Compressor Wheel With Supports

In one aspect of the present disclosure, a compressor wheel is disclosed that includes a body, a plurality of blades, and one or more supports. The supports add strength to the compressor wheel and may be configured as ribs, for example. The body has a first face (e.g., an outer or front face), which may include the blades, and a second face (e.g. an inner or rear face), which may include the supports. The supports may include an arcuate configuration curving forward in a direction of rotation of the compressor wheel.

BACKGROUND

Compressor wheels in forced induction devices (e.g., turbochargers or superchargers for internal combustion engines) accelerate at high rates (e.g., up to 200,000 rpm per second) and rotate in steady state at high speeds (e.g., up to 300,000 rpm), which can subject the compressor wheel to high stress. For example, during acceleration, the wheel may be subject to higher torsional loading and, thereby, higher stress (e.g., shear stress) as torque is transferred radially outward from the drive shaft through the compressor wheel. More particularly, as the inner regions of the compressor wheel move ahead of the outer regions, stress (i.e., shear stress) is created and builds in the material comprising the compressor as torque is transferred radially outward.

Conventional compressor wheels are typically made of metallic materials and have a solid body in which the metal material extends continuously in an axial direction from a first face (e.g., an outer or front face) to a second face (e.g., an inner or rear face). In known compressor wheels, the first (outer) face is generally curved and includes a plurality of blades, while the second (inner) face is generally planar and/or extends axially away from the first face. This construction (i.e., materials and structure) allows conventional compressor wheels to distribute and manage torsional loading and stress during acceleration.

Compressor wheels including (e.g., formed from) composite materials may offer various advantages over metallic compressor wheels, such as, for example, reduced mass and reduced moment of inertia, which can facilitate quicker response and/or allow for reduced motor size (e.g., in electric motor-driven forced induction devices). Composite compressor wheels, however, may be subject to different strength considerations. The present disclosure addresses the concern by providing composite compressor wheels that include strengthening supports to increase structural rigidity and the ability of the composite compressor wheels to withstand the torsional loads and stresses created during acceleration.

SUMMARY

In one aspect of the present disclosure, a compressor wheel is disclosed that includes a body, a plurality of blades, and one or more supports. The supports add strength to the compressor wheel and may be configured as ribs, for example. The body has a first face (e.g., an outer or front face), which may include the blades, and a second face (e.g. an inner or rear face), which may include the supports. The supports may include an arcuate configuration curving forward in a direction of rotation of the compressor wheel.

In certain embodiments, the body, the blades, and the supports may be integrally formed. For example, the body, the blades, and the supports may be injection molded from a composite material (e.g., glass-filled nylon).

In certain embodiments, the blades may have a width that increases from an intermediate region to inner and outer regions spaced radially inward and outward from the intermediate region, respectively.

In certain embodiments, the blades may have a substantially constant width (e.g., over a majority of a radial length thereof).

In certain embodiments, the supports may increase in thickness moving in an axial direction toward a rear surface of the rear face of the body.

In certain embodiments, the supports may have a filleted transition to the rear face of the body, which may have a substantially constant radius over a majority of a radial length thereof.

In certain embodiments, a radially inner end of each support may be offset relative to the axis.

In certain embodiments, the compressor wheel may include a hub with a shaft coupling that protrudes radially rearward form the rear face of the body.

In certain embodiments, the hub and the shaft coupling may be integrally formed with the body.

In certain embodiments, a trailing edge of each support may be positioned in tangential relation to the hub.

In certain embodiments, an end of the hub may have a diameter that defines a minimum radial dimension extending across the hub in perpendicular relation to the axis of rotation.

In certain embodiments, the trailing edge of each support may be positioned in tangential relation to the diameter defined by the end of the hub.

In certain embodiments, a leading edge of each support may intersect the trailing edge of an adjacent support.

In certain embodiments, the diameter of the hub may intersect the leading edge of one or more of the supports and the trailing edge of one or more of the supports.

In certain embodiments, the leading edge may be offset relative to the axis.

In certain embodiments, the leading and trailing edges of each support may be positioned in tangential relation to the hub, but in opposite directions.

In certain embodiments, the blades may curve in a direction opposite to the direction of curvature of the supports.

In certain embodiments, the body may include one or more cavities on the rear face thereof located between adjacent supports.

In certain embodiments, the compressor wheel may be incorporated into a forced induction device, such as an exhaust driven turbocharger.

In another aspect of the present disclosure, a compressor wheel is disclosed that includes a body having opposing first and second faces, and a hub that is configured and dimensioned for mechanical connection to a shaft to facilitate rotation of the compressor wheel about an axis of rotation. The compressor wheel also includes a plurality of blades included on the first face of the body and extending radially outwardly from the hub, and a plurality of supports included on the second face of the body.

Each support includes a first end that is positioned adjacent to the hub and an opposing second end that is spaced radially from the first end (i.e., in certain embodiments, the supports may extend radially outward from the hub). The supports are configured and dimensioned to transfer torque radially outward across the body of the compressor wheel to reduce stress in the body during acceleration.

In certain embodiments, the body, the blades, and the supports may be integrally formed.

In certain embodiments, the compressor wheel may be formed from a composite material, for example, glass-filled nylon.

In certain embodiments, each of the supports may include a first end that is positioned adjacent the hub and an opposing second end that is spaced radially from the first end. In such embodiments, each of the supports may be arcuate in configuration and may curve from the first end to the second end. For example, the supports may curve from the first end to the second end in correspondence with a direction of rotation of the compressor wheel.

In certain embodiments, the blades may include an arcuate configuration, and may curve in a direction opposite to the supports.

In certain embodiments, the supports may each define a thickness extending orthogonally in relation to the axis of rotation. The thickness may be constant or variable between the first and second ends of the supports. For example, the supports may each include a first section adjacent the first end of the support, a second section adjacent the second end of the support, and an intermediate section positioned between the first section and the second section, wherein the first section defines a first thickness, the second section defines a second thickness, and the third section defines a third thickness that is less than the first thickness and the second thickness.

In certain embodiments, the supports may each define a centerline that intersects the axis of rotation. Alternatively, however, the supports may each define a centerline that is offset from the axis of rotation whereby the supports extend tangentially from the hub.

In certain embodiments, the supports may each include a leading edge spaced a first radial distance from the axis of rotation and a trailing edge spaced a second radial distance from the axis of rotation less than the first radial distance.

In certain embodiments, the supports may be configured, dimensioned, and positioned such that the leading edge of each support intersects the trailing edge of an adjacent support.

In another aspect of the present disclosure, a compressor wheel is disclosed that includes a body having opposing first and second faces (e.g., outer/front and inner/rear faces), a plurality of blades included on the first face, and a plurality of supports included on the second face.

The body of the compressor wheel also includes a hub that is configured and dimensioned for mechanical connection to a shaft to facilitate rotation of the compressor wheel about an axis of rotation.

In certain embodiments, the blades may extend radially outward from the hub and may curve in a first direction (e.g., in correspondence with a direction of rotation of the compressor wheel), whereas the supports may extend radially outward from the hub and may curve in a second direction opposite the first direction.

Each of the supports defines a thickness extending orthogonally in relation to the axis of rotation. In certain embodiments, the thickness of each support may be constant between first and second ends thereof. Alternatively, however, the thickness of each support may vary. For example, in certain embodiments, the supports may each include a first section adjacent a first end of the support, a second section adjacent an opposing second end of the support, and an intermediate section positioned between the first section and the second section, wherein the first section defines a first thickness, the second section defines a second thickness, and the third section defines a third thickness less than the first thickness and the second thickness.

In another aspect of the present disclosure, a compressor wheel is disclosed that includes a body having opposing first and second faces (e.g., outer/front and inner/rear faces), a plurality of blades included on the first face, and a plurality of supports included on the second face.

The body of the compressor wheel also includes a hub that is configured and dimensioned for mechanical connection to a shaft to facilitate rotation of the compressor wheel about an axis of rotation.

In certain embodiments, each of the supports may define a centerline that is offset from the axis of rotation whereby the supports extend tangentially from the hub.

In certain embodiments, the supports may each include a leading edge that is spaced a first radial distance from the axis of rotation and a trailing edge that is spaced a second radial distance from the axis of rotation less than the first radial distance. In such embodiments, the leading edge of each support may intersect the trailing edge of an adjacent support.

DETAILED DESCRIPTION

The present disclosure describes a compressor wheel for use in a forced induction device, such as a turbocharger or a supercharger, which may be formed from non-metallic materials, such as polymers and/or composite materials. The presently disclosed compressor wheel is configured and dimensioned to distribute and/or otherwise manage torsional loading and stress created during acceleration. More specifically, the compressor wheel includes strengthening supports that are configured and dimensioned to transfer torque radially through the compressor wheel, such as, for example, via compression during acceleration, to reduce stress. The strengthening supports may be curved and/or linear in configuration, and may be facilitate uniformity in radial growth of the compressor wheel in outer portions thereof.

With reference toFIGS. 1-7, a forced induction device100is illustrated that includes a housing140and a compressor wheel210that is positioned within the housing140. In use, the forced induction device100may be configured as part of a powertrain of a vehicle and be arranged to supply compressed air to an internal combustion engine of the powertrain. The compressor wheel210may be actuated (i.e., rotated) through connection to, or communication with, any suitable drive source. For example, the compressor wheel210may be configured and dimensioned for connection to an electric motor. Additionally, or alternatively, it is envisioned that the compressor wheel210may be configured, dimensioned, and positioned for rotation via exhaust gas from the engine (e.g., in the context of a turbocharger) or via mechanical power transfer from the engine (e.g., in the context of a supercharger).

The compressor wheel210may be formed from any suitable material, such as, for example, polymer(s), composite materials, such as glass-filled nylon, and/or other non-metallic materials. In certain embodiments, it is envisioned that the compressor wheel210may be unitary in construction, and that the compressor wheel210may be formed, for example, through a molding process, such as injection or insert molding.

The compressor wheel210includes a body212(FIGS. 2, 3) having a first (outer/front) face214and a second (inner/rear) face216. The body212includes a hub217that facilitates connection to a drive shaft152(FIG. 1) such that the compressor wheel210is rotatable about an axis of rotation212a(FIG. 2) via connection to, or communication with, the aforementioned drive source. In the illustrated embodiment, for example, the hub217includes a shaft coupling218formed integrally with the body212that incorporates an engagement structure219. In the embodiment seen inFIGS. 2 and 3, for example, the engagement structure219includes a circular bore219aand a series of recesses219bthat collectively define a generally cruciform configuration. It should be appreciated, however, that in alternate embodiments of the disclosure, the specific configuration and components of the engagement structure219may be varied in alternate embodiments of the disclosure. For example, it is envisioned that the engagement structure219may include a hexagonal cross-sectional configuration. Additionally, or alternatively, the engagement structure219may include any structure suitable for the intended purpose of connecting the drive shaft152to the compressor wheel210for rotation in the manner described herein, such as, for example, ribs, detents, etc.

The hub217extends axially with respect to inner and outer surfaces216a,216bof the body212so as to define respective inner and outer faces217a,217bhaving transverse cross-sectional dimensions (e.g., a diameters) that extends in orthogonal relation to the axis of rotation212a. Although illustrated as including a generally cylindrical configuration in the illustrated embodiments, whereby the hub217defines a circular cross-section, it is envisioned that the hub217may assume alternate geometrical configurations. For example, it is envisioned that the hub217may be generally frusto-conical in configuration.

Although the engagement structure219is shown and described as being integrally formed with the hub217in the embodiment illustrated inFIGS. 1-7, in an alternate embodiment, the engagement structure219may be provided on a separate insert that is configured and dimensioned for receipt by the hub217. For example, with reference toFIG. 8, an insert219cis disclosed that is positionable within an opening217cdefined by the hub217. The insert219cincludes a series of projections219dthat are configured and dimensioned for engagement with corresponding projections217ddefined by the hub217. In such embodiments, it is envisioned that the insert219cand the hub217may be connected in any suitable manner, such as, for example, via a press-fit engagement, welding, etc., and that the hub217and the insert219cmay include any suitable cross-sectional geometry, e.g., square, hexagonal, flat, etc.

It is envisioned that the insert219cmay be formed from the same material as the hub217and the compressor wheel210, or that the hub217and the insert219cmay be formed from different materials. For example, the hub217may be formed from a non-metallic material, such as glass-filled nylon, whereas the insert219cmay be formed from a metallic material, such as aluminum, steel, etc.

It is envisioned that the insert219cmay serve as a compression limiter to reduce or eliminate load on the hub217. Additionally, it is envisioned that the insert219cmay increase achievable tip speeds by reducing bore stress on the hub217.

With reference again toFIGS. 1-7, the outer face214of the body212includes (e.g., defines or forms) the outer surface216a(FIG. 3), and is generally convex in configuration. The outer face214includes a plurality of blades220that extend outwardly from the outer surface214a. The blades220are configured and dimensioned to draw air from an intake (not shown) and compress the air such that it is expelled from an outlet (not shown) at a higher pressure for forced induction into an internal combustion engine, for example. It is envisioned that the plurality of blades220may be formed integrally with the body212(e.g., as part of the molding process), and thus, that the blades220and the body212may be formed from the same material. Alternatively, it is envisioned that the blades220may be formed separately from the body212and attached thereto, such as, for example, via welding. In such embodiments, the body212and the blades220may be formed from the same or different materials.

In certain embodiments, the blades220may include a curved configuration, as shown inFIG. 3, for example. More particularly, it is envisioned that the curvature of the blades220may oppose the direction of rotation of the compressor wheel210, which is indicated by arrow1, or that the curvature of the blades220may be configured in correspondence with the direction of rotation of the compressor wheel210.

The inner face216of the body212includes (e.g., defines or forms) the inner surface216b, and approaches/intersects the outer face214an outer periphery215of the body212. The inner face216is generally concave in configuration, and includes one or more supports222, as well as one or more recess224. The recess(es)224extend between adjacent supports222and are collectively defined by the inner surface216a, the hub217, and the supports222. In certain embodiments, it is envisioned that the recesses224may reduce the overall wall thickness, and thus, the overall weight of the body212, and/or that the recesses224may be positioned to increase consistency in the wall thickness of the body212, which may be advantageous in forming the compressor wheel210using an injection molding process. The recesses224may thus “hollow” the body212in contrast to the solid design employed in many known conventional compressor wheels, as described above.

The supports222are configured, dimensioned, and positioned to transfer torque radially outward across the body212of the compressor wheel210so as to reduce stress in the body212during acceleration. Although configured as a plurality of ribs in the illustrated embodiments, the supports222may assume any configuration suitable for the intended purpose of transferring torque radially outward in the manner described herein, such as, for example, struts, brackets, walls, etc.

It is envisioned that the supports222may be formed integrally with the body212(e.g., as part of the molding process), as illustrated inFIGS. 2 and 3, for example, and thus, that the supports222and the body212may be formed from the same material. Alternatively, it is envisioned that the supports222may be formed separately from the body212and attached thereto, such as, for example, via welding. In such embodiments, it is envisioned that the body212and the supports222may be formed from the same or different materials. As seen inFIGS. 2 and 3, forming the supports222integrally with the body212eliminates any physical division between the hub217and the supports222, whereby the transverse cross-sectional dimension of the hub217(e.g., the diameter) acts as an imaginary dividing line separating the hub217from the supports222.

Each of the supports222each includes a first end222apositioned adjacent (e.g., coupled to or formed integrally with) the hub217and a second end222bspaced radially from the first end222a. It is envisioned that ends222bof the supports222may extend into an outer/peripheral region of the compressor wheel210, as shown inFIG. 2, for example, or alternatively, that the ends222bmay extend to the outer periphery215of the body212. The supports222each define a first edge222c(e.g., an inner or leading edge) spaced a first radial distance R1(FIG. 4) from the axis of rotation212a, a second edge222d(e.g., an outer or leading edge) spaced a second radial distance R2from the axis of rotation212athat is greater than the first distance, and a centerline222epositioned equidistant from the first edge222cand the second edge222d.

As shown inFIG. 2, for example, it is envisioned that the supports222may be spaced evenly across the inner face216. For example, the compressor wheel210may include four supports222spaced at 90-degree intervals. In alternate embodiments, however, the number of supports222included on the compressor wheel210may be varied. For example, the compressor wheel210may include three supports222spaced at 120-degree intervals, five supports222spaced at 72-degree intervals, etc.

In one embodiment, the supports222may include a curved configuration, as shown inFIG. 2, for example. More particularly, it is envisioned that the supports222may curve in the direction of rotation of the compressor wheel210, which indicated by arrow1inFIG. 2, or alternatively, that the supports222may curve in a direction opposite that of rotation of the compressor wheel210. It is envisioned that the curvature of the supports222may be chosen to facilitate the transfer of torque radially outward during acceleration of the compressor wheel210as a compressive load along the supports222. As can be appreciated through reference toFIGS. 2 and 3, it is envisioned that the curvature defined by the supports222may be opposite that defined by the blades220.

It is envisioned that the configuration, dimensions, and positions of the supports222may be varied in alternate embodiments of the compressor wheel210. For example, based upon the desired performance of the compressor wheel210and/or the loads/stresses experienced by the compressor wheel210during operation, the curvature, cross-sectional shape, and/or location of the supports222may be varied. In particular, the curvature of the supports222may be varied such that, during acceleration, the supports222are loaded primarily in compression and minimize any bending load or moment. The curvature of the supports222may also be chosen to inhibit or prevent drawing lubricants (e.g., oil or grease) from bearings positioned adjacent the inner face216of the compressor wheel210(e.g., by creating a small positive pressure on the second face216).

As shown inFIG. 2, it is envisioned that the supports222may define a thickness T that varies between the ends222a,222b. For example, the supports222may each include a first portion223aadjacent the end222adefining a first thickness Ta, a second portion223badjacent the end222bdefining a second thickness Tb, and one or more intermediate portions223cpositioned between the portions223a,223bdefining a third thickness Tc. In the particular embodiment shown inFIG. 2, for example, the supports222are configured and dimensioned such that the thickness Ta is greater than the thickness Tb, whereby the supports222widen to define a fillet adjacent the hub217, but less than the thickness Tc. It should be appreciated, however, that in alternate embodiments, the thicknesses Ta, Tb, Tc may be altered or varied to achieve any desired effect or to apply structural support to the compressor wheel210as needed. For example, the thicknesses Ta, Tb, Tc may be equivalent to each other, the thickness Ta may exceed the thickness Tc, etc. It is envisioned that increasing the thickness of the supports222adjacent the ends222bmay offset a reduction in material used in construction of the blades220(e.g., to further limit stress concentrations).

Although shown as including first, second, and third portions inFIG. 2, it should be appreciated that the number of the portions may be increased or decreased in alternate embodiments of the disclosure.

With continued reference toFIG. 2, it is envisioned that the supports222may define a curvature with a substantially constant radius (e.g., a simple curve) over a majority of the length of the support222(e.g., 50% or more of the overall length of the support222). Alternatively, is envisioned that the curvature of the supports222may vary between the ends222a,222b. For example, in one embodiment, the curvatures of the portion223a,223b,223cmay be unequal (e.g. the curvature of the portion223amay exceed the curvature of the portion223bwhich may exceed the curvature of the portion223c). It is envisioned that the curvature of the supports222may be defined as elliptical or exponential curvature, or any other suitable shape.

With reference toFIGS. 4-7, the supports222define a height H that may be varied between the ends222a,222b. For example, in the illustrated embodiment it is envisioned that the height H may decrease from the end222ato the end222b. It is envisioned that the variation in height H may be gradual, such that the supports222include a generally “tapered” configuration, as illustrated inFIGS. 5-7, for example, or that the height H may be reduced incrementally in step-wise fashion.

Dependent upon the desired operation and structural reinforcement provided by the supports222, it is envisioned that the specific location and/or orientation of the supports222may be varied. For example, with reference toFIG. 4, the supports222may be positioned such that the centerlines222eare offset or spaced radially from the axis of rotation212a, whereby the supports222extend tangentially from the hub217. Alternatively, it is envisioned that the supports222may be positioned such that the centerlines222eintersect the axis of rotation212a. As seen inFIG. 4, in certain embodiments, the supports222may be positioned such that the edges222dintersect, or are otherwise joined to, the edges222cof adjacent supports222.

As discussed above, the supports222reduce stress in the body212during acceleration when compared to similarly configured compressor wheels without such supports222, and the effect of these stress reductions is amplified by the curvature of the supports222.FIG. 11Aprovides an illustration of a computer simulation performed with respect to the compressor wheel210illustrated inFIGS. 2 and 3, for example, whereasFIG. 11Bprovides an illustration of a computer simulation performed with respect to a similar compressor wheel310that is devoid of the supports222, andFIG. 11Cprovides an illustration of a computer simulation performed with respect to a similar compressor wheel410that includes linear supports422.

The simulations reflected inFIGS. 11A-11Cwere performed in both accelerating and steady state conditions for the compressor wheels210,310, and410to determine stress concentrations. During the simulations, the respective outer peripheries215,315,415of the compressor wheels210,310,410, were held in place while torque was applied to the respective hubs217,317,417. The regions having different shading indicate different levels of stress (see the legend associated withFIG. 11A). As shown inFIG. 11B, the compressor wheel310experiences large stress concentrations of greater than 200 MPa in areas surrounding the hub317, as well as in inner regions of the body312, which are reduced gradually as the radial distance from the hub317is increased. Stress reduction is also visible in regions associated with the blades320. As shown inFIG. 11C, the compressor wheel410also experiences large stress concentrations of greater than 200 MPa in areas surrounding the hub417, as well as in inner regions of the body412, and in the areas of transition between the supports422and the body412. In contrast, as shown inFIG. 11A, the compressor wheel210experiences substantially smaller stress concentrations of greater than 200 MPa, which are localized to the areas of transition between the supports222and the hub217.

FIGS. 12A-12Cprovide illustrations of computer simulations performed in steady state conditions in which the hubs217,317,417were restrained and a1-barload, representative of aerodynamic loading, was applied the blades220,320,420in conjunction with a centrifugal load of 70,000 RPM. As shown inFIG. 12B, the compressor wheel310experienced the lowest magnitude stress concentrations, peaking at approximately 70,000 MPa. As shown inFIG. 12C, however, the compressor wheel410experienced peak stress concentrations of approximately 100,000 MPa in the areas of transition between the supports422and the body412(e.g., as the supports422constrain radial growth of the body412). As shown inFIG. 12A, the compressor wheel210also experienced peak stress concentrations of approximately 100,000 MPa in the areas of transition between the supports222and the body212with the highest stress concentrations being located in outer regions of the compressor wheel210(e.g., as the supports222expand radially outward in an attempt to straighten).

FIGS. 13A-13Cprovide illustrations of computer simulations performed in steady state conditions to identify and measure radial displacement (e.g., growth) experienced by the compressor wheels210,310,410. InFIGS. 13A-13C, regions having different shading indicate different amounts of radial growth (see the legend associated withFIG. 13A). As compared to metallic compressor wheels, growth of polymer or composite compressor wheels may be up to 20 times greater. As shown inFIG. 13B, the compressor wheel210experiences generally even radial growth. Aerodynamic loading of the blades220, for example, tends to compress the compressor wheel210radially inward, so as to partially offset centrifugal forces. As shown inFIG. 13C, the compressor wheel410experiences uneven radial growth with the supports422constraining growth at 90-degree intervals. As shown inFIG. 13A, the compressor wheel210experiences generally even radial growth but in slightly greater magnitude than the compressor wheel310.

The simulations reflected inFIGS. 11A-13Cillustrate that the compressor wheel210experienced substantial reductions in stress when compared to the compressor wheels310,410during acceleration, but higher stresses than the compressor wheel310during steady state conditions. Additionally, the simulations illustrate that the compressor wheel210experienced slightly greater radial growth than the compressor wheel310, and substantially more uniformity in radial growth than the compressor wheel410, during steady state rotation. As a result, the compressor wheel210may provide a better compromise of stress in acceleration and steady state conditions, while providing generally even radial growth, which may be provide better durability and/or fatigue life of the compressor wheel210. Furthermore, the use of curved supports222may be particularly advantageous in different applications, such as in exhaust-driven turbochargers, that operate the compressor wheel210at higher pressures and/or at higher temperatures (e.g., as compared to electronic or mechanically driven forced induction devices) that may cause greater stress and/or shape distortion.

In the preceding description, reference may be made to the spatial relationship between the various structures illustrated in the accompanying drawings, and to the spatial orientation of the structures. However, as will be recognized by those skilled in the art after a complete reading of this disclosure, the structures described herein may be positioned and oriented in any manner suitable for their intended purpose. Thus, the use of terms such as “above,” “below,” “upper,” “lower,” “inner,” “outer,” etc., should be understood to describe a relative relationship between structures, and/or a spatial orientation of the structures.

Additionally, terms such as “approximately” and “generally” should be understood to allow for variations in any numerical range or concept with which they are associated. For example, it is envisioned that the use of terms such as “approximately” and “generally” should be understood to encompass variations on the order of 25%, or to allow for manufacturing tolerances and/or deviations in design.