COVER STORY SUSPENSION SYSTEMS EFFICIENT CONCEPT DESIGN OF TWIST BEAM REAR AXLES Twist beam rear axles are lighter and less expensive than multi-link suspensions but can’t be developed easily. Thus, the University of Siegen developed a new analytical method for concept design, with which stiffness and kinematics of twist beam axles can be evaluated within a few seconds. © iammacintosh | fotolia 24 www.autotechreview.com AUTHORS MOTIVATION AND STATEMENT OF complex interactions between the differ- THE PROBLEM ent variables, since local improvements of one requirement may have negative With cost and weight advantages, the effects on the others. twist beam rear axle has been increas- This fact is the main challenge for the ingly used for vehicles in low and middle concept design of the twist beam axle. classes. However, in comparison to multi- According to the state-of-the-art technol- PROF. DR.-ING. XIANGFAN FANG is Director of the Institute of link suspensions, more development ogy, the kinematics of the rigid axle and Automotive Lightweight Design at efforts are required to improve the stiff- the independent suspension are usually the University of Siegen (Germany). ness under lateral force and the axle kine- calculated using multi-body simulation matics during cornering, which can cause (MBS) and then optimised with numeri- over-steering behaviours. The develop- cal optimisation tools. Compared to the ments of the last decade led to significant twist beam axle, in which especially the improvements in axle stiffness and kine- cross member is designed relatively soft, matics, so that an increasing use of the the components of the rigid axle and the twist beam axle can be observed cur- independent suspension are much stiffer DIPL.-ING. KANLUN TAN rently, also in higher class vehicles. and can be considered as rigid bodies in is Research Associate of the Institute of Automotive The main requirements for the concept those simulations. This assumption can- Lightweight Design at the design of the twist beam rear axle include, not be applied to the twist beam axle, University of Siegen (Germany). (a) the lateral, toe and camber stiffness, since the deformation of the axle compo- as mentioned above; and (b) the kine- nents, particularly the bending and twist- matic toe and camber. The latter show the ing of the cross member, determine the changes of the toe and camber angles properties of the axle kinematics and during parallel and opposite wheel trav- must not be neglected. els. The lateral stiffness is defined as the For this reason, a highly detailed, para- ratio of an applied lateral force at the metric MBS model with deformable com- wheel contact point to the displacement ponents is required to enable the concept of the point in the vehicle transverse design and optimisation of the twist beam direction. Similarly, the toe and camber axle. The large number of optimisation stiffness are the ratios of the same lateral variables and the high complexity of flexi- force to the changes of the toe and cam- ble multi-body models require a huge ber angles. computing capacity and a very long com- As can be seen in 1, all requirements putation time. Therefore, this CAE optimi- are simultaneously influenced by many sation method is rarely being used in the factors and there is also a strong depend- industrial practice for the twist beam axle. ence between the requirements. The most The commonly used approach in the important influencing factors are the hard development of the twist beam axle starts points, the three-dimensional form of the usually with several “empirical” or on components and the sectional properties. benchmarking-based concepts. They are These influencing factors are also the vari- at first roughly designed with CAD and ables, which must be defined during the then converted into finite-element and concept design. This means that the axle MBS models. A concept evaluation con- stiffness and kinematics are mainly deter- cerning the stiffness and kinematics can mined by its basic concept. Other factors, only be carried out after the simulations. such as design details, do have influence The best concept must be further on the strength and durability of the axle; developed and optimised via many opti- however, they have only small influence misation steps. For this reason, many on the axle stiffness and kinematics and resources must be invested in the CAD will not be further considered in the cur- and CAE works before the concept eval- rent investigation. uation. Furthermore, the quality of the In addition to the illustration of the concepts is highly dependent on the complex interactions, ① also clearly personal experiences of the engineers, shows an enormous design potential. On so that unsuitable concepts might be one hand, the large number of the varia- followed and optimised for a long time bles can provide a large variety of concept without having a good result at the end. possibilities, while on the other hand, the To solve these problems, a new method design and optimisation of the twist beam for concept design was developed in the axle become very difficult due to these work presented here. In this method, all autotechreview February 2015 Volume 4 | Issue 2 25 COVER STORY SUSPENSION SYSTEMS Lateral stiffness Toestiffness Camber stiffness Other axle stiffnesses cross member with a high bending stiff- ness but lower torsion stiffness. In the example axle showed here, the cross member has a hat profile cross section Three-dimensional Hard points Sectionalproperties Other factors with reinforcements at each of the two form of components transition areas to the side arms, which have a nearly circular cross section. Each component can be idealised as Other kinematic Kinematic toe Kinematic camber five straight and homogeneous beams. characteristics This subdivision is sufficient enough to 1 Complex interactions between the concept variables and requirements represent the three-dimensional form of the components. In order to describe the strong variation of the cross sections of Ul Ur the axle components in reality, each beam can be defined with a separate property. For example, the cross member in the axle is idealised to have a rectangular profile at (a) the ends, a hat profile in the central region and a partially closed profile in the transitional areas. To improve the accu- racy of the model, extra beams can be introduced; however, it causes a signifi- RAS cantly higher computation time. RAS FS Besides a cross member and two side Ul Ur arms, a twist beam axle usually has also components to connect with spring damper elements. Traditional spring damper seats, such as the one shown in (b) ②, are connected to the stiff side arms. They can be nearly neglected in the ana- lytical method because of their small influence on the axle stiffness. However, some modern spring-damper RAS RAS FS seats connect the cross member with the side arms at the same time, so that the relatively weak cross member is signifi- cantly reinforced. This leads to an increase of the total axle stiffness. Because of the complex geometry of the (c) seats, their implementation into the ana- lytical method is difficult and can be con- sidered as a further development perspec- tive of the current method. In the second step, all loads on the nodes and bearings are calculated analyti- cally. For this purpose, the axle is 2 Idealisation of the example axle as a beam model and the calculation of its bearing and node loads with the mounted as a statically determined sys- statically determined constraints tem, which requires exactly six con- straints for its freedom of movement, ② the complex interactions in ① were NEW APPROACH OF ANALYSIS (b), ② (c). The two guide bearings, Ul mathematically, purely analytically and and Ur, are idealised as ball joints here, completely determined and imple- The basic approach of the stiffness analy- where Ur can also move translational in mented into a software tool. Once the sis based on this new method can be the car’s y-direction. While the lateral concept variables are entered, the axle divided into four steps. In the first step, force acts on the left wheel contact point stiffness and kinematics can be calcu- the axle is idealised as a beam model, 2 with a short offset RASFS, the right wheel lated with a good accuracy in a few sec- (a). A twist beam axle usually consists of contact point RAS must have no move- onds. The CAD data and CAE calcula- two side arms with high bending and tor- ment in the car z-direction. With these tion are not required at all. sion stiffness, which are connected by a statically determined constraints, all 26 www.autotechreview.com forces and moments acting on the bear- ings and nodes can be calculated analytically. In reality, the two guide bearings are not ideal ball joints but rubber bushings, (a) whose characteristics can also affect the axle stiffness additionally. However, because the effects of the rubber bushing on the axle characteristic are often consid- ered separately in the industrial practice, the assumption here of idealised ball joints can be considered as sufficient. In the third step, the three-dimen- sional and manifold deformations of each beam are calculated analytically. They consist of tension, compression and bending deformations, as well as pure torsion and warping torsion. The corre- (b) sponding equations or systems of equa- tions are developed in matrix form and solved analytically. To complete the stiffness analysis, the individual beam deformations are assem- bled in the fourth and last step and then the total axle stiffness is determined. As can be seen in 3 (a), the deformation begins at the left side arm, while the cross member moves only slightly with- out deformation.