Experimental Investigation on Geometric Error …
89
Fig. 5 Point cloud data of 60° wall angle pyramid imported in SolidWorks software
This results in more stretching of sheet with relatively more elastic recovery. Thus,
there is more spring-back at large step size in case of contoured/incremental tool
path which is not the case in spiral tool path. As the wall angle increases, RMSE
increases. This is because, at high wall angle, elastic recovery is more which leads
to increased spring-back. Since, at higher wall angle, stretching is predominant and
high localized deformation takes place which results in more spring-back. Since feed
rate has no significant influence on RMSE. Therefore, high feed rate can be used to
reduce forming time. In fact, there is slight decrease in RMSE as feed rate increases
which is desirable. This is due to the fact that frictional heat which is generated due to
sliding contact between the tool and sheet metal blank, which softens the material and
plastic deformation takes place with less elastic recovery. So, as feed rate increases,
RMSE decreases. Figure 5 shows the point cloud data of 60° wall angle pyramid
which is imported in SolidWorks software and the difference between scanned and
target profile.
4 Predictive Model for Geometrical Error (RMSE)
Using experimental results, an empirical relation is proposed to represent the
geometrical error (RMSE). It is given by Eq. (2) in actual factors.
Geometrical Error (RMSE) = {0.4 + (1.2 × t d ) − (0.8 × z)
+(0.01 × ϕ) + (0.000017 × f )}
(2)
where t d = dummy sheet thickness; z = step size, ϕ = wall angle; f = feed rate.
Confirmation tests are carried out in order to verify adequacy and suitability of developed mathematical model. Process parameters settings are randomly finalized within
range of design space. Results of confirmation experiments are given in Table 4.
89
Fig. 5 Point cloud data of 60° wall angle pyramid imported in SolidWorks software
This results in more stretching of sheet with relatively more elastic recovery. Thus,
there is more spring-back at large step size in case of contoured/incremental tool
path which is not the case in spiral tool path. As the wall angle increases, RMSE
increases. This is because, at high wall angle, elastic recovery is more which leads
to increased spring-back. Since, at higher wall angle, stretching is predominant and
high localized deformation takes place which results in more spring-back. Since feed
rate has no significant influence on RMSE. Therefore, high feed rate can be used to
reduce forming time. In fact, there is slight decrease in RMSE as feed rate increases
which is desirable. This is due to the fact that frictional heat which is generated due to
sliding contact between the tool and sheet metal blank, which softens the material and
plastic deformation takes place with less elastic recovery. So, as feed rate increases,
RMSE decreases. Figure 5 shows the point cloud data of 60° wall angle pyramid
which is imported in SolidWorks software and the difference between scanned and
target profile.
4 Predictive Model for Geometrical Error (RMSE)
Using experimental results, an empirical relation is proposed to represent the
geometrical error (RMSE). It is given by Eq. (2) in actual factors.
Geometrical Error (RMSE) = {0.4 + (1.2 × t d ) − (0.8 × z)
+(0.01 × ϕ) + (0.000017 × f )}
(2)
where t d = dummy sheet thickness; z = step size, ϕ = wall angle; f = feed rate.
Confirmation tests are carried out in order to verify adequacy and suitability of developed mathematical model. Process parameters settings are randomly finalized within
range of design space. Results of confirmation experiments are given in Table 4.