-operational state. The alignment process considers any relation between two adjacent pieces of rotating machines. The term machine can refer to any device comprising a rotating mechanism, and should be considered synonymous with machine, equipment, device, apparatus, and the like.

A first alignment offset for a pair of coupled shaft assemblies 110, 120 is an axial or parallel offset, which is illustrated in FIG. 1. A second alignment offset for a pair of coupled shaft assemblies 110, 120 is an angular offset, which is illustrated in FIG. 2. These two alignment offsets are address using commonly known processes. Addressing a backlash condition, as illustrated in FIG. 3, increases the complexity of the process.

Each shaft assembly 110, 120 includes a first shaft coupling flange 114, 124 affixed to a coupling end of a respective shaft 112, 122. The first shaft coupling flange 114 and second shaft coupling flange 124 are coupled together using any known suitable coupling mechanism. Examples of suitable coupling mechanisms can include threaded fasteners, mechanical interlocks (such as a twist and lock, a jaw coupling, shaft collars, a quick clamp interface, a rigid shaft coupling, a bellows shaft coupling, a flexible beam coupling, a disc shaft coupling, and the like), and the like. It is recognized that a coupling insert (not shown) may be inserted between the first shaft coupling flange 114 and second shaft coupling flange 124.

Alignment between the first shaft 112 and second shaft 122 can be referenced using a first shaft rotational axis 116 and a second shaft rotational axis 126 of the first shaft 112 and second shaft 122, respectively. An exemplary axial offset is identified as a radial offset distance 230. A laser alignment system provides a method for determining the radial offset distance 230 between the first shaft rotational axis 116 and the first laser line 216 as illustrated in FIG. 1. An exemplary angular offset is identified as an angular offset 232. The laser alignment system can also provide a method for determining the angular offset 232 between the first shaft rotational axis 116 and the first laser line 216 as illustrated in FIG. 2. The laser alignment system can include a first shaft alignment laser assembly 210 and a second shaft alignment laser assembly 220. The first shaft alignment laser assembly 210 includes a first shaft laser sensor support member 214 having a distal or sensor end and an attachment end, a first shaft alignment laser sensor 212 attached to the sensor end of the first shaft laser sensor support member 214, and any known mechanical attachment member (not shown) attached to the attachment end of the first shaft laser sensor support member 214. The first shaft alignment laser sensor 212 is temporarily affixed to the first shaft 112 by the mechanical attachment member. Similarly, the second shaft alignment laser assembly 220 includes a second shaft laser sensor support member 224 having a distal or sensor end and an attachment end, a second shaft alignment laser sensor 222 attached to the sensor end of the second shaft laser sensor support member 224, and any known mechanical attachment member (not shown) attached to the attachment end of the second shaft laser sensor support member 224. The second shaft alignment laser sensor 222 is temporarily affixed to the second shaft 122 by the mechanical attachment member. The first shaft laser sensor support member 214 and second shaft laser sensor support member 224 are oriented extending radially from the first shaft rotational axis 116 and second shaft rotational axis 126, respectively, wherein the first shaft laser sensor support member 214 and second shaft laser sensor support member 224 are arranged in parallel alignment with one another when viewed along the rotational axis 116, 126, as illustrated in FIG. 4.

The exemplary embodiment presents a first shaft alignment laser sensor 212 attached to the first shaft 112 and a second shaft alignment laser sensor 222 attached to the second shaft 122. The laser alignment system can be provided as a single laser system or a dual laser system. For a single laser system, the first shaft alignment laser sensor 212 can include a laser and/or a sensor and the second shaft alignment laser sensor 222 would include the pairing element, i.e. if the first shaft alignment laser sensor 212 includes a laser, the second shaft alignment laser sensor 222 would include the sensor. For a dual laser system, each of the first shaft alignment laser sensor 212 and the second shaft alignment laser sensor 222 would include a laser and a sensor. In the preferred embodiment, it is desired to use a dual laser system. The parallel alignment illustrated in FIG. 1 shows how the radial offset distance 230 of a true radial measurement referred to as d' can be measured by observing changes in the linear measurement referred to as d on the shaft alignment laser sensor 212, 222.

However in the case of laser heads which emit a continuous line of laser light which crosses a one (1) dimensional sensor, then an angular mismatch between the two heads also causes a change in the linear displacement on the sensor without an actual change in radial displacement. Any angular mismatch introduces an error in the alignment process. The subject disclosure teaches a method compensating for this error.

Precision is critical during a shaft alignment procedure. In an optimal process, the first shaft laser sensor support member 214 and second shaft laser sensor support member 224 are arranged in parallel alignment with one another when viewed along the rotational axis 116, 126, as illustrated in a shaft end view presented in FIG. 4. The radial alignment of the first shaft laser sensor support member 214 and second shaft laser sensor support member 224 is represented by a first laser radial reference line 215. Various key points or intersections are defined by subscripted letters. Lines spanning between two points are defined by a combination of each of the respective subscripted letters associated with each end of the line. A true linear displacement 312 defines movement relative to a fixed point on the first shaft alignment laser sensor 212, wherein an exemplary fixed sensor point 213, 223 (referenced by the subscripted letter Za) and the intersection between the first laser line 216 and the first shaft alignment laser sensor 212 is defined by an optimal laser alignment sensor intersection 250 (referenced by the subscripted letter Aa). The true linear displacement 312, referenced by the subscripted letter ZaAa, spans between the first shaft laser fixed sensor point 213 (referenced by the subscripted letter Za) and the optimal laser alignment sensor intersection 250 (referenced by the subscripted letter Aa). The true radial displacement 310, referenced by the subscripted letter OaAa, spans between the first shaft rotational axis 116 (referenced by the subscripted letter Oa) and the optimal laser alignment sensor intersection 250 (referenced by the subscripted letter Aa). The true linear displacement 312 provides the service person with the information (dimensions) for resolving any alignment offsets between the two shafts 112, 122.

A factor referred to as backlash can introduce error into to the alignment process. Backlash is presented in the illustration shown in FIG. 3 and in the representative graphical illustration shown in FIG. 5. Backlash results from differences in angular movement between mating parts, more specifically angular differences between the first shaft 112 and the second shaft 122, represented by a first shaft rotational offset 118 and second shaft rotational offset 128 respectively. Coupling backlash is common, and to a point, desirable in many types of couplings. Coupling backlash causes a backlash generated laser angular offset 234 between the first shaft laser sensor support member 214 and second shaft laser sensor support member 224, represented by a first laser radial reference line 215 and second laser radial reference line 225, respectively. The backlash generated laser angular offset 234 is also defined by a backlash generated laser angular offset 234, which is geometrically represented by the symbol Θ. The backlash generated laser angular offset 234 introduces an offset, which changes the intersection between the first laser radial reference line 215 and the first laser line 216 (identified by the optimal laser alignment sensor intersection 250)(referenced by the subscripted letter Aa) to the intersection between the first laser radial reference line 215 and the second laser line 226 (identified by the radially offset linear displacement sensor intersection 252)(referenced by the subscripted letter Ab). The result is an error in a radial direction, referred to as a first radial alignment error 320 (referenced by the subscripted line AaAb). The graphical representation presents the impact of the backlash or angled offset between the first laser radial reference line 215 and the second laser radial reference line 225. The first radial alignment error 320 impacts the other dimensions, wherein the angular relation changes the true linear displacement 312 to an erroneous linear displacement 322 (referenced by the subscripted line ZaAb) and the true radial displacement 310 to an erroneous radial displacement 324 (referenced by the subscripted line OaAb). The present invention presents a process for compensating for potential error introduced by backlash.

Other elements noted in the graphical representation of FIG. 5 include a second laser line 226, which defines a second laser alignment sensor intersection 254 (referenced by the subscripted letter Ae) at an intersection with the second laser radial reference line 225. A respective distance between the first shaft rotational axis 116 (referenced by the subscripted letter Oa) and the second laser alignment sensor intersection 254 (referenced by the subscripted letter Ae) is referred to as an angled radial displacement 336

(referenced by the subscripted line OaAe).

Graphical representations utilized in mathematical equations to compensate for the angular offset caused by backlash are presented in FIGS. 5 through 8. Each of the two (2) shaft alignment laser assemblies 212, 222 initiates their rotation about the first shaft rotational axis 116 (referenced by the subscripted letter Oa). The true radial

displacement 310 (referenced by the subscripted line OaAa) determines the actual radial displacement. When the second laser radial reference line 225 is offset in radial alignment respective to the first laser radial reference line 215, the laser intersection is referred to as a second laser alignment sensor intersection 254 (referenced by the subscripted letter Ae). The radial displacement measure by the radially offset laser spans between the first shaft rotational axis 1 16 and the second laser alignment sensor intersection 254, wherein the radial displacement measure is referred to as an angled radial displacement 336 (referenced by the subscripted line OaAe). The true radial displacement 310 is determined by rotating the angled radial displacement 336 (referenced by the subscripted line OaAe) along the second laser radial reference line 225 by the backlash generated laser angular offset 234

(referenced by the symbol Θ), in accordance with a superimposed corrected radial displacement offset 270, to align and superimpose the angled radial displacement 336 upon the first laser radial reference line 215.

The backlash generated laser angular offset 234 (referenced by the symbol Θ) rotates the second laser line 226 (represented by a second laser radial reference line 225) into a misaligned configuration. The second laser line 226 projects a line that intersects the first laser radial reference line 215 at an intersection referred to as a radially offset linear displacement sensor intersection 252 (referenced by the subscripted letter Ab). The radially offset linear displacement sensor intersection 252 defines an erroneous radial displacement 324 (referenced by the subscripted line OaAb), which is an effective radial measurement between the first shaft rotational axis 116 and the radially offset linear displacement sensor intersection 252. A first laser line 216 defines a reference line extending from the optimal laser alignment sensor intersection 250 perpendicularly from the first laser radial reference line 215. A radially offset effective laser radial distance 227 defines a reference line extending from the radially offset linear displacement sensor intersection 252 perpendicularly from the first laser radial reference line 215. The result of the backlash generated laser angular offset 234 (referenced by the symbol Θ) is an erroneous dimension referred to as a first radial alignment error 320 (referenced by the subscripted line AaAb). It is noted that the length of true radial displacement 310 (referenced by the subscripted line OaAa) and angled radial displacement 336 (referenced by the subscripted line OaAe) are the same.

Using trigonometry, it is noted that:

OaAe

Cos (Θ) =

OaAb

OaAa OaAe

Therefore: OaAb = =

cos (Θ) cos (Θ)

OaAa

Or Alternatively: (OaAa + AaAb) =

Cos (Θ)

1

Therefore AaAb = OaAa * (

Cos (Θ)

It is noted that in a condition where first laser radial reference line 215 and second laser radial reference line 225 are in alignment, the resulting backlash generated laser angular offset 234 (referenced by the symbol Θ) equals zero. In this condition, the error is zero as expected.

The desired dimension between the first shaft laser fixed sensor point 213

(referenced by the subscripted letter Za) and the optimal laser alignment sensor intersection 250 (referenced by the subscripted letter Aa) is identified as a true linear displacement 312 (referenced by the subscripted line ZaAa). In a condition where the first laser radial reference line 215 and the second laser radial reference line 225 are misaligned, the misalignment (illustrated as a backlash generated laser angular offset 234) a first radial alignment error 320 is introduced (referenced by the subscripted line AaAb), wherein the first radial alignment error 320 (referenced by the subscripted line AaAb) is added to the true linear displacement 312 (referenced by the subscripted line ZaAa) to become an erroneous linear displacement 322 (referenced by the subscripted line ZaAb).

The goal of the process is to determine the value of the first radial alignment error 320 to determine the desired, accurate value for the true radial displacement 310.

A complex backlash error amplifies the complexity of the alignment process. An exemplary complex backlash scenario is presented in FIG. 7 and detailed in the enlarged view presented in FIG. 8. The complex backlash error introduces an offset between the first shaft rotational axis 116 and either of the shaft alignment laser sensors 212, 222.

The offset between the first shaft rotational axis 116 and either of the shaft alignment laser sensors 212, 222 is illustrated by a sensor offset dimension 360

(referenced by the subscripted line CaCg) spanning between a sensor shaft centerline registration reference point 260 (referenced by the subscripted letter Ca) and a sensor shaft centerline offset reference point 262 (referenced by the subscripted letter Cg). The centerline of the shaft alignment laser sensors 212, 222 is identified as an offset laser centerline reference 117. The offset between the first shaft rotational axis 116 and the offset laser centerline reference 117 introduces another level of complexity into the alignment process. In a condition where the laser sensor radial reference line 215 is offset, the revised reference line is identified as an offset laser radial reference line 245. The second laser line 226 is extended to intersect with the offset laser radial reference line 245, wherein the intersection is defined by a radially and angular offset laser sensor intersection 258.

The sensor offset dimension 360 (referenced by the subscripted line CaCg) is oriented perpendicular to each of the first laser radial reference line 215 and offset laser radial reference line 245.

When aligning a pair of mated shafts having an offset between the first shaft rotational axis 116 and either of the shaft alignment laser sensors 212, 222 aggravates the error introduced during the alignment process. The complex scenario introduces a second radial alignment error 330, which further aggravates the measurement error from the desired measurement of the true radial displacement 310 (referenced by the subscripted line OaAa). The extended second laser line 226 intersects the offset laser radial reference line 245 at a radially and angular offset laser sensor intersection 258 (referenced by the subscripted letter Ag). A complex radially offset effective laser radial distance 237 defines a reference line extending from the radially and angular offset laser sensor intersection 258 perpendicularly from the offset laser radial reference line 245. In a configuration having a simple angular offset between the first laser radial reference line 215 and the second laser radial reference line 225, the resulting error is defined by the first radial alignment error 320 (referenced by the subscripted line AaAb). The complex scenario introduces an additional error identified by a second radial alignment error 330 (referenced by the subscripted line AaAg). A complex erroneous linear displacement 332 (referenced by the subscripted line AzAg) is a measurement between the shaft laser fixed sensor point 213 (referenced by the subscripted letter Za) and the complex radially offset effective laser radial distance 237.

Several other intersecting coordinates are noted for reference. An optimal laser alignment sensor intersection from offset laser centerline 259 is a projection of the optimal laser alignment sensor intersection 250 (referenced by the subscripted letter Aa) onto the offset laser radial reference line 245. The optimal laser alignment sensor intersection from offset laser centerline 259 (referenced by the subscripted letter Ah) is located at a distance from the offset laser centerline reference 117 (referenced by the subscripted letter Og) which is equals the length of the true radial displacement 310 (referenced by the subscripted line OaAa) initiating from the first shaft rotational axis 116 (referenced by the subscripted letter Oa). Similarly, a projected radially offset linear displacement sensor intersection 256 (referenced by the subscripted letter Af) is located at a distance from the offset laser centerline reference 117 (referenced by the subscripted letter Og) which is equals the length of the erroneous radial displacement 324 (referenced by the subscripted line OaAb) initiating from the first shaft rotational axis 116 (referenced by the subscripted letter Oa).

In this scenario, the distance measured is referred to as a complex erroneous linear displacement 340 (referenced by the subscripted line OgAg), which measures the distance between the offset laser centerline reference 117 (referenced by the subscripted letter Og) and the radially and angular offset laser sensor intersection 258 (referenced by the subscripted letter Ag). In order to determine the desired dimension of the true radial displacement 310 (referenced by the subscripted line OaAa), the process must determine the first radial alignment error 320 (referenced by the subscripted line AaAb) and the second radial alignment error 330 (referenced by the subscripted line AaAg), then subsequently subtract the values of the first radial alignment error 320 and the second radial alignment error 330 from the value of the complex erroneous linear displacement 340, wherein:

OaAa = OgAg - (AaAb + AaAg)

The following are other geometric relationships that can be used to correct for a complex backlash error:

AaAg AaAg

Tan (Θ)

AfAb CaCg

It is understood that AfAb = CaCg.

Therefore: AaAg = CaCg * tan (Θ)

This provides a calculation for the dimension of OgAg as:

OaAa

OgAg + (CaCg * Tan (0))

Cos (Θ)

Or Alternatively:

OaAa

(OaAa + (AaAb + AaAg)) + ( CaCg * Tan (0))

Cos (Θ)

Therefore:

The total error = AhAg = (AaAb + AaAg) Wherein:

1

(AaAb + AaAg) = OaAa * ( 1) + CaCg * Tan (Θ)

Cos (Θ)

This means that the total error in our measurement of true radial displacement 310 (referenced by the subscripted line OaAa) has two components: one is related to the true measurement of true radial displacement 310 (referenced by the subscripted line OaAa) divided by Cos (Θ), the other is the sensor offset dimension 360 (referenced by the subscripted line CaCg) multiplied by Tan (Θ). This latter term is independent of the true measurement and is principally dominated by distance of the sensor-offset dimension 360 (referenced by the subscripted line CaCg), which is typically fixed by the design of the laser heads.

Again note that if Θ is 0 the error is 0 and OaAb = OaAa = OaAe as expected.

The following refers to a compensation method for errors due to backlash:

Compensation for errors due to backlash relies on measuring the rotation angles of each shaft alignment laser sensor 212, 222 and compensating for errors due to angular mismatches between them. We can refer to the two errors as follows:

AaAb = OaAa * (

Cos and

AaAg CaCg tan (Θ)

The error referred to as second radial alignment error 330 (referenced by the subscripted line AaAg) is the simplest to compensate for, as the value does not vary with the actual measurement. The second radial alignment error 330 (referenced by the subscripted line AaAg) also tends to dominate for typical measurements. For example if CaCg = 5mm and ZaAa = 100mm then for errors in the range ±0.5° these terms are as follows: θ AaAb (mm) AaAg (mm) Total Error (mm)

-0.5° -0.0038 -0.0436 -0.0474

-0.4° -0.0024 -0.0349 -0.0373

-0.3° -0.0014 -0.0262 -0.0276

-0.2° -0.0006 -0.0175 -0.0181

-0.1° -0.0002 -0.0087 -0.0089

0.0° 0.0000 0.0000 0.0000

0.1° -0.0002 0.0087 0.0086

0.2° -0.0006 0.0175 0.0168

0.3° -0.0014 0.0262 0.0248

0.4° -0.0024 0.0349 0.0325

0.5° -0.0038 0.0436 0.0398

The following describes the compensation for errors; the difference between the angles measured by each head is calculated:

Initially, using the following from above:

OaAa

(OaAa + (AaAb + AaAg)) = + ( CaCg * Tan (Θ))

Cos (Θ) where the complex erroneous linear displacement 340 (referenced by the subscripted line OgAg) is also recognized as:

OgAg = (OaAa + (AaAb + AaAg))

The complex erroneous linear displacement 340 (referenced by the subscripted line OgAg) is the apparent distance from the first shaft rotational axis 116 (referenced by the subscripted letter Oa), based on the observed reading. The compensation can be calculated as follows:

OaAa

OgAg = + ( CaCg * Tan (0))

Cos (Θ)

Therefore:

OaAa = Cos (Θ) * (OgAg - CaCg * Tan (Θ)) = Cos * (θι - θ₂) * (CaCg * Tan (θι - θ₂) Where θι is the measured radial displacement value measured for the first shaft alignment laser sensor 212 and θ₂ is the measured radial displacement value measured for the second shaft alignment laser sensor 222.

In other words, to compensate for the first radial alignment error 320 (referenced by the subscripted line AaAb), a compensation value (ci) is calculated as follows:

Ci = - (CaCg * Tan (θι - θ₂)) and added to the measured radial displacement value (where ( and 6 are the angles measured at each head, and so ( - 6 = Θ in FIGS. 5-8).

To compensate for the second radial alignment error 330 (referenced by the subscripted line AaAg), a compensation value (C₂) is calculated as follows:

and the adjusted radial displacement value is multiplied by the compensation value (C₂).

Note that the true radial displacement 310 (referenced by the subscripted line OaAa) is the total height from the first shaft rotational axis 116 (referenced by the subscripted letter Oa) to the point where the laser line 216 impinges on the sensor 212, and so the user needs to provide an additional piece of information (in the simplest case, the distance from the first shaft rotational axis 116 (referenced by the subscripted letter Oa) to the first shaft laser fixed sensor point 213 (referenced by the subscripted letter Za)) in order to provide accurate compensation.

It is noted that the process enables partial compensation in those conditions where only part of the error is required.

Typically if the shaft alignment laser sensor 212, 222 is offset so that it is not in line with the first shaft rotational axis 116, then the contribution of the first radial alignment error 320 (referenced by the subscripted line AaAb) is much more significant than the second radial alignment error 330 (referenced by the subscripted line AaAg). In this case it may be a suitable compromise to only compensate for this error, by calculating the following: d = - (CaCg * Tan (Q₁ - θ₂)) and adding this to the measured value.

This has the advantage that the user need not supply a value for the height of the sensor 212, 222 above the first shaft rotational axis 116, wherein these values are required for full compensation.

It is noted that the information can be entered into a computing device. The computing device would include a processor, digital memory, a user interface for entering and obtaining information between the user and the computing device, and a set of instruction steps, the steps comprising a method of entering measurements, interpreting the measurements, assigning the measurements to variables of pre-established equations, and one or more calculations to determine the true radial displacement 310 between a first shaft 112 and a second shaft 122.

Since many modifications, variations, and changes in detail can be made to the described preferred embodiments of the invention, it is intended that all matters in the foregoing description and shown in the accompanying drawings be interpreted as illustrative and not in a limiting sense. Thus, the scope of the invention should be determined by the appended claims and their legal equivalence.

Ref. Description Geometric No. Reference

110 first shaft assembly

112 first shaft

114 first shaft coupling flange

116 first shaft rotational axis Oa

117 offset laser centerline reference Og

118 first shaft rotational offset

120 second shaft assembly

122 second shaft

124 second shaft coupling flange

126 second shaft rotational axis

128 second shaft rotational offset

210 first shaft alignment laser assembly

212 first shaft alignment laser sensor

213 first shaft laser fixed sensor point

214 first shaft laser sensor support member

215 first laser radial reference line

216 first laser line

220 second shaft alignment laser assembly

222 second shaft alignment laser sensor

223 second shaft laser fixed sensor point

224 second shaft laser sensor support member

225 second laser radial reference line

226 second laser line

227 radially offset effective laser radial distance

230 radial offset distance

232 angular offset

234 backlash generated laser angular offset Θ

237 complex radially offset effective laser radial distance

245 offset laser radial reference line

250 optimal laser alignment sensor intersection Aa

252 radially offset linear displacement sensor intersection Ab

254 second laser alignment sensor intersection Ae

256 projected radially offset linear displacement sensor intersection Af

258 radially and angular offset laser sensor intersection Ag

259 optimal laser alignment sensor intersection from offset laser centerline Ah

260 sensor shaft centerline registration reference point Ca 262 sensor shaft centerline offset reference point Cg 270 superimposed corrected radial displacement offset

310 true radial displacement OaAa

312 true linear displacement ZaAa

320 first radial alignment error AaAb

322 erroneous linear displacement ZaAb

324 erroneous radial displacement OaAb

330 second radial alignment error AaAg

332 complex erroneous linear displacement ZaAg

336 angled radial displacement OaAe

340 complex erroneous linear displacement OgAg

360 sensor offset dimension CaCg

Claims

What is claimed is:

1. A method of aligning a pair of mating shafts, the method comprising the steps of: attaching a first laser sensor (212) to a first shaft (112) of a pair of mating shafts; attaching a second laser sensor (222) to a second shaft (122) of the pair of mating shafts; determining an initially read erroneous radial displacement (324); determining a backlash generated laser angular offset (234); calculating a true radial displacement (310) by using a formula including the initially read erroneous radial displacement (324) and the backlash generated laser angular offset (234).

2. A method of aligning a pair of mating shafts as recited in claim 1 , the method comprising the additional steps of: utilizing the true radial displacement to correct radial displacement between the pair of mating shafts along a distance that is parallel to a first laser radial reference line, wherein the first laser radial reference line is a radial centerline of the laser located from a respective shaft rotational axis

3. A method of aligning a pair of mating shafts as recited in claim 1 or 2, the method comprising the additional steps of: transmitting a laser emitting line from the first laser sensor to the second laser sensor, wherein the second laser sensor determines an intersecting location of the laser emitting line thereon.

4. A method of aligning a pair of mating shafts as recited in any one of claims 1 to 3, wherein the step of calculating a true radial displacement (310) is accomplished by using formulas of:

AaAb = OaAb - OaAa 1

and OaAa = AaAb / ( - 1)

Cos (Θ) wherein:

OaAa is the true radial displacement (310);

OaAb is the initially read erroneous radial displacement (324);

AaAb is a radial alignment error (320); and

Θ is the backlash generated laser angular offset (234).

5. A method of aligning a pair of mating shafts as recited in any one of claims 1 to 4, the method comprising the additional steps of: aligning the first laser sensor (212) to a first shaft rotational axis (116) of the first shaft (112); and aligning the second laser sensor (222) to a second shaft rotational axis (126) of the second shaft (122).

6. A method of aligning a pair of mating shafts as recited in any one of claims 1 to 5, the method comprising the additional steps of: entering the following information into a computer:

A) the first radial alignment error (320); and B) the backlash generated laser angular offset (234); using a processor, digital memory, and a set of instructions programmed within the computer to calculate the true radial displacement (310).

7. A method of aligning a pair of mating shafts as recited in any one of claims 1 to 6, the method comprising the additional step of determining if a value of the backlash generated laser angular offset (234) is zero, wherein when the value of the backlash generated laser angular offset (234) is zero, then the true radial displacement (310) is determined to equal the initially read erroneous radial displacement (324).

8. A method of aligning a pair of mating shafts, the method comprising the steps of: attaching a first laser sensor (212) to a first shaft (112) of a pair of mating shafts; attaching a second laser sensor (222) to a second shaft (122) of the pair of mating shafts; determining an initially read complex erroneous linear displacement (340); determining a backlash generated laser angular offset (234); determining a sensor offset dimension (360), the sensor offset dimension being a linear distance between a radial line extending from a shaft rotational axis (116) and an offset laser radial reference line (245); and calculating a true radial displacement (310) by using a formula including the initially read erroneous radial displacement (324) and the backlash generated laser angular offset (234).

9. A method of aligning a pair of mating shafts as recited in claim 8, the method comprising the additional steps of: utilizing the true radial displacement to correct radial displacement between the pair of mating shafts along a distance that is parallel to a first laser radial reference line, wherein the first laser radial reference line is a radial centerline of the laser located from a respective shaft rotational axis

10. A method of aligning a pair of mating shafts as recited in claim 8 or 9, the method comprising the additional steps of: transmitting a laser emitting line from the first laser sensor to the second laser sensor, wherein the second laser sensor determines an intersecting location of the laser emitting line thereon.

11. A method of aligning a pair of mating shafts as recited in any one of claims 8 to

10, wherein the step of calculating a true radial displacement (310) is accomplished by using a formula of

OaAa = Cos (Θ) * (OgAg - CaCg * Tan (Θ))

wherein:

OaAa is the true radial displacement (310); CaCg is the sensor offset dimension (360)

OgAg is a initially read complex erroneous linear displacement (340); and Θ is the backlash generated laser angular offset (234) for the first laser.

12. A method of aligning a pair of mating shafts as recited in any one of claims 8 to

11, the method comprising the additional steps of: aligning the first laser sensor (212) to a first shaft rotational axis (116) of the first shaft (112); and aligning the second laser sensor (222) to a second shaft rotational axis (126) of the second shaft (122).

13. A method of aligning a pair of mating shafts as recited in any one of claims 8 to

12, the method comprising the additional steps of: entering the following information into a computer:

A) the first radial alignment error (320);

B) the backlash generated laser angular offset (234); and

C) the sensor offset dimension (360), using a processor, digital memory, and a set of instructions programmed within the computer to calculate the true radial displacement (310).

14. A method of aligning a pair of mating shafts as recited in any one of claims 8 to

13, the method comprising the additional step of determining if a value of the backlash generated laser angular offset (234) is zero, wherein when the value of the backlash generated laser angular offset (234) is zero, then the true radial displacement (310) is determined to equal the initially read erroneous radial displacement (324).