Design, manufacture, and performance evaluation of a single-axle tractor-operated potato digger elevator

Abstract This study presents the design, manufacture, and test of a two-wheel tractor-mounted potato digger elevator for harvesting potatoes. The experimental design for the prototype evaluations is a split plot where the conveyor slope (10°, 15°, and 20°) is the main plot and the rake angle (15°, 20°, and 25°) is a sub-plot with three replications. It was discovered that increasing the blade angle reduced tuber damage loss while increasing the conveyor slope. The greatest exposure effectiveness of 96.47% is recorded at a conveyor slope of 15° and a rake angle of 20°. At this optimum condition, damage percentage, conveyance efficiency, cleaning efficiency, drawbar pull, fuel consumption, wheel slip, soil swelling factor, soil mean weight diameter, pulverization ratio, and field capacity are 3.39%, 89.64%, 91.87%, 2959.1 N, 14.87 l/ha, 17.67%, 20.25%, 17.44 mm, 78.09%, and 0.127 hectares per hour, respectively. In comparison to manual hand hoe harvesting, the prototype can save 86.6% on labor and 63.36% on harvesting costs. The equipment is acceptable with its high promise for deployment to small to medium-sized farmers, and the authors advise re-evaluating at greater rake angles and conveying slope using multiple potato varieties and a double axel tractor.


PUBLIC INTEREST STATEMENT
Designing a root crop harvester and elevator requires understanding engineering properties, tuber characteristics, and manufacturing materials.Safety of the soil cutter relies on soil strength, and soil mechanics must be studied for mechanical and structural components.The blade and conveyor are crucial components in the root crop harvester machine, and understanding their dynamic interaction can improve harvest and post-harvest operations and reduce economic losses.A single-axle tractor-operated potato digger elevator can benefit smallholder potato producers by minimizing losses, drudgery, production costs, time, and energy during harvesting.Prototype evaluations showed that the equipment saved 86.6% on labor and 63.36% on harvesting costs compared to manual hand hoe harvesting.This equipment is suitable for small to medium-sized farmers and can minimize losses, drudgery, production costs, time, and energy losses during harvesting.

Introduction
Potato (Solanum tuberosum L.) is the fourth most important tuber crop in the world and first in volume among root crops, which more than 125 countries, and a billion people consume daily (Hayilu et al., 2017).The occurrence of a prolonged famine happened at the end of the nineteenth century, rapidly increasing the adoption of potatoes in Ethiopia due to their high nutrition and being an adaptive species to climate change since they were introduced in 1858 (Dawit & Alemayehu 2021).Ethiopia has 70% of the 13.50 million ha of arable land suitable for potato cultivation, which is the highest potential in Africa.Around 1,288,146 household farmers are dependent on potato production, and about 67,361.87ha of land is under potato production (Wubet et al., 2022;Yazie et al., 2017).Potato is the best smallholder farmers' crop in the highlands, with a short cropping cycle (3-4 months) and a high yield (40 t/ha), making it a suitable crop where land is limited, but labor is abundant, allowing it to serve both cash and food security (Gebru et al., 2017).Potatoes can fill a gap in the food supply during the hungry months of October to December before the grain crops are harvested (Wegi et al., 2017).It rapidly became a source of cash income as demand by the food-processing sector increased to meet the fast and snack foods, the growth of urban populations, rising incomes, and the diversification of diets (Devaux et al., 2021).
In Ethiopia, hand hoeing and oxen ploughing are the most common methods of potato production (Tadesse et al., 2017;Tschopp et al., 2010).Harvesting potatoes was done either manually with a hand hoe or with an oxen-drawn local Maresha [10].However, the reduction in fuel consumption, turn-around time, labor requirements, and machinery wear and tear is increasing interest in single-axle tractors among smallholder farmers in Asia and Africa (Diao et al., 2014).The challenge is delivering machines operated by 2 WT, demonstrating them, adopting them in the target market, and then developing a supply chain for the commercialization of these machines (Haque et al., 2016).Studies showed that there are 2 WT service providers, model farmers, and farmer unions that started their businesses recently in Ethiopia that offer ploughing and transportation services and have started making money.Similarly, corporate unions have now expanded their businesses and started offering 2 WT-based services (Workneh et al., 2021).DF-15 L and DF-12 L model two-wheel tractors (2WTs) with 15hp and 12 hp capacities, respectively, started to be used in Ethiopia (Kebede & Getnet, 2017).This shows that the demand for 2 WT-based technologies will have a positive impact on smallholder farmers due to on-farm power in Sub-Saharan Africa declining due to the collapse of tractor hiring; the decline in draft animals; and human labor stemming from rural-urban migration.This leads to high labor drudgery, with women disproportionately weeding, threshing, shelling, and transporting by head-loading (Ayele, 2022).However, nowadays, potato crop harvesting is done using traditional methods, including an animal-drawn, locally produced plough called Maresha and a bamboo or metal funnel attached to the plough.In small areas, manual harvesting is practiced by making holes or slits with a stick or tool and collecting the tubers by hand.These bruised tubers caused considerable losses due to damaged and unexposed tubers that affect the tuber shelf life and decrease market values.Tuber damage also promotes the spread of vector-borne pathogens (Musita et al., 2019).Hand tools (hoe, spade, etc.) are a labor-intensive and time-consuming process that requires about 210 person-days per hectare (Ebrahem et al., 2011).Similarly, the harvest and post-harvest loss of potatoes in Ethiopia is more than 25%, partly due to poor harvesting.It is caused by potato production of 13.7 tons per hectare, which is very low in comparison to the potential yield (40 tons per hectare) obtained in Ethiopia under research conditions (Wassihun et al., 2019).In Ethiopia, developing a machine to reduce labor costs, harvesting losses, and labor-intensive employment for potato harvesting is crucial (Dagninet et al., 2015).Hence, the objective of this research is to design, and manufacture a two-wheel tractor-operated potato digger elevator, and evaluate the effect of rake angle and conveyor slope on the performance of the prototype machine.

Materials and methods
The design and manufacturing process started in January 2018, but field tests were conducted in December 2018.The field was irrigated to maintain the soil moisture at 11.08% on a dry basis, which was adequate for digging operations to avoid the soil sticking to the potatoes (Reddy et al., 2018).The average digging depth was 15 cm, and the oscillation amplitude was 20 mm (Al-Dosary, 2016).The trial was carried out on the Belete potato variety.

Experimental site
Manufacturing and performance evaluation of the machine have been done at the Melkassa Agricultural Research Center (MARC) in the agricultural mechanization research workshop and research field, which is found in Oromia, Ethiopia, located at an altitude of 1550 m.a.s.l. and lies between 8°24'0"and 8°30' 12'"N latitude and 39°21" 0" and 39°35'14'' E longitude.

Working principles of the machine
A detailed assembly view of the potato digger elevator machine components is presented in Figure 1 and Figure 2. The major parts were the soil cutting blade (5), shanks (8), chain conveyor rods (17), depth control wheels (11), tuber delivery hopper (14), side flanges (12), drawbar hitch (4), transmission system (22) (spur gears, pulleys, V-belts, input, and output shafts), and eccentric discs (10).The depth control wheels (11) were designed based on the power screw principle, which enabled control of the depth of operation and support during transport.The power from the singleaxle tractor engine clutch is transmitted into two components of a machine: conveyor and oscillation systems using a combination of pulleys and V-belts with chain and sprocket for oscillation and conveying purposes.The other is through the drawbar of a 2 WT and the drawbar hitch (4) of a machine using pin joint hitching that is used for draft pull.The machine was elevating the tuber soil mix directly to the conveyor from the soil cutting blade (5) while providing an adequate sieving area to lose soil.When the tractor moved forward, the V-shaped blade (5) broke and split the ridges up to the desired depth and lifted the potato tubers and soil clods with the rest of the plant body.Eccentric discs (10) were fixed to both ends of the output shaft, which was hinged by a connecting rod (9) to the lower conveyor shaft (20) to shake and sieve the entire lifted material and transport the tuber to the delivery hopper (14).While digging, soil clods feed along with tubers but are broken by the oscillation of eccentric discs (10) that are connected by rods to the lower conveyor shaft (20) and dropped to the spacing provided between the rods (17) on the elevator.Small steel guide plates (19) were welded on both sides of the blade and side flange (12) to guide and throw the potato soil mass into the elevator.The elevator transports tubers to the rear end of the elevator through rods ( 17) and is exposed to manual pick-up.The description and analysis of parts of the machine are illustrated in Figure 1, Figure 2 and Table 1.

Selection of manufacturing materials
Material selection is crucial to the design of any machine or process plant, especially when it is to be used for soil cutting.Hence, it is of utmost importance to ensure that the components of the machine meet the desired performance requirements.Some components of the machine will be in direct contact with soil and must not corrode or shear.The material must be resistant to wear and shear to give the machine a long life and be durable.To ensure high-quality standards, materials with the appropriate engineering properties were carefully chosen for the design to cope with the varying degrees of stress, strain, torque, and frictional loads (Table 2).Most of the materials used for the manufacturing of this machine were mild steel containing 0.16-0.30%carbon (AISI 1020).Mild steel has a relatively low tensile strength but is easily available, cheap, malleable, and used where ductility is important.The basic parameters to be considered were the determination of conveyor slope, conveyor oscillation amplitude, rake angle, digging depth, pulley diameters, shaft diameter, chain length, belt length, selection of pulleys and chain and sprockets, selection of spur gears and eccentric discs, and so on, which were decided based on different research outputs earlier and applying theories, principles, and practices of machine design, particularly root crop harvesters, and cleaners.The detaile about the material selection is presented in Table 2. Provisions for adjustments were used to maintain different rake angles, conveyor slope, depth control, the length of the connecting rod, the tension on the transmission belt, and the conveyor chain.

Power required for soil cutting
The blade has a minimum depth (d) and width (w) of 15 cm and 55 cm, respectively; this is the depth-to-width ratio of 0.27.Therefore, it is less than 0.5 and is called wide blades [22].Hence, the  cutting force of the blade was calculated using Equation 1.The detailed input data for the design equations of soil-engaged components of the machine (blade and shank detailed presented in Table 3).
The N factors for an intermediate roughness of blade shape interface can be interpolated using Equation 2 as given below (Obermayr et al., 2011): Where, F s = cutting force of the blade, N q = mass surcharge on the soil, kg γ = soil densities, kg/m 3 c = soil cohesion, Pa  1)

2.
Passive resistance force parallel to soil cutting blade F bh 1140.67N (from Equation 3)

5.
Frictional soil cohesion cutting factor N c 5.13 (from Equation 2) Power required for soil cutting P sc 3251.72 W, (from Equation 5)

8.
The thickness of soil cutting blade t b 10mm (from Equation 10)
Horizontal forces acting on the shank F sh 2358.3N(from Equation 11) 12.
Vertical forces acting on the shank F vs 2358.3N(from Equation 14)  20)
Power at the mechanical system of the tractor P t 4585.88W(from Equation 23)  The values N δ equal 0 and Ф, where the corresponding values of the N-factor at δ = 0and δ = Ф, respectively, obtained from a graph of passive soil cutting factors (Obermayr et al., 2011).
For the estimation of soil passive resistance (F s ), the optimum parameters are summarized as a literature recommendation (Coetzee & Els, 2009;Saakuma et al., 2016;Ukritchon et al., 2017), where γ = 1450 kg/m 3 , C = 6965.1 N/m 2 , Ф = 25°, δ = 20°, α = 25°and d = 0.15 m.The passive resistance force (F s ) is loaded at an angle of friction (δ) to the interface of a blade.Hence, the component of forces in parallel (F bh ) and perpendicular (F bv ) to the blade face with forward working speed (V) is consecutively given as follows (Dhananchezhiyan et al., 2020) (Figure 3).The power for soil cutting (P sc ) was using Equation 3 -Equation 5  61)

38.
The force of gravity on the connecting rod P g 571.66 W (from Equation 63)

39.
Total power for driving the reciprocating system P r 3965.48W (from Equation 64)

Design of soil cutting blade
An angle of the cutting edge of the blade was sharpened to have a 16° taper (Dhananchezhiyan et al., 2020).The rake angle of a blade was adjustable through a semicircular slot that slides on the shank and a fixed shaft that allowed changing the blade angle from 0° to 30°.The perpendicular component of the soil load can be caused by the bending moment, whereas the horizontal component induces direct stress on the blade (Dhananchezhiyan et al., 2020).The average soil resistance of the blade acts at a distance of 20% of the depth of cut measured from the cutting edge (Boson et al., 2016).The blade is supported on the shank at a distance of 300 mm from the cutting edge (Figure 3).The detailed Input data for the design equations of soil-engaged components of the machine (blade and shank are presented in Table 3.) The bending moment (BM), bending stress on the blade (σ b ), direct stress (σ d ), and total stress (σ tb ) induced were estimated using Equation 6-Equation 9, respectively.
Usually, the factor of safety (fos) for agricultural machines was 3. Hence, total stress (σ t ) with safe stress of 294.74MPa of AISI 1020 carbon steel, the thickness (t) determined using a theorem of quadratic equations as estimated in Equation 10

Design of shank
The shanks were two mild steel straight rectangular shanks that connected the blade to the drawbar hitch through the hollow rectangular toolbar.The force required to move the machine was the sum of the horizontal forces (F sh ) and the vertical forces (F sv ) on the blade.Horizontal forces (F sh ) can be found using Equation 11.The detailed Input data for the design equations of soil-engaged components of the machine (blade and shank are presented in Table 3).Therefore, the bending moment (BMs) on the shank is due to horizontal forces (F sh) .Although the bending stress (σ bs ), direct stress (σ ds ) on bade is caused by the vertical soil cutting resistance force.Hence, total stress (σ ts ) was computed using Equation 12-Equation 16, respectively.

Analysis of drawbar power
The draught force is the horizontal component (F sh ) of the soil cutting force (Fs) (Obermayr et al., 2011).Soil reaction force/thrust (H) and equilibrium of the external horizontal forces acting on the tractor, where the drawbar power (P d ) and rolling resistance force (R) were estimated through Equation 17 and Equation 18shown below (Bao et al., 2019).The detailed Input data for the design equations of soil-engaged components of the machine (blade and shank are presented in Table 3).
It was graphically illustrated that the coefficient of rolling resistance of a 1000-mm-diameter tractor rubber wheel on the stubble surface was interpolated to 0.124 (Bao et al., 2019).The total weight (W) is the sum of the weight of the machine (w m ) and the weight of tuber soil (W s ).Rolling resistance (R) is the weight (W) multiplied by rolling resistance (μ) as shown in Equation 19: The comparative slip-pull performance of the wheel slip of the two-wheel-drive tractor on stubble, uncultivated, and loamy surface soil at 3138.72 N drawbar pull is about 1-5% (Bao et al., 2019).Thus, at 3.5 km/hr or 0.975 m/s actual forward speed (V), the theoretical linear velocity (V o ) of the ground wheel of a tractor was calculated and could be 1.03 m/s at 5% wheel slip.The efficiency of power transmission for tractors between transmission inputs to PTO is around 90-92% and power losses in the mechanical transmission systems of 2WTs are usually small and less than 10% (Bao et al., 2019).Power at a variable speed V-belt drive pulley (used as a clutch) of the 2 WT tractor (Pi) divided into conveyor elevator and drawbar systems of the potato digger elevator.Power loss (P l ) of 2 WT by wheel slip (i), rolling friction, and power at a mechanical system of the tractor (P t ) are at 90% transmission efficiency (η) using Equation 20-Equation 23, respectively.
Where: P sc = Power required for soil cutting, P w = Wheel power, w, and P d = Drawbar power, w

Conveyor mechanism
The conveyor mechanism consists of conveyor rods spaced and fixed on each peg connected end to both ends (Figure 4).The slope of the conveyor was adjustable from 0° to 25° through a semicircular slot produced on both sides of the side flange.The rotation of the shaft and eccentric discs produced the oscillation motion of the conveyor.The detailed Input data for the design of the conveyor components of the machine are presented in Table 4.

Velocity component on the conveyor system.
The load due to tensions on the chain conveyor could analyze the movement of the soil tuber mass.Assume that point A locates at the end of the blade and at the beginning of the conveyor, which has a certain angle to the ground (Strobel et al., 2020).The velocity chart of a conveyor chain is shown in Figure 5 below: The relative speed of the chain and tractor was the speed of soil tuber mass on a conveyor.Using trigonometric relation, the relative speed of soil tuber mass in the X and Y-direction can be computed, then the relative speed of soil tuber mass V f/e was evaluated using Equation 24Figure 4. Profile of conveyor mechanism.
Where: A = a point of potato tuber moving to chain elevator.V f = travel speed of a machine, (0.975 m/s (Reddy et al., 2018)); V c = speed of the conveyor, (1.5 m/s (Dorokhov et al., 2022;Mostofi, 2009)) V f = machine forward velocity, m/s V e = resultant velocity of elevator chain, m/s V ex and V ey is X and Y component of Ve, m/s V f/e = relative speed of soil tuber mass and tractor, m/s; V f/e = relative velocity of 2 WT forward speed and elevator speed, m/s; β = the angle between the movement direction and the chain conveyor speed, (°) 2.4.5.2.Conveyed materials.The mass of soil tuber material flow on the conveyor was analyzed to estimate the conveyed materials, it was used that the ideal bulk densities for plant growth were 1.4 g/cm 3 [32] .The mass of conveyor parts is very small and can be neglected; the volume of the material flow on the conveyor (Ms) was computed from Equation 25to Equation 27shown below (Wei et al., 2019).The optimum operation depth for potato harvesting is 15 cm (Al-Dosary, 2016).The weight of the tuber on a conveyor was a product of the width of the conveyor, (w c ), speed of the conveyor (v f/e ), and yield(y) (Dhananchezhiyan et al., 2020) as shown in Equation 29 below.
Where: W t = Mass of tuber, kg,w c = width of conveyor, 0.75 m, y = Average yield of tuber, kg/m 2 The national average productivity of potatoes in Ethiopia is 8 tons/ha, which is below the African continent average (10.8 tons/ha) (Birch et al., 2012).By equating the volume of material flow with the volume of the conveyor, assume the material was spread uniformly on the conveyor with a thick layer (t c ), using Equation 29The time is taken (t k ) a material remaining on the conveyor also estimated as stated in Equation 30: The total mass of soil tuber (M m ) was carried by a conveyor, and the upper chain tension (F su ) of the elevator and down chain tension (F i ) were illustrated using Equation 31to Equation 33, respectively.
For the inclined chain, the lifting chain and the power required to drive the conveyor (P c ) are required to lift mass computed from Equation 34 to Equation 37 below.
Where: T t = Total chain tension, N V c = velocity of the conveyor f 1 = Down chain friction factor (0.10-0.15) f = Upper chain friction factor (0.25-0.35) h = height of elevator, m l= center length of elevator/conveyor, m θ= conveyor inclination, o Q t = Weight of conveyed material, kg/s Q c = Total chain mass, kg.s −1 Q r = Total elevator rod mass, kg.s −1 Fs = Upper chain tension, N Fi = Down chain tension, N Fg = Lift chain tension, N μ = friction coefficient between elevator rod and soil tuber mass 2.4.5.3.Selection of conveyor chain and sprocket.The conveyor contains three chains and sprockets, one on each side of the conveyor web, while the other transmits power from the machine output shaft to the conveyor system.The chain selection corresponds to a pinion speed of 300 rpm; chain number 10B was selected (Bhandari, 2010).However, this chain was not capable of making flat pegs to weld onto the chain plate for the conveyor rod; hence, the next chain number, 12B, was selected.The detailed Input data for the design of the conveyor components of the machine are presented in Table 4.

Conveyor rod.
The diameter of the conveyor rod and minimum tuber diameter (D min ) was taken at 15 mm and 30 mm, respectively (Liao et al., 2012).Hence, the length of the chain conveyor spacing (S) between rods was from Equation 38and Equation 39, respectively.

Power transmission system
The power of 2 WT was divided at the main clutch into two machine systems; one from the main clutch to a small gearbox, which drives the ground wheels through a chain and sprocket.The other was used to drive the attached machines as drawbar power.The conveyor and shaker were driven by the main clutch of the 2 WT through two V-belts (B-74).The driven pulley of 260 cm diameter was fixed to the input shaft and then to the output shaft through the spur gear.The spur gears were used for speed reduction and to change the rotation of the 2 WT engine to a clockwise rotation that operated the conveyor web opposite to the forward motion of a 2 WT (Figure 6).The detailed Input data for the design of the power transmission system of the machine are presented in Table 4.

Determination of total transmission ratio
The recommended actual forward speed of the potato harvester was 0.975 m/s or 3.5 km/hr (Reddy et al., 2018).The ratio of the conveyor speed to the forward speed of the tractor was 1.2-1.5 (Dorokhov et al., 2022;Mostofi, 2009).The elevator speed should be 1.52 m/s at 1-1.5 forwarding speeds.Finally, to get 1.5 m/s conveyor speed, the speed ratio between, the engine pulley and engine clutch, the engine clutch and machine pulley, the input and output shaft, and the conveyor shaft and output shaft were computed using Equation 41From the 15 hp of the 2 WT manufacturers' catalog, the rated engine rpm (N e ), the diameter of the engine pulley (D e ), and the diameter of a clutch (D c ) were 2000 rpm, 12.5 cm, and 21.5 cm, respectively.The power transmission from the 2 WT engine flywheel to the clutch is through a V-belt.The engine power at a tractor clutch was divided to drive two basic systems.First, power from the clutch is transmitted to the input shaft through the V-belt and pulley.The input shaft also drives the output shaft through a combination of spur gears and then drives both oscillation and conveyor systems.The second was to drive the axle of a tractor through a chain and sprocket mechanism.The machine pulley was fixed at the input shaft with a diameter (D m ) of 26 cm, rpm of machine pulley (N m ).The driver sprocket was fixed at the output shaft with rpm (N o ) and pitch diameter (D o ) of 360.1 rpm and 66.1 mm, respectively.The transmission ratio between the input and output shaft is estimated using Equation 40: Where: D o and D i = pitch diameter of driven and driver gear on output and input shaft, respectively, cm, Distance from the center of the driving gear to the center of the driven gear (C d ) is the sum of the pitch radii of two gears estimated using Equation 41 (Huzaim et al., 2022): The pitch diameter and the number of teeth of the driving and driven gear were 10.5 cm; 24 cm, 30, and 70, respectively, were selected and purchased from the market.The gear standards, based on availability and low-cost through-hardened cast iron (FG-150), were chosen for gear material (Huzaim et al., 2022).Power was transmitted between the shafts using a chain and sprocket inclined 20° to the horizontal.The conveyor speed (V c ) is 1.5 m/s.The transmitted force, (F t ) and normal force, (F n ) on spur gear were estimated using Equation 42, and Equation 43Figure 6. Detail of power transmission system.

Selection of power transmission chain and sprocket
Corresponding to a pinion speed of 360.1 rpm, chain no.10B has been selected which is capable of transmitting 4191.6W per strand (Bhandari, 2010).Hence, the (D1), pitch line velocity of the driver sprocket (V 1 ) and load on chain (W) was computed using Equation 44, to Equation 46, respectively (Liao et al., 2012).
The load on the driving of the chain is the sum of the tangential force (F t ), centrifugal tension on the chain (F c ), and the tension due to sagging (F sg ) (Khurmi & Gupta, 2005).From Equation 47 The total tension load to the driving transmission chain (T t ) and power required for driving (P r ) was estimated using Equation 50 and Equation 51, respectively.
The conveyor power (P c ) transmitted by this chain and sprocket was 983.97 W at an input speed of 360.1 rpm and an output speed of conveyor 300 rpm.In a roller chain, the minimum number of teeth on the driver sprocket (T 1 ) for a velocity ratio of 1.2 should be 13.Similarly, it received 1038.04W of power (P r ) from the output shaft of a machine.

Oscillation system
It is used to convert the rotary motion of the output shaft to reciprocating motion to oscillate, shake, and separate soil tuber mass at the recommended maximum amplitude of 40 mm (Alexander, 2010).A conveyor consists of parallel rods welded on the chain plate.A vertical reciprocating motion produced by pairs of eccentric discs at both ends of the output shaft oscillates and shakes the conveyor system to separate soil tuber mass.The detailed Input data for the design of the scillation system of the machine are presented in Table 4.

Design and analysis of connecting rod
The connecting rod is a hinged member between the crank pin and lower conveyor shaft on both sides of the conveyor (Figure 6).The total force (F v ) applied on the connecting rod of the reciprocating system was estimated using Equation 52 (Khurmi & Gupta, 2005).
Where: F v = total force acting on the connecting rod, N F i = Inertia force of reciprocating parts, N F ss = net force acting to the line of stroke, N M R = Mass of the reciprocating parts, kg g = acceleration due to gravity, m/s 2 The maximum vertical component force on the connecting rod at a crank angle (θ) is zero.Then the total and maximum vertical load applied on the connecting rod is estimated using Equation 53where: α= linear acceleration of the disc, m/s 2 m = Mass of reciprocating component, kg r = Radius of a crank, m, ω ¼the angular speed of the output shaft, rad/s The component of force (F ss ) is applied by the eccentric disc through the connecting rod during the rotation of the output shaft (Figure 7).Linear acceleration α ð Þof the disc and net force (F ss ) on the connecting rod due to the rotation of the eccentric disc using Equation 54 and Equation 55, respectively, are given.
The inertia force of reciprocating parts (Fi) on the connecting rod was calculated using Equation 56below (Khurmi & Gupta, 2005).Where: l = Length of connecting rod and the centers; mr = Radius of the cranks, m θ = Inclination of connecting rod to the line of stroke, (°) n = Ratio of length to the radius of crank = l/r.
The maximum inertia force of reciprocating parts, θ ¼ 0:Gravitational resistance force (F g ) on the reciprocation system of a machine, and total maximum vertical load (F v ) applied to the connecting rod were calculated using Equation 57

Driving power of connecting rod
The turning moment at the eccentric disc (T g ) was evaluated using Equation 59 (Khurmi & Gupta, 2005).Then, the power required to drive the connecting rod, (P dc ), with the velocity of the piston (V), the power loss to overcome the inertia effect (P i ), the power required to overcome the force of gravity (P g ) on the connecting rod, and the total power required for driving the reciprocating system (P r ) were estimated using from Equation 59to Equation 64

Design and analysis of shafts
Power from the 2 WT clutch was transmitted to the machine pulley using a V-belt drive.Two parallel shafts (input and output shafts) were used.The clockwise (CW) rotation is negative, whereas the counter-clockwise (CCW) rotation is positive, which was assumed during the estimation of shear force and bending moment.
2.6.3.1.Design and analysis of output shaft.The output shaft was driving oscillation and conveyor systems.It was subjected to both torsion and bending in combination, which is the profile shown in Figure 7.
The power driven by the output shaft (P o ) was divided to drive the conveyor (P c ) and oscillation mechanism (P r ) using Equation 65Hence, the torque developed by the output shaft (T o ) at N o = 360.1rpmusing Equation 66 was: The output shaft was subjected to both horizontal and vertical loads acting on the shaft (Figure 8).
Where: F rl and F rr = Eccentric disc reaction force at E and J, φ =Angle of bearing reaction act at F F bl and F br = Bearing reaction force at F and H, respectively, F g = Gear reaction force at G ϕ = Angle of bearing reaction force act at H, Fc = Tension of chain at I γ=Inclination of chain to horizontal at I ε= Gear pressure angle act at G All applied loads and tensions from the output shaft through spur gear were acting on the shaft both in horizontal (XZ) and vertical (YZ) directions.

Shear force and bending moment diagram on horizontal (XZ plane)
Shear force and bending moment diagram on horizontal (XZ plane) on the horizontal forces with the output shaft (XZ plane) using trigonometric relations were evaluated as follows.
To evaluate the horizontal component of bearing reaction forces F blx and F brx , was considered bending moment at F: F c =T = 821.23N(Chain tension, determined in section 2.5.1) The chain drive was inclined to 20° to horizontal.Hence,F c cos γ ¼ 821:23N � cos 20 o ¼ 771:7N, then Similarly, the horizontal bearing reaction forces F blx , were calculated using total load at H: The horizontal bending moments on the output shaft were:

Shear force and bending moment diagram on horizontal (XZ plane)
Similarly, the shear force and bending moment diagram on the horizontal (YZ plane) are evaluated at which forces acting on the vertical direction (YZ) plane) of the output shaft are estimated using trigonometric relations.
The force required for oscillation on both ends of the shaft was 5260.46N (section 3.4.7.2).It was assumed that the horizontal components of forces that existed and applied to the connecting rod were equally divided between both ends of the output shaft at 2630.23 N. The chain tension was set at 20° from horizontal.
Normal force (F n ) on the gear was estimated at which the pressure angle of the gear was 20°.Hence, Vertical components of bearing reaction forces F bry , were evaluated using moment at F.
∑ M F ¼0. Hence, F br sin ϕ ¼ 3544:46N The vertical component of bearing reaction forces F bly , the total vertical forces (Fv): The shear force and bending moment on the horizontal planes containing the spur gear, eccentric disc, and conveyor chain of the output shaft were plotted as follows (Figure 9):

Resultant bending moment and shear force diagram
The resultant bending moment (M R ) was computed using Equation 67 Therefore the bending moment and shear force diagram was presented in Figure 10 with the maximum bending moment being 398.2 Nm at point G (Figure 10).

The diameter of the output shaft
From the bending moment diagram, the maximum bending moment and maximum torque transmitted by the output shaft were 132.2 Nm and 398.2 Nm at point G, respectively.Assume K b = 1.5 and K t = 1, and allowable stress of 40 MPa (for a steel shaft with a keyway).Hence, using the maximum shear stress theory, the diameters were estimated using Equation 67 as follows [38]: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi The permissible angle of twist through the torque on the shaft was computed using Equation 68The maximum allowable angle of twist is 1°/m, so the shaft is within a safe range (Kibi, 2016).The calculated angle of twist was less than the permissible angle of twist (1°/m).
2.6.8.1.Design and analysis of input shaft.The power to drive the input shaft was a 2 WT clutch through a pair of V-belts and pulleys.The shaft is supported by bearings and supports a pulley and driver gear subjected to torsion and bending in combination (Figure 11).The input shaft was subjected to belt tension and load due to the driver gear.Load on the input shaft is applied vertically and horizontally in the XYZ plane as shown in Figure 12: All applied load and tensions from the 2 WT clutch were loaded on the shaft both in horizontal (XZ) and vertical (YZ) planes.

Shear force and bending moment diagram on horizontal (XZ plane)
The trigonometric relation, for the XZ plane, was given as, F blx ¼ F bl cos α, andF brx ¼ F br cos θ Gear forces and belt tension from section 2.5.1 and section 2.6.4,respectively, were: Reaction forces F brx and F blx , through the moment at L and O, were: Then, the horizontal moment of the input shaft would be: 2.6.10.Shear force and bending moment diagram on a vertical plane (YZ) (Figure 13) Using trigonometric relations: Assume no slip of gear and belt, the vertical component of bearing reaction force was using moments at L and O, respectively: The equilibrium of vertical forces (F y ) is calculated as: Total bending moments of input shaft on a vertical plane (YZ) Shear force and bending moment diagram on the vertical plane (YZ) plane as shown below (Figure 18): Based on the magnitude and location of forces acting on the input shaft, shear force and bending moment on the horizontal of the shaft were computed and plotted as follows (Figure 13).

The direction of forces on the input shaft
The direction of bearing reaction force using vertical and horizontal components:F bl sin α ¼ 86:34N F bl cos α ¼ 751:3N, respectively, was: tan α ¼ Load including chain and belt tensions acting on the shaft was resolved into vertical and horizontal components.Hence, the resultant bending moment was estimated using Equation 66; the input shaft shear force and bending moment on horizontal and vertical planes containing the pulley and driving gear were plotted in Figure 14:

The diameter of the input shaft
From Figure 14, the shear force and bending moment diagram for the input shaft, the maximum bending moment was 110.05 Nm at point N.The maximum torque on the input shaft (M t ) developed through the machine pulley (section 2.6.4),was: T t = 530.45Nand T s = 138.5 Nm.Using Equation 67, the diameters of the input shaft were determined as follows: The permissible angle of twist caused by torque on the shaft was using Equation 68: Note that the maximum permissible angle of twist = 1°/m and the calculated angle of twist was less than the permissible angle of twist of (1°/m).Hence, the shaft is within the safe limit of torsional deflection satisfied (Vitos et al., 2014).

Belt and pulley selection
A driver and driven pulley were assembled on the clutch of a 2 WT engine and the input shaft of a machine, respectively.The clutch diameter is 215 mm.The rpm at the driver pulley/clutch of a tractor and driven/machine pulley were 1162.8rpm and 961.5 rpm, respectively.The diameter of the driven pulley was determined using Equation 40, where The V-belt belt service of 8 hours per day, transmitted a net power of 10.2 kW from the 2 WT clutch at 1162.8 rpm and 961.5 rpm, respectively (section 2.5.1), with a correction factor (fa) of 1.2.Belt selection for such load, B-section V-belt was used to drive 1162.8rpm.The power at the input shaft (P is ) was 5003.52W, which drives both the conveyor and oscillation system (Bhandari, 2010).T t and T s are tensions on the tight and slack sides.Hence, the velocity (V b ) and power transmitted by a belt (P is ) were estimated using Equation 70 to Equation 725003:52W ¼ ðT t À T s Þ � 13:1m=s, then, 381:95N ¼ ðT t À T s Þ Where: μ = 0.42 (coefficient of friction between rubber belt and aluminum (Khurmi & Gupta, 2005), α = angle of wrap for driving pulley, rad The wrap angle can be determined using Equation 73to Equation 74Using the Equation 74 of tensions on the tight and slack sides are estimated as follows.

Selection of bearings
Four radial bearings were required for the design of the machine: two for supporting the output shaft and the other two for the input shaft.The radial load on the left and right bearings that support each shaft was assumed to be a pure radial force with no axial load on bearings; thus, the operating range for machines used for short periods and intermittently was 4000-8000 (Khurmi & Gupta, 2005).Using the standard methods, the radial ball bearing was selected (Bhandari, 2010).

Depth control systems
The mechanism for the depth control system was constructed to set a harvesting depth.During operation, the clearance between the cutting edge of the blade and the bottom of the wheel was controlled using a fork pushed through a screw.The mechanism was very similar to that of power screws.The power screw is rotated manually by a handle that is fixed on both sides of the operator's seat on side flanges.The depth of the lift arm was designed to be adjusted and varied within a range of zero to 200 mm vertically (Al-Dosary, 2016).

Determination of total power
The power at transmission input (P i ) on the clutch in 2 WT is about 91.08% of the 2 WT engine brake power (P b ) ((Romanelli & Milan,)-)].DF-15 L 2 WT tractor brake power (P b ) was 11,1855W.The power at transmission input using Equation 75 was: Pi = 10,187.75W The total power (P dt ) to drive the machine was as Equation 76: Power at the input shaft (P is ) was power at the output shaft (p o ) assuming that there were no frictional and slippage losses in gears.Power at the mechanical system of the tractor (P t) and power at the input shaft (P is ) were 4585.88W and 5003.52W, respectively, as computed in sections 2.4.4 and 2.6.2.Hence, the total power (P dt ) was:

Performance evaluation of the prototype machine
Test and performance evaluations of the machine were conducted at the MARC research site.
Looking to local growing practices and the recommendation of an agronomist, land preparation for potato production, and planting on a trapezoidal cross-sectional ridge were applied (Vitos et al., 2014).Planting potatoes through irrigation was done with manual row planting.The average height of the ridges and spacing between and within the rows were 15 cm, 75 cm, and 30 cm, respectively (Tadesse et al., 2017).It was planted and fertilized with di-ammonium phosphate (DAP), and urea was applied at the rates of 195 kg/ha and 165 kg/ha, respectively (Vučajnk et al., 2017).The potato crop was ready for harvest after 150 days of planting.An area of 57 m × 108 m with a 10 m × 15 m plot size was used to conduct the test run.

Parameters measured
Field tests were conducted in November and December 2018; the field was irrigated to condition the soil moisture at 11.08% on a dry basis, which was adequate for digging operations to avoid the soil sticking to the potatoes (Reddy et al., 2018).The average digging depth was 15 cm, and the amplitude was 20 mm (Al-Dosary, 2016).The trial was carried out on the Belete potato variety.

Physical properties of potato tuber
The properties of potatoes, for the design of the digger, were identified and determined.The properties were shape, shape factor, bulk density, angle of friction, size, mass, bulk density, and static friction coefficient.These were measured, and an average value was computed.
2.7.2.1.Size.About 50 potato tubers were selected, with three ranges of minimum, medium, and maximum sizes.Their three principal dimensions were measured using an electronic digital caliper made in Taiwan that has an accuracy of 0.02 mm and was used to measure the physical property of tubers.Arithmetic and geometric mean diameter, spherically, surface area, bulk density, volume, and angle of repose of tubers were analyzed using standard procedures with three replications.

Coefficient of static friction.
The coefficient of static friction ðμÞon galvanized steel sheets, mild steel sheets, rubber, and timber sheets was measured for potato tubers using the inclined plane method.

Properties of soil during harvest
2.7.3.1.Moisture content.To determine the soil moisture content of the field, soil samples were taken up to a depth of 15 cm.The samples were collected randomly from three locations on each test plot.The samples were weighed and dried in a microwave oven dryer made in Germany for 24 hours at 105°C.It was a percentage of the mass difference before and after the oven was evaluated.

Bulk density.
A core sampler was used for taking the soil sample.Samples were weighed and kept in the oven at 105 ± 5° C for 24 hours, and then bulk density on a dry weight basis was estimated.

Penetration resistance and cone index.
A penetrometer with a proving ring having a dial gauge, the Netherlands-made Eijkelkamp 14.05 field vane tester (16 × 32 mm, extra), type IB, with a measuring range of 0-10 000 kPa and an accuracy of 1% of the reading value, was used to measure the soil resistance to penetration before harvesting (Arvidsson & Keller, 2011).It had 322.5 mm 2 base areas, and 30° cone angles were used to measure the penetration resistance and the cone index of the soil before harvesting at three random points in each plot to a depth of 15 cm. Where: P z = penetration resistance, MPa, Fa =Force applied, N, A b = Cone base area, mm 2 2.7.3.4.Shear strength.It was using a shear vane tester with the Eijkelkamp type IB from the Netherlands, with a measuring range of 0-10,000 kPa and an accuracy of 10% of the reading value in 15 cm depth.To measure the undrained shear strength (S uv ) in the soil before harvesting, a vane tester with a height-to-diameter ratio of one or two was used.Equation 78indicated below (Arvidsson & Keller, 2011;ASTM, 2004).
Where: T = torque, Nm D = diameter of the vane, m 2.7.3.5.The Angle of Soil-Metal Friction.The static friction between steel sheet metal and the soil was measured using soil block using the inclined plane method.The soil block was kept on a horizontal plane and gradually increased.The angle of the impending slip was calculated using Equation 79, as shown below [22].

Experimental design
Performance evaluation of the prototype machine was designed for three levels of rake angles: A 1 = 15°, A 2 = 20°, and A 3 = 25° as subplot factors; different authors suggested these optimum values [24,[47][48]; and three levels of elevator slope: S 1 = 10°, S 2 = 15°, and S 3 = 20° as the main plot factor; the literature recommended these elevator slopes [49-51].The experimental design was a split plot design with 3 2 factorial experiments and 3 replicates as blocks, giving 27 total experimental units.
The elevator slope was taken as the main plot, while rake angles were taken as a subplot.The working speed and working depth of a two-wheel tractor throughout the experiment were kept constant at 3.5 km/h (third gear system) and 15 cm, respectively, as stated by Belay (2021) Kebede & Getnet (2017).

Independent variables
2.8.1.1.Conveyor slope.During performance evaluation, the elevator digger was attached to a 2 WT drawbar hitch and 2 WT clutch with pins and V-belts, respectively.The elevator was designed to adjust the slope angle by sliding the upper conveyor shaft on a semicircular slot with a pointer to fix the angle at 10°, 15°, and 20°, as shown in Figures 3 and 5.The selection of a constant and optimum 2 WT speed level was adjusted by correcting the position of the fuel control throttle of the engine as soon as a constant value was reached, which was at 3/4 th , i.e., 270° of 360° total rotation, with third gear setting at 2000 rpm rated engine speed (Kebede & Getnet, 2017).The oscillation amplitude and speed of the conveyor were settled at 20 mm and 1.5 m/s, respectively (Alexander, 2010).The angles adjusted and selected for every unit of the test were applied, and, then, the values of the independent variable, conveyor slope (C), were determined.
2.8.1.2.Rake angles.The cutting angle of a blade was also adjusted at 15°, 20°, and 25°during the test.The blade can slide/rotate on a fixed shaft.The shaft was connected to both sides of the side flange through bearing openings to determine and fix the selected angle when the blade slides on it, as shown in Figure 1.There were levers both on the right and left sides of the blade at which a rake angle was adjusted along the semicircle slot hole on the shanks to fix the required cutting angle when sliding.The maximum depth of a blade cut was set at 15 cm, with a moisture content of 11.08%.The test rake angle was adjusted and selected, and the values of an independent variable known as the rake angle (A) were recorded.

Dependent variables
Data collection of dependent variables was applied through randomly selected three samples from each experimental unit.Variables examined were: 1.The percentage of damageðη d Þ: was computed on a 2 m length of raw demarcated randomly, collected, and weighed all visible tubers through an outlet of a machine.The damaged tubers were separated, counted (serious damage and avoid slight damage), and undamaged potato tubers after harvesting and recorded as η d in percentage, using Equation 81, below (Ibrahim et al., 2008).
Where: M D = Mass of damaged or cut root crop, kg M ND = Mass of root crop exposed not damaged, kg.
2. Exposure efficiencyðη p Þ: was also computed as a 2 m length of raw was marked randomly and the visible tubers were collected and weighed.These were the exposed tubers.The ones that were still contained in the soil, but not visible, were the unexposed tubers, which were collected by manual digging.It was the ratio of exposed/lifted tuber to the sum of exposed and unexposed tuber and recorded asη p , in %, as illustrated in Equation 82 as shown below (Ibrahim et al., 2008;Mehta et al., 2018). Where: M L = Mass of lifted root crop over the soil surface, kg M UL = Mass of un-lifted root crop, kg 3. Conveyance efficiencyðη y Þ: was computed by selecting a sample of 2 m distance on a raw randomly.Then measure the collected tubers at the hopper of a machine and the tubers fall on the ground and recorded asη y , in %. η y was the ratio of the weight of collected tubers at the hopper outlet to the sum of collected tuber at the hopper outlet and leaked tuber to the ground.It was defined in Equation 83, as follows (Ashraf et al., 2018).
Where: M h = Mass of tubers picked by conveying unit, kg, M L = Total mass of tubers dig, kg 4. Cleaning efficiency (η l ): was computed through a sample of 2 m distance on a raw was randomly marked and measured the potato tubers and impurities/soil clod by collecting them at the outlet of a machine.Then cleaning efficiency is the ratio weight of the tuber to the sum of tuber and impurities and recorded asη l , in %.The cleaning efficiency of a machine was expressed in Equation 80, shown below (Ashraf et al., 2018).

Drawbar pull (D f
): was measured using a drawbar dynamometer using two tractors and a dynamometer between them; the first tractor was the power source while the second was 2 WT towed and served as a machine attached to it and recorded as D f in kN (Bao et al., 2019).
6. Actual field capacity (C f ): was computed by the time consumed during the digging operation (lost time and productive time) and recorded as C f in ha/h, as shown (Moayad et al., 2014).
Where: Ef = Field efficiency, %, EFC = Effective field capacity, ha/h.and C t = Theoretical field capacity, ha/h.7. Fuel consumption (f c ) of a tractor: the fuel tank was filled up to the neck of the fuel tank before and after the digging operation.The amount of refilling measured after the test was the fuel consumption for the digging operation and it was expressed as litter per hour.The amount of fuel used to refill the fuel tank was recorded as f c in ml, f c using Equation 86, as follows (Bao et al., 2019).
Where: f c = fuel consumption rate, l/ha,C r = reading of cylinder, L.,A = area, ha 8. Wheel slip (s % ): The wheel slip of the machine with load and without load was measured at a 15 m distance.Wheel slip can be calculated by counting the number of revolutions in a given distance and recorded as S% in %.Slip is defined in Equation 87and Equation 88Where: B = base distance, m, L = loaded distance, m, The total drive-wheel revolution under load (R) and no-load (r) should record during testing.Hence: 9. Soil swelling factor (sf): Soil samples were taken using a soil sampler before and after harvesting.Then, the swell factor, sf, was computed in Equation 89 (Obermayr et al., 2011): Where: V f =the soil volume after cutting, m 3 , V o =soil volume before cutting, m 3 γ f = the soil density after cutting, kg/m 3 10.Soil aggregate size: The soil samples collected from the harvested plots were air-dried to remove moisture.After drying, a known weight was placed on the topmost sieve of a series of sieves, which were vertically arranged.By separating the portion retained on the 2.0mm sieve into a series of fractions using the 75, 50, 37.5, 25.0, 19.0, 9.5, 4.75, and 2.0mm sieves to test (Usaborisut & Prasertkan, 2019).After manually shaking the weight and then the diameter of each clod were measured using a Vernier caliper and the Equation 90and Equation 91 was used to calculate the mean weight diameter (SMWD) of the soil aggregates.
Where: Gs=grain size distribution, M r =mass of retained, kg, Mt=total mass of soil, kg Soil mean weight diameter was also determined using the standard dry-sieving method as (Parent et al., 2012).
Where: MWD = soil mean weight diameter, mm, X i = mean diameter of any size range i of any aggregate, mm W i = weight of aggregate in size range i as a fraction of total dry weight, g 11.Soil pulverization ratio (Ф ≤ 25 mm), %: It is the percentage of the soil weight fraction composed of soil clods less than or equal to 25 mm (Ф ≤ 25 mm) which passes the sieve mesh of 25 mm to the total clods produced by potato digger in % (Usaborisut & Prasertkan, 2019).

Economic evaluation of machine
The economic evaluation of the prototype machine analyzed economic aspects including fixed cost, variable cost, the breakeven point (BEP), benefit-cost ratio (BCR), and payback period (PBP) (Ashraf et al., 2018;Dagninet et al., 2015;Dhananchezhiyan et al., 2020;Fouda, 2009;Kempenaar & Struik, 2007).It was compared to the conventional practice of digging by hand hoe with a field capacity of 0.0025 ha/h i.e.50 men-h/day18.Similarly, the workforce required for potato haulm killing by hand sickle was taken 20 to 25 man-h/ha (Kempenaar & Struik, 2007).

Statistical analysis
Data were subjected to analysis of variance using Statistix-10 statistical soft wares.When the effects of the treatments were found significant, the LSD test was performed to assess the difference between the treatments at a 5% level of significance.

Properties of potato tubers
Table 5 was the average values of the physical properties of Belete and Gudene potato varieties, which were the most common in Ethiopia.Physical properties were the basis to design and manufacture the machine.The outcome was sequentially lined but differed slightly from the two Iranian cultivars (Azizi et al., 2014;Dalvand, 2011).It revealed that moisture content, length, width, thickness, arithmetic mean and geometric mean diameters, sphericity, volume, mass, density, surface area, and angle of repose were 86.32%, 70.36 mm, 52.64 mm, 45.87 mm, 56.30 mm, 54.80 mm, 80.32%, 91.86 cm3, 125.66 g, 1.52 g.cm-3, 94.47 cm2, and 26.083, respectively, for the Belete variety; and 79.63%, 60.
Similarly, Table 6 presented the static coefficient of friction of Belete and Gudene varieties using the inclined plane method at different surfaces that were used to estimate design parameters during the design and construction of the machine, and finally, the mean value of the inclination angle was calculated.

Properties of soil during harvesting
Table 7 shows the average soil's physical attributes at harvesting time throughout the measurement performance of the equipment.An essential component of the suggested potato digger is the share, which is engaged in the soil to dig up the potato tubers and send them to the conveyor.Therefore, soil factors play a vital role in developing and manufacturing the machine, which impacts the performance of the root crop digger during the harvesting operation.The soil data were recorded immediately at the moment of harvesting that includes moisture content, bulk density, soil PH, strength characteristics, and penetration resistance as given in Table 7.

3.3. The Parameters of potato crop
Table 8 shows the physical properties of harvested potato tubers that were recorded after evaluation using randomly selected harvested tubers.Hence, the results of the observations on the characteristic dimensions of the potato tubers were relevant to the study.To determine the position of tubers concerning the ground surface, the quantity of the material to be handled by the digger for separation, and the throat height of the digger measurements were given in Table 8.

Mechanical damage of tubers η d ð Þ
Table 9 presents the effect of the conveyor slope (C) and rake angle (A) of the machine on the mechanical damage to tubers in percent (%).Mechanical damage to tubers (η d ) was highly influenced by the angle of the cut and conveyor slope.The ANOVA revealed that the conveyor slope (C) and the cutting angle of a blade (A) had a significant effect on the mechanical tuber damage (η d ) of the machine at (P 0.05).Maximum tuber damage was 4.32%, observed at 15°A and 20 °C; whereas it was 1.82% when the C and A were 10° and 25°, respectively (Table 9).At 15°A of the blade, maximums were observed, because the point of action of the digging blade tip was directly on the tuber zone in the soil.This was increasing the field capacity at a low A and caused a clear increase in potato losses due to shallow penetration depth.Furthermore, it decreased the raised potato soil layer, which leads to a direct impact between the blade and tubers; hence, more damaged tubers were expected.This is also the same result indicated in related literature (Tawfik & Abdellah, 2012).Generally, decreases were observed by increasing A, but a narrow increase was observed with the increase of C. Similar

Potato tuber parameters Mean values
The center-to-center distance of the ridge (cm) 74.3 Ridge height (cm) 17.49 The bottom width of the ridge (cm) 41.91 Depth of tubers from the ground surface (cm) 9.73 The arithmetic mean diameter of maximum tuber (mm) 70.85 The arithmetic mean diameter of medium tuber (mm) 56.42 The arithmetic mean diameter of minimum tuber (mm) 35.51 The geometric diameter of the maximum tuber (mm) 57.39 The geometric mean diameter of medium tuber (mm) 45.74 The geometric mean diameter of minimum tuber (mm) 33.64 trends of an increase in cut potatoes with an increase in rake angle were observed during the evaluation of root crop diggers for potatoes (Narender et al., 2019).However, the interaction effect of A, and C, on the tuber was not significantly affected (P < 0.05).The regression analysis was made for a relationship between the A and C of the machine.Hence, In the regression equation above, A had the greatest negative impact, whereas C had a positive impact.

Exposure efficiency η p � �
Table 10 shows the effect of the rake angle (A), and conveyor slope (C) of the machine on the exposure efficiency (η p ) in percentage (%) of the machine.ANOVA on the exposing efficiency (η p ) of the prototype potato digger elevator showed that interactions of conveyor slope (C) and rake angle (A) had a highly significant effect on the mean of the machine at (p < 0.05).The maximum of 96.47% was obtained when the machine was operated at C, 15°, and A, 20°, whereas the minimum of 84.75% was observed when the machine was operated at C, 20° and A, 15°, respectively (Table 10).Increases in A and C up to 20° and 15°, respectively, increased, while they gradually declined at 25° and 20°, respectively.It was initially increased with an increase in A and C but was later marginally decreased.This could lead to the fact that at higher A and C, more soil pulverization occurred, but at the same time, a dangerous accumulation of  soil slices on the surface of the blade that imparted on tubers was high, hence causing a decrease in exposed tubers.An increase in A may have increased soil penetration below the potato tuber zone, which in turn dressed the tubers with more soil layers.As a result, it was reduced to the maximum A and C values.Similar trends were observed with an increasing conveyor slope and decreasing efficiency of an inclined Teflon grain cleaning machine (Awgichew & FANTA, 2015).The greater force acting on the soil tuber mixture as it slides down the slope, as well as the difference in gravity and inertia components of forces, cause the mixture to slide down rather than be supplied to the conveyor at C. However, it was a little bit deviated from the findings that the percent of exposed potatoes decreased with an increase in blade angle from 17-23 o, and 23° was optimum for root crop digger evaluation for potatoes (Narender et al., 2019).Nonetheless, this result contradicted the findings of a rotary blade potato digger, which revealed that the blade slope cannot be greater than 15 degrees for high exposure due to soil accumulation (Gavino et al., 2018).
Multiple regressions were analyzed as: The C made a high contribution to the exposed efficiency (in %).

Conveyance efficiency n y À �
The effect of rake angle (A) and conveyor slope (C) on the conveyance efficiency of the potato digger elevator is shown in Table 11 as a percentage (%).The ANOVA results for conveyance efficiency showed that blade rake angle (A) and conveyor slope (C) had a significant effect at (P < 0.05).The increase in C, from 10° to 15°, decreased from 94.42 to 89.93%; a further increase in C to 20° resulted in a decrease of 85.76%, as shown in Table 11.Also, an increase in A, from 15° to 20° increased from 88.69% to 89.97%; a further increase in A, to 25°, increased by 91.44%.The interaction effect of A and C was not significant at (P < 0.05, revealing the maximum was 95.6% at 10 °C and 25°A; whereas the minimum was 84.51% at 20 °C, and 15°A, combinations (Table 11).At the higher C of the tubers, rolling friction over the elevator caused rolling back effects of the soil tuber mass to cause the soil tuber poured to move out of the blade faces because of the greater force acting on the entire material down and leading to accumulating soil tuber at the face of the blade.The result implies that at a 25° rake angle, the tends to a minimum and causes a maximum conveying loss.The result coincided with a four-wheel tractor-driven potato digger cum elevator of 94-96% efficiency (Reddy et al., 2018).The equations, for the relationship, could be expressed by the equation: The equation revealed that C contributed the most to the in % when compared to the other variables.This implies that it also had a direct relationship with A and an indirect relationship with C.

Cleaning efficiency η l ð Þ
Table 12 shows the effects of cleaning efficiency on the percent (%) of the potato digger elevator at various blade rake angles and conveyor inclinations.It showed that the blade rake angle (A), conveyor slope (C), and interaction had a significant effect on the machine under study (P < 0.05).
The maximum of 96.63% was obtained when the machine was operated at 15°A and 20 °C, while the minimum was 86.78% at 25°A and 15 °C.In general, it increased with an increase in the C, while it declined with an increase in the A, because when A increased, it gave the worst results due to the large amount of soil cut and soil clods that caused the lodging effect of the soil, which exceeded the clearances of the conveyor rod, but the increase in the C caused the rapid break-up of the soil clods.It is the same trend for a vibrator digger with a four-wheel tractor drive at a rake angle of 14° at a 2.30 km/h working speed (Tawfik & Abdellah, 2012).From regression equations: A has an indirect effect, but C directly affects it, with an intermediate correlation of R 2 = 0.71.

Drawbar pull (D f )
Table 13 shows the effects of the rake angle (A) and conveyor slope (C) of the machine on the drawbar pull (N).The ANOVA on the drawbar pull (Df) data at different blade rake angles (A) and conveyor slopes (C) revealed that the interaction has a significant effect on Df both with A and C (P < 0.05).The LSD comparison test revealed that the maximum Df inspected was 3132.2 kN at 20 °C and 25°A, while the minimum Df was 2848.9 kN at 10 °C and 15 °A, as shown in Table 13.This revealed that more draft was exerted for the prototype machine compared to the 2362.37N drawbar pull of 2 WT on the mouldboard plough and power tiller (Kebede & Getnet, 2017).Moreover, Df was increased by increasing both C and A. The fact that at higher A, and C, greater penetration with an accumulation of soil tuber mass around a blade was high and the mass of soil tuber carried by a conveyor, which imparted the energy, required penetrating, sieving, and carry caused a higher Df.Increasing the component of the gravitational force of dead load (soil tuber mass) in a direction opposite to the drag force of the elevator increased the energy required.This was also a similar result as per the angle of the blade if less than 14° will not disturb the soil sufficiently and an angle greater than 20° will tend to collect soil in front of the blade, unnecessarily increasing draft reported during the evaluation of a digger for harvesting onion (Gavino et al., 2018).The regression analysis to establish a relation between Df (N), A, and C was: The A has affected the D f as compared to the C.Both A and C, have a direct effect on D f with R 2 = 0.88.

Fuel consumption (fc)
Table 14 shows the effects of the rake angle (A), and conveyor slope (C) of the potato digger elevator, on the fuel consumption (l/ha).The ANOVA, on the fc data of the potato digger elevator, revealed that A, and C, had significant effects on the fc (P < 0.05).The maximum fc was 16.73 l/ha at maximum fc and A, of 20° and 25°, respectively.When the machine was running at minimum C and A of 10° and 15°, respectively, the observed minimum mean fc was 13.54 l/ha.Furthermore, fc rose sharply from 13.54 l/ha to 16.73 l/ ha, while C and A rose to 10-20° and 15-25°, respectively.The fc result was higher than 9.36 lit/ha and reached 12.56 lit/ha during a field test of the same tractor with different types of attached seeder and depths of ripping (Kebede & Getnet, 2017).The increase in both A and C increased fuel usage during the harvesting operation.Multiple regression analysis was done to establish the relationship between fc, A, and C.   A made a greater contribution to fc as compared to C. Both A and C have a direct relationship with fc.

Wheel slip (S % )
Table 15 shows the effects of the rake angle (A), and conveyor slope (C) of the potato digger elevator machine, on the wheel slip (S % ) in (%).The rake angle (A) was significantly influenced by the wheel slip (S % ) of a 2 WT.The analysis of variance of the data of the wheel slip of 2 WT revealed that A had a highly significant effect, but the elevator slope (C), as well as the interaction of A and C, did not show a significant effect at (P < 0.05).As shown in Table 15, the S % was directly proportional to the A, which increased with the A. The maximum S % recorded was 22.04% at 25°A and 10 °C; whereas the minimum S % of 13.64% was at 15° and 20° A and C, respectively, where the grand mean and CV were 17.51%, and 6.99%, respectively.The maximum slip was significantly lower than the average S percentage of 39.35% obtained when the same 2 WT was tested during tillage (Kebede & Getnet, 2017).Multiple regression analysis was done to establish a relationship between S % , A, and C.
When compared to C, A made a larger contribution to fc, R 2 = 0.77.

Swelling factors (S f )
Table 16 shows the effects of the machine's rake angle (A) and conveyor slope (C) on the swelling factors (sf) in percent.As shown in Table 16, the blade rake angle (A) and conveyor slope (C) had a highly significant effect on the soil swelling factor (Sf) at P < 0.05), based on an ANOVA.It revealed that an increase in A, and C, leads to increased Sf.The maximum mean Sf of soil achieved was 32.382% at 20 °C and 25° A, but at 10 °C and 15° A, the minimum mean Sf of soil was 14.75%, at which the grand mean and CV were 23.96% and 10.07%, respectively.A multiple regression analysis was conducted to establish a relationship between Sf, A, and C.
A had the greatest effect on the S f as compared to the C.Both A and C have a direct relationship with S f .

Soil Mean Weight Diameter (SMWD)
Table 17 shows soil mean weight diameter (SMWD) data (in mm) at different rake angles and conveyor slopes of the potato digger elevator.The ANOVA indicated that the SMWD of the prototype machine was significantly affected by the elevator slope (C) and blade rake angle (A) at (P < 0.05).The maximum SMWD observed was 25.54 mm at 10 °C and 25°A, but the minimum SMWD recorded was 11.08 mm at 20 °C and 15°A of a blade, as shown in Table 17.It showed that the A of a blade increases with SMWD; inversely, the C increases as SMWD decreases.At maximum C, the soil clod tends to be exposed to more impact load due to the reciprocating and oscillating of the elevator, resulting in the crashing of clods to a minimum diameter that moves downward between conveyor rods.A is directly proportional to SMWD in a blade, and increasing A causes an increase in cutting depth and the formation of large clods.Multiple regression analysis was done to establish the relationship between SMWD, A, and C. SMWD ¼ 0:87A À 0:29C þ 3:61, R 2 ¼ 0:54 A was the greatest contributor to the SMWD as compared to C. A has a direct contribution, while C has an indirect contribution to SMWD with an intermediate correlation of R 2 = 0.54

Soil pulverization ratio (λ)
Table 18 shows the effects of the rake angle (A), and conveyor slope (C) of the machine on the soil pulverization ratio (λ) in percent (%).The percentage of the soil weight fraction composed of soil clods less than or equal to the clearance between the conveyor rod, i.e., 30 mm, which passes from the sieve mesh size of 25 mm to the total weight of all clods produced by the potato digger was significant, affected by conveyor slope (C) and rake angle (A) at P < 0.05.At P 0.05, Table 18 Table 18.The effects of rake angle (A), and conveyor slope (C), on the soil pulverization ratio (λ) in (%) shows that A and C had significant effects on the level of (%).The least λ, 67.11%, was recorded at an A of 25°and a C of 10°.The maximum λ of 89.31% occurred when the machine was operated at 15°A and 20 °C.The results showed that it was directly proportional to C, which increased with slope, but indirectly proportional to A, which decreased with A. The relationship between A and C was established using the multiple regression analysis shown below.

Field capacity (Fca)
Table 19 shows the effects of rake angle (A) and conveyor slope (C) on the field capacity (Fca) of the machine.According to the ANOVA, Fca was not significantly affected by the elevator slope (C) but was significantly affected by the rake angle (A) of a blade (P < 0.05), as shown in Table 19.The maximum Fca at a 15° rake angle and a 10° conveyor slope was 0.135 ha/h.This increases A and C as well as drawbar force; it also causes a small change in Fca.The F ca of 0.127 ha/h was also at the highest A, and C, at 25° and 20°, respectively.Similarly, the maximum field efficiency observed was 81.90% at 15° A and 10° of C, a machine, respectively, whereas the minimum field efficiency was 77.04% at 20°C, and 25°A.However, the result was contradicted by the same two-wheel tractor harvesting onions with a field capacity of 0.086 ha/ hr [65] .The following regression analysis was performed to determine the relationship between actual Fca, A, and C.
F ca ¼ 0:143 À 0:00051A À 0:00021C, R 2 ¼ 0:44 As shown, both A and C have an indirect contribution to the actual F ca , but A made a greater contribution as compared to C, with a medium correlation of R 2 = 0.44

Economic evaluation
The cost and benefit that can be obtained by using the potato digger elevator machine have been evaluated in terms of raw material, production (machine and labor), and operation costs.The cost of operation associated with the existing practise (manual hand hoe digging) of potato digging was compared with the cost of operation of a developed potato digger elevator.The estimated cost of the machine was around 330.64 USD, with a cost of operation of 32.92 USD/ha and total labor of 116 man-hours/ha, including hauling, removing, and picking during harvesting by this machine.The cost of operation of manual hand hoe digging was computed at 146.03 USD/ha, with total labor of 620 man-h/ha required for hauling, digging, and picking during potato harvesting operations (Bouman, 1993;Varshney et al., 1989;Younus & Jayan, 2016).The developed machine had 0.14 h/ha capacities.The saving in cost per hectare with the use of the potato digger elevator was found to be 113.11USD/ha.It saved 86.6% labor (percentage of labor involved relative to manual hand hoe harvesting) and 63.36% cost of harvesting in comparison to the manual hand hoe harvesting practise.The breakeven point (BEP) for the potato digger elevator was 104.25 h/yr, i.e., annual coverage (Ac) or annual utility of 35.75 ha/yr.The percentage of BEP was 37.9%.BEP is achieved at about 37.9% of the annual utility or area coverage in 275 h/yr. of use of the operation of a machine.The payback period (PBP) was also 1.59 years, and the benefit-cost ratio (BCR) was 4.33; when more than unity shows the machine could be worthwhile, it can provide additional benefit returns over the costs of a machine.

Conclusion
Ethiopia's traditional potato crop harvesting involves hand hoes, ploughs, and a bamboo/metal funnel attached to a country plough (Maresha).Over 25% of harvest and post-harvest loss in Ethiopia is due to poor harvesting, resulting in damage to tubers.To minimize harvesting loss, drudgery, labor requirement, production cost, and time and energy, a 2 WT operated potato digger elevator was designed, tested, and fabricated.The prototype showed maximum tuber damage of 4.32% at 15° blade rake angle and 20° conveyor slope, while minimum damage was 1.824% at 10° and 25° rake angles.The maximum exposure efficiency was 96.47% at 15° and 20° rake angles, while the minimum exposes efficiency was 84.75% at 20° and 15° rake angles.The soil pulverization ratio was directly proportional to the elevator slope, increasing with slope but decreasing with angle.Tuber damage loss decreased when increasing the rake angle, but increased with the conveyor slope.Increasing the rake angle and conveyor slope up to 20° and 15° resulted in increased exposure efficiency, while it declined gradually at 25° and 20° rake angle and conveyor slope, respectively.The potato digger elevator prototype machine effectively performed, with the rake angle being the most affected.The study indicated the optimum combination of rake angle and elevator slope to be 15° and 20°, respectively.The regression analyses and equations developed can be used to select the optimum combination of variable parameters to improve potato digging, tuber, and soil separating and cleaning mechanisms.Systematic, coordinated, and relentless efforts and further tests are needed to improve the machine's use in double axel tractors and other root crop harvesting.Mechanisms related to control of conveyor inclination, depth, vibration amplitude, rake angles, and tension of elevator, belt, and chain drives are essential mechanisms to improve the mechanism easily, uniformly, and consistently.An automatic control system can be developed and used to produce quality potato digger elevators that will fetch high income for manufacturers and farmers.

Figure 1 .
Figure 1.Assembly of the potato digger elevator machine components.

Figure
Figure 2. Orthographic view of potato digger elevator machine.
cutting factor N = the four passive soil cutting factors ϕ= angle of internal shearing resistance δ= angle of soil±blade interface friction N δ = the value of the appropriate N factors like N γ or N c
volume of soil flow, m 3 ; V m = volume of soil flow, m 3 /s d = depth of operation, 0.15 m, A b = base area of the trapezoidal blade, m 3 , ρ s = density of soil, kg/m 3 w = Effective width/minor width of the blade, 0.55 m,

Figure 5 .
Figure 5. Soil tuber velocity analysis on a conveyor.
to Equation 49 illustrated forces on a chain.Hence, Where: m = Mass of the chain in kg/m x = Centre distance, m k = Constant based on chain drive arrangement v = Velocity of chain, m.s −1

Figure 7 .
Figure 7. Output shaft with a driven gear, chain, sprocket, and eccentric disc mounted with on bearings.
Figure 8.The output shaft shows forces acting on the output shaft.

Figure
Figure 9. Shear force and bending moment diagrams on the horizontal (XZ) plane (a) and vertical direction (YZ) plane (b) existed on the output shaft, respectively.

Figure
Figure 10.Resultant bending moment and shear force diagram.

Figure 11 .
Figure 11.Input shaft profile with a driven gear and pulley mounted with on bearings.

Figure 12 .
Figure 12.The input shaft shows forces acting on it.

Figure 13 .
Figure 13.Shear force and bending moment diagrams on horizontal (XZ) plane (a) and vertical direction (YZ) plane (b) existed on the input shaft, respectively.

Figure 14 .
Figure 14.Shear force and bending moment diagram for the input shaft.

Table 9 . The effect of conveyor slope (C) and rake angle (A) on mechanical damage of tubers
Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 10 . The effect of rake angle (A), and conveyor slope (C), on the exposure efficiency (η
SED: Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 11 . The effect of rake angle (A), and conveyor slope (C), on the conveyance efficiency
SED: Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 12 . The effects of rake angle (A), and conveyor slope (C), on the cleaning efficiencyðη l Þin %
Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 13 . Drawbar pull (N) of the machine at different rake angles and conveyor slope
Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 14 . The effects of rake angle (A), and conveyor slope (C), on the fuel consumption (fc) in (l/ha)
SED: Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 15 . The effects of rake angle (A), and conveyor slope (C), on the wheel slip (S
Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability. % ) in (%)

Table 16 . The effects of rake angle (A), and conveyor slope (C), on the swelling factors (s f ) in (%)
SED: Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 17 . The effects of rake angle (A), and conveyor slope (C), on the soil mean weight diameter (SMWD) in (mm)
SED: Standard errors of differences of means; LSD: Least significance difference; CV: Coefficient of variation; Means followed by the same letters are not significantly different at a 5% level of probability.

Table 19 . The effects of rake angle (A), and conveyor slope (C) on the field capacity (Fca) in (ha/hr.)
Standard errors of differences of means; LSD: least significant difference; CV: Coefficient of variation; means that at a 5% level of probability, two words followed by the same letters are not significantly different.