**3.3. The influence of weights and knot vector to the fluctuations of ram velocity and acceleration**

To check the influence of weights and knot vector to the ram motions, let [*ω*1] = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [*ω*2] = [1, 0.5, 0.6, 0.8, 1, 0.9, 0.8, 0.4, 0.8, 1.2, 0.5, 0.8, 1], [*ω*3] = [1, 1, 1, 1, 0.5, 0.6, 0.8, 0.05, 0.8, 1.2, 0.5, 0.8, 1], and *U*2 = [0, 0, 0, 0, 0.0476, 0.1111, 0.254, 0.4444, 0.619, 0.7619, 0.8571, 0.92, 0.995, 1, 1, 1, 1]. The corresponding ram motions are dicpited in Figure 13 resepctively. It can be found that the peak velocity and acceleration of the return period can be lowered up to 20%-30% and the ram velocity lowered 40% when the upper die touches the workpiece by adjusting the knots corresponding to quick return period.

**Figure 12.** Ram motion under different weights

168 Metal Forming – Process, Tools, Design

0 1

R R

1

012

RRR

weights and knots.

**and acceleration** 

<sup>2</sup> 2 3 <sup>n</sup> n n (1) i i,k j j,k i i,k i i,k

(j 1) (j 1)

− − − +− + +− +

u uu u

ip i ip1 i1

5678 6 <sup>7</sup> <sup>5678</sup>

RRRR P RRRR P

<sup>8</sup> 7 8 9 10

<sup>P</sup> RRRR

10 11

R R

8 9 10 11

RRRR

(25)

= − − − (26)

2

P

0 (1) s (2) s 1 2 3 4 5 6 7 (2) e (1) e 8

Q D D Q Q Q Q Q Q Q D D Q

P

 

P

9

=

(27)

P

P

P

(2) (2) 10

<sup>11</sup> (1) <sup>11</sup> <sup>12</sup>

**(2) 12 (1) 12**

<sup>R</sup> <sup>P</sup> 1

**R R**

<sup>+</sup>

(j) i,p 1 i 1,p 1

N (x) N (x) N (x) p( )

i 0 i 0 i 0 / ω N (x) 2ω N (x) ω N (x) / ω N (x) = = =

i,p

Combining Eqs.(16), and (22) through (26), following equation can be got:

 

operation, and decrease the peak power demand of the servomotors.

By solving Eq.(27), the control points *P*0, *P*1*…*, and *P*12 are determined and therefore the ram motion can be solved according to Eq.(16). Thanks to the locality of NURBS, the ram motion can be refined piecewisely through the manipulation of corresponding control points,

**3.2. The influence of weights to the fluctuations of ram velocity and acceleration**  To check the influence of weights to the ram motions, let [*ω*1] = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [*ω*2] = [1, 0.5, 0.6, 0.8, 1,0.9, 0.8, 0.4, 0.8, 1.2, 0.5, 0.8, 1], and [*ω*3] = [1, 1, 1, 1, 0.5, 0.6, 0.8, 0.1, 0.8, 1, 1, 1, 1]. The corresponding ram motions are dicpited in Figure 12 resepctively. It can be found that weight *ω<sup>i</sup>* (*i*=8) should be adjusted that can lower the fluctuation of the ram velocity and acceleration and decrease the shock, vibration and noise during stamping

**3.3. The influence of weights and knot vector to the fluctuations of ram velocity** 

To check the influence of weights and knot vector to the ram motions, let [*ω*1] = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [*ω*2] = [1, 0.5, 0.6, 0.8, 1, 0.9, 0.8, 0.4, 0.8, 1.2, 0.5, 0.8, 1], [*ω*3] = [1, 1, 1, 1, 0.5,

(1) (1) 0

(2) (2) (2) 1

<sup>1234</sup> <sup>3</sup> <sup>2345</sup> <sup>4</sup> 3456 5

RRRR <sup>P</sup> RRRR P RRRR P

**Figure 13.** Ram motion under different weights and knot vectors

#### **3.4. The self-adaption of the weights due to optimization of the ram motioin**

Under the same group of demands over the displacement, velocity of the ram motion, a large number of NURBS curves can be achieved and hence the optimized one is able to select by optimization.

#### *3.4.1. The self-adaption due to the ram displacement*

Due to the local support of the NURBS expression, the ram motion can be discretized into several segments to set up the constraint inequalities. The *m* curve segments are denoted as 1 *<sup>l</sup>* , 2 *<sup>l</sup>* , …, and *<sup>l</sup> <sup>m</sup>* . Supposed displacement demands over curve segement *<sup>l</sup> <sup>j</sup>* , <sup>1</sup>*s* ≤ *<sup>l</sup> <sup>j</sup>* ≤ <sup>2</sup>*s* , i.e.

$$\mathbf{s}\_1 \le \frac{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}} d\_i^{\boldsymbol{\mu}} \boldsymbol{\Lambda}\_{i,k}^{N\_i(\boldsymbol{u})}}{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}} \boldsymbol{\alpha}\_i^{\boldsymbol{\mu}} \boldsymbol{\Lambda}\_{i,k}^{N\_i(\boldsymbol{u})}} \le \mathbf{s}\_2 \quad \text{where knot vector } \boldsymbol{\mu} \in \left[ \boldsymbol{\mu}\_{j\_1 \boldsymbol{\mu}} \quad \boldsymbol{\mu}\_{j\_2} \right]. \text{ To satisfy this in-equality demand, let } \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}} \text{ and } \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}} \text{ denote the vector } \{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}, \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}\} \text{ and } \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}} \text{ denote the vector } \{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}, \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}\} \text{ and } \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}} \text{ denote the vector } \{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}, \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}\} \text{ of } \{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}, \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}\}. \text{ The vector } \{\boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}, \boldsymbol{\Sigma}\_{i=0}^{\boldsymbol{\mu}}\} \text{ is defined as}$$

the two endpoints, maximum and minimum values over *<sup>l</sup> <sup>j</sup>* locate at the domain formed by <sup>1</sup>*s* and 2*s* , i.e.

$$\mathbf{s}\_1 \le \frac{\Sigma\_{i=0}^{\mu} d\_i^{\alpha} d\_{i,k}^{N\_{i,k}(\mu\_{j1})}}{\Sigma\_{i=0}^{\mu} d\_i^{\alpha} N\_{i,k}(\mu\_{j1})} \le \mathbf{s}\_2 \tag{28}$$

The Design of a Programmable Metal Forming Press and Its Ram Motion 171

≤ ≤ (36)

≤ ≤ (37)

<sup>=</sup> = (38)

*<sup>t</sup>* <sup>0</sup> *<sup>v</sup>* .

, 0.5, 1, 0.8, 0.5, 0.8,

2 3 1 () () 1 2 ( ) max *pu pu p u v v* <sup>−</sup> 

2 3 1 () () 1 2 ( ) min *pu pu p u v v* <sup>−</sup> 

To lower the velocity fluctuation and ease the shock, vibration and noise to improve the workpiece's stamping quality, goal function can be defined by controlling the velocity of the

( ) ( ) |() <sup>0</sup> F min *<sup>n</sup> <sup>v</sup> i ii*

Considering some of the weights have no relation to the stamping operation, these weights are prescribed and other weights are selected to be optimized under the demands of

Take the deep drawing operation as example. The performance demands include: (1) uniform stamping operation: nearly constant stamping velocity (100-300mm/s) for drawing period, (2) quick return: high ram speed (330-500mm/s) for return period, and (3) small

To express the relationship between the ram motion and time by NURBS, the ram

Correspondingly, the velocity constraints are normalized to be nominal velocity *v*<sup>0</sup>

ω

only affects the curve shape over the knot span [ *ui* , <sup>1</sup> *ui k* + + ] ∈[ *uk* , <sup>1</sup> *un*<sup>+</sup> ],

= [0.5, 1, 3

are selected as optimized variables that relate to the drawing and

ω , 4 ω , 5 ω , 6 ω

<sup>d</sup> . The real ram velocity can be derived as *v* = *<sup>s</sup>*

fluctuation of ram velocity and acceleration during drawing and releasing periods.

ω

Σ

ω

displacement, velocity and above goal function by iterative solution.

displacement and time are normalized firstly as follows:

0

releasing periods. The total weights are set as

*t s s t* d

ω

ω , <sup>4</sup> ω , <sup>5</sup> ω , <sup>6</sup> ω

<sup>0</sup>*t t* / =[0, 0.67/4, 0.99/4, 1.80/4, 2.25/4, 2.97/4, 3.37/4, 3.69/4, 1], and

<sup>0</sup>*s s*/ =[1, 186.78/400,106.67/400,44.44/400,0,62.22/400,177.78/400,275.56/400,1].

*3.4.3. The solution of the optimized weights* 

' ( ) () , *n <sup>i</sup> <sup>v</sup> R ud i i ik i*

<sup>=</sup> <sup>=</sup> .

ram as follows:

where, 0

**3.5. Case study** 

*3.5.1. The problem definition* 

*3.5.2. The optimization* 

expressed as 0 *v* = <sup>0</sup>

Because weights *<sup>i</sup>*

here weights 3

0.7, 0.9].

ω

$$\mathbf{s}\_1 \le \frac{\Sigma\_{i=0}^{\mu} d\_i^{\mu} d\_{i,k}^{N\_{i,k}}(u\_{j,2})}{\Sigma\_{i=0}^{\mu} d\_i^{\mu} i\_{i,k}(u\_{j,2})} \le \mathbf{s}\_2 \tag{29}$$

$$\mathbf{s}\_1 \le \max \left( \frac{\Sigma\_{i=0}^\mu a\_i^{d\_i} \mathbf{s}\_{i,k}^{N\_{i,k}}(\boldsymbol{u})}{\Sigma\_{i=0}^\mu a\_i^{o\_i} \mathbf{s}\_{i,k}^{N\_{i,k}}(\boldsymbol{u})} \right) \le \mathbf{s}\_2 \tag{30}$$

$$\mathbf{s}\_1 \le \min \left( \frac{\Sigma\_{i=0}^{\mu} d\_i^{\alpha} d\_i^{N\_{i,k}} \mu}{\Sigma\_{i=0}^{\mu} a\_i^{\alpha} N\_{i,k} \mu} \right) \le \mathbf{s}\_2 \tag{31}$$

#### *3.4.2. The self-adjustment due to velocity of the ram*

Supposed velocity demand over curve section *<sup>l</sup> <sup>j</sup>* <sup>1</sup> *v* ≤ *lj <sup>v</sup>* ≤ <sup>2</sup> *v* , where *u*∈[ <sup>1</sup> *uj* , 2 *uj* ]. For 0 ' ( ) , *n lj <sup>i</sup> v R ud ik i* <sup>=</sup> <sup>=</sup> , we have 1 *v* ≤ <sup>0</sup> ' ( ) , *n <sup>i</sup> R ud ik i* <sup>=</sup> ≤ <sup>2</sup> *v* , i.e.

$$\upsilon\_1 \le \sum\_{i=0}^{u} \left| \frac{\frac{a \circ N\_{i,k}^{\cdot}(u)}{\sum\_{j=0}^{u} a \circ N\_{j,k}(u)} \cdot a \circ N\_{i,k}(u) \sum\_{j=0}^{u} a \circ N\_{j,k}(u)}{\left(\sum\_{j=0}^{u} a \circ N\_{j,k}(u)\right)^2} \right|\_{i} \le \upsilon\_2 \tag{32}$$

$$\textbf{Let } p\_1 = \left| \sum\_{j=0}^{n} a\_j N\_{j,k}(u) \right|^2 \text{, } p\_2 = \sum\_{i=0}^{n} \left( \frac{a\_i N\_{i,k}(u)}{\sum\_{j=0}^{n} a\_j N\_{j,k}(u)} \right) d\_{i'} \quad \text{and} \quad p\_3 = \sum\_{i=0}^{n} \left( a\_i N\_{i,k}(x) \sum\_{j=0}^{n} a\_j N\_{j,k}(x) \right) l\_i \quad \text{Eq. (32) is a constant } \forall i \text{ that } \sum\_{i=0}^{n} a\_i N\_{i,k}(x) \text{ if } \sum\_{j=0}^{n} a\_j N\_{i,k}(x) \neq 0 \text{ and } \forall i \text{ are integers such that } \sum\_{j=0}^{n} a\_j N\_{i,j}(x) \neq 0 \text{ and } \forall i \text{ are integers.}$$

transformed as

$$
v\_1 \le \frac{p\_2 - p\_3}{p\_1} \le v\_2\tag{33}$$

To satisfy Eq.(33), make sure the values of the first point and endpoint, maximum and minimum values over *lj <sup>v</sup>* locating within the domain spaned by 1 *v* and 2 *v* , i.e.

$$\upsilon\_1 \le \frac{\upsilon\_2(u\_{j1}) - \upsilon\_3(u\_{j1})}{\upsilon\_1(u\_{j1})} \le \upsilon\_2 \tag{34}$$

$$\upsilon\_1 \le \frac{p\_2(u\_{j\_2}) - p\_3(u\_{j\_2})}{p\_1(u\_{j\_2})} \le \upsilon\_2 \tag{35}$$

The Design of a Programmable Metal Forming Press and Its Ram Motion 171

$$\forall v\_1 \le \max\left(\frac{p\_2(u) - p\_3(u)}{p\_1(u)}\right) \le v\_2 \tag{36}$$

$$v\_1 \le \min\left(\frac{p\_2(u) - p\_3(u)}{p\_1(u)}\right) \le v\_2\tag{37}$$

#### *3.4.3. The solution of the optimized weights*

To lower the velocity fluctuation and ease the shock, vibration and noise to improve the workpiece's stamping quality, goal function can be defined by controlling the velocity of the ram as follows:

$$\mathcal{F}(o\boldsymbol{\theta}) := \min \{ \boldsymbol{\Sigma}\_{i=0}^{n} \mid \boldsymbol{v}\_{i}(o\_{i}) \} \tag{38}$$

where, 0 ' ( ) () , *n <sup>i</sup> <sup>v</sup> R ud i i ik i* ω<sup>=</sup> <sup>=</sup> .

Considering some of the weights have no relation to the stamping operation, these weights are prescribed and other weights are selected to be optimized under the demands of displacement, velocity and above goal function by iterative solution.

#### **3.5. Case study**

170 Metal Forming – Process, Tools, Design

<sup>1</sup>*s* and 2*s* , i.e.

0 '( ) ,

Let <sup>1</sup> *p* = <sup>2</sup> <sup>0</sup> [ ( )] , *n <sup>j</sup> N u j jk* <sup>=</sup> ω

transformed as

*lj <sup>i</sup> v R ud ik i* <sup>=</sup> <sup>=</sup> , we have 1 *v* ≤ <sup>0</sup>

, <sup>2</sup> *p* = <sup>0</sup>

*n*

the two endpoints, maximum and minimum values over *<sup>l</sup>*

*3.4.2. The self-adjustment due to velocity of the ram* 

Supposed velocity demand over curve section *<sup>l</sup>*

'( ) ,

0

' ( ) , ( ) ,

 

*N u i ik N u j jk*

=

ω

ω

*<sup>i</sup> R ud ik i* <sup>=</sup> ≤ <sup>2</sup> *v* , i.e.

'

*N u*

0 2 0

*n j*

=

ω

*n*

*n j*

0

ω <sup>=</sup> =

ω

=

*n i n j*

( ) <sup>0</sup> , 1 1 2 ( ) <sup>0</sup> , 1 *<sup>n</sup> dN u <sup>i</sup> i i ik j <sup>n</sup> N u <sup>i</sup> i ik j s s* ω

( ) <sup>0</sup> , 2 1 2 ( ) <sup>0</sup> , 2 *<sup>n</sup> dN u <sup>i</sup> i i ik j <sup>n</sup> N u <sup>i</sup> i ik j s s* ω

ω

ω

( ) <sup>0</sup> , 1 2 ( ) <sup>0</sup> , max *<sup>n</sup> dN u <sup>i</sup> i i ik <sup>n</sup> N u <sup>i</sup> i ik s s* ω

( ) <sup>0</sup> , 1 2 ( ) <sup>0</sup> , min *<sup>n</sup> dN u <sup>i</sup> i i ik <sup>n</sup> N u <sup>i</sup> i ik s s* ω

0

=

 ω

*di* , and 3 *p* = <sup>0</sup> <sup>0</sup>

≤ ≤ (32)

*n n*

ω

*<sup>i</sup> N x N xd <sup>j</sup> <sup>i</sup> i ik j jk* <sup>=</sup>

*v v* <sup>−</sup> ≤ ≤ (33)

≤ ≤ (34)

≤ ≤ (35)

 ω= 

*n*

( ) , ' ( ) ( ) , , ( ) ,

*i ik Nu Nu i ik j jk N u j jk <sup>d</sup> N u j jk v v*

 <sup>−</sup>

1 2 [ ( )] ,

ω

*i n i j*

2 3 <sup>1</sup> 1 2 *p p p*

To satisfy Eq.(33), make sure the values of the first point and endpoint, maximum and

2 3 1 ()() 1 1 1 2 ( ) <sup>1</sup> *pu pu j j p uj v v* <sup>−</sup>

2 3 1 ()() 2 2 1 2 ( ) <sup>2</sup> *pu pu j j p uj v v* <sup>−</sup>

minimum values over *lj <sup>v</sup>* locating within the domain spaned by 1 *v* and 2 *v* , i.e.

 <sup>=</sup> <sup>≤</sup> <sup>=</sup>

 <sup>=</sup> <sup>≤</sup> <sup>=</sup>

<sup>=</sup> <sup>≤</sup>

<sup>=</sup> <sup>≤</sup>

ω

ω

<sup>=</sup>

<sup>=</sup>

*<sup>j</sup>* locate at the domain formed by

≤ (28)

≤ (29)

≤ (30)

≤ (31)

*<sup>j</sup>* <sup>1</sup> *v* ≤ *lj <sup>v</sup>* ≤ <sup>2</sup> *v* , where *u*∈[ <sup>1</sup> *uj* , 2 *uj* ]. For

'( ) ( ) , ,

. Eq.(32) is

#### *3.5.1. The problem definition*

Take the deep drawing operation as example. The performance demands include: (1) uniform stamping operation: nearly constant stamping velocity (100-300mm/s) for drawing period, (2) quick return: high ram speed (330-500mm/s) for return period, and (3) small fluctuation of ram velocity and acceleration during drawing and releasing periods.

#### *3.5.2. The optimization*

To express the relationship between the ram motion and time by NURBS, the ram displacement and time are normalized firstly as follows:

$$1. t\_0 / t = [0, 0.67/4, 0.99/4, 1.80/4, 2.25/4, 2.97/4, 3.37/4, 3.69/4, 1], \text{and } 1$$

<sup>0</sup>*s s*/ =[1, 186.78/400,106.67/400,44.44/400,0,62.22/400,177.78/400,275.56/400,1].

Correspondingly, the velocity constraints are normalized to be nominal velocity *v*<sup>0</sup> expressed as 0 *v* = <sup>0</sup> 0 *t s s t* d <sup>d</sup> . The real ram velocity can be derived as *v* = *<sup>s</sup> <sup>t</sup>* <sup>0</sup> *<sup>v</sup>* .

Because weights *<sup>i</sup>* ω only affects the curve shape over the knot span [ *ui* , <sup>1</sup> *ui k* + + ] ∈[ *uk* , <sup>1</sup> *un*<sup>+</sup> ], here weights 3 ω , <sup>4</sup> ω , <sup>5</sup> ω , <sup>6</sup> ω are selected as optimized variables that relate to the drawing and releasing periods. The total weights are set as ω = [0.5, 1, 3 ω , 4 ω , 5 ω , 6 ω , 0.5, 1, 0.8, 0.5, 0.8, 0.7, 0.9].

To assure the continousness of ram displacement, velocity and acceleration, NURBS of *k* = 3 is applied here. The constraints relating the punching speed are listed as:

The Design of a Programmable Metal Forming Press and Its Ram Motion 173

**Figure 15.** The servo press prototype with 2-servomotor redundant actuation of 200 tonnage (photo)

In this chapter, a new concept of programmable metal forming press of redundant parallel actuation is presented to make it possible to develop a larger servo mechanical press using servomotors available. Based on the above discussions, following conclusions can be drawn: 1. A servo mechanical press is different from a traditional mechanical press in such a way that it involves servo actuation design with programmable motors and punching

2. The tonnage of servo mechanical presses is limited by the capacity of servomotors available to some extent. The new servo mechanical press with redundant actuation proposed in this chapter is a feasible option to develop a larger machine based on servomotors available. This redundant actuation scheme is able to accommodate an un-

3. The mechanism design for the redundant actuation should be considered carefully that

4. The ram motion of the servo press can be optimized that requires a tool to express. The pseudo-NURBS representation proposed is effective to model the ram motion and form an optimization problem. Simulation shows that the optimized ram motion improves stamping operation with higher productivity and avoids large transient force and

5. A computer programme based on the pseudo-NURBS method is developed in the

*State Key Lab of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, China* 

The author thanks the partial financial supports under the projects from the National Natural Science Foundation of China (NSFC Grant No. 50875161), Program for New

laboratory embedded in the servo press that facilitates the press operation.

mechanism design with higher mechanical advantage.

maintains the performance of the redundant actuation.

vibration by smooth approaching and slow releasing of the ram.

synchronization between the two servomotors.

**4. Conclusion** 

**Author details** 

Weizhong Guo and Feng Gao

**Acknowledgement** 


To limit the velocity fluctuation, the goal function is defined as *F*( ) ω = min ( | | <sup>0</sup> *<sup>n</sup> <sup>v</sup> i i* <sup>Σ</sup> <sup>=</sup> ).

Hence, we can get the optimized weights 3 ω =0.5, 4 ω =0.7, 5 ω =0.8, and 6 ω=0.7.

#### *3.5.3. Performance analysis*

*c*

As discussed above, the optimized weights are

*a* ω= [0.5, 1, 0.5, 0.7, 0.8, 0.7, 0.5, 1, 0.8, 0.5, 0.8, 0.7, 0.9].

Here another two weights are set for comparison as:

*b* ω = [0.5, 1, 0.9, 0.4, 0.5, 0.2, 0.5, 1, 0.8, 0.5, 0.8, 0.7, 0.9] ω= [0.5, 1, 0.3, 0.5, 0.1, 1, 0.5, 1, 0.8, 0.5, 0.8, 0.7, 0.9]

Figure 14 displays the ram motion curves under weights *<sup>a</sup>* ω , *<sup>b</sup>* ω , and *<sup>c</sup>* ω respectively. From the figures, it can be seen that the ram motion of *<sup>a</sup>* ω is the nearest to the desired trajectory for drawing and releaseing period, the ram velocity curve of *<sup>a</sup>* ω is more flat for drawing period, and the fluctuation of the ram acceleration of *<sup>a</sup>* ω is the least that helps to decrease shock, vibration and noise. This is consistent with the comparison of goal functions. The goal function values are 20441, 20457 and 20606 under *<sup>a</sup>* ω , *<sup>b</sup>* ω and *<sup>c</sup>* ωrespectively.

**Figure 14.** The optimized ram motion

#### *3.5.4. The prototype development*

To validate the new concept, a servo press prototype with 200 ton punching force has been developed in our lab. As shown in Figure 15, the machine is more than 5 meters high and 2 meters wide. Experimental studies are being performed on this prototype including dynamic performance, dynamic control and stamping process planning.

The Design of a Programmable Metal Forming Press and Its Ram Motion 173

**Figure 15.** The servo press prototype with 2-servomotor redundant actuation of 200 tonnage (photo)
