How to Analyze Accessory Belt Drive in Powertrain using Simulation and Metamodeling

When automotive engineers use simulation software there are various challenges when designing robust and optimized accessory drive systems for engines. Most original equipment manufacturers (OEMs) rely on different suppliers for their engine belts and accessories. This leads to challenges in obtaining input engine data from different suppliers to incorporate in a system-level simulation. Fundamentally, a belt supplier’s input data is the belt, but it is difficult to get other inputs related to the accessories and tensioner since they mainly come from other suppliers.  

In case of an issue in the accessory drive system, it is challenging to get a common model to analyze the entire system in one simulation platform. Most of the time, sharing input data of one supplier with other leads to proprietary issues. It is necessary for OEMs to create their own common simulation platform and system-level models using inputs collected from their various suppliers. 

A System-level Approach to Analyze Accessory Drives 

Due to simulation tool limitations, crank loading on the accessory drive is modeled as an enforced input of a crank hub torsional. But this approach does not consider the dynamic coupling between crank and accessory drive system dynamics. GT-SUITE has an integrated system-level capability in which a detailed model coupled with belt, accessories, tensioners, and detailed cylinder pressure-based cranks can be modeled. This model helps design a robust product and optimizes the accessory drive using a system-level approach. For example, in a single integrated model, the change in torsional vibration damper (TVD) of a crank can be analyzed from both perspectives. In this blog, I studied the crankshaft torsionals and their coupled effect on accessory drive system dynamics. 

Using GT-SUITE, it is also possible to model the accessory drive system for hybrid electric vehicle (HEV) applications. HEVs fundamentally use dual arm tensioners for boosting/re-generation or start/stop applications. 

Note: Using GT-SUITE, even detailed cranktrains, timing drives, and valvetrain subsystems can be integrated to perform a detailed system-level analysis of the entire powertrain (see Figure 1 below). 

Figure 1: System-level Modeling of an Accessory Drive in GT-SUITE

Longitudinal and Transverse Vibration in Belt Drive 

In belt drive systems there are fundamentally two major vibration issues which can cause failure: 

Torsional Vibration: A belt and pulley system can be conceptualized as a rotational system of torsional spring and inertia. The span between two pulleys acts as a spring and the pulley as inertia in a simplified way. Based on this, the system can get excited at the torsional natural frequency due to the crank excitation. When there is an alternator decoupler in the system, which has soft springs (used to decouple the heavy inertia of the generator), it can create a first natural frequency in the range of 10-20 Hz.  

Transverse/Span Vibration: The belt segment between two pulleys has its own stiffness and can be conceptualized as span stiffness. This span stiffness depends on span length and initial belt installation tension. The shorter the span length, the higher the stiffness and higher the span natural frequency. In many cases, due to the packaging, it is difficult to reduce the span length. In this case, installation tension becomes a critical parameter to reduce transverse vibration. 

See Figure 2 to see the difference between torsional and transverse vibrations.

Figure 2: Torsional and Transverse Vibration in an Accessory Drive

Main Simulation Results to be Analyzed 

For analyzing the accessory drive system, below are the main results that need to be analyzed with defined design targets: 

• Maximum and minimum belt tension 
• Maximum and minimum hub loads 
• Tensioner arm angular motion 
• Slips at each pulley 
• Transverse belt span deflections 

Among these, maximum belt tension and tensioner arm motion is the most critical output as failing these criteria can lead to the mechanical failure of the belt. There is often a hard stop in the tensioner. Once the angular arm motion reaches this limit, then there is an abrupt increase in belt tension which leads to breakage of the belt. Hub load outputs are also important for bearing design and durability considerations. Minimum belt tension, hub load, slip, and span deflection are important for efficient design. For example, if the minimum belt tension reaches zero, the belt loses contact with the pulley, reducing the system’s efficiency. 

In Figure 3 below, here are some examples of the results in GT-SUITE (e.g., belt tension and global slip %). 

Figure 3: Belt Tension and Global Slip%

Use of Metamodels to Provide Early Design Direction to the Product Team  

Once a baseline model is defined, including the ability to qualify design guidelines, constraints, and identify failing criteria, it is ready to leverage GT-SUITE’s built-in Machine Learning Assistant (MLA). The MLA can be used to either optimize the system or correct part selection and sizing when the issues are related to failing a design target for a given operating condition. Cost optimization can be achieved by reducing the number of ribs on the belt, removing the idler, choosing the appropriate supplier for belt or accessories, and more. If the design is failing, the system sensitivity could be known to the different input which have some scope for modification with the actual hardware. 

In below plots (Figure 4), one example shown, in which some parameters like belt pre-tension, water pump/alternator torque, belt axial stiffness, idler diameter, and tensioner position are studied for a given model for the weighted sensitivity. In general, these parameters have some flexibility to change while designing the actual system. Based on the sensitivity analysis, a design direction can be given to the production team.  

Figure 4: Main Effects Plots for Specified Attributes or Inputs Ranking

Also, there is another plot which shows variational analysis results (Figure 5) within the range specified for the different input factors taken. This will help the production team to choose the right system. For example, in this case based on the sensitivity analysis, a user can first try to optimize the system-based on the belt dynamic tension and tensioner angular motion by changing the selected input within the range. The effect on the dynamic belt tension and tensioner motion within the range can be seen by the slider bar results as shown in Figure 5. 

Figure 5: Variational Analysis for Specified Attributes

Video Demonstration of Kriging and Multilayer Perceptron (MLP) Metamodeling Methods   

Learn More About our Accessory Drive Belt Dynamic Simulation  

If you would like to learn more or are interested in trying accessory drive belt dynamic simulation, contact us!  

Stay tuned for the next blog which will be focused on the details of the use of GT-SUITE’s Machine Learning Assistant for accessory drives!