# Mechanical Devices for Mass Distribution Adjustment: Are They Really Convenient?

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{D}) during the tests (Figure 2).

_{e}), engine torque (T

_{e}) and selected gear to be acquired simultaneously, while the engine power (P

_{e}) was calculated using the method reported in Molari et al. [28]. Tests were performed on a loam soil [29] field with a moisture content [30] of 16.87% (dry basis) and plastic limit and liquid limit [31] of 22.6% and 36.2%, respectively. In order to reduce data scattering, drawbar tests were carried out using the constant draught test procedure [32,33] for all the three tested weight distribution configurations. Thus, the TT during the tests was always maintained at full throttle, while the drawbar pull could be varied by manipulating the throttle lever and the engaged gear of the LU. Tests were carried out at 3 different gears of the TT (7th, 8th and 9th) and 5 different travelling speeds were obtained for each gear by changing the drawbar pull applied by the LU. The gear ratios ($\tau $) of the tractor rear wheels to the engine crankshaft are reported in Table 3.

_{l}− N

_{u}

_{l})/N

_{l},

_{l}and N

_{ul}are the number of revolutions performed by the TT engine crankshaft over the 30 m of running length with and without drawbar pull applied by the LU, respectively, and are calculated by integrating n

_{e}over the time duration of each test run. The mean values of F

_{D}, v and P

_{e}over each of the 30 m runs were also calculated. Moreover, the evaluation of the standard deviation of F

_{D}(σ

_{FD}) and v (σ

_{v}) over each run were used to verify that tests were performed in almost steady-state conditions. Indeed, samples that achieved values of σ

_{FD}greater than 500 N or of σ

_{v}greater than 0.2 km/h were not considered valid. Then, traction efficiency (η

_{T}) and the net traction ratio (NTR) were calculated, respectively, as:

#### 2.1. Interpolation of Data Obtained from Experiments

_{T}as a function of s, of NTR as a function of s and of η

_{T}as a function of NTR for each of the three tractor configurations tested. The regression models used are shown in Table 4.

^{®}, Mathworks, Inc., Natick, MA, USA). For each regression model, the same upper and lower bounds of the independent variable were chosen for the three tractor configurations, and, for each regression curve, the area enclosed between the upper and the lower prediction bounds was determined (Figure 3).

#### 2.2. Field Productivity and Fuel Consumption Prediction

_{plough}) was estimated using the ASAE/ D497.7 standard [35]:

_{plough}= {0.7 × [652 + 5.1 v

^{2}] × W

_{i}× D

_{i}}/M

_{i}(in meters) is the implement width, set equal to 2.2 m, and D

_{i}(in centimeters) is the working depth, set at 35 cm. As for the plough parameters, soil parameters were chosen to simulate a plausible working condition for the TT.

_{Dplough}) and the power absorbed (P

_{plough}) by the implement are computed as follows:

_{Dplough}= NTR M g

_{plough}= F

_{Dplough}v

_{i}. η

_{f}

_{f}is the field efficiency, equal to 0.85, which is the standard value for a moldboard plough [35].

_{T ic,min}, η

_{T ic,reg}, η

_{T ic,max}

_{e}= P

_{plough}/η

_{T}

_{Dplough}previously determined (Figure 6).

_{th}) is determined:

_{th}= v/(1 − s)

_{e}= [v

_{th}/(r

_{r}τ)] (60/2π)

_{e}= (60 P

_{e})/(2π n

_{e})

_{s}) of the TT during the reference operation, an empirical equation was developed and validated through tests performed at the PTO test bench located at the Agricultural Mechanics Laboratory of University of Bologna located in Cadriano, Italy:

_{s}= 460.1 − 26.28 (n

_{e}/n

_{rated}) − 606.4 (T

_{e}/T

_{max}) + 72.97 (n

_{e}/n

_{rated})

^{2}− 12.11 (n

_{e}/n

_{rated}) (T

_{e}/T

_{max})) + 325.4 (T

_{e}/T

_{max})

^{2}

_{s}is known, the hourly fuel consumption (C

_{h}) and the fuel consumption per hectare (C

_{ha}) are obtained as follows:

_{h}= (C

_{s}× P

_{e})/ρ

_{ha}= C

_{h}/Π

^{3}.

## 3. Results

#### 3.1. Tractive Performance

_{T}with respect to the case of FE. However, the difference between the two curves is very limited, with the maximum difference in η

_{T}for a given value of tractor slip being 0.02. Furthermore, a comparison of the prediction bound areas (Figure 7b) confirms that FE and R regressions deeply overlap: 73% of the R prediction bound area is included in that of FE. The prediction bound area for configuration FC significantly overlaps with that of FE only for values of tractor slip lower than 20%, whereas globally the two areas overlap for the 31% of their extension.

_{T}-s and NTR-s regression models; in particular, the area for the FC configuration is 17 and 56% wider than that for the FE and R configurations, respectively. There is a pronounced overlap between the three prediction bound areas; indeed, 64 and 66% of the R configuration area is included in the FE and FC areas, respectively. FC and FE areas overlap for 50% of their extension.

#### 3.2. Cost-Effectiveness Analysis in FE and FC Configurations

_{T}to the regression model to the upper prediction bound. This is due to the engine characteristic curve (Equation (12)): albeit n

_{e}is the same, different values of η

_{T}result in different working points of the engine in terms of torque T

_{e}and engine power P

_{e}(Table 10), and, ultimately, in different values of the specific fuel consumption. The fact that the engine working point changes also affects the hourly fuel consumption estimation (Equation (13)), which exhibits an opposite trend with respect to C

_{s}.

_{s}determined using the regression equation, consumption for the FE configuration is only 1% higher than that for the FC configuration. Even considering the hourly fuel consumption C

_{h}, no significant differences arise; for the FE configuration, C

_{h}is only 0.4 L/h (1%) lower than the one in the FC configuration. A similar trend is found for C

_{ha}(the difference between the two configurations is 0.4 L/ha, i.e., 1%). This is due to the fact that C

_{ha}is proportional to C

_{h}.

_{h}is 2 L/h (4.7%) lower and C

_{ha}is 1.9 L/ha (4.7%) lower than in the FC configuration. Moreover, if the opposite scenario is considered, where consumption is estimated using the traction efficiency lower prediction bound for the FE configuration and the upper prediction bound for the FC configuration, results are the opposite (C

_{h}and C

_{ha}higher in FE configuration than in FC).

## 4. Discussion and Conclusions

_{T}with respect to tractor mass distribution. However, a more detailed analysis conducted on the basis of the overlaps in the model prediction bound areas shows that there are significant overlaps; hence, it does not seem possible to draw reliable conclusions on the beneficial or detrimental effects of the use of the MC on traction efficiency. Theoretical [19,26,37] and experimental [4,5,38] studies have proved that η

_{T}is influenced by the tractor static mass distribution. However, devices such as the MC are able to change the mass distribution by an amount that is insufficient to experimentally observe any effects. Changes in the mass distribution could be amplified by using a heavier ballast; however, this solution could not be applied in this study, since the weight on the front axle in the FE configuration was close to the maximum value allowed by the manufacturer.

_{T}[40] and even considering the best-case scenario where the difference between the η

_{T}in the FE and FC configurations is the maximum that the regression models can indicate, fuel hourly and per-hectare consumptions in the FE configuration are only 4.7% lower (i.e., 2.1 L/h and 1.9 L/ha lower) than those in the FC configuration.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Parameter | Value (mm) |
---|---|

Wheelbase (WB) | 2884 |

Longitudinal distance of the front hitch from the front wheel hubs (x_{fh}) | 1665 |

Height above ground of the front hitch (h_{fh}) | 850 |

Longitudinal distance of the rear hitch from the rear wheel hubs (x_{rh}) | 1200 |

Height above ground of the rear hitch (h_{rh}) | 655 |

Longitudinal length of the ballast over the rear hitch (x_{rb}) | 400 |

Longitudinal length (hitch to hitch) of the MC (MC_{l}) | 690 in FC 1690 in FE |

Longitudinal length of the ballast over the MC hitch (B_{l}) | 280 |

Vertical distance between tractor front lower hitch and MC lower hitch (MC_{hl}) | 120 |

Vertical distance between tractor front upper hitch and MC lower hitch (MC_{hh}) | 480 |

## Appendix B

**Figure A4.**NTR-v regression curves(E1)obtained from the field tests performed in 8th gear in FC and FE configurations.

Regression Parameters | FC | FE |
---|---|---|

Coefficient p_{1}(with 95% confidence bounds) | −2789 (−3955, −1623) | −2624 (−3838, −1410) |

Coefficient p_{2}(with 95% confidence bounds) | 1.864 × 10^{4}(7424, 2.986 × 10 ^{4}) | 1.660 × 10^{4}(5432, 2.776 × 10 ^{4}) |

Coefficient p_{3}(with 95% confidence bounds) | 2.645 × 10^{4}(40.67, 5.285 × 10 ^{4}) | 3.328 × 10^{4}(9004, 5.755 × 10 ^{4}) |

R^2 | 0.97 | 0.97 |

## Appendix C

**Figure A5.**NTR-s regression curves (E2)) obtained from the field tests performed in 8th gear in FC and FE configuration.

Regression Parameters | FC | FE |
---|---|---|

Coefficient p_{1}(with 95% confidence bounds) | −14.31 (−20.65, −7.972) | −13.24 (−19.63, −6.842) |

Coefficient p_{2}(with 95% confidence bounds) | 1405 (1032, 1779) | 1378 (961.8, 1795) |

Coefficient p_{3}(with 95% confidence bounds) | 2.298 × 10^{4}(1.797 × 10 ^{4}, 2.799 × 10^{4}) | 2.361 × 10^{4}(1.822 × 10 ^{4}, 2.900 × 10^{4}) |

R^2 | 0.97 | 0.97 |

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**Figure 1.**Multiplier Counterweight in (

**a**) fully extended configuration (FE); (

**b**) fully closed configuration (FC). (

**c**) The test configuration R, where a standard 1000 kg ballast was mounted on the rear three-point hitch. Schematics for the calculation of tractor mass distribution are reported in Appendix A.

**Figure 2.**Drawbar test setup with the TT in the R configuration. The plough on the Case IH Maxxum 115 (LU) tractor was mounted for the sole purpose of making the LU tractor reach the weight necessary to brake the TT.

**Figure 3.**Regression analysis for net traction ratio (NTR) as a function of s for tractor configuration FE. The experimental data points, the regression curve R2 and the upper and lower prediction bounds (95% confidence level) are visible. The yellow-shaded region is the area used for data comparison.

**Figure 4.**Example of the expected working condition of the tractor-plough system for TT in FE configuration and 8th gear.

**Figure 5.**Example of traction efficiency estimation for tractor configuration FE and 8th gear. η

_{T FE,reg}is the estimation based on the regression model; η

_{T FE,min}is based on the lower prediction bound and η

_{T FE,maxg}is based on the upper prediction bound for the model.

**Figure 6.**Example of the tractor slip estimation starting from the expected value of F

_{Dplough}. Tractor configuration FC and 8th gear.

**Figure 7.**(

**a**) η

_{T}-s regression curves, and (

**b**) prediction bound areas for tractor configurations FE, FC and R. Regression coefficients are listed in Table 7. The lower and upper slip values for the models are 11 and 52%, respectively.

**Figure 8.**(

**a**) NTR-s regression curves and (

**b**) prediction bound areas for tractor configurations FE, FC and R. Regression coefficients are listed in Table 8. The lower and upper slip values for the models are 11 and 52%, respectively.

**Figure 9.**(

**a**) NTR-η

_{T}regression curves and (

**b**) prediction bound areas for tractor configurations FE, FC and R. Regression coefficients are listed in Table 9. The lower and upper net traction ratio values for the models are 0.40 and 0.64, respectively.

**Figure 10.**Predicted values of (

**a**) C

_{s}, (

**b**) C

_{h}and (

**c**) C

_{ha}, for tractor configurations FE and FC in 8th gear. For each configuration, the blue, orange and yellow bars refer to estimations determined using, respectively, the lower prediction bound of the model, the regression model R3, and the upper prediction bound of the model.

Specification | Value/Description |
---|---|

Engine speed at the maximum engine power (n_{rated}) (rpm) | 2000 |

Max engine power @ n_{rated} (kW) | 191 |

Max torque (T_{max}) @1500 rpm (Nm) | 1100 |

Torque @ n_{rated} (Nm) | 912 |

Unballasted mass (kg) | 8590 |

Transmission | Full Powershift (gears: 19 forward, 6 reverse) |

Front tires | Michelin MACHXBIB 600/65 R28 (50 kPa) speed radius index r _{f} = 0.700 m |

Rear tires | Michelin MACHXBIB 710/70 R38 (50 kPa) speed radius index r _{r} = 0.925 m |

**Table 2.**Tractor static weight distribution over the axles in fully closed (FC), fully extended (FE) and standard ballast on the rear three-point linkage (R) configurations.

Tractor Configuration | Total Tractor Mass (M) (kg) | Mass on the Front Axle (%) | Mass on the Rear Axle (%) |
---|---|---|---|

MC Fully Extended (FE) | 9590 | 59 | 41 |

MC Fully Closed (FC) | 9590 | 56 | 44 |

Standard ballast on the rear three-point linkage (R) | 9590 | 32 | 68 |

Gear | Gear Ratio $\left(\mathit{\tau}\right)$ |
---|---|

7th | 7.475 × 10^{−3} |

8th | 8.932 × 10^{−3} |

9th | 1.074 × 10^{−2} |

Curves | Fitting Method | Model Equation |
---|---|---|

η_{T} as a function of s (R1) | Non-linear least squares | η_{T} = a^{(b s)} + c^{(d s)} |

NTR as a function of s (R2) | Linear least squares | NTR = p_{1} s^{2} + p_{2} s + p_{3} |

η_{T} as a function of NTR (R3) | Non-linear least squares | η_{T} = a^{(b} ^{NTR}^{)} + c^{(d} ^{NTR}^{)} |

Curves | Fitting Method | Model Equation |
---|---|---|

NTR as a function of v (E1) regression curve and parameters are reported in Appendix B | Linear least squares | NTR = p_{1} v^{2} + p_{2} v + p_{3} |

Curves | Fitting Method | Model Equation |
---|---|---|

F_{Dplough} as a function of s(E2) regression curve and parameters are reported in Appendix C | Linear least squares | F_{Dplough} = p_{1} s^{2} + p_{2} s + p_{3} |

Regression Parameters | FE | FC | R |
---|---|---|---|

Coefficient a (with 95% confidence bounds) | 2943 (−1.907 × 10 ^{12}, 1.907 × 10^{12}) | 37.56 (−4.421 × 10 ^{6}, 4.421 × 10^{6}) | −2199 (−6.029 × 10 ^{11}, 6.029 × 10^{11}) |

Coefficient b (with 95% confidence bounds) | 1.036 × 10^{−2}(−699.3, 699.3) | 1.060 × 10^{−2} (−10.33, 10.36) | 1.366 × 10^{−2}(−399.5, 399.5) |

Coefficient c (with 95% confidence bounds) | −2942 (−1.907 × 10 ^{12}, 1.907 × 10^{12}) | −37.06 (−4.421 × 10 ^{6}, 4.421 × 10^{6}) | 2200 (−6.029 × 10 ^{11}, 6.029 × 10^{11}) |

Coefficient d (with 95% confidence bounds) | 1.036 × 10^{−2}(−699.4, 699.4) | 1.077 × 10^{−2} (−10.42, 10.44) | 1.366 × 10^{−2}(−399.4, 399.5) |

R^2 | 0.97 | 0.96 | 0.94 |

Regression Parameters | FE | FC | R |
---|---|---|---|

Coefficient p_{1} (with 95% confidence bounds) | −1.561 × 10^{−4}(−1.839 × 10 ^{−4}, −1.284 × 10^{−4}) | −1.290 × 10^{−4}(−1.716 × 10 ^{−4}, −8.637 × 10^{−5}) | −1.761 × 10^{−4}(−2.033 × 10 ^{−4}, −1.488 × 10^{−4}) |

Coefficient p_{2}(with 95% confidence bounds) | 1.535 × 10^{−2}(1.350 × 10 ^{−2}, 1.720 × 10^{−2}) | 1.313 × 10^{−2}(1.053 × 10 ^{−2}, 1.573 × 10^{−2}) | 1.704 × 10^{−2}(1.555 × 10 ^{−2}, 1.860 × 10^{−2}) |

Coefficient p_{3}(with 95% confidence bounds) | 0.254 (0.228, 0.282) | 0.291 (0.255, 0.327) | 0.223 (0.203, 0.242) |

R^2 | 0.97 | 0.94 | 0.97 |

Regression Parameters | FE | FC | R |
---|---|---|---|

Coefficient a (with 95% confidence bounds) | −505.1 (−1.103 × 10 ^{11}, 1.103 × 10^{11}) | −7.706 (−3.584 × 10 ^{5}, 3.584 × 10^{5}) | 173.9 (−1.000 × 10 ^{9}, 1.000 × 10^{9}) |

Coefficient b (with 95% confidence bounds) | 3.769 (−7.257 × 10 ^{4}, 7.258 × 10^{4}) | 2.710 (−1302, 1307) | 2.909 (−6541, 6547) |

Coefficient c (with 95% confidence bounds) | 505.3 (−1.103 × 10 ^{11}, 1.103 × 10^{11}) | 8.050 (−3.584 × 10 ^{5}, 3.584 × 10^{5}) | −173.6 (−1.000 × 10 ^{9}, 1.000 × 10^{9}) |

Coefficient d (with 95% confidence bounds) | 3.769 (−7.256 × 10 ^{4}, 7.257 × 10^{4}) | 2.660 (−1284, 1289) | 2.912 (−6545, 6551) |

R^2 | 0.92 | 0.84 | 0.90 |

MC Configuration | F_{Dplough} (kN) | NTR_{plough} | v (km/h) | s (%) | Π (ha/h) | η_{T} | P_{e}(kW) |
---|---|---|---|---|---|---|---|

FC | 43.4 | 0.46 | 5.6 | 17.7 | 1.05 | η_{T FC,min} = 0.45η _{T FC,reg} = 0.48η _{T FC,max} = 0.50 | 148@ η_{T FC,min}142@ η _{T FC,reg}136@ η _{T FC,max} |

FE | 43.9 | 0.47 | 5.6 | 17.7 | 1.05 | η_{T FE,min} = 0.47η _{T FE,reg} = 0.49η _{T FE,max} = 0.51 | 144@ η_{T FE,min}139@ η _{T FE,reg}135@ η _{T FE,max} |

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## Share and Cite

**MDPI and ACS Style**

Varani, M.; Mattetti, M.; Maraldi, M.; Molari, G.
Mechanical Devices for Mass Distribution Adjustment: Are They Really Convenient? *Agronomy* **2020**, *10*, 1820.
https://doi.org/10.3390/agronomy10111820

**AMA Style**

Varani M, Mattetti M, Maraldi M, Molari G.
Mechanical Devices for Mass Distribution Adjustment: Are They Really Convenient? *Agronomy*. 2020; 10(11):1820.
https://doi.org/10.3390/agronomy10111820

**Chicago/Turabian Style**

Varani, Massimiliano, Michele Mattetti, Mirko Maraldi, and Giovanni Molari.
2020. "Mechanical Devices for Mass Distribution Adjustment: Are They Really Convenient?" *Agronomy* 10, no. 11: 1820.
https://doi.org/10.3390/agronomy10111820