Shyam and Singh (1990) designed and developed a potato grader. Design consideration, constructional details, method of operation and performances have been reported. On an average, the grader sorted 20 to 25 q h-1 of seed potato into 4 to 5 sizes employing 0 to 14 attendants. The screen efficiency of the oscillatory sieves ranged from 80 to 90% and average tuber damage was to be within 2%. Doriaswatny (2000) developed a sieve type grader for grading groundnuts into three different sizes. The output capacity was 600 kg h-1 and was powered by one horsepower 3-phase electric motor. Re-orientation of pods in sieve holes was observed that required modification in shaking system. Adler reviewing the literature it was concluded that sieve type graders faced a same problem of sieve hole blocking. Roy et al (2005) developed a low cost potato grader. There were three sieves at an angle of 15° with the horizontal and sieves were made of rubber impregnated al wires. The grader was capable to size the potatoes into four sizes with the capacity of 2,030 kg h-1. Trapping of potatoes in the sieves was observed and to eliminate the potato trapping, a mechanism for re-orientation of potato tubers was recommended. Narvankar et al (2005) studied on rotating screen grader suitable for fruits like lemon, ber, aonla to grade the samples into 4 grades. The grader was tested for capacity and optimum grading performance as a function of rotating speed of screen, diameter of screen, exposure length and input each at four levels by using second order response surface design in 80 design points. Capacity of the grader varied from 45 to 327.27 kg h-1 for lemon, 43.63 to 464.51 kg h-1 for aonla and 46.75 to 436.36 kg h-1 for ber. The maximum grading efficiency for lemon, aonla and ber was found to be 79%, 93.8% and 97.96% respectively.

As the grader was versatile in nature for grading all types of spherical fruits, the grader was tested by using Nagpur mandarin, Kagzi lime, guava and onion. For grading Nagpur mandarin fruits, the partitions of outlets were provided where the spacing between two pipes of each pair was 40 mm, 50 mm, 60 mm, 70 mm and 80 mm thereby receiving the fruits of 40 to 50 mm diameter 50 to 60 mm diameter , 60 to 70 mm diameter and 70 to 80 mm diameter. For grading kagzi lime fruits, the spacing between two pipes of each pair was reduced and the partition of outlets were  provided where the spacing between two pipes of each pair was 25 mm, 30 mm, 35 mm, 40 mm and 45 mm thereby receiving the fruits of <30 mm diameter, 30 to 35 mm diameter, 35 to 40 mm diameter and 40 to 45 mm diameter. . For grading guava  fruits, the partitions of outlets were provided where the spacing between two pipes of each pair was 40 mm, 50 mm, 65 mm, 80mm and 90 mm thereby receiving the fruits of less than  50 mm diameter,50 to 65 mm diameter , 65 to 80 mm diameter and greater than  80mm diameter. For grading onions, the spacing between two pipes of each pair was reduced and the partition of outlets were  provided where the spacing between two pipes of each pair was 25 mm, 35 mm, 45 mm,  and 55 mm thereby receiving the fruits of <35 mm diameter, 35 to 45 mm diameter and greater than 45 mm diameter .

The grading efficiency is sensitive to feed rate and slope of the pipes (feed end to opposite end). Hence these two factors were considered for optimization for better grading efficiency by using response surface methodology.
The experimental plan selected was for two variables and five levels in response surface methodology (Cochran and Cox, 1975) for optimization of factors for maximum grading efficiency. The two independent variables,  feed rate kg/min (x₁) and slope, percent, (x₂) and their levels, coded and uncoded are shown in Table 1 for Nagpur mandarin, kagzi lime, guava and onion. The centre point values were chosen as 30 kg/min feed rate and 32.5 per cent slope for Nagpur mandarin, guava and onion grading and 25 kg/min and 32.5 per cent slope for kagzi lime grading respectively, from previous results at this centre. The two higher and two lower levels were added using equation.
Central level  + (   √2 x interval) ……………(1)

The second order polynomial equation of the following form can be assured to appropriate the true functions.
Y = b₀ + b₁x₁ + b₂x₂ + b₁₁x₁² + b₂₂ x₂²  + b₁₂ x₁x₂ ……..(2)

Where b₀, b₁, b₂, b_11, b₂₂ and b₁₂ are the constant co-efficients and x₁ and x₂ are the coded independent variales. These coded variables (x_i) in any particular application are linearly related to X_i by the following equation (Khuri and Cornell, 1987).

2Xi  - (X_iH  + X_iL)

x_i=  -----------------------------    ………………(3)

X_iH –X_iL

Where,
x_i = Coded variable 

X_i = Decoded variable 

X_iH = High level (+1) of X_i

X_iL = Low level (-1) of X_I

The test lot of onion (variety-PKV Selection white )  was consisting of 378 fruits weighing 15 kg (Table 4). Out of which there were 114 fruits weighing 8.52 kg of major diameter greater than 45 mm (A), 114 fruits, weighing 3.680 kg of major diameter ranging between 35 to 45 mm (B), 150 fruits weighing 2.800 kg of  major diameter less than 35 mm (C). The average weight of each fruit of grade A, B and C  was  0.075, 0.032 and  0.019 kg respectively as given in Table 4.
The test lot of kagzi lime fruits was consisting of 357 fruits weighing 12 kg (Table 5). Out of which there were 114 fruits weighing 5.44 kg. of major diameter greater than 40 mm (A), 115 fruits, weighing 3.900 kg of major diameter ranging between 35 to 40 mm (B), 94 fruits weighing 2.200 kg of major diameter ranging between 30 to 35 (C) mm and 34  fruits weighing 0.460 kg of major diameter less than 30 mm (D). The average weight of each fruit of grade A, B, C and D was  0.048, 0.034, 0.023 and 0.014 kg respectively as given in Table 5.

After testing the grader by using Nagpur mandarin, guava, onion and kagzi lime as per treatment combinations given in Table 1 replicated thrice, the grading efficiency was calculated by dividing the weight of correctly graded fruits by total weight of fruits taken for grading. After optimizing the input parameters (feed rate and slope) for maximum grading efficiency by using response surface methodology, the grader was tested by using the optimized input parameters. The percent overall effectiveness of separation was also calculated as described in Annexure A by using optimized input parameters.

The experimental average results of three replications for grading efficiency are depicted in Table 6 for Nagpur mandarin, guava, onion and kagzi lime. The observed data was fitted in second order polynomial model equation. The partial regression coefficients obtained after multiple regression analysis are presented in Table 7. The regression analysis resulted the following second order polynomial equations for grading efficiency.

For Nagpur mandarin

For guava

Y = 90.42 + 0.514 x1 –2.463 x2 – 1.056 x1² – 1.473 x2² – 0.5 x1x2 (R² = 0.852)----(5)

For onion

Y = 72.254 + 0.05x1 + 3.271x2 – 1.030 x1² – 1.410x2² – 0.9 x1x2 (R² = 0.853)------(6)

For kagzi lime

Y = 76.620 + 3.052x1 + 3.382x2 – 1.513 x1₂ – 4.682x2² – 3.13 x1x2 (R² = 0.878)----(7)

The stationary point where the slope of the curve on the first derivative is zero was located as described by Khuri and Cornell (1987). Results in Table 9 show that the stationary points for the responses was lying inside the experimental region defined by x1 = + 1.414 and x2 = +1.414. The model were tested whether the function has maximum or minimum prediction values. It was observed that, the function possesses maximum value for all types of fruits taken for grading. The co-ordinates (x1 = 0.279 & x2 = 0.335) correspond to the uncoded values as 31.67 kg/min feed rate ad 35.01 per cent slope of pipes for Nagpur mandarin grading, The co-ordinates (x1 = 0.460 & x2 = - 0.914) correspond to the uncoded values as 32.76 kg/min feed rate and 25.65 per cent slope of pipes for guava grading and coordinates (x1 = - 0.306 and x2 = 1.221) correspond to the uncoded value as 28.16 kg/min feed rate and 41.66 per cent slope for onion grading  and coordinates (x1 = 0.973 and x2 = 0.035) correspond to the uncoded value as 29.86 kg/min feed rate and 32.67 per cent slope for kagzi lime.  Using these input factors the grading efficiency  was calculated to be 76.24 per cent for Nagpur mandarin, 91.66 per cent for guava , 74.37 per cent for onion and 78.16 per cent for kagzi lime respectively.

The response surface and contour plots were generated on computer screen in order to study the pictorial form of behavior of response variables using the prediction model equation as shown in Fig. 2, 3, 4 and 5 for grading efficiency for Nagpur mandarin , guava, onion and kagzi lime respectively.

Table 10 presents the statistical analysis of joint test on the two parameters involving one particular factor. For example, test x1 tests the hypothesis that parameters of model equation viz. x1, x12and x1x2 are all zero. Similar is the case for x2. Table 10 revealed that, x2 (slope) is highly significant at 10% level than x1 (feed rate). This shows that, the effect of slope is much effective than the feed rate for the response.

The mathematical model was evaluated for its adequacy by testing the grader by using Nagpur mandarin for three samples (sample size 30 kg) with factors constant at above level (32 kg/min feed rate and 35% slope). The grading efficiency of grader was found to be 75.62 per cent with + 0.82  standard deviation. The corresponding average overall effectiveness of separation was 24.42 per cent with + 0.24  standard deviation. The mathematical model was evaluated for its adequacy by testing the grader by using guava  for three samples (sample size 20 kg) with factors constant at above level (32.76 kg/min feed rate and 25.65% slope). The grading efficiency of grader was found to be 90.53 per cent with + 0.87 standard deviation. The corresponding average overall effectiveness of separation was 75.00 per cent with + 0.11 standard deviation. Similarly the mathematical model was evaluated for its adequacy by testing the grader by using onion  for three samples (Sample size 20 kg) with factors constant at above level (28.16 kg/min feed rate and 41.66% slope). The grading efficiency was found to be 73.80 per cent with + 0.63 standard deviation.  The corresponding average overall effectiveness of separation was 47.00 per cent with + 0.39 standard deviation. Similarly the mathematical model was evaluated for its adequacy by testing the grader by using kagzi lime for three samples (Sample size 50 kg) with factors constant at above level (30 kg/min feed rate and 33% slope). The grading efficiency was found to be 76.83 per cent with + 0.71 standard deviation.  The corresponding average overall effectiveness of separation was 24.65 per cent with      + 0.31 standard deviation. This lower overall effectiveness of separation can be attributed to the difference between the major and minor diameter of fruit (fruit being not perfectly spherical) ranging from zero to 9 mm and the orientation of fruit (either major diameter/ minor diameter perpendicular to slope) while conveying within the diverging gap between two pipes of each pair, which caused the mixing of various grades of fruits. Moreover, the overall effectiveness of separation is the multiplication of effectiveness of separation of each grade /outlet.

With the optimized feed rate the capacity of grader for grading Nagpur mandarin comes out to be 15.20 tonnes per day of eight hours and with 80 per cent efficiency,  the capacity of the grader is 12.16 tonnes of per day of eight hours for Nagpur mandarin. With the optimized feed rate the capacity of grader for grading guava comes out to be 15.76 tonnes per day of eight hours and with 80 per cent efficiency,  the capacity of the grader is 12.61 tonnes of per day of eight hours for guava. With the optimized feed rate, the capacity of the grader for grading onion comes out to be 13.52 tonnes per day of eight  hours and with 80 per cent efficiency, the capacity of the grader is10.82 tonnes per day of eight hours. Similarly with the optimized feed rate the capacity of the grader for grading kagzi limes comes out to be 14.33 tonnes per day of eight hours and with 80 per cent efficiency, the capacity of the grader is 11.46 tonnes per day of eight hours.

The PDKV Fruit grader is techno economically feasible unit with BEP 44% (Table 11)  Pay back period for equipments 1.75 yrs. and the Annual net profit of Rs. 56560/- can be earned by using this equipment. The employment generated is 300 man days /year.(Annexure B.)

Y = 75.461 + 1.820 x1 + 3.120 x2 – 2.592 x1² – 4.192 x2² – 1.112 x1x2 (R² = 0.886)----(4)

The analysis of variance (Table 8) for the effect of factors on response indicated that the regression was significant (at 10% level) and lack of fit was non significant and hence the mathematical model can be considered as quite adequate for the  Nagpur  mandarin, guava, onion and Kagzi lime grading.

Table 8. Analysis of variance for the effect of input variables on grading efficiency (Y)

Source	Nagpur mandarin		Guava		Onion		Kagzi lime
	df	SS	df	SS	df	SS	df	SS
Model (Reg.)	5	261.099*	5	71.998*	5	107.718*	5	374.999*
Residual	4	33.605	4	12.520	4	18.637	4	52.295
Lack of fit	3	33.495	3	12.48	3	18.535	3	52.068
Pure error	1	0.110	1	0.0398	1	0.102	1	0.228
F ratio (LDF)	-	101.991	-	104.52	-	60.387	-	76.298
R2	-	0.886	-	0.852	-	0.853	-	0.878

*Significant at 10% level
 Table 9. Predicted levels of factors yielding optimum response 

Factors	Grading efficiency (Y)
	Nagpur mandarin		Guava		Onion		kagzi lime
	Coded	Uncoded	Coded	Uncoded	Coded	Uncoded	Coded	Uncoded
Feed rate, kg/min	0.279	31.67	0.460	32.76	-0.306	28.16	0.973	29.86
Slope, percent	0.335	35.01	-0.914	25.65	1.221	41.66	0.035	32.67
Response, per cent	76.24		91.66		74.37		78.16

Table 10. Analysis of variance for the overall effect of individual factor 

Factor	df	S.S.	Mean square	F ratio
Nagpur mandarin
x1	3	69.253	23.084	2.041
x2	3	181.632*	60.544	5.352
Guava
x1	3	10.14	3.38	0.80
x2	3	59.28*	19.76	4.70
Onion
x1	3	9.065	3.021	0.481
x2	3	87.496*	29.165	4.644
Kagzi lime
x1	3	113.737	37.912	2.156
x2	3	258.999*	86.333	4.909

Significant at 10% level
  Table 11. Cost economics of PDKV fruit grader

1	BEP,%	44
2	Pay back period for equipment, yr	1.75
3	Pay back period for project,yr	1.92
4	Return on investment	43.02
5	Employment generation mandays/ year	300
6	Annual Net profit, Rs	56560

Appendix - A

Effectiveness of Separation
          Let a feedlot of X oranges contain four sizes of oranges, viz. X1, X2, X3 and X4. of Grade I, Grade II, Grade III and Grade IV respectively.
Now,
             X’1    =        No. of oranges of X1 collected in grade I
             X”1    =        No. of oranges of X1 collected in other outlet
             X’2    =        No. of oranges of X2 collected in grade II
             X”2    =        No. of oranges of X2 collected in other outlet
             X’3    =        No. of oranges of X3 collected in grade III
             X”3    =        No. of oranges of X3 collected in other outlet
             X’4    =        No. of oranges of X4 collected in grade IV
             X”4    =        No. of oranges of X4 collected in other outlet
Then for material balance,
             X       =        X1 + X2 + X3 + X4
                       =        X’1 + X’’1 + X’2 + X’’2 + X’3 + X’’3 + X’4 + X’’4
Effectiveness for X1,
                                                           X’1
             Effectiveness X1 =          ---------------             ........(1)
                                                          X’1  + X’’1
Effectiveness for X2,
                                                                X’2
             Effectiveness X2 =           ---------------          ........(2)
                                                        X’2  + X’’2
 
Effectiveness for X3,
                                                            X’3
             Effectiveness X3 =          ---------------            ........(3)
                                                        X’3  + X’’3
 
Effectiveness for X4,
                                                           X’4
             Effectiveness X4 =        ---------------               ........(4)
                                                      X’4  + X’’4
Overall Effectiveness of separation according to size,
=          Eff. X1 x Eff. X2  x Eff. X3  x Eff. X4             .........(5)

Fig. 1. PDKV Fruit Grader developed at Akola Center

Fig.1 Contour Plot And Response Surface Showing Effect Of Feed Rate And Slope On Grading Efficiency Of Nagpur Mandarin

Fig.2 Contour plot and response surface showing effect of feed rate and slope on grading efficiency of Guava

Fig.3 Contour plot and response surface showing effect of feed rate and slope on grading efficiency of Onion

Fig.4 Contour plot and response surface showing effect of feed rate and slope on grading efficiency of Kagzi Lime