ABSTRACTA method is presented for precise mounting of a hose modelwith any specified twist. Once mounting points and directionsare specified, a hose of a specified length can be developedusing discrete beams. A divide and conquer approach isemployed to position, orient, decouple the free end of thehose model in a twist free state that is then twisted to aspecified angle. The development of the kinematic elementsnecessary to do this is presented. Some Cosserat models havebeen shown to branch into multiple solutions while themethod presented here has always converged to the minimumenergy solution. The method for linking the hose model toother linkages is discussed as well one common errorcommitted by users in implementing the link.

In order to model the torsional properties of the hose, thetorsional stiffness must be modified. A method for doing thisusing digital scans is discussed. Failure to consider preset andhysteresis of the hoses can cause considerable error inpredicting interference as is demonstrated. Simply taking themount orientations out of a common plane can causesignificant stress to build up in the model from torsionalcoupling during a simple linear translation.

INTRODUCTIONMany methods for modeling hydraulic have been developed.Cosserat models [1, 2], finite element models [3], anddiscrete beam models [4,5,6,7,8,9,10] have all beensuccessfully employed. They all have their strengths, but itcould be argued that beam models in a multi-body modelingsystem are the easiest to deploy. A person with a bachelor ofscience in mechanical engineering and an interest in

kinematics can be taught to develop hose models in a matterof hours using a multi-body modeling system whereasCosserat models can be quite daunting. Sugiyama and Otakipointed out that “good” initial conditions can be important fora good solution. Some models can branch into multiplesolutions if care is not taken.

The authors have been using a divide and conquer method tomove hose models into position. Using this method, there hasnever been a case where models have branched into anassembled into an incorrect position. The steps of this methodwill be outlined. The resulting model can integrated into anexisting suspension model, but it is very easy to do thisincorrectly. An example of implementing the modelincorrectly will be presented. Finally, The SAE standard,SAE J1927 [11], states that “hoses should flex in only oneplane”. A brief explanation will be given on how nearness toone plane can be quantified. The models presented here weredeveloped in the multi-body modeling system, ADAMSusing Timoshenko beams [12]. The techniques presented herecould be implemented in any multi-body modeling system.

BUILDING A MODELThe first step in building a model is determining the mountpoints and the attachment directions at those points. Figure 1shows two cylinders that might represent mounts with theircenterlines determining directions. The sense of this directionis important because there are several ways that a hose couldbe assembled as shown in Figure 2. Once the sense has beendetermined a length can be selected.

A Method for Precise Placement of Hose Models 2013-01-0603Published

04/08/2013

Mitchel KeilWestern Michigan Univ.

Jai ThomasCaterpillar Inc.

Copyright © 2013 SAE International

doi:10.4271/2013-01-0603

Figure 1. Candidate attachment locations for a hose.

Figure 2. Possible assembly configurations.

The exact desired length of the hose is used to build a seriesof cylindrical solids connected with short beam elements asshown in Figure 3. In the example, 100 cylinders wereconnected with 99 beams because it made for a relativelysmooth looking model. Fifty cylinders also works well, butthere is no significant difference in run time. The model hereran in a few minutes. Regarding the smoothness of the model,it is obviously not as smooth as the Cosserat models, butthese models are constructed in an interactive environmentwhere properties can be modified quickly. The models canalso be coupled directly into existing suspension model in thesame environment. Also, the deviations from a smoothrepresentation (less than a millimeter as shown here) are faroutweighed by factors such as improper simulationtechniques or improperly characterizing material which canresult in very large errors as described below.

Figure 3. Hose model built on one mount.

Once the model has been built, a divide and conquer strategycan be used to isolate components of motion necessary toplace the free end of the model properly on the other mount.Conceptually, the easiest motion is translation to the mountpoint. This was done using a prismatic joint with a unit stepfunction that was multiplied by the magnitude necessary tomove the proper distance.

Figure 4. Free end moved to the other mount.

To get the proper rotation, a rotary joint was used. Thedirection rotary joint axis was determined from the crossproduct of the attachment direction vectors. Thus, therotational axis is normal to both attachment vectors. Theangle of rotation was then determined by the dot product ofthe two attachment vectors. Again a unit step function wasused and multiplied by the magnitude necessary to rotate theproper angle for alignment with the mount. A second rotaryjoint was created with its axis collinear with the centerlineaxis of the free-end cylinder. This second rotary joint wasused to allow the free-end to be positioned with zero torquealong the axis of the hose. The angle of rotation was recordedand a third unit step function was used rotate the end and lockthis angle. The final placement result is shown in Figure 5.The resulting model could then be integrated into asuspension model. The placement motions would becompleted before suspension movement began.

Figure 5. Free end rotated to the proper orientation.

Potential Errors in the Implementationof the ModelThe authors have seen people dismiss that last rotational lockalong the axis of the hose. The reason for this dismissal wasdue to the fact that the hose model was being used forinterference checks in a vehicle assembly. Users needed tocollect model configurations for many positions of asuspension, so they would assemble the model integrate itinto the assembly. Then they would reconfigure thesuspension and assemble the model again. This had the effectof moving the suspension with a torque free coupling. Figure6 illustrates what can happen. Two models were built onegold one red. The gold model was fixed to the suspensionlinks at both ends. The red model was allowed to rotate freelyabout its attachment axis on the mount nearest to the largegray tire. The suspension was articulated through steer,jounce, and rebound. At the start of the run, the models were

coincident. Later in the run, the models separated as shown.The difference at maximum separation is about one inch. Thisis not acceptable since one inch clearance is often used as anacceptable clearance.

Figure 6. A comparison of a simulation of two hosemodels with both ends fixed(gold) and one end free (red).

The model must be attached to the suspension assembly atboth ends as the hose in the vehicle will be. Figure 7reinforces how tight the routing for a hose can be with thefingers of an inspector fitting between a strut and a vehicle'ssheet metal.

Figure 7. Hydraulic hose on front suspension shownrouting between sheet metal and strut.

A second source of error can come from neglecting to adjustthe torsional stiffness of a hose model. The torsional stiffnesscan be 10 to 15 times that of an isotropic hose. For purebending, the torsional stiffness doesn't matter. Simplebending deflection tests will yield acceptable values forbending stiffness. Twist testing has not given good results inthe experience of the authors. Comparing twisted hosemodels to digital scans has proven to work much better. Withthis method, the torsional stiffness along the axis of the hoseis adjusted until the model approaches the scans as shown inFigure 8. Figure 9 shows the difference between an isotropic

model and an anisotropic model. Both models had the sameend twisted 180°. Neglecting the torsional stiffness has nearlythe same effect as a torque free coupling at one end.

Figure 8. Twisted model compared to digital scans.

Figure 9. Comparison of isotropic model and anisotropicmodel at 180° twist.

Recent ObservationsA recent observation with the model is a confirmation of thestatement “hoses should flex in only one plane” whichappears in the SAE standard SAE J1927. When the twodirection vectors at the ends of the hose model can becontained in one plane, there is very little differential torquebuilt up between beam elements. It does not matter if the endsare displaced from one another or twisted with respect to oneanother. However, if the respective planes which are normalto the cross product of those vectors become separated, thedifferential torque rises very quickly for cases of both relativedisplacement and relative twist of one end. This supports theaforementioned statement in the standard very well.

Mathematically, this separation can be developed from Figure

10. The tails of vectors and are located at the hosemount points. The directions of the vectors determine themount orientations at each end. The direction of the normalvector is determined from the cross product of Equation

(1). is the vector from the first mount point to the second.

is the projection of that is perpendicular to . issized to satisfy the vector loop in Equation (2). Ideally, the

magnitude of is zero, and is equal to .

(1)

(2)

Figure 10. Vector diagram for determiningperpendicular separation of mount points.

Another observation is that hysteresis and preset can distortthe predictive quality of any model. A study [13] showed thatmultiple scans were necessary in developing a more precisenon-linear hose model. Figure 11 helps to illustrate this point.One 16 inch hose was scanned multiple times with no torqueapplied at either end. The mount points were about 7 inchesapart and the orientation vectors were coplanar. The line ofsight is approximately parallel to the plane containing theorientation vectors. One end of the hose was twisted andreleased and a scan was taken. The free end was then twistedin the other direction and released and scanned. Then, theother end of the hose was rotated 90 degrees and the processand the process was repeated. The multiple scans show aseparation of 2.33 inches. One should plan for this potentialstatic deviation in order to maintain clearance.

Figure 11. Multiple digital scans of a 16 inch hose.

SUMMARY/CONCLUSIONSThe modeling method presented here places a hose model ofan exact length with precision using a multi-body dynamics

modeler. It will work in any 3 dimensional multi-bodydynamics modeler that supports the beam elements outlinedhere. There are still significant opportunities for using themethod improperly.

The observation of high differential torque when the mountdirections are not coplanar should be studied further. Thisdifferential torque can certainly damage a structure likehydraulic hose which resists twisting. There may bekinematic solutions that can compensate for this effect, butthey would have to be effective through the full range ofsteer, jounce and rebound.

REFERENCES1. Sugiyama, S. and Otaki, T., “Mathematical Model forBrake Hose Layout,” SAE Technical Paper 922123, 1992,doi: 10.4271/922123.

2. Gregoire, M, and Schomer, E., “Interactive Simulation ofOne-Dimensional Flexible Parts”, Computer-Aided Design39 (2007) 694-707.

3. Kusunoki, K and Miyashita, Y., “Brake Hose RoutingSimulation for Layout Design”, www.estech.co.jp/list.pdf/estl32.pdf, 2004. (accessed 10 July 2009).

4. Elliott, A. S., “Hydraulic Hose Validation Report”,Mechanical Dynamics, Inc. internal document, June 17, 1996.

5. Chipperfield, K. A., Vance, J. M., “VRHOSE - VirtualHose Routing Design”, Industrial Virtual Reality SymposiumProceedings, November 1-2, 1999, Chicago, Illinois, pp.67-72.

6. Keil, M., Rodriguez, J., and Hemmye, M., “Modeling andValidation of Large Hydraulic Hose Deflections,” SAETechnical Paper 2002-01-2589, 2002, doi:10.4271/2002-01-2589.

7. Thomas, J. “Modeling and Validation of a Brake Hose”Master's Thesis, Western Michigan University, UniversityMicrofilms, Ann Arbor, MI, 2004.

8. Alexander, D., “Technical Innovations - Virtual Layout ofHydraulic Hoses,” SAE Off-Highway Engineering Online,June 2005.

9. Fischer, A. G., Chipperfield, K.A. & Vance, J.M. (2002,).“VRHose-Hydraulic hose routing in virtual reality withJack™”, 9th AIAA/ISSMO Symposium on Multidisciplinaryanalysis and optimization, September, 2002, Atlanta, USA.

10. Kang, M., “A Study on Prediction of the Brake HosesDeformation Associated with a Vehicle Motion,” SAETechnical Paper 2012-01-0224, 2012, doi:10.4271/2012-01-0224.

11. SAE International Surface Vehicle Information Report,“Cumulative Damage Analysis for Hydraulic HoseAssemblies,” SAE Standard J1927, Reaf. March, 2009.

12. ADAMS™ Software Reference Manual. (2007).

13. Thomas., “Experimentally Reducing Preset andHysteresis Effects in Creating a Non-Linear Model for BrakeHoses”, Dissertation, Western Michigan University,University Microfilms, Ann Arbor, MI, 2010.

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