Linear Motion – Calculating Acceleration for Linear Motion Control Applications

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Unit Converter
Conversion Type Units Units

Newton’s Second law:

 F = m xa
Force = Mass x Acceleration

To size a stage properly the force must be known. If force is not known it must be calculated from this equation. The mass is the total mass of the customer payload plus the mass of the moving components of the stage. If the acceleration component is not known it must be calculated. Calculators are provided under the Acceleration tab for estimating the acceleration of a system. Once the force is determined, the duty cycle for all of the specific forces must be determined to calculate the RMS force, which is the average required force. The Force RMS tab provides the tools needed to determine the RMS Force of a motion profile.

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Variable Description Units Calculation
m Moving mass
a Acceleration
F Force 0
*accelerations up to 10 g’s are possible under closed loop control
*accelerations up to 20 g’s are possible under open loop control

 

        

triangular formula graph
$$ \Large \alpha = \frac{4 \times d }{t^2 \times G} $$
 

 

 

Variable Description Units Calculation
d Distance moved
t Time to complete move (sec)
G Gravitational constant
a Acceleration (g’s) 0
*accelerations up to 10 g’s are possible under closed loop control
*accelerations up to 20 g’s are possible under open loop control

 

Trapezoidal formula graph
$$\Large a = {2 \times d \over t_{a}^2 \times G} $$
Known Variables
Time and Distance are known
Velocity and Distance are known
Time and Velocity are known

 

Variable Description Units Calculation
d Distance moved
t Time to complete move (sec)
v Velocity
G Gravitational constant
a Acceleration (g’s) 0
*accelerations up to 10 g’s are possible under closed loop control
*accelerations up to 20 g’s are possible under open loop control

sinusoidal formula graph

$$ \Large a = {2 \pi^2f^2 D \over G} $$
Known Variables
Frequency and Distance are known
Velocity and Frequency are known
Distance and Velocity are known

 

Variable Description Units Calculation
d Distance moved
f Frequency (Hz)
v Velocity
G Gravitational constant
a Acceleration (g’s) 0
*accelerations up to 10 g’s are possible under closed loop control
*accelerations up to 20 g’s are possible under open loop control

force formula graph

$$ \Large F_{rms} = \sqrt{\left ( F_{a} \right )^2 \times t_{a} + \left ( F_{c} \right )^2 \times t_{c} + \left ( F_{d} \right )^2 \times t_{d} \over \left ( t_{on} + t_{off} \right )} $$

 

Variable Description Units Calculation
Fa Acceleration Force
Fc Constant Velocity Force
Fd Deceleration Force
ta Time to accelerate (sec)
tc Time at constant velocity (sec)
td Time to decelerate (sec)
ton ta + tc + td (sec)
toff Dwell time (sec)
Frms Average required force 0

$$ \Large Duty Cycle\left ( \% \right ) ={ t_{on} \over \left ( t_{on} + t_{off}\right )} \times 100 $$
Variable Description Calculation
ton Time with power applied (sec)
toff Dwell time (sec)
Duty Cycle (%) Percentage of total time spent active 0
Example
Duty Cycle = 1 sec on, 3 sec off

Duty Cycle = 1/(1+3) = 1/4

Duty Cycle = 25%

Note: Duty Cycle is only for DC motors.

$$ \Large F@100\% = Force At DutyCycle \div \sqrt{ 1 \over DutyCycle} $$
Variable Calculation
Duty Cycle %
Force at Duty Cycle
Force at 100 % 0
Example
Force at 10% Duty Cycle = 1 lb X (1/10%)1/2

Force at 10% Duty Cycle = 1 lb X 3.16

Force at 10% Duty Cycle = 3.16 lbs

Note: This calculation is only for DC motors.
Use the following formula for AC motors:

AC Duty Cycle Calculations
Force @ 50% = Force @ 100% * 1.75
Force @ 15% = Force @ 100% * 5
Force @ 3% = Force @ 100% * 8

For the easy to use Calculator or the App CLICK HERE

H2W Technologies, Inc. is dedicated to the design and manufacture of linear and rotary motion products that are used in the motion control industry. The complete line of linear electric motors includes: Single and dual axis linear steppers, DC brush and brushless linear motors, voice coil actuators, and AC induction motors. Also offered is a complete line of ball screw, lead screw and belt driven positioning stages.

Other motion control products include: Limited angle torque motors for compact, limited angular excursion rotary servo applications, 3 phase brushless rotary servo motors with matching digital servo amplifiers and permanent magnet linear brakes for fail-safe, zero power braking for baggage handling and people moving applications as well as amusement park rides.

With over 75 years combined experience in the linear and rotary motion field, the H2W Technologies team of engineers offers the optimal solution to the most demanding motion control, requirements.

For additional information contact Mark Wilson at H2W Technologies, 26380 Ferry Ct, Santa Clarita,  CA 91350; Tel: 888-702-0540 FREE, Fax: 661-251-2067, E-Mail: info@h2wtech.comor visit the website at http://www.h2wtech.com

 

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Linear Motion Control – Single Rail Positioning Stage H Gantry from H2W Technologies.

H2W Technologies Single Rail Positioning System

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Santa Clarita, CA —– H2W Technologies’ latest single rail positioning stage H-gantry design is an open frame XY positioning system. It has two bottom parallel axes with one cross axis connecting the two (H-gantry).

Each linear axis uses H2W’s brushless linear motors (BLDM-B04), and each has a total stroke length of 25.67 in [652 mm]; can generate 6.2 lbs [27.8 N] of continuous force and 18.7 lbs [83.3 N] of peak force, or a combined 12.4 lbs [55.6 N] continuous force and 37.4 lbs [166.6 N] of peak force on the bottom axis. The non-contact 1-micron resolution encoders allow for precise positioning. The moving tables are guided by a precision recirculating linear ball bearing system.

The linear axes are assembled on a single piece of aluminum extrusion, thus reducing the overall weight of the system. The top cross axis is mounted to the bottom parallel axis using rigid aluminum extrusions, 90-degree right angle gussets, and custom extrusion end plates. The system is mounted to a flat aluminum tooling plate base. There are also provisions that allow customer cables to be routed within the cable carriers. It has end-of-travel rubber bumper stops.

Additional options include, a home positioning sensor, end-of-travel-sensors, and custom mounting holes. Single extrusion length of up to 6 m long, allows for longer stroke applications.

Features:

  • Low system weight
  • Built using standard extrusion profiles
  • Cable carriers to route payload cables
  • Three axis of coordinated motion

About H2W Technologies, Inc.

H2W Technologies, Inc. is dedicated to the design and manufacture of linear and rotary motion products that are used in the motion control industry. The complete line of linear electric motors includes: Single and dual axis linear steppers, DC brush and brushless linear motors, voice coil actuators, and AC induction motors. Also offered is a complete line of ball screw, lead screw and belt driven positioning stages.

Other motion control products include: Limited angle torque motors for compact, limited angular excursion rotary servo applications, 3 phase brushless rotary servo motors with matching digital servo amplifiers and permanent magnet linear brakes for fail-safe, zero power braking for baggage handling and people moving applications as well as amusement park rides.

With over 75 years combined experience in the linear and rotary motion field, the H2W Technologies team of engineers offers the optimal solution to the most demanding motion control, requirements.

See Article: https://www.h2wtech.com/article/single-rail-positioning-stage-h-gantry

See Video at Youtube: https://youtu.be/y25d5vgx838

See Product: https://www.h2wtech.com/page/single-rail-positioning-stage-h-gantry

For additional information contact Mark Wilson at H2W Technologies, 26380 Ferry Ct, Santa Clarita, CA 91350; Tel: 888-702-0540, Fax: 661-251-2067, E-Mail: info@h2wtech.com or visit the website at http://www.h2wtech.com

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Motion Control – Dual Feedback Voice Coil Positioning Stage.

H2W Technologies Dual Feedback Positioning-Stage

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Santa Clarita, CA —– Motion Control – The VCS20-020-CR-01-MC-F3K voice coil positioning stage has dual feedback capability. It can operate either under closed loop position control with force monitoring or closed loop force control with position monitoring. It uses H2W voice coil motor NCC20-18-020-1A to generate a continuous/peak force of 2.0 lbs [8.9 N]/6.0 lbs [26.7 N] with a total stroke length of 2.0 in [50.8 mm]. The 1-micron resolution encoder allows for precise positioning. The 3kg rated force transducer allows for 0.01-3kg of push/pull force feedback control.

It comes supplied with a high accuracy crossed roller bearing. The motor coil is the moving part of the assembly in order to reduce the moving mass of the system. Power is supplied to the motor via a high flex, high reliability flat ribbon cable.

Features:

  • Ability to close the control loop via position (utilizing the 1-micron resolution encoder) or force (utilizing the 3 kg rated force transducer), and the ability to switch between the two within the motion controller.
  • High resolution and repeatability
  • Low moving mass
  • High reliability
  • Ability to run in horizontal or vertical orientation

About H2W Technologies, Inc.

H2W Technologies, Inc. is dedicated to the design and manufacture of linear and rotary motion products that are used in the motion control industry. The complete line of linear electric motors includes: Single and dual axis linear steppers, DC brush and brushless linear motors, voice coil actuators, and AC induction motors. Also offered is a complete line of ball screw, lead screw and belt driven positioning stages.

Other motion control products include: Limited angle torque motors for compact, limited angular excursion rotary servo applications, 3 phase brushless rotary servo motors with matching digital servo amplifiers and permanent magnet linear brakes for fail-safe, zero power braking for baggage handling and people moving applications as well as amusement park rides.

With over 75 years combined experience in the linear and rotary motion field, the H2W Technologies team of engineers offers the optimal solution to the most demanding motion control, requirements.

See Article: https://www.h2wtech.com/article/dual-feedback-voice-coil-positioning-stage

See Video at Youtube: https://youtu.be/uuSXKYWAv9k

See Product: https://www.h2wtech.com/product/voice-coil-stages/VCS20-020-CR-01-MC-F3K

For additional information contact Mark Wilson at H2W Technologies, 26380 Ferry Ct, Santa Clarita, CA 91350; Tel: 888-702-0540, Fax: 661-251-2067, E-Mail: info@h2wtech.com or visit the website at http://www.h2wtech.com

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Motion Control – XYZ Voice Coil Positioning Stage from H2W Technologies!

H2W Technologies XYZ Voice Coil Positioning Stage

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Santa Clarita, CA —– Motion Control Components – H2W Technologies designed the VCS20-20-03-MC-01-XYZ as a 3-axis positioning solution where compact size and cost were important. Using voice coil motors, instead of 3-phase brushless linear motors, significantly reduced the overall size, weight, and cost of the system.

The VCS20-20-03-MC-01-XYZ is a closed loop voice coil driven XYZ positioning stage. It is ideal for three axis positioning applications. It uses H2W voice coil motors NCC20-18-020-1A (XY Horizontal Axis) and NCC03-15-050-2X (Vertical Z-Axis). The XY Horizontal Axis motors have a 2.00″ [50.8 mm] stroke; generate 2.0 lbs [8.9 N] of continuous force and 6.0 lbs [26.7 N] of peak force. The Vertical Z-Axis motor has a 0.25″ [6.4 mm] stroke; generates 5.0 lbs [22.3 N] of continuous force and 15.0 lbs [66.8 N] of peak force. The 1.0-micron resolution encoders allow for precise positioning. It comes supplied with precise linear bearings that allow for smooth and rigid motion. The motor coil is the moving part of the assembly in order to reduce the moving mass of the system. Power is supplied to the motor via a high flex, high reliability flat ribbon cable.

Features include:

  • Compact, small footprint positioning stage 
  • Light moving mass 
  • Three axes of coordinated motion 
  • Custom strokes, forces, and feedback resolution configurations available

About H2W Technologies, Inc

H2W Technologies, Inc. is dedicated to the design and manufacture of linear and rotary motion products that are used in the motion control industry. The complete line of linear electric motors includes: Single and dual axis linear steppers, DC brush and brushless linear motors, voice coil actuators, and AC induction motors. Also offered is a complete line of ball screw, lead screw and belt driven positioning stages.

Other motion control products include: Limited angle torque motors for compact, limited angular excursion rotary servo applications, 3 phase brushless rotary servo motors with matching digital servo amplifiers and permanent magnet linear brakes for fail-safe, zero power braking for baggage handling and people moving applications as well as amusement park rides.

With over 75 years combined experience in the linear and rotary motion field, the H2W Technologies team of engineers offers the optimal solution to the most demanding motion control, requirements.

See Video at Youtube: https://youtu.be/IGy9d2L0TAA

See Product: https://www.h2wtech.com/page/xyz-voice-coil-positioning-stage”

For additional information contact Mark Wilson at H2W Technologies, 26380 Ferry Ct, Santa Clarita, CA 91350; Tel: 888-702-0540, Fax: 661-251-2067, E-Mail: info@h2wtech.com or visit the website at http://www.h2wtech.com

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Linear Motion Control – Six-Axis Linear and Rotary Positioning Stage!

H2W Technologies Six Axis Linear Motion Rotary Positioning Stage

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Santa Clarita, CA —– Linear Motion Control – The SRS-080-10-020-01-3EXRTS is a six-axis positioning stage that consists of three rotary motors, with encoders, each mounted to three independently moving linear axis. It is ideal for applications that require independent multiple motions on a single travel plane.

Each linear axis uses a H2W brushless linear motor BLDM-D06 to generate a continuous/peak force of 24.8 lbs [110 N]/74.5 lbs [331 N] with each moving table capable of a total stroke length of 82 in [2083 mm]. Each linear axis has an independent non-contact 1.0-micron resolution encoder head reading a single encoder scale allowing for precise positioning using any multi-axis motion controller. Each moving table is guided by a rigid recirculating ball linear bearing block sharing a single linear bearing rail.

Each rotary axis consists of a standard 34-frame rotary stepper motor with a 40,000 counts/rev resolution encoder. Using a state-of-the-art motion control electronics package provided by H2W, each rotary stepper motor can operate as a 2-phase rotary brushless motor. Each motor can generate a continuous torque of 27.1 oz-in [3.06 N-m]. Each rotary axis is removable, which, in turn, reduces the moving weight of the linear axis to which it was mounted. This allows for larger payloads on each linear axis.

The entire stage is assembled on a single piece of aluminum extrusion, thus reducing the overall weight of the system. It has end-of-travel rubber bumper stops, a home positioning sensor, end-of-travel-sensors, and custom mounting holes are available upon request. There are also provisions that allow customer cables to be routed within the cable carriers.

Features:

  • Multiple linear motors on single magnet track Combined linear and rotary displacement
  • Rotary axis is capable of full 360-degree rotation
  • Ability to run closed loop rotary stepper motors
  • Rotary axis can be easily removed
  • Six axis of coordinated motion
  • Assembled on a single piece of aluminum extrusion
  • Cable carriers to route customer payload cables

About H2W Technologies, Inc.

H2W Technologies, Inc. is dedicated to the design and manufacture of linear and rotary motion products that are used in the motion control industry. The complete line of linear electric motors includes: Single and dual axis linear steppers, DC brush and brushless linear motors, voice coil actuators, and AC induction motors. Also offered is a complete line of ball screw, lead screw and belt driven positioning stages.

Other motion control products include: Limited angle torque motors for compact, limited angular excursion rotary servo applications, 3 phase brushless rotary servo motors with matching digital servo amplifiers and permanent magnet linear brakes for fail-safe, zero power braking for baggage handling and people moving applications as well as amusement park rides.

With over 75 years combined experience in the linear and rotary motion field, the H2W Technologies team of engineers offers the optimal solution to the most demanding motion control, requirements.

See Article: https://www.h2wtech.com/article/six-axis-linear-and-rotary-positioning-stage

See Video at Youtube: https://youtu.be/cfnl7wxrLCs

See Product: https://www.h2wtech.com/page/six-axis-linear-and-rotary-positioning-stage

For additional information contact Mark Wilson at H2W Technologies, 26380 Ferry Ct, Santa Clarita, CA 91350; Tel: 888-702-0540, Fax: 661-251-2067, E-Mail: info@h2wtech.com or visit the website at http://www.h2wtech.com

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