Vehicle rear body structure and method for manufacturing thereof

A vehicle rear body structure containing a rear rail extending in a longitudinal direction and a rear bumper beam, extending transversely to the longitudinal direction, the rear rail having a rear end and a front end, spaced apart along the longitudinal direction, the rear end being connected to the rear bumper beam and the rear rail extending towards the front of the vehicle from its rear end, wherein the rear rail comprises at least a front portion, an intermediate portion and a rear portion, the front portion being intended for extending alongside a fuel tank of the vehicle, the resistance to plastic deformation of the front portion being greater than the resistance to plastic deformation of the intermediate portion, which is itself greater than the resistance to plastic deformation of the rear portion.

FIELD OF THE INVENTION

The present invention relates to a vehicle rear body structure.

BACKGROUND OF THE INVENTION

Conventionally, the rear body structure of a vehicle includes a series of structures, located at the rear of the fuel tank, which are intended to absorb impact energy by deforming in response to an impact at the rear of the vehicle, and thus protect the fuel tank in the case of such an impact. These structures include a rear bumper beam and crash boxes, located between the rear ends of the rear rails of the rear body structure and the bumper beam.

The rear rails are located in front of the crash boxes. They conventionally have a resistance that is greater than that of the bumper beam and of the crash boxes and are intended for transferring the impact forces to the structural elements of the vehicle body. A front portion of the rear rails extends alongside the fuel tank of the vehicle, which is usually located at the rear end of the vehicle, in front of the wheel casings.

It appears that, in the case of high speed impacts on the rear of the vehicle, the conventional shock absorbing structures mentioned above may not sufficiently absorb the impact energy and the impact may result in a crushing of the rear rail(s). Such an uncontrolled crushing may result in an intrusion of some elements of the rear body structure into the gas tank, thus causing damage to the fuel tank, which might lead to spilling of the fuel and may ultimately result in an explosion of the vehicle. Therefore, damage to the fuel tank should be avoided, even in the case of high speed impacts.

BRIEF SUMMARY OF THE INVENTION

An object of the invention is to provide a vehicle rear body structure which provides for an improved crashworthiness in the case of a rear impact on the vehicle, and in particular which provides for an improved protection of the fuel tank in the event of such an impact.

The invention therefore provides a vehicle rear body structure comprising a rear rail extending in a longitudinal direction and a rear bumper beam, extending transversely to the longitudinal direction, the rear rail having a rear end and a front end, spaced apart along the longitudinal direction, the rear end being connected to the rear bumper beam and the rear rail extending towards the front of the vehicle from its rear end, wherein the rear rail comprises at least a front portion, an intermediate portion and a rear portion, the front portion being intended for extending alongside a fuel tank of the vehicle, the resistance to plastic deformation of the front portion being greater than the resistance to plastic deformation of the intermediate portion, which is itself greater than the resistance to plastic deformation of the rear portion, and wherein the vehicle rear body structure further comprises a guide structure intended for guiding the deformation of the rear rail so as to prevent a deformation thereof in a direction perpendicular to the longitudinal direction.

In certain embodiments, the guide structure is intended for guiding the deformation of the rear rail so as to prevent an upward deformation of the rear rail.

In certain embodiments, the guide structure comprises two legs intended for bearing vertically downwards on the guide rail in bearing areas spaced apart from each other.

In certain embodiments, one bearing area is located in the intermediate portion while the other bearing area is located in the front portion.

In certain embodiments, the product of the square of wall thickness of the front portion by the yield strength of the front portion is greater than the product of the square of the wall thickness of the intermediate portion by the yield strength of the intermediate portion, which is itself greater than the product of the square of the wall thickness of the rear portion by the yield strength the rear portion.

In certain embodiments, the yield strength of the front portion is greater than the yield strength of the intermediate portion, which is itself greater than the yield strength of the rear portion and/or the wall thickness of the front portion is greater than the wall thickness of the intermediate portion, which is itself greater than the wall thickness of the rear portion.

In certain embodiments, the rear portion is adjacent to the intermediate portion along the longitudinal direction and the intermediate portion is adjacent to the front portion along the longitudinal direction.

In certain embodiments, the rear portion is a press-hardened steel part having, after press-hardening, a yield strength Recomprised between 360 and 400 MPa or a press-hardened steel part having, after press hardening, a yield strength Recomprised between 700 and 950 MPa and the front portion is a press-hardened steel part having, after press hardening, a yield strength Recomprised between 950 and 1200 MPa or a press-hardened steel part having, after press hardening, a yield strength Regreater than 1260 MPa.

In certain embodiments, the rear portion is a press-hardened steel part having, after press-hardening, a yield strength Recomprised between 360 and 400 MPa and has a wall thickness of about 1.6 mm or a press-hardened steel part having, after press hardening, a yield strength Recomprised between 700 and 950 MPa having a wall thickness of about 1.4 mm.

In certain embodiments, the intermediate portion has a wall thickness of about 1.7 mm.

In certain embodiments, the front portion is a press-hardened steel part having, after press hardening, a yield strength Recomprised between 950 and 1200 MPa and has a wall thickness of about 1.7 mm or the front portion is a press-hardened steel part having, after press hardening, a yield strength Regreater than 1260 MPa and has a wall thickness of about 1.6 mm.

In certain embodiments, a front part of the intermediate portion is a press-hardened steel part having, after press hardening, a yield strength Recomprised between 700 and 950 MPa.

In certain embodiments, the rear portion of the rear rail comprises crumple zones to allow the rear rail to controllably deform during an impact.

In certain embodiments, the rear body structure further comprises a fuel tank, the front portion of the rear rail extending alongside the fuel tank.

In certain embodiments, the rear body structure comprises two rear rails, a rear intermediate transversal beam, a front intermediate transversal beam and a front transversal beam, the front intermediate transversal beam, the front transversal beam and the rear rails delimiting among themselves a frame for receiving the fuel tank, the front portion of the rear rails extending between the front transversal beam and the front intermediate transversal beam.

In certain embodiments, the front transversal beam extends between the front ends of the rear rails.

In certain embodiments, the front portion of the rear rails extends from the front transversal beam at least up to the front intermediate transversal beam.

The invention also provides a vehicle body comprising the vehicle rear body structure as defined above.

The invention also provides a method for manufacturing a rear body structure of a vehicle, the method comprising a step of manufacturing a rear rail, said step comprising successive steps of: providing a tailor welded blank, the tailor welded blank being obtained by welding together at least as many different blanks as there are portions having different compositions or thicknesses in the rear rail, each of these blanks having a composition and/or thickness depending on the desired properties of the corresponding rear rail portion; and forming this tailor welded blank into the desired shape. In some of these embodiments, the forming step is a step of hot forming the tailor welded blank, and said hot forming is followed by a step of cooling the hot formed tailor welded blank at a controlled cooling rate.

In certain embodiments of the method for manufacturing a rear body structure of a vehicle, at least two portions of the rear rail have the same composition and are subjected to a different heat treatment during or after forming so as to obtain a different yield strength in each portion.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, the terms inner, outer, front, rear, transversal, longitudinal, vertical, horizontal, top and bottom are construed with reference to the usual orientation of the illustrated elements, parts or structures when assembled on a vehicle structure, the vehicle lying on a horizontal plane.

A vehicle rear body structure2according to an embodiment is illustrated onFIG. 1. The vehicle front body structure2may be a rear body structure of any kind of four wheel vehicle, in particular a front body structure of a unitized body.

The vehicle front body structure2comprises a frame assembly4. The frame assembly4comprises two rear rails10,12and a rear bumper beam21.

Each rear rail10,12extends substantially along the longitudinal direction of the vehicle. The rear rail10extends on one side of the vehicle in a front-rear direction of the vehicle body. It comprises a rear end10aand a front end10b. Similarly, the rear rail12comprises a rear end12aand a front end12b.

The rear bumper beam21extends substantially transversely to the longitudinal direction. It extends at the rear of the rear rails10,12. The rear end10a,12aof each rear rail10,12is connected to the rear bumper beam21, in particular through crash boxes31,33. More particularly, the rear bumper beam21bears longitudinally on the rear ends10a,12aof the rear rails10,12, in particular through said crash boxes31,33.

The front end10b,12bof each rear rail10,12is connected to a structural element of the vehicle's body.

In the example shown inFIG. 1, the frame assembly4further comprises a rear intermediate transversal beam23, a front intermediate transversal beam25and a front transversal beam27.

The front transversal beam27extends between the front ends10b,12bof the rear rails10,12. It is intended for extending at the front of the wheel casings of the vehicle.

The rear and front intermediate transversal beams23,25extend between the rear transversal beam21and the front transversal beam27. They are connected to the rear rails10,12at their lateral ends. The rear and front intermediate transversal beams23,25are located at the wheel casings of the vehicle and reinforce the vehicle rear body in this area.

The front intermediate transversal beam25, the front transversal beam27and the rear rails10,12delimit among themselves a frame35intended for receiving the fuel tank of the vehicle. The fuel tank has not been shown in the drawings in order not to overly complicate the drawings.

The rear rails10,12are provided as pairs in left-right symmetry with respect to the lateral direction. In the following, the description will be made with reference to the right rear rail10, on the understanding that the same description applies to the left rear rail12.

As can be seen onFIGS. 2 and 3, the rear rail10is substantially U-shaped. It comprises an outer flank34, oriented towards the exterior of the vehicle, and an inner flank35parallel to the outer flank34, oriented towards the interior of the vehicle. The rear rail10further comprises a bottom36oriented towards the bottom of the vehicle, the bottom being substantially orthogonal to the inner and outer flanks34,35. The U-shaped rear rail10opens upwardly.

The rear rail10extends in a substantially longitudinal direction. It comprises, from the front end10bto the rear end10a, a front portion37, an intermediate portion39and a rear portion41. The intermediate portion39extends the front portion37rearwards, and is itself extended rearwards by the rear portion41. The front portion37, intermediate portion39and rear portion41are adjacent to one another along the longitudinal direction.

In this example, the front end of the intermediate portion39is connected directly to the rear end of the front portion37. The rear end of the intermediate portion39is connected directly to the front end of the rear portion41.

The front portion37is intended for extending longitudinally alongside the fuel tank of the vehicle. Its front end forms the front end10bof the rear rail10. In the example shown inFIG. 1, the front portion37extends between the front transversal beam27and the front intermediate transversal beam25. The front portion37is curved in a longitudinal plane extending substantially horizontally.

The intermediate portion39is substantially straight. It extends between the front portion37and the rear portion41along the longitudinal direction. In the example shown inFIG. 1, the intermediate portion39extends towards the rear of the vehicle rear body structure from the front intermediate transversal beam25. In this example, the back intermediate transversal beam27extends transversely between the intermediate portions39of the rear rails10,12.

The rear portion41is substantially straight. The rear end of the rear portion41forms the rear end10aof the rear rail10.

Each of the rear portion41, the intermediate portion39and the front portion37is U-shaped and comprises an inner wall, an outer wall and a bottom, which each form a section of the inner wall35, the outer wall34and the bottom36of the rear rail10.

The rear rail10is made of steel, for instance dual-phase steel or press hardened boron steel.

According to the invention, the front portion37, the intermediate portion39and the rear portion41each have a different resistance to plastic deformation, the resistance to plastic deformation increasing from the rear end10aof the rear rail10to the front end10bof the rear rail10.

More particularly, the resistance to plastic deformation of the front portion37is greater than the resistance to plastic deformation of the intermediate portion39, which, in turn is greater than the resistance to plastic deformation of the rear portion41.

The resistance to plastic deformation increases with increasing wall thickness t of the considered rear rail portion, as well as with increasing yield strength of the material forming said rear rail portion. More particularly, the resistance to plastic deformation of each portion of the rear rail10may be characterized by the product P of the square of wall thickness t of the considered portion of the rear rail10by the yield strength Reof said portion.

Advantageously, this product P increases from the rear end10ato the front end10bof the rear rail10.

More particularly, the product P for the front portion37is greater than the product P of the intermediate portion39and the product P is greater than the product P of the rear portion41. In other words, for each portion of the rear rail10, the thickness t and the yield strength Reare chosen such that the product P increases from one section to the next from the rear to the front of the rear rail10.

According to one particular embodiment, the yield strength Refof the material forming the front portion37is greater than the yield strength Rei, of the material forming the intermediate portion39, which in turn, is greater than the yield strength Rer, of the material forming the rear portion41. Thus, Ref>Rei>Rer.

For example, the yield strength Re, of the steel forming the rear portion41may be comprised between 200 and 700 MPa, while the yield strength Re, of the steel forming the intermediate section39is comprised between 300 and 1300 MPa and the yield strength Refof the steel forming the front portion37is comprised between 400 and 1500 MPa.

In particular, the yield strength Refof the material forming the front portion37is greater by at least 100 MPa than the yield strength of the material forming the rear portion41.

As an alternative, the wall thickness t of the rear rail10increases from the rear end10ato the front end10b.

More particularly, the wall thickness tfof the front portion37is greater than the wall thickness ti, of the intermediate portion39, which is itself greater than the wall thickness tr, of the rear portion41. In other words, tf>ti>tr.

For example, the thickness tfof the wall of the front portion37may be comprised between 1.4 and 3 mm, while the thickness tr, of the wall of the intermediate portion39is comprised between 1.4 and 3 mm and the thickness ti, of the wall of the rear portion41is comprised between 1 and 2 mm.

In particular, the wall thickness tfof the front portion37is greater by at least 0.4 mm than the wall thickness tr, of the rear portion41.

Advantageously, both the yield strength Reand the wall thickness t of the rear rail10increase from the rear end10ato the front end10bof the rear rail10. More particularly, the following relationships apply: tf>ti>trand Ref>Rei>Rer.

This gradual increase in the resistance to plastic deformation along the length of the rear rail10from the rear portion41to the front portion37results in an improved crashworthiness of the vehicle in the event of an impact at the rear of the vehicle.

Indeed, in the case of such an impact of sufficient strength, the rear portion41of the rear rail10will deform and absorb a considerable portion of the impact energy. Since the resistance to plastic deformation of the front portion37is greater than that of the rear portion41, it will stay substantially intact as a result of the impact, thus preventing an intrusion of other components of the rear body structure into the fuel tank, alongside which the front portion37extends. This feature is important in order to avoid damage to the fuel tank due to an impact and fuel spillage possibly resulting therefrom, as well as to reduce the risk of explosion resulting from an impact at the rear of the vehicle. The intermediate portion39, which has a resistance to plastic deformation that is intermediate between those of the front portion37and of the rear portion41, deforms only once the rear portion41has been deformed, and, by deforming, absorbs impact energy and protects the front portion37. It helps manage the plastic hinge between the rear portion41and the front portion37by keeping the front and intermediate portions37,39of the rear rail10intact while the rear section is absorbing most of the crash energy by deforming at the earliest crash phase and avoiding unwanted material failure risk when the local plastic hinge occurs in a later phase of crash.

According to one embodiment, each of the front, rear and intermediate portions37,41,39has the same yield strength along its entire length.

For example, the rear portion41is a press-hardened steel part having, after press-hardening, a yield strength Recomprised between 360 and 400 MPa. It is more particularly made of a press-hardenable steel having a carbon content comprised between 0.04 wt. % and 0.1 wt. % and a manganese content comprised between 0.3 wt. % and 2.0 wt. %. Even more particularly, the steel composition of the rear portion41comprises in % weight: 0.04%≤C≤0.1%, 0.3%≤Mn≤2.0%, Si<0.3%, Ti≤0.08%, 0.015≤Nb≤0.10%, Cu, Ni, Cr, Mo≤0.1%, the remainder being iron and unavoidable impurities resulting from the elaboration. This rear portion41advantageously has a wall thickness of about 1.6 mm.

The rear portion41may also have a wall thickness of about 1.4 mm and be a press-hardened steel part having, after press hardening, a yield strength Recomprised between 700 and 950 MPa. More particularly, the rear portion41is made of a press-hardenable steel having a carbon content comprised between 0.06 wt. % and 0.1 wt. % and a manganese content comprised between 1.4 wt. % and 1.9 wt. %. Even more particularly, the steel composition of the rear portion41may further comprise Nb, Ti, B as alloying elements.

The front portion37has a wall thickness of about 1.7 mm. It is a press-hardened steel part having, after press hardening, a yield strength Recomprised between 950 and 1200 MPa. More particularly, it is made of a press-hardenable steel having a carbon content comprised between 0.20 wt. % and 0.25 wt. % and a manganese content comprised between 1.1 wt. % and 1.4 wt. %. Even more particularly, the steel composition of the front portion37comprises in % weight: 0.20%≤C≤0.25%, 1.1%≤Mn≤1.4%, 0.15%≤Si≤0.35%,≤Cr≤0.30%, 0.020%≤Ti≤0.060%, 0.020%≤Al≤0.060%, S≤0.005%, P≤0.025%, 0.002%≤B≤0.004%, the remainder being iron and unavoidable impurities resulting from the elaboration.

The front portion37may also have a wall thickness of about 1.6 mm and be made of a press-hardened steel part having, after press hardening, a yield strength Regreater than 1260 MPa. More particularly, the steel composition comprises for example, in % weight: 0.24%≤C≤0.38%, 0.40%≤Mn≤3%, 0.10%≤Si≤0.70%, 0.015%≤Al≤0.070%, Cr≤2%, 0.25%≤Ni≤2%, 0.015%≤Ti≤0.10%, Nb≤0.060%, 0.0005%≤B≤0.0040%, 0.003%≤N≤0.010%, S≤0.005%, P≤0.025%, %, the remainder being iron and unavoidable impurities resulting from the elaboration.

The intermediate portion39has a wall thickness of about 1.7 mm and be a press-hardened steel part having, after press hardening, a yield strength Recomprised between 700 and 950 MPa. More particularly, the intermediate portion39is made of a press-hardenable steel having a carbon content comprised between 0.06 wt. % and 0.1 wt. % and a manganese content comprised between 1.4 wt. % and 1.9 wt. %. Even more particularly, the steel composition of the intermediate portion39may further comprise Nb, Ti, B as alloying elements.

According to a second example of the rear rail10, at least two portions among the portions37,39,41of the rear rail10may have the same thickness and the same composition, but different yield strengths, the difference in yield strength being obtained by subjecting the different portions to a different heat treatment.

For example, the front portion37and the intermediate portion39have a same thickness of 1.7 mm and the same composition. More particularly, the steel composition of the front portion37and the intermediate portion39comprises in % weight: 0.20%≤C≤0.25%, 1.1%≤Mn≤1.4%, 0.15%≤Si≤0.35%,≤Cr≤0.30%, 0.020%≤Ti≤0.060%, 0.020%≤Al≤0.060%, S≤0.005%, P≤0.025%, 0.002%≤B≤0.004%, the remainder being iron and unavoidable impurities resulting from the elaboration. However, the front portion37has a yield strength Recomprised between 950 and 1200 MPa, while the intermediate part39has a yield strength between 700 and 950 MPa.

As shown inFIG. 3, the rear rail10may comprise, in its rear portion41, crumple zones47to allow the rear rail10to controllably deform during an impact. In this embodiment, the crumple zones47are formed only in a rear area of the rear portion41, and particularly in the rear half of the rear portion41.

The crumple zones may include, for example, apertures or cavities or ribs formed on the walls of the rear portion41. In the embodiment shown inFIG. 3, the crumples zones47are formed by ribs formed in a bottom of the rear portion41. The ribs extend transversely to the longitudinal direction, i.e. substantially vertically. They are substantially parallel to one another. In this example they are spaced regularly along the longitudinal direction and present a uniform width along the longitudinal direction. Each rib extends from the one lateral side to the other of the rear portion41of the rear rail10.

In this example, the intermediate portion39and the front portion37do not comprise any crumple zones.

In the example shown inFIG. 2, the cross-sectional areas of the rear portion41and of the intermediate portion39are substantially constant. The cross-sectional area of the front portion37increases from its rear end to its front end. The cross-sectional area is taken in a transverse plane normal to the longitudinal direction. This feature also contributes to increasing the resistance to deformation of the front portion37.

As can be seen onFIG. 2, the vehicle rear body structure2further comprises, for each of the rear rails10,12, a guide structure51configured for guiding the deformation of the corresponding rear rail10,12during an impact at the rear of the vehicle. In particular, this guide structure51is configured for preventing a deformation of the rear rail10,12along a direction perpendicular to the longitudinal direction, and more particularly along the vertical direction. The guide structure51is in particular configured for preventing part of the rear rail10,12from moving upwards when subjected to impact forces along the longitudinal direction.

The guide structure51is therefore configured for retaining the rear rail10,12against an upward deformation when subjected to impact forces along the longitudinal direction. Such an upward deformation would result in lower energy absorption by the rear portion41and more deformation of the front portion37causing higher unwanted intrusion in the fuel tank area.

The guide rail10,12therefore deforms mainly along the longitudinal direction as a result of such impact forces.

For this purpose, each guide structure51comprises at least two legs53bearing upon the rear rail10,12in bearing areas which are spaced apart along the longitudinal direction. The legs53extend along a direction substantially perpendicular to the longitudinal direction, and more particularly vertically. They extend above the rear rail10,12.

In the example shown inFIG. 2, the legs53have a bottom end and a top end. The bottom end of each leg53bears on the bottom36of the U-shaped rear rail10. The legs53extend upwards from the rear rail10towards an upper structure of the vehicle body (not shown in the drawings), and in particular towards a floor element, extending transversely substantially between the wheel casings.

The top ends of the legs53are, in the example shown inFIG. 2, connected to each other through a connection element55.

At its top end, the guide structure51is attached to said upper structure of the vehicle body, and in particular to the rear wheel casings and the rear floor of the vehicle body.

The bottom ends of the legs53are inserted into the U-shaped rear rail10so as to bear on the bottom36thereof and be located between the outer and inner flanges34,35. The legs53are further fixed to the rear rail10by any adapted fixing means.

In the example shown inFIG. 2, the guide structure51extends across the junction between the intermediate portion39and the front portion37so as to avoid any upwards deformation of the rear rail10in this area. More particularly, a front leg53of the guide structure51bears on the front portion37of the rear rail10, while a back leg53of the guide structure51bears on the front portion37of the rear rail10.

The positions of those legs53are highly limited to maximize the luggage compartment area.

From a crash management and car body torsional stiffness point of view, a connection of the legs53in the intermediate portion39of the rear rails10,12ensures the highest possible energy absorption in high speed rear crash test and highest possible torsional stiffness.

At least two adjacent portions37,39,41of the rear rail10are connected to each other through a weld. According to one embodiment, all three portions37,39,41of the rear rail10are connected to each other through a weld.

Advantageously, the rear rail10is manufactured from a corresponding tailor welded blank, the tailor welded blank being obtained by welding, and in particular laser welding, of at least as many different blanks as there are portions having different compositions or thicknesses in the rear rail10,12, each of these blanks having a thickness and/or a composition depending on the desired properties of the corresponding rear rail portion.

For example, the tailor welded blank is obtained by welding together at least three blanks, each of these blanks corresponding to a portion37,39,41of the rear rail10and having a thickness and/or a composition depending on the desired properties of the corresponding portion37,39,41of the rear rail10,12.

More particularly, a method for manufacturing a rear rail10comprises the following successive steps:welding together, in particular through laser welding, at least as many different blanks as there are portions having different compositions or thicknesses in the rear rail10,12, each of these blanks having a composition and/or thickness depending on the desired properties of the corresponding rear rail portion;forming this tailor welded blank into the desired shape, in particular through drawing.

The step of forming the tailor welded blank is, in particular, a step of hot forming. The hot forming step is followed by a step of cooling of the part, i.e. of the hot formed tailor welded blank, at a controlled cooling rate.

In particular, depending on the desired final properties of each portion of the rear rail10, these portions may be subjected to a different cooling treatment after forming of the blank. For example, the front portion37may be cooled at a higher cooling rate than the rear portion41. In particular, the front portion37may be quenched, while the rear portion41is cooled more slowly so as to obtain the desired yield strength.

The skilled person, based on his general knowledge, is able to determine the cooling rate to be used depending on the desired yield strength of each portion of the rear rail10.

Depending on the desired final properties of each section of the rear rail10, these sections may be subjected to a different heat treatment during or after forming the blank into the half-shell52,54.

For example, if two adjacent portions have the same composition, but are intended to have different yield strengths in the final part, these different yield strengths may be obtained by one or a combination of the following methods:during hot forming, the portion intended to have a lower yield strength is heated to a lower temperature than the portion intended to have a higher yield strength;after hot forming, the portion intended to have a lower yield strength is cooled at a slower rate than the section intended to have a higher yield strength; and/orthe portions are subjected to an identical hot forming and cooling after hot forming treatment, but the portion intended to have a lower yield strength is subsequently subjected to an additional heat treatment in order to decrease yield strength.

While the invention has been described in detail in connection with only a limited number of embodiments, it should be readily understood that the invention is not limited to such disclosed embodiments.