MMP SA-2550A
Page 14 of
24
Midwest Motion Products
DESIGN, MANUFACTURING & DISTRIBUTION - MOTION CONTROL EQUIPMENT
email:
These energy terms can be broken down into the approximate mechanical and electrical terms - capacitive, kinetic, and potential
energy. The energy equations for these individual components are as follows:
𝐸
𝑐
=
1
2
𝐶𝑉
𝑁𝑂𝑀
2
𝐸
𝑟
=
1
2
𝐽𝜔
2
1
1
𝐸
𝑝
= 𝑚𝑔ℎ
𝐸
𝑐
– Energy stored in capacitor (J)
C – Capacitance (F)
𝑉
𝑁𝑂𝑀
– Nominal bus voltage of the system
𝐸
𝑟
– mechanical energy of the load (J)
J – moment of inertia of the load (kg-m
2
)
𝜔
– angular velocity of the load (rad/s)
𝐸
𝑝
– potential energy of load (J)
m – mass of the load (kg)
g – gravitational acceleration (9.81 m/s
2
)
h – vertical height of the load (m)
During regeneration the kinetic and potential energy will be stored in the power supply’s capacitor. To determine the final power
supply voltage following a regenerative event, the following equation may be used for most requirements:
(𝐸
𝑐
+ 𝐸
𝑟
+ 𝐸
𝑝
)
𝑖
= (𝐸
𝑐
+ 𝐸
𝑟
+ 𝐸
𝑝
)
𝑓
1
2
𝐶𝑉
𝑁𝑂𝑀
2
+
1
2
𝐽𝜔
𝑖
2
+ 𝑚𝑔ℎ
𝑖
=
1
2
𝐶𝑉
𝑓
2
+
1
2
𝐽𝜔
𝑓
2
+ 𝑚𝑔ℎ
𝑓
Which simplifies to:
𝑉
𝑓
= √𝑉
𝑁𝑂𝑀
2
=
𝐽
𝐶
(𝜔
𝑖
2
− 𝜔
𝑓
2
) +
2𝑚𝑔(ℎ
𝑖
− ℎ
𝑓
)
𝐶
The V
f
calculated must be below the power supply capacitance voltage rating and the drive over voltage limit. If this is not the case,
a shunt regulator is necessary. A shunt regulator is sized in the same way as a motor or drive, i.e. continuous and RMS power
dissipation must be determined. The power dissipation requirements can be determined from the application move profile.
MIDWEST M
O
TION
P
RODUCTS
