Production Rate (Rp)
The production rate for an specific processing assembly operation is generally expressed as an hourly rate that means. parts/hr. Let us assume how this is calculated for three types of production systems namely Job shop, batch and mass production?
In a typical processing operation, such like machining, Tc consists of
1. Actual machining time (T0),
2. Work part handling time (Th), and
3. Tool handling time per workpiece (Tth).
Equation 1
∴ Tc = T0 + Th + Tth
For a batch production, assume the batch (Q) processing time is Tb, then
Tb = Tsu + Q . T0
Setup is needed only once for one batch of product.
Thus the processing time for each of the product (Tp) is computed as following:
Equation 2
T p = Tb /Q
Equation 3
∴ Production rate (Rp) =60/ Tp
For job shop production system (Q = 1) and the production rate is calculated by using
Eq. (3).
Equation 4
∴ Tp = Tsu + Tc
For mass production system Tp = Tc (non-operational times and setup time are neglected)
where Tc = Tr + Max. T0
Tr is time to transfer the workpart among stations.
In all of the above equations, calculation of T0 is process dependent. If the process is machining process, operation time is frequently referred as machining time. The machining times for several machining processes and the significance of it is explained in the following sections.
The Basic endeavour in any production process is to generate acceptable components with maximum production rate and minimum production cost. But no single effort had been found fully successful due to the complexities involved in the process. For example if the cutting speed, feed and depth of cut are enhanced rapidly to decrease the machining time then the tool life shortens and thus, tooling cost enhance and so that the total production cost also enhance. Alternatively if the cutting speed is drop to improve the tool life the metal removal rate is decreased and therefore the production cost is again increased. Therefore, to keep a balance, optimal process parameters (feed, speed and depth of cut) are to be calculated. Their choice is somewhat hard and a lot depends upon the shop practices in addition to the experience of the operator/planner.
In viewpoint of the above a thorough knowledge on the estimation of machining cost and time is significant.
The cutting speed in turning is the surface speed of the work piece. Therefore
Equation 5
V = π DN /1000
where V = cutting speed (surface), m/min,
D = diameter of the workpiece, mm, and
N = rotational speed of the workpiece, rpm.
The diameter D to be utilized can be either the initial diameter of the blank or the last diameter of the workpiece after giving the depth of cut. Though, there is practically not much change in the values attained by using either of the values. To be realistic, the average of the two diameters would be better.
From the above equation, we have
Equation 6
N = 1000 / π D V
The spindle speed (rpm) attained from the Eq. (10) might not be an exact value of the speed available on the lathe machine, as any lathe would only have limited range of spindle speeds available. Therefore it is necessary to adjust the value so attained to that available in the speed range considering the work and tool material combination. It is demonstrated later by using an example. Thus the machining time in turning (t) is estimated as following
Equation 7
t = (L + L0 )/2 f N
Where L = length of the job, mm ≅ L/ fn if L ≡ L0 ,
L0 = over travel of the tool beyond the length of the job to help in the setting of the tool, mm (sometimes approach length is also included), and
f = feed rate, mm/rev.
The over travel to be provided based upon the operator's choice however usual values could be 2 to 3 mm on either side. The reason of providing over travel in a machining process is to make certain smooth exit of tool from the zone of machining, to apparent the burr produced on the part and to compensate for the elastic deflections as of the tool/work system.
The number of passes needed to machine a component based upon the left over stock (stock allowance). Also based upon the specified surface finish and the tolerance on a given dimension, the choice would need to be made as to the number of finishing passes (1 or 2) whereas the rest of the allowance is to be removed through the roughing passes. The roughing passes Pr is given by following
Pr = A - Af / dr
where A = total machining allowance, mm,
Af = finish machining allowance, mm, and
dr = depth of cut in roughing, mm.
The value determined from the above equation is to be rounded to the next integer. Likewise, the finishing passes, Pf, is given by following
Pf = Af /dr
where df = depth of cut in finishing, mm.