Research & Development Center

# YANMAR Technical Review

## Design Method for Hydro-Mechanical Transmission for Vehicle: Prediction of Noise Based on 1D and 3D Simulation

### Abstract

For agricultural tractor, these two performances have been very important; high efficiency and maneuverability because the operator has increasingly required the fewer fuel consumption and easier and more precise control of the tractor. Therefore, new hydraulic mechanical transmission (HMT) has been developed specially to fit their demands. HMT is well known for the high efficiency level thanks to their splitting power flow between mechanical and hydraulic path. Moreover, its step-less variable speed feature is suitable for the operator demand such as quick and smooth speed change. However, HMT is hydraulic powered system then hydraulic noise may more often occur than the pure mechanical transmission; such as power-shift transmission or dual clutch system. Purpose of this paper is to show how to design tractor transmission with HMT concerning with hydraulic noise.

### 1. Developed HMT

#### 1.1. Structure Overview

Conventional tractors transmission technology mainly consists of "mechanical" or "hydraulic" types. Fig.1 shows appearance of newly developed HMT (Hydraulic Mechanical Transmission), which has the concept that it brings both high transmission efficiency of mechanical type and high maneuverability of hydraulic type. The main features of this HMT are as following;

- Only one plunger block into which plungers of pump and motor are inserted.
- Spool mechanism which switch hydraulic oil path while the expansion and compression process.
- Continuous variable speed control with the electromagnetic proportional valves.

### 2. Procedure of Sound Pressure Level Prediction

#### 2.1. Procedure

In order to predict the hydraulic noise level, calculation procedure has been developed as shown in Fig.2.

Each steps of the procedure are as following;

##### (a) Hydraulic pressure simulation on HMT

For the purpose of reducing the hydraulic noise, one-dimensional numerical model has been developed (Fig.3). This 1D model provides all forces and moments produced by the pressure in each plunger chambers, high and low-pressure ports. Hydraulic Oil flow from Plunger chamber is switched from low (high) pressure port to high (low) pressure port. It is well known that V-shaped notch on the valve plate is effective to reduce the high frequency noise of axial piston pumps ^{[1]}. This HMT has same functional part, which is named timing spool as shown in Fig.4. The spool geometry determines how quickly opens or closes the fluid path.

##### (b) Transmission vibration simulation

By using the calculated forces and moments, vibration speed of transmission cover has been calculated with FE frequency response analysis (Fig. 5). Forces calculated by 1D model was used to predict the transmission cover vibration. The axial forces have been applied to the cover surface where HMT is fastened and the whole edge of the cover has been treated as the fixed end.

##### (c) Sound pressure calculation

Sound pressure level has been calculated by using the vibration acceleration of the transmission cover's surface and equation (1), which was derived from the wave equation (2)^{[2]}.

where, SPL, are sound pressure level [dB], height and width of sound source [m], air density [kg/m^{3}]，frequency spectrum of vibration velocity in discrete-time system, sound speed [m/s]，distance from the sound source [m] and Laplacian; which means in Cartesian coordinate system of x, y, z-axis. is known as velocity potential function, which is expressed in formula (3) and (4); where sound pressure and medium particle velocity .

### 3. Results of Simulation

#### 3.1. Hydraulic Pressure Simulation

1D model which calculates each plunger chamber and port pressure brought all forces and moments affecting to the cover where HMT is mounted. Table 1 shows the condition of the simulation. This condition represents the tractor operating mode in which tractor runs at quite slow speed; 0.35km/h with no traction load.

Table 1 Condition of Simulation

Fig.6 is a one example of the result which shows the pressure frequency spectrum in high pressure port. In this case, the plunger block rotates 2,800min^{-1}; thus, the pump's 1st harmonic order is 327Hz because pump has 7 plungers, and the motor's 1st harmonic order is 302Hz because motor has also 7 plungers and motor rotates at the differential speed between input speed 2,800min^{-1} and output speed 210min^{-1}. This result shows that the higher the harmonic order is, the lower the pressure spectrum peak becomes.

#### 3.2. Transmission Cover Vibration

Fig.7 shows the vibration acceleration on the transmission cover surface calculated with FE frequency response analysis. The frequency spectrum has great peaks around 3kHz by the effect of a plurality of characteristic oscillation modes of the cover.

#### 3.3. Sound Pressure Calculation

Fig.8 shows the result of sound pressure level prediction by using the vibration acceleration of the transmission cover and equations (1) and (2). This sound pressure level was simulated where the distance from the transmission cover is 1.0m.

### 4. Conclusion

This paper showed the method that predicts the transmission noise produced by the hydraulic pressure in HMT with using only design parameters. The result of the pressure simulated by 1D model was shown and the vibration acceleration on the transmission surface and the sound pressure level were predicted. In the next step, the experimental data will be measured and compared with this simulated result to be verified the prediction method.

### 5. References

- T. Grahl: 8 AFK, 1988, pp187-204.
- M. Ota: Basic information sound engineering, 1990, p. 86.

### -IMPORTANT-

The original technical report is written in Japanese.

This document was translated by Research & Development Management Division.