Abstract:
The present invention is directed to a driveline configuration for a heavy-duty truck having multiple drive axles. The driveline configuration reduces the torsional vibrations associated with second order torsional excitation produced by the driveline&#39;s universal joints in both nominal and off-design conditions. The forward drive axle ( 101 ) and rearward drive axle ( 102 ) are oriented such that the interaxle drive shaft ( 110 ) utilizes a parallel shaft geometry with small joint operating angles. A double cardan joint ( 115 ) connects the main drive shaft ( 107 ) to the forward drive axle.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]    This application is a continuation of U.S. application Ser. No. 09/768,743, filed Jan. 23, 2001, priority from the filing date of which is hereby claimed under 35 U.S.C. § 120. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    Drivelines for vehicles having at least two drive axles and, more particularly, to configurations of such drivelines exhibiting torsional vibrations.  
         BACKGROUND OF THE INVENTION  
         [0003]    The large trucks that are used to transport freight on our nation&#39;s highways—including, for example, Class 8 trucks—are most commonly tractor-semitrailer combinations having a tractor configured with a steerable axle at the front and tandem driving axles at the rear. Typically, these trucks utilize a “conventional” power train arrangement, depicted schematically in FIGS. 1 and 2. In this conventional power train arrangement, power produced by the engine (not shown) is transmitted through the transmission  108  to the forward drive axle  101  through a main drive shaft  107 . Although a single drive shaft is shown, it is common, and contemplated by the present invention, that a compound main drive shaft structure (i.e., two or more drive shafts rotatably connected with universal joint(s)) may be used.  
           [0004]    In this prior art driveline, the forward end  107 A of the main drive shaft  107  connects to the output shaft of the transmission  108  with a first universal joint  109 A. As used herein, “output shaft” refers to a shaft, typically but not necessarily a pinion shaft, on a component such as a transmission or an axle, that is driven by or through the component to provide power to another downstream component, and an “input shaft” refers to a shaft, again typically but not necessarily a pinion shaft, on a component such as an axle, which is externally driven to provide power to and/or through the component.  
           [0005]    The rearward end  107 B of the main drive shaft  107  connects to the input shaft  128  of the forward drive axle  101  with a second universal joint  109 B (FIG. 2). A similar but generally shorter interaxle drive shaft  110  transmits power between the forward drive axle  101  and the rearward drive axle  102 . The forward end  110 A of the interaxle drive shaft  110  connects to the output shaft  130  of the forward drive axle  101  with a third universal joint  109 C, and the rearward end  110 B of the interaxle drive shaft  110  connects to the input shaft  132  of the rearward drive axle  102  with a fourth universal joint  109 D.  
           [0006]    The universal joints  109  allow the interconnected shafts to rotate about their respective axes, notwithstanding nonalignment between the shafts. Various types of universal joints are commonly used in automotive drivelines, but the most prevalent by far, particularly in heavy-duty applications, is the so-called cardan joint (also known as a Hooke joint). Cardan joints have the advantages of mechanical simplicity, good reliability, and low cost. A disadvantage of the cardan joints, however, is that uniform rotational motion at the input yoke of the joint results in non-uniform motion at the output yoke of the joint unless the joint operating angle is zero, that is, unless the shafts connected by the cardan joint rotate about a common axis. (The joint operating angle is defined herein to be the absolute value of the acute angle defined by the axes of the two shafts connected through the universal joint.)  
           [0007]    The relationship between the input motion and the output motion across a simple cardan joint is well known. For small joint operating angles, a constant rotational velocity at the input yoke of the joint will produce nonconstant rotational motion at the output yoke having a maximum angular (or torsional) acceleration that increases approximately in proportion to the square of the shaft rotational speed and approximately in proportion to the square of the joint operating angle. In typical vehicle power trains, the drive shafts typically rotate at several thousand revolutions per minute. Therefore, even small joint operating angles can produce large angular accelerations. The angular accelerations are periodic, with a frequency of twice the shaft speed.  
           [0008]    Large torsional accelerations can produce high dynamic torques on the universal joints and other driveline components. These dynamic forces can be very damaging to the internal components of the transmission, as well as the axle gearing and the universal joints themselves. Moreover, the dynamic forces are periodic, and can occur at resonant frequencies of the driveline, thereby amplifying the stresses and strains induced in the driveline. Consequently, designers strive to achieve driveline geometries with small joint operating angles that limit the torsional accelerations to levels that are consistent with long component life.  
           [0009]    In drivelines having appropriately-phased, multiple cardan joints, non-uniform motion produced by one joint may be at least partially offset by one or more of the remaining joints. Referring now to FIGS. 3A and 3B, in a drive shaft  143  interconnecting an input shaft  141  with an output shaft  145 , using a pair of cardan joints  109 A,  109 B, there are two configurations whereby the angular accelerations introduced at the input joint  109 A will be ideally compensated for at the output cardan joint  109 B. In the first ideal configuration, shown in FIG. 3A, the input shaft  141  is parallel to the output shafts  145  (“parallel shaft geometry”), so the joint operating angles (angles A and B) are equal. In the second ideal configuration, shown in FIG. 3B, the input shaft  141  is not parallel to the output shaft  145 , but the shafts are configured so that the joint operating angles are again equal (“intersecting shaft geometry”). If the joint angles A and B are equal and the joints are phased appropriately, uniform rotary motion of the input shaft  141  will produce uniform rotary motion at the output shaft  145  with either the parallel shaft or the intersecting shaft geometries. However, the drive shaft  143  located between the universal joints  109 A,  109 B will still exhibit non-uniform motion and angular accelerations, and the inertia of the drive shaft  143  will generate second order (twice shaft speed) dynamic torsional loads on the joint assemblies  109 A,  109 B. If the two joint angles A and B are not equal, then uniform rotation of the input shaft  141  will produce non-uniform rotation of output shaft  145 . The difference between the joint operating angles of the two joints (i.e., A minus B) is known as the “cancellation error.” 
           [0010]    In order to avoid the angular vibrations introduced by cardan joints, so-called constant velocity (CV) joints have been developed. Several different types of CV joints have been developed, including, for example, ball-and-groove type joints such as Rzeppa, Weiss joints, helical or skewed groove joints, tracta joints, cross-groove joints, double-offset joints, tripot joints and flexing type joints. CV joints introduce little or no rotational non-uniformity. CV joints are commonly used in particular applications, notably on the axle shafts of front wheel drive automobiles. The primary disadvantages of CV joints are that they are complex and expensive compared to cardan joints, and they tend to have lower mechanical efficiency and poorer reliability than cardan joints. Consequently, CV joints are typically used only where acceptable performance cannot be achieved with cardan joints.  
           [0011]    A near-constant-velocity joint can be achieved through the use of a “double cardan joint” or a “centered double cardan joint,” as shown in FIG. 4. Conceptually, a centered double cardan joint  50  is made by combining two conventional cardan joints into a single joint by merging the two inner yokes into a single, two-sided “coupling yoke”  53 . A centering bearing  57  is incorporated into the joint that constrains the operating angles of the two joint halves to remain nearly equal. While not a true constant velocity joint, the departure from ideal behavior is small until the operating angle becomes quite large.  
           [0012]    In drive trains configured as depicted in FIG. 2, the transmission  108  is usually installed such that the axis of the transmission output shaft  126  is directed generally toward the input shaft  128  of the forward drive axle  101 , such that the two universal joints  109  at either end of the drive shaft  107  operate at equivalent and small, but non-zero, joint operating angles. A joint operating angle of zero is generally avoided to ensure that the joint bearings (not shown) rotate as the drive shaft revolves in order to distribute lubrication within the bearing and avoid premature wear or “brinelling” of the bearing elements.  
           [0013]    Driveline engineers strive to achieve drive shaft geometries that provide small joint operating angles and minimal cancellation error so that second-order torsional accelerations are minimized throughout the driveline. On trucks with tandem drive axles, this has been difficult to accomplish because the two drive axles  101 ,  102 , are closely spaced. Typically, the output shaft  130  on the forward drive axle  101  and the input shaft  132  on the rear drive axle  102  are vertically offset due to the presence of a power-dividing differential in the forward axle  101 . Additionally, the drive axles  101 ,  102 , are generally provided with a suspension system  111  that permits the axles to move vertically relative to each other, and relative to the vehicle chassis during operation of the vehicle. Because the drive axles  101 ,  102 , are closely spaced, the joint operating angles on the interaxle shaft  110  are very sensitive to relative vertical motion between the drive axles  101 ,  102 , caused by motion of the suspension  111 .  
           [0014]    [0014]FIG. 1 shows a trailing arm air suspension  111 , of the type commonly used in modern commercial trucks, wherein the forward and rearward drive axles  101  and  102  are clamped rigidly to the trailing arm springs  103  (also called main support members). The forward end of the trailing arm springs  103  is connected with pivots  106  to frame brackets  104 , which mount to frame structure  114  shown in phantom view. Air springs  105  act on the rear part of the trailing arm springs  103  and carry a portion of the sprung load. The remaining share of the sprung load is carried on the forward portion of the trailing arm springs  103 . The trailing arm springs  103  have very high flexural stiffness compared to the air springs and, under normal vertical deflections of the suspensions  111 , the axles  101 ,  102  articulate approximately about the trailing arm pivots  106 .  
           [0015]    A parallel shaft geometry driveline configuration is shown in FIG. 5, with the trailing arm springs  103  shown in phantom. Here, both the transmission  108  and the forward drive axle  101  are inclined at an angle that provides the desired small operating angles on the drive shaft universal joints  109 A and  109 B. The rearward drive axle  102  is installed in a parallel configuration with the forward drive axle  101 . Due to the vertical offset between the forward drive axle output shaft  130  and the rearward drive axle input shaft  132 , this configuration results in large joint operating angles on the interaxle drive shaft  110  at joints  109 C and  109 D, which produce high torsional accelerations in the interaxle shaft. Due to poor reliability of the interaxle shaft universal joints  109 C and  109 D, this configuration has been largely replaced with an intersecting shaft geometry, as shown in FIG. 6, which provides for smaller joint operating angles on the interaxle shaft joints  109 C and  109 D. In the intersecting shaft geometry, the rearward drive axle  102  is rotated such that the intersection of the axis of the forward drive axle output shaft  130  and the axis of the rearward drive axle input shaft  132  lies midway between the interaxle shaft joints  109 C and  109 D to provide approximately equal shaft joint angles.  
           [0016]    The driveline geometry is usually established to provide optimal performance at the nominal operating position of the suspension  111  (shown in FIG. 1). However, the driveline must also accommodate the geometry changes that occur as a result of motions of the suspension  111 . As the chassis moves up and down on the suspension  111 , the axles  101  and  102  articulate about their respective trailing arm spring pivots  106  some distance ahead of the axle. Consequently, the pitch angle of the axles  101  and  102  relative to the chassis frame structure  114  (shown in phantom in FIG. 1) also changes. Both the vertical motion and the pitch rotation of the axles cause the driveline geometry and joint angles to change.  
           [0017]    In a truck utilizing the parallel shaft geometry shown in FIG. 5, the joint operating angles on the interaxle shaft  110  will increase as the chassis frame  114  moves downward (with respect to the axles), compressing the suspension whereby the trailing arm springs  103  pivot about the pivots  106  (shown in phantom), and decrease as the chassis frame  114  moves upward. However, in a parallel shaft geometry, the two joint operating angles on the interaxle shaft  110  will remain approximately equal. So while the large joint operating angles create high torsional accelerations in the interaxle shaft  110 , the lack of any significant cancellation error limits or mitigates the torsional accelerations from being propagated beyond the interaxle shaft  110 .  
           [0018]    In a truck utilizing the intersecting shaft geometry shown in FIG. 6, however, an entirely different result is obtained. As the suspension  111  (shown in FIG. 1) compresses, the joint operating angles at joint  109 C at the forward end of the interaxle shaft  110  increases, while the joint operating angles at joint  109 D at the rear of the interaxle shaft  110  decreases. Therefore, small movements of the suspension  111  rapidly generate large cancellation errors within the interaxle shaft  110 . The cancellation error increases until one joint operating angle passes through zero, at which point the cancellation error is constant. The large cancellation error in the interaxle shaft joints  109 C and  109 D produces high amplitude second order torsional vibrations in the main drive shaft  107 , which can damage internal components of the transmission  108  and other power train components.  
           [0019]    As noted earlier, one possible solution for eliminating torsional vibrations is to use CV joints. Installing CV joints at both ends of the interaxle shaft  110  and at the forward drive axle input shaft  128  would largely eliminate second order torsional vibrations. However, the shortcomings of CV joints make this an expensive and unappealing solution. An additional limitation is that CV joints generally cannot operate at the large operating angles that occur in the interaxle drive shaft  110  during “cross-articulation”—i.e., when one of the drive axle suspensions is fully compressed and the other is fully extended, as often occurs when the vehicle traverses obstacles such as curbs at low speeds or otherwise operates in rough terrain. The extremely short length of the interaxle shaft  110  may also be insufficient for packaging two CV joints and also provide for the slip needed to accommodate the change in length under articulation. So the use of CV joints in the interaxle drive shafts where the largest cancellation errors occur is impractical. For these reasons, conventional highway tractors typically do not utilize CV-equipped interaxle shafts.  
         SUMMARY OF THE INVENTION  
         [0020]    The present invention is directed to a low-vibration driveline for a vehicle having a plurality of rearwardly disposed, driven axles. In a preferred embodiment the low-vibration driveline includes a forward and a rearward drive axle interconnected with an interaxle drive shaft. The drive axles are oriented with the output shaft from the forward drive axle directed generally towards the input shaft on the rearward drive axle, such that the interaxle assembly is in a parallel shaft geometry with joint operating angles that are small. The interaxle drive shaft is connected to the drive axles with universal joints. A main drive shaft that transmits power to the drive axles is connected to the forward drive axle input shaft using a constant velocity, or near-constant velocity universal joint.  
           [0021]    In a preferred embodiment, the joint operating angles on both ends of the interaxle drive shaft are not more than 5 degrees. In another preferred embodiment these joint operating angles are less than about 2 degrees.  
           [0022]    In embodiments of the present invention that utilize constant velocity universal joints to connect the main drive shaft to the forward drive axle, the constant velocity joint may be of the Rzeppa, Weiss, tripot type, double-offset type, or derivative designs.  
           [0023]    In an embodiment of the present invention that utilizes a near-constant velocity joint to connect the main drive shaft to the forward drive axle, a double-cardan type near constant velocity joint may be used.  
           [0024]    In another aspect of the present invention, the forward end of the main drive shaft connects to a transmission with a universal joint, the universal joint having a small joint operating angle.  
           [0025]    In an aspect of the present invention, the nonconstant velocity and non-near-constant velocity joints may be of the cardan type of universal joint.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0026]    The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:  
         [0027]    [0027]FIG. 1 is a schematic side view of a prior art driveline configuration for a truck having tandem drive axles with trailing arm air suspensions with a chassis frame member shown in phantom.  
         [0028]    [0028]FIG. 2 is a schematic side view of the prior art driveline shown in FIG. 1 with the suspension components removed to expose the driveline components.  
         [0029]    [0029]FIGS. 3A and 3B are schematic diagrams illustrating a parallel shaft geometry utilizing cardan joints and an intersecting shaft geometry utilizing cardan joints.  
         [0030]    [0030]FIG. 4 is a partially cutaway view of a centered double cardan joint.  
         [0031]    [0031]FIG. 5 is a schematic side view of a prior art driveline substantially similar to that shown in FIG. 2, and having a parallel shaft geometry interaxle drive shaft.  
         [0032]    [0032]FIG. 6 is a schematic side view of a prior art driveline substantially similar to that shown in FIG. 2, but having an intersecting shaft geometry interaxle drive shaft.  
         [0033]    [0033]FIG. 7 is a schematic side view of a driveline according to the present invention.  
         [0034]    [0034]FIG. 8 is a schematic side view of the driveline illustrated in FIG. 7, but with the suspension deflected (compressed) from its nominal design position.  
         [0035]    [0035]FIG. 9 shows a surface plot of the calculated torsional accelerations as a function of the forward and rear drive axle ride height (suspension deflection) for a prior art intersecting driveline such as that depicted in FIG. 2, rotating at 2,500 rpm.  
         [0036]    [0036]FIG. 10 shows a surface plot of the calculated torsional accelerations as a function of the forward and rear drive axle ride height (suspension deflection) for the driveline configuration according to the present invention, such as that depicted in FIG. 7, rotating at 2,500 rpm. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0037]    The present invention is directed to a driveline configuration that greatly reduces driveline vibrations, and in particular reduces U-joint generated second-order torsional vibrations in the driveline. Further, the amplitude of the torsional vibrations at the transmission end of the driveline are relatively insensitive to normal operating changes in the suspension height and remain near zero for any suspension position.  
         [0038]    In a preferred embodiment, shown in FIG. 7, the forward drive axle  101  and the rearward drive axle  102  are arranged such that the output shaft  130  of the forward drive axle  101  is parallel to, and directed approximately towards, the input shaft  132  of the rear drive axle  102 . The installation angles of the drive axles  101  and  102  are selected to provide small joint operating angles on the interaxle drive shaft  110  at universal joints  109 C and  109 D when the vehicle is at the nominal design position. In the preferred embodiment, the joint operating angles at joints  109 C and  109 D are preferable between 1 degree and 5 degrees, and more preferably less than about 2 degrees.  
         [0039]    The forward drive axle output shaft  130  is approximately parallel to the rearward drive axle input shaft  132 . Therefore, the interaxle drive shaft  110  utilizes a parallel shaft geometry. Standard cardan type joints  109 C, and  109 D are used at each end of the interaxle drive shaft  110 .  
         [0040]    The transmission  108  is installed so that the transmission output shaft  126  is directed generally toward the forward drive axle input shaft  128 , and at an angle that provides for a small but non-zero joint operating angle at the transmission output shaft  126 . The joint operating angle is preferably 1 to 5 degrees, and more preferably about 1 to 2 degrees. A standard cardan joint  109 A is also used at the forward end  107 A of the main drive shaft  107 .  
         [0041]    At the rearward end  107 B of the main drive shaft  107 , a near-constant-velocity double cardan joint  115  connects the rearward end  107 B of the main drive shaft  107  to the forward drive axle input shaft  128 . Although the double cardan joint  115  is preferred due to its simplicity, reliability and low cost, it is also contemplated by this invention that any other suitable near-constant velocity, or true CV joint, could be used in place of the double cardan joint  115 .  
         [0042]    At the nominal design geometry shown in FIG. 7, all of the joint operating angles are small, except at the double cardan joint  115  connecting the main drive shaft  107  to the forward drive axle input shaft  128 . However, since the double cardan joint is a near-constant-velocity joint, it introduces minimal cancellation error. Consequently, the torsional acceleration amplitudes at any point in the driveline will be small at the nominal design condition.  
         [0043]    As the suspension compresses or extends from the design position whereby the trailing arm springs  103  rotate about their respective pivots  106 , the joint operating angles at joints  109 C and  109 D on the interaxle drive shaft  110  will change. However, the magnitudes of these joint operating angles will remain smaller than what would be produced in prior art parallel shaft or intersecting shaft geometries because the initial (nominal) joint operating angles are very small. In addition, because the present invention utilizes a parallel shaft geometry for the interaxle drive shaft  110 , the interaxle joint operating angles will remain approximately equal under suspension deflections. Hence, the interaxle drive shaft  110  does not introduce any significant cancellation error into the driveline, even when the suspension is deflected away from its nominal position.  
         [0044]    For example, FIG. 8 shows the driveline configuration of FIG. 7, but with the suspension deflected, i.e., the trailing arm springs  103  that support the drive axles  101 ,  102 , have pivoted about the pivots  106 . The displacement of the axles  101  and  102  about their respective trailing arm pivots  106  produces an increase in the joint operating angles on joints  109 C and  109 D on the interaxle drive shaft  110 , and the joint operating angles remaining equal.  
         [0045]    The flexure in the suspension will also change the joint operating angle at joint  115  between the main drive shaft  107  and the forward drive axle input shaft  128 , but because a near-CV (or CV) joint is utilized, no significant cancellation error is introduced. As can be seen in FIG. 8, the flexure in the suspension causes very little or no change in the joint operating angle at the joint  109 A between the transmission  108  and the drive shaft  107  because the trailing arm pivot  106  for the forward drive axle  101  is typically very close to the location of joint  115  and the main drive shaft  107  is relatively long. Changes in the position of the suspension results in only small changes in the vertical position of the double cardan joint  115  and, consequently, very small changes in the joint operating angle at the transmission cardan joint  109 A.  
         [0046]    It will be apparent to one of ordinary skill in the art that the present invention, can be implemented in a straightforward manner on vehicles having more than one driven axle, by orienting each of the driven axles such that the output shaft of each driven axle is directed towards the input shaft of the next rearward axle, and utilizing a constant velocity, or a near-constant velocity joint at the input shaft of the forwardmost drive axle. It will also be apparent that the present invention can be implemented using other types of suspensions.  
         [0047]    A second order torsional acceleration analysis of a driveline configured according to the present invention was conducted and compared with an equivalent analysis performed for a conventional intersecting shaft geometry driveline configuration. FIG. 9 shows the calculated second order torsional accelerations for the conventional intersecting shaft geometry driveline (FIG. 5) rotating at 2,500 rpm, as a function of the forward and rearward suspension ride deflection. Significant torsional accelerations are introduced as the forward and rearward drive axle suspensions deflect through ±1.5 inches from nominal, rising rapidly from about zero at the design condition to well over 2,000 rad/sec/sec through a significant portion of the parameter space.  
         [0048]    [0048]FIG. 10 shows the corresponding torsional accelerations calculated for a driveline configured according to the present invention (FIG. 7) under the same operating conditions. The maximum torsional accelerations are significantly lower than the prior art configuration, and in particular a large portion of the parameter space is relatively flat (less than 500 rad/sec/sec). The only portion of the parameter space wherein high torsional accelerations are found is where one suspension is significantly extended while the other suspension is simultaneously and significantly compressed. Although such counter-deflected suspension configurations can occur when a truck is traversing very irregular terrain, for example, over a curb or other obstacle in a roadway, such conditions generally occur at low speeds when the drive shafts  107  and  110  are rotating at relatively low rotational speeds. Because the torsional accelerations are proportional to the square of the shaft rotational speed, the joint-induced torsional accelerations in the driveline are generally not important at low speeds.  
         [0049]    As discussed above, the torsional accelerations induced by the universal joints increase as the square of the rotational speeds. Therefore, the highest torsional accelerations generally occur when the vehicle is running at full speed. A common scenario involving significant suspension deflections and full shaft speeds occurs when a truck is cruising at highway speeds and dynamic factors such as accelerations or road conditions produce a vertical bounce at the rear of the truck, resulting in generally equal deflections in both suspensions. In such a scenario, the forward and rearward axle suspensions move generally in unison, and vertical displacement of the axles follow a diagonal path in FIGS. 9 and 10, shown as line  99 .  
         [0050]    Comparing FIGS. 9 and 10, it is apparent that approximately equal vertical deflections of the forward and rearward axles produce markedly different torsional accelerations in the driveline when comparing the conventional intersecting shaft geometry (FIG. 9) with the present invention (FIG. 10). The intersecting shaft geometry produces very sharply increasing torsional accelerations as the drive axles move in tandem away from the design condition in either directions. The driveline of the present invention, in contrast, produces almost no torsional accelerations as the drive axles move up and down in unison.  
         [0051]    The driveline configuration of the present invention results in near-zero torsional acceleration amplitudes at the transmission output shaft and almost complete insensitivity to suspension ride height changes. Torsional amplitudes of the shaft between the two cardan joints on the interaxle shaft are near zero at the nominal design position and remain low over a broad range of suspension positions.  
         [0052]    As noted earlier, frequently trucks will utilize a compound main drive shaft, having more than one drive shaft between the transmission and the forward drive axle. For example, if the chassis has a long wheel base, the distance from the transmission to the first axle may exceed the preferred maximum length for a single drive shaft. In this case, two or more shafts may be employed. Typically, the universal joint connecting a first (forward) main drive shaft with a second (rearward) main drive shaft is mounted to the chassis somewhere between the transmission and the forward drive axle. The geometry of the drive shafts is normally configured to provide small joint operating angles with proper cancellation on the forward shaft(s). The forward-most shaft(s) is attached only to the chassis and therefore its joint operating angle is not affected by suspension articulations. The rearward main drive shaft is attached to the chassis at its front end. In these embodiments, the rear-most main drive shaft is configured in a similar manner to the single main drive shaft arrangement described above—i.e., with a constant- or near-constant-velocity universal joint at its rearward end and a standard cardan joint at its forward end.  
         [0053]    An additional benefit to the present invention is that the small joint operating angles and the parallel shaft geometry, reduce the sensitivity of the driveline to the pinion angle settings (where “pinion angles” refers to the angle that the drive axle input and output shafts make with the chassis, or a horizontal plane). As noted above, the torsional acceleration induced by the universal joint increase as the square of the joint operating angle. Therefore, in prior art driveline configurations employing relatively large joint operating angles in the interaxle drive shaft  110 , truck manufacturers will typically precisely set the drive axle pinion angles after the truck is manufactured. This is an expensive and time-consuming step. In the present invention, the interaxle joint operating angles are small and the driveline is therefore much less sensitive to minor variations in pinion angle settings. The step of precisely setting the pinion angles after assembly of the truck can therefore be avoided, simplifying the manufacturing process.  
         [0054]    While the preferred embodiment of the invention has been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention.